multilinear 0.2.1 → 0.2.2
raw patch · 19 files changed
+3335/−3372 lines, 19 filesdep ~containersdep ~criteriondep ~deepseqsetup-changed
Dependency ranges changed: containers, criterion, deepseq, mwc-random, primitive, statistics, vector
Files
- ChangeLog.md +6/−0
- LICENSE +674/−674
- README.md +32/−32
- Setup.hs +2/−2
- benchmark/Bench.hs +35/−35
- multilinear.cabal +19/−17
- src/Multilinear.hs +188/−188
- src/Multilinear/Class.hs +0/−5
- src/Multilinear/Form.hs +173/−173
- src/Multilinear/Generic.hs +1030/−1070
- src/Multilinear/Index.hs +105/−105
- src/Multilinear/Index/Finite.hs +85/−85
- src/Multilinear/Index/Infinite.hs +71/−71
- src/Multilinear/Matrix.hs +147/−147
- src/Multilinear/NForm.hs +168/−168
- src/Multilinear/NVector.hs +134/−134
- src/Multilinear/Tensor.hs +289/−289
- src/Multilinear/Vector.hs +142/−142
- test/Spec.hs +35/−35
+ ChangeLog.md view
@@ -0,0 +1,6 @@+# 0.2.2, 2018-11-01 +## Dependencies update +- ported to LTS-12.16 resolver + +# 0.2.1, 2018-10-31 +Initial release
LICENSE view
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No Surrender of Others' Freedom. + + If conditions are imposed on you (whether by court order, agreement or +otherwise) that contradict the conditions of this License, they do not +excuse you from the conditions of this License. If you cannot convey a +covered work so as to satisfy simultaneously your obligations under this +License and any other pertinent obligations, then as a consequence you may +not convey it at all. For example, if you agree to terms that obligate you +to collect a royalty for further conveying from those to whom you convey +the Program, the only way you could satisfy both those terms and this +License would be to refrain entirely from conveying the Program. + + 13. Use with the GNU Affero General Public License. + + Notwithstanding any other provision of this License, you have +permission to link or combine any covered work with a work licensed +under version 3 of the GNU Affero General Public License into a single +combined work, and to convey the resulting work. The terms of this +License will continue to apply to the part which is the covered work, +but the special requirements of the GNU Affero General Public License, +section 13, concerning interaction through a network will apply to the +combination as such. + + 14. Revised Versions of this License. + + The Free Software Foundation may publish revised and/or new versions of +the GNU General Public License from time to time. Such new versions will +be similar in spirit to the present version, but may differ in detail to +address new problems or concerns. + + Each version is given a distinguishing version number. If the +Program specifies that a certain numbered version of the GNU General +Public License "or any later version" applies to it, you have the +option of following the terms and conditions either of that numbered +version or of any later version published by the Free Software +Foundation. If the Program does not specify a version number of the +GNU General Public License, you may choose any version ever published +by the Free Software Foundation. + + If the Program specifies that a proxy can decide which future +versions of the GNU General Public License can be used, that proxy's +public statement of acceptance of a version permanently authorizes you +to choose that version for the Program. + + Later license versions may give you additional or different +permissions. However, no additional obligations are imposed on any +author or copyright holder as a result of your choosing to follow a +later version. + + 15. Disclaimer of Warranty. + + THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY +APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT +HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY +OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, +THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM +IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF +ALL NECESSARY SERVICING, REPAIR OR CORRECTION. + + 16. Limitation of Liability. + + IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING +WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS +THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY +GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE +USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF +DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD +PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), +EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF +SUCH DAMAGES. + + 17. Interpretation of Sections 15 and 16. + + If the disclaimer of warranty and limitation of liability provided +above cannot be given local legal effect according to their terms, +reviewing courts shall apply local law that most closely approximates +an absolute waiver of all civil liability in connection with the +Program, unless a warranty or assumption of liability accompanies a +copy of the Program in return for a fee. + + END OF TERMS AND CONDITIONS + + How to Apply These Terms to Your New Programs + + If you develop a new program, and you want it to be of the greatest +possible use to the public, the best way to achieve this is to make it +free software which everyone can redistribute and change under these terms. + + To do so, attach the following notices to the program. It is safest +to attach them to the start of each source file to most effectively +state the exclusion of warranty; and each file should have at least +the "copyright" line and a pointer to where the full notice is found. + + {one line to give the program's name and a brief idea of what it does.} + Copyright (C) {year} {name of author} + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see <http://www.gnu.org/licenses/>. + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + {project} Copyright (C) {year} {fullname} + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +<http://www.gnu.org/licenses/>. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +<http://www.gnu.org/philosophy/why-not-lgpl.html>.
README.md view
@@ -1,32 +1,32 @@-# README #--[](https://travis-ci.org/ArturB/Multilinear)--Multilinear is general - purpose linear algebra and multi-dimensional array library for Haskell. It provides generic and efficient implementation of linear algebra operations on vectors, linear functionals, matrices and its higher - rank analoges: tensors. It can also be used as simply a miltidimensional arrays for everyone. --### AS FOR NOW, THE LIBRARY IS IN PRODUCTION PHASE - DO NOT USE IT FOR PRODUCTION!! ###--## Scripting ##--Multilinear is optimized to being used from GHCi. It uses easy and concise notation of Einstein summation convention to calculate complex tasks. Using this, you are able to write for example a deep learnin neural network from scratch in just a few lines of interpreter code. If you want to know more about Einstein convention, see the Wikipedia: https://en.wikipedia.org/wiki/Einstein_notation--## Machine learning ##--Multi-dimensional algebra is especially useful to quickly write machine learning algorithms (eg. neural networks) from scratch. When library will be stable, some examples will be available. --### Installation ###--Installation using Stack. Invoke this command in library folder:--```-stack build-```--### Contribution guidelines ###--If you want to contribute to this library, contact with me. --### Who do I talk to? ###--All copyrights to Artur M. Brodzki.-Contact mail: artur@brodzki.org+# README # + +[](https://travis-ci.org/ArturB/Multilinear) + +Multilinear is general - purpose linear algebra and multi-dimensional array library for Haskell. It provides generic and efficient implementation of linear algebra operations on vectors, linear functionals, matrices and its higher - rank analoges: tensors. It can also be used as simply a miltidimensional arrays for everyone. + +### AS FOR NOW, THE LIBRARY IS IN PRODUCTION PHASE - DO NOT USE IT FOR PRODUCTION!! ### + +## Scripting ## + +Multilinear is optimized to being used from GHCi. It uses easy and concise notation of Einstein summation convention to calculate complex tasks. Using this, you are able to write for example a deep learnin neural network from scratch in just a few lines of interpreter code. If you want to know more about Einstein convention, see the Wikipedia: https://en.wikipedia.org/wiki/Einstein_notation + +## Machine learning ## + +Multi-dimensional algebra is especially useful to quickly write machine learning algorithms (eg. neural networks) from scratch. When library will be stable, some examples will be available. + +### Installation ### + +Installation using Stack. Invoke this command in library folder: + +``` +stack build +``` + +### Contribution guidelines ### + +If you want to contribute to this library, contact with me. + +### Who do I talk to? ### + +All copyrights to Artur M. Brodzki. +Contact mail: artur@brodzki.org
Setup.hs view
@@ -1,2 +1,2 @@-import Distribution.Simple-main = defaultMain+import Distribution.Simple +main = defaultMain
benchmark/Bench.hs view
@@ -1,35 +1,35 @@-{-|-Module : Bench-Description : Benchmark of Multilinear library-Copyright : (c) Artur M. Brodzki, 2018-License : BSD3-Maintainer : artur@brodzki.org-Stability : experimental-Portability : Windows/POSIX---}--module Main (- main-) where--import Control.DeepSeq-import Criterion.Main-import Criterion.Measurement as Meas-import Criterion.Types-import Multilinear.Generic-import qualified Multilinear.Matrix as Matrix--m1 :: Tensor Double-m1 = Matrix.fromIndices "ij" 1000 1000 $ \i j -> fromIntegral (2*i) - exp (fromIntegral j)--m2 :: Tensor Double-m2 = Matrix.fromIndices "jk" 1000 1000 $ \i j -> sin (fromIntegral i) + cos (fromIntegral j)--main :: IO ()-main = do- putStrLn "Two matrices 1000x1000 multiplying..."- (meas,_) <- Meas.measure ( nfIO $ (m1 * m2) `deepseq` putStrLn "End!" ) 1- putStrLn $ "Measured time: " ++ show (measCpuTime meas) ++ " s."- return ()-+{-| +Module : Bench +Description : Benchmark of Multilinear library +Copyright : (c) Artur M. Brodzki, 2018 +License : BSD3 +Maintainer : artur@brodzki.org +Stability : experimental +Portability : Windows/POSIX + +-} + +module Main ( + main +) where + +import Control.DeepSeq +import Criterion.Main +import Criterion.Measurement as Meas +import Criterion.Types +import Multilinear.Generic +import qualified Multilinear.Matrix as Matrix + +m1 :: Tensor Double +m1 = Matrix.fromIndices "ij" 1000 1000 $ \i j -> fromIntegral (2*i) - exp (fromIntegral j) + +m2 :: Tensor Double +m2 = Matrix.fromIndices "jk" 1000 1000 $ \i j -> sin (fromIntegral i) + cos (fromIntegral j) + +main :: IO () +main = do + putStrLn "Two matrices 1000x1000 multiplying..." + (meas,_) <- Meas.measure ( nfIO $ (m1 * m2) `deepseq` putStrLn "End!" ) 1 + putStrLn $ "Measured time: " ++ show (measCpuTime meas) ++ " s." + return () +
multilinear.cabal view
@@ -1,11 +1,13 @@--- This file has been generated from package.yaml by hpack version 0.28.2. +cabal-version: 1.12 ++-- This file has been generated from package.yaml by hpack version 0.31.0. -- -- see: https://github.com/sol/hpack ----- hash: 303f9bcc9eca604310b89a96ec09fc72e7e996959cc498ef5d730cb3051669c3+-- hash: 8c8b8435434271d1b1843d492d988ebe7197f269825a8f98478d0b939b63b23f name: multilinear-version: 0.2.1+version: 0.2.2 synopsis: Comprehensive and efficient (multi)linear algebra implementation. description: Comprehensive and efficient (multi)linear algebra implementation, based on generic tensor formalism and concise Ricci-Curbastro index syntax. More information available on GitHub: <https://github.com/ArturB/multilinear#readme> category: Machine learning@@ -17,9 +19,9 @@ license: BSD3 license-file: LICENSE build-type: Simple-cabal-version: >= 1.10 extra-source-files: README.md+ ChangeLog.md source-repository head type: git@@ -44,15 +46,15 @@ hs-source-dirs: src default-extensions: DeriveGeneric FlexibleContexts FlexibleInstances MultiParamTypeClasses- ghc-options: -O2 -Wall+ ghc-options: -O2 -Wall -fllvm -optlo-O3 build-depends: base >=4.7 && <5- , containers- , deepseq- , mwc-random- , primitive- , statistics- , vector+ , containers >=0.5+ , deepseq >=1.4+ , mwc-random >=0.13+ , primitive >=0.6+ , statistics >=0.14+ , vector >=0.12 default-language: Haskell2010 test-suite multilinear-test@@ -63,11 +65,11 @@ hs-source-dirs: test default-extensions: DeriveGeneric FlexibleContexts FlexibleInstances MultiParamTypeClasses- ghc-options: -O2 -Wall -threaded -rtsopts -with-rtsopts=-N+ ghc-options: -O2 -Wall -fllvm -optlo-O3 -threaded -rtsopts -with-rtsopts=-N build-depends: base >=4.7 && <5- , criterion- , deepseq+ , criterion >=1.2+ , deepseq >=1.4 , multilinear default-language: Haskell2010 @@ -79,10 +81,10 @@ hs-source-dirs: benchmark default-extensions: DeriveGeneric FlexibleContexts FlexibleInstances MultiParamTypeClasses- ghc-options: -O2 -Wall -threaded -rtsopts -with-rtsopts=-N+ ghc-options: -O2 -Wall -fllvm -optlo-O3 -threaded -rtsopts -with-rtsopts=-N build-depends: base >=4.7 && <5- , criterion- , deepseq+ , criterion >=1.2+ , deepseq >=1.4 , multilinear default-language: Haskell2010
src/Multilinear.hs view
@@ -1,189 +1,189 @@-{-|-Module : Multilinear-Description : A (multi)linear algbra library.-Copyright : (c) Artur M. Brodzki, 2018-License : BSD3-Maintainer : artur@brodzki.org-Stability : experimental-Portability : Windows/POSIX--Multilinear library provides efficient and terse way to deal with linear algebra in Haskell. It is based on concept of tensor - a multidimensional indexed array of numbers. Vectors, matrices and linear functionals are examples of low-order tensors.--= Quick tutorial--Tensors are indexed, each having one or several indices numbering its components. A scalar has no indices, as being simply a value. A vector has one index, because it is a one-dimensional list of numbers. A matrix has two indices, being a bidimensional table of numbers. Tensors are arbitrarily - dimensional, so you can have a vector of matrices (third-order tensor) and so on. Such tensors are especially useful when dealing with more complex task, such as programming neural networks e.g. for deep learning.--Index may be either __lower (contravariant)__ or __upper (covariant)__, depending on its function.--A vector has one __upper__ or __contravariant__ index, because it represents a value, point in a space. A linear functional (called in this library as a __form__) is represented as a list of numbers, similar to vector, but it does not indicate a value, but rather a coefficients of __linear map__ or __transformation__ that takes a vector and returns a number, simply by calculating a linear combination of vector components with weights being a linear functional coefficients. So elements of linear functional are indexed by __lower__ or __covariant__ index.--A matrix also represents a linear transformation, similar to linear functional, but it take a vector and return a vector, not a scalar. So matrix is simply a bunch of linear functionals - each one is a matrix row and returns a one element of resulting vector. These linear functionals are also indexed - of course by an contravariant index, as vector, which is returned by a matrix. So matrix is a tensor with two indices - one uppper (contravariant) and one lower (covariant).--A dot product is - what a surprise! - a linear transformation. But it is different from matrix - it takes two vectors to multiplicate and returns one number. So it needs two lower (covariant) indices. In fact, a dot product is represented as a bidimensional table of numbers - as matrix - but with two lower indices, instead of one upper and one lower. Tensors with several lower indices are called n-forms. Actually, many linear maps that takes two vectors and returns a number are represented in such notation. A dot product is a table filled with zeros but having a 1-s in diagonal of the table - it look visually identical like unit matrix, but it isn't a matrix - it's actually a 2-form. In this library dot product is called (as in abstract maths) a __Kronecker delta__ (in "Multilinear.NForm"").--A cross product takes two vectors and returns a vector of numbers. So, as you can guess, it has three indices - two covariant (lower) and one upper (contravariant). A tensor that corresponds to cross product is called Levi-Civita symbol and is implemented under "Multilinear.Tensor".--As you see, multidimensional indexed arrays - tensors - provide a unified way to deal with linear algebra - such with data (vectors) and functions operating on them (matrices, n-forms). Using tensors instead of limited number of pre-defined functions, you gain a power of universal formalism, where you can express any linear function you want to deal with.--When you apply a linear functional to a vector, you compute a linear combination - or a weighted sum - of its components. It is so common operation in linear algebra,-that it requires a convenient way to note. Einstein (1905) introduced a summation rule:--If you multiply a tensor with lower index __/i/__ by a tensor with upper index with same name __/i__ then the linear combination of its components is automatically computed. The only condition is that an index of vector and index of corresponding linear transformation must have the same name.--== Examples--@-->>> v = Vector.fromIndices "i" 5 $ \\i -> i + 2 (vector v has 5 elements and v[i] = i + 2, indexing from 0)->>> v-\<i:5\>- | 2- | 3- | 4- | 5- | 6->>> f = Form.const "i" 5 1 (linear functional has 5 elements and f[i] = 1)->>> f-[i:5] [1,1,1,1,1]->>> f * v-20-@--If you want to apply a vector to matrix, you must simply multiply them. The only condition is - as you can guess - that lower (indicating that matrix is a linear transformation) index of matrix must have the same name as the upper index of vector (indicating that this vector is a argument of matrix linear transformation; an upper index of matrix here indicates that this linear transformation returns a vector)--@-->>> m = Matrix.fromIndices "ij" 5 5 $ \\i j -> i + j->>> m-\<i:5\>- | [j:5] [0,1,2,3,4]- | [j:5] [1,2,3,4,5]- | [j:5] [2,3,4,5,6]- | [j:5] [3,4,5,6,7]- | [j:5] [4,5,6,7,8]->>> v = Vector.fromIndices "j" 5 $ \\j -> j (vector v has 5 elements and v[j] = j, indexing from 0)->>> v-\<j:5\>- | 0- | 1- | 2- | 3- | 4->>> m * v-\<i:5\>- | 30- | 40- | 50- | 60- | 70-@-Note, that result vector is indexed with "i" - the same index as uppper index of our matrix.--If you want to do a matrix multiplication, a lower index of first matrix must have the same name as upper index of second matrix.--@-->>> m1 = Matrix.fromIndices "ij" 3 5 $ \\i j -> i + j->>> m1-\<i:3\>- | [j:5] [0,1,2,3,4]- | [j:5] [1,2,3,4,5]- | [j:5] [2,3,4,5,6]->>> m2 = Matrix.fromIndices "jk" 5 4 $ \\j -> i + j (vector v has 5 elements and v[j] = j, indexing from 0)->>> m2-\<j:5\>- | [k:4] [0,1,2,3]- | [k:4] [1,2,3,4]- | [k:4] [2,3,4,5]- | [k:4] [3,4,5,6]- | [k:4] [4,5,6,7]->>> m1 * m2-\<i:3\>- | [k:4] [30,40,50,60]- | [k:4] [40,50,60,70]- | [k:4] [50,60,70,80]-@--Note, that rule that first matrix lower index must be the same as the second matrix upper index corresponeds to the fact, that to multiply two matrices, the widht of first matrix must be the same as width of the second matrix. The rule of matrix multiplication guarantees, that this operation is equivalent to linear functions composition.--The dot product of vectors may be done by simply making one of vectors with lower index, or - more correctly - by applying two vectors to Kronecker delta:--@-->>> v1 = Vector.fromIndices "i" 5 $ \\i -> i + 2 (vector v has 5 elements and v[i] = i + 2, indexing from 0)->>> v1-\<i:5\>- | 2- | 3- | 4- | 5- | 6->>> v2 = Vector.fromIndices "j" 5 $ \\j -> j (vector v has 5 elements and v[j] = j, indexing from 0)->>> v2-\<j:5\>- | 0- | 1- | 2- | 3- | 4->>> v1 * (lower "j" v2)-50->>> NForm.dot 5 "ij" * v1 * v2 (A Kronecker delta - representing a dot product - of size 5 with indices \"i\" and \"j\" is multiplied by v1 and v2)-50--@--If you want to know more about linear algebra and Einstein convention, read Wikipedia:--- <https://en.wikipedia.org/wiki/Matrix_(mathematics)>-- <https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors>-- <https://en.wikipedia.org/wiki/Einstein_notation>---}--module Multilinear (- {-module Form,- module Generic,- module Index,- module Index.Finite,- module Index.Infinite,- module Matrix,- module NForm,- module Tensor,- module Vector,- module X-}-) where---- Re-export other library modules-{-import Multilinear.Class as Multilinear-import qualified Multilinear.Form as Form-import Multilinear.Generic as Generic-import qualified Multilinear.Index as Index-import qualified Multilinear.Index.Finite as Index.Finite-import qualified Multilinear.Index.Infinite as Index.Infinite-import qualified Multilinear.Matrix as Matrix-import qualified Multilinear.NForm as NForm-import qualified Multilinear.NVector as NVector-import qualified Multilinear.Tensor as Tensor-import qualified Multilinear.Vector as Vector--import Statistics.Distribution as X-import Statistics.Distribution.Beta as X-import Statistics.Distribution.Binomial as X-import Statistics.Distribution.CauchyLorentz as X-import Statistics.Distribution.ChiSquared as X-import Statistics.Distribution.Exponential as X-import Statistics.Distribution.FDistribution as X-import Statistics.Distribution.Gamma as X-import Statistics.Distribution.Geometric as X-import Statistics.Distribution.Hypergeometric as X-import Statistics.Distribution.Laplace as X-import Statistics.Distribution.Normal as X-import Statistics.Distribution.StudentT as X-import Statistics.Distribution.Uniform as X--import System.IO.Unsafe as X-import Control.Monad.Trans.Class as X-import Control.Monad.Trans.Either as X-import Control.Exception.Base as X+{-| +Module : Multilinear +Description : A (multi)linear algbra library. +Copyright : (c) Artur M. Brodzki, 2018 +License : BSD3 +Maintainer : artur@brodzki.org +Stability : experimental +Portability : Windows/POSIX + +Multilinear library provides efficient and terse way to deal with linear algebra in Haskell. It is based on concept of tensor - a multidimensional indexed array of numbers. Vectors, matrices and linear functionals are examples of low-order tensors. + += Quick tutorial + +Tensors are indexed, each having one or several indices numbering its components. A scalar has no indices, as being simply a value. A vector has one index, because it is a one-dimensional list of numbers. A matrix has two indices, being a bidimensional table of numbers. Tensors are arbitrarily - dimensional, so you can have a vector of matrices (third-order tensor) and so on. Such tensors are especially useful when dealing with more complex task, such as programming neural networks e.g. for deep learning. + +Index may be either __lower (contravariant)__ or __upper (covariant)__, depending on its function. + +A vector has one __upper__ or __contravariant__ index, because it represents a value, point in a space. A linear functional (called in this library as a __form__) is represented as a list of numbers, similar to vector, but it does not indicate a value, but rather a coefficients of __linear map__ or __transformation__ that takes a vector and returns a number, simply by calculating a linear combination of vector components with weights being a linear functional coefficients. So elements of linear functional are indexed by __lower__ or __covariant__ index. + +A matrix also represents a linear transformation, similar to linear functional, but it take a vector and return a vector, not a scalar. So matrix is simply a bunch of linear functionals - each one is a matrix row and returns a one element of resulting vector. These linear functionals are also indexed - of course by an contravariant index, as vector, which is returned by a matrix. So matrix is a tensor with two indices - one uppper (contravariant) and one lower (covariant). + +A dot product is - what a surprise! - a linear transformation. But it is different from matrix - it takes two vectors to multiplicate and returns one number. So it needs two lower (covariant) indices. In fact, a dot product is represented as a bidimensional table of numbers - as matrix - but with two lower indices, instead of one upper and one lower. Tensors with several lower indices are called n-forms. Actually, many linear maps that takes two vectors and returns a number are represented in such notation. A dot product is a table filled with zeros but having a 1-s in diagonal of the table - it look visually identical like unit matrix, but it isn't a matrix - it's actually a 2-form. In this library dot product is called (as in abstract maths) a __Kronecker delta__ (in "Multilinear.NForm""). + +A cross product takes two vectors and returns a vector of numbers. So, as you can guess, it has three indices - two covariant (lower) and one upper (contravariant). A tensor that corresponds to cross product is called Levi-Civita symbol and is implemented under "Multilinear.Tensor". + +As you see, multidimensional indexed arrays - tensors - provide a unified way to deal with linear algebra - such with data (vectors) and functions operating on them (matrices, n-forms). Using tensors instead of limited number of pre-defined functions, you gain a power of universal formalism, where you can express any linear function you want to deal with. + +When you apply a linear functional to a vector, you compute a linear combination - or a weighted sum - of its components. It is so common operation in linear algebra, +that it requires a convenient way to note. Einstein (1905) introduced a summation rule: + +If you multiply a tensor with lower index __/i/__ by a tensor with upper index with same name __/i__ then the linear combination of its components is automatically computed. The only condition is that an index of vector and index of corresponding linear transformation must have the same name. + +== Examples + +@ + +>>> v = Vector.fromIndices "i" 5 $ \\i -> i + 2 (vector v has 5 elements and v[i] = i + 2, indexing from 0) +>>> v +\<i:5\> + | 2 + | 3 + | 4 + | 5 + | 6 +>>> f = Form.const "i" 5 1 (linear functional has 5 elements and f[i] = 1) +>>> f +[i:5] [1,1,1,1,1] +>>> f * v +20 +@ + +If you want to apply a vector to matrix, you must simply multiply them. The only condition is - as you can guess - that lower (indicating that matrix is a linear transformation) index of matrix must have the same name as the upper index of vector (indicating that this vector is a argument of matrix linear transformation; an upper index of matrix here indicates that this linear transformation returns a vector) + +@ + +>>> m = Matrix.fromIndices "ij" 5 5 $ \\i j -> i + j +>>> m +\<i:5\> + | [j:5] [0,1,2,3,4] + | [j:5] [1,2,3,4,5] + | [j:5] [2,3,4,5,6] + | [j:5] [3,4,5,6,7] + | [j:5] [4,5,6,7,8] +>>> v = Vector.fromIndices "j" 5 $ \\j -> j (vector v has 5 elements and v[j] = j, indexing from 0) +>>> v +\<j:5\> + | 0 + | 1 + | 2 + | 3 + | 4 +>>> m * v +\<i:5\> + | 30 + | 40 + | 50 + | 60 + | 70 +@ +Note, that result vector is indexed with "i" - the same index as uppper index of our matrix. + +If you want to do a matrix multiplication, a lower index of first matrix must have the same name as upper index of second matrix. + +@ + +>>> m1 = Matrix.fromIndices "ij" 3 5 $ \\i j -> i + j +>>> m1 +\<i:3\> + | [j:5] [0,1,2,3,4] + | [j:5] [1,2,3,4,5] + | [j:5] [2,3,4,5,6] +>>> m2 = Matrix.fromIndices "jk" 5 4 $ \\j -> i + j (vector v has 5 elements and v[j] = j, indexing from 0) +>>> m2 +\<j:5\> + | [k:4] [0,1,2,3] + | [k:4] [1,2,3,4] + | [k:4] [2,3,4,5] + | [k:4] [3,4,5,6] + | [k:4] [4,5,6,7] +>>> m1 * m2 +\<i:3\> + | [k:4] [30,40,50,60] + | [k:4] [40,50,60,70] + | [k:4] [50,60,70,80] +@ + +Note, that rule that first matrix lower index must be the same as the second matrix upper index corresponeds to the fact, that to multiply two matrices, the widht of first matrix must be the same as width of the second matrix. The rule of matrix multiplication guarantees, that this operation is equivalent to linear functions composition. + +The dot product of vectors may be done by simply making one of vectors with lower index, or - more correctly - by applying two vectors to Kronecker delta: + +@ + +>>> v1 = Vector.fromIndices "i" 5 $ \\i -> i + 2 (vector v has 5 elements and v[i] = i + 2, indexing from 0) +>>> v1 +\<i:5\> + | 2 + | 3 + | 4 + | 5 + | 6 +>>> v2 = Vector.fromIndices "j" 5 $ \\j -> j (vector v has 5 elements and v[j] = j, indexing from 0) +>>> v2 +\<j:5\> + | 0 + | 1 + | 2 + | 3 + | 4 +>>> v1 * (lower "j" v2) +50 +>>> NForm.dot 5 "ij" * v1 * v2 (A Kronecker delta - representing a dot product - of size 5 with indices \"i\" and \"j\" is multiplied by v1 and v2) +50 + +@ + +If you want to know more about linear algebra and Einstein convention, read Wikipedia: + +- <https://en.wikipedia.org/wiki/Matrix_(mathematics)> +- <https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors> +- <https://en.wikipedia.org/wiki/Einstein_notation> + +-} + +module Multilinear ( + {-module Form, + module Generic, + module Index, + module Index.Finite, + module Index.Infinite, + module Matrix, + module NForm, + module Tensor, + module Vector, + module X-} +) where + +-- Re-export other library modules +{-import Multilinear.Class as Multilinear +import qualified Multilinear.Form as Form +import Multilinear.Generic as Generic +import qualified Multilinear.Index as Index +import qualified Multilinear.Index.Finite as Index.Finite +import qualified Multilinear.Index.Infinite as Index.Infinite +import qualified Multilinear.Matrix as Matrix +import qualified Multilinear.NForm as NForm +import qualified Multilinear.NVector as NVector +import qualified Multilinear.Tensor as Tensor +import qualified Multilinear.Vector as Vector + +import Statistics.Distribution as X +import Statistics.Distribution.Beta as X +import Statistics.Distribution.Binomial as X +import Statistics.Distribution.CauchyLorentz as X +import Statistics.Distribution.ChiSquared as X +import Statistics.Distribution.Exponential as X +import Statistics.Distribution.FDistribution as X +import Statistics.Distribution.Gamma as X +import Statistics.Distribution.Geometric as X +import Statistics.Distribution.Hypergeometric as X +import Statistics.Distribution.Laplace as X +import Statistics.Distribution.Normal as X +import Statistics.Distribution.StudentT as X +import Statistics.Distribution.Uniform as X + +import System.IO.Unsafe as X +import Control.Monad.Trans.Class as X +import Control.Monad.Trans.Either as X +import Control.Exception.Base as X -}
src/Multilinear/Class.hs view
@@ -154,7 +154,6 @@ {-| Multidimensional array treated as multilinear map - tensor -} class ( Num (t a), -- Tensors may be added, subtracted and multiplicated - Monoid (t a), -- Tensors are monoids with concatenation as monoid operation Functor t -- Tensor should be a Functor for convenience ) => Multilinear t a where @@ -301,10 +300,6 @@ infixl 9 <<<| (<<<|) :: t a -> String -> t a t <<<| n = shiftLeftmost t n - - {-| Concatenation of two tensors by common index -} - {-| Tensors must be equivalent: 'equiv' t1 t2 == True -} - augment :: t a -> t a -> String -> t a {-| Simple mapping -} {-| @map f t@ returns tensor @t2@ in which @t2[i1,i2,...] = f t[i1,i2,...]@ -}
src/Multilinear/Form.hs view
@@ -1,173 +1,173 @@-{-|-Module : Multilinear.Form-Description : Linear functional constructors (finitely- or infinitely-dimensional)-Copyright : (c) Artur M. Brodzki, 2018-License : BSD3-Maintainer : artur@brodzki.org-Stability : experimental-Portability : Windows/POSIX--- This module provides convenient constructors that generates a linear functionals-- Finitely-dimensional functionals provide much greater performance that infinitely-dimensional---}--module Multilinear.Form (- -- * Generators- -- ** Finite functionals- Multilinear.Form.fromIndices, - Multilinear.Form.const,- Multilinear.Form.randomDouble,- Multilinear.Form.randomDoubleSeed,- Multilinear.Form.randomInt, - Multilinear.Form.randomIntSeed,- -- ** Infinite functionals- Multilinear.Form.fromIndices', - Multilinear.Form.const'-) where--import Control.Monad.Primitive-import Multilinear.Generic-import Multilinear.Index.Infinite as Infinite-import Multilinear.Tensor as Tensor-import Statistics.Distribution--invalidIndices :: String-invalidIndices = "Indices and its sizes not compatible with structure of linear functional!"---- * Finite functional generators--{-| Generate linear functional as function of indices -}-{-# INLINE fromIndices #-}-fromIndices :: (- Num a- ) => String -- ^ Index name (one character)- -> Int -- ^ Number of elements- -> (Int -> a) -- ^ Generator function - returns a linear functional component at index @i@- -> Tensor a -- ^ Generated linear functional--fromIndices [i] s f = Tensor.fromIndices ([],[]) ([i],[s]) $ \[] [x] -> f x-fromIndices _ _ _ = Err invalidIndices--{-| Generate linear functional with all components equal to some @v@ -}-{-# INLINE Multilinear.Form.const #-}-const :: (- Num a- ) => String -- ^ Index name (one character)- -> Int -- ^ Number of elements- -> a -- ^ Value of each element- -> Tensor a -- ^ Generated linear functional--const [i] s = Tensor.const ([],[]) ([i],[s])-const _ _ = \_ -> Err invalidIndices--{-| Generate linear functional with random real components with given probability distribution.-The functional is wrapped in the IO monad. -}-{-| Available probability distributions: -}-{-| - Beta : "Statistics.Distribution.BetaDistribution" -}-{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -}-{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -}-{-| - Exponential : "Statistics.Distribution.Exponential" -}-{-| - Gamma : "Statistics.Distribution.Gamma" -}-{-| - Normal : "Statistics.Distribution.Normal" -}-{-| - StudentT : "Statistics.Distribution.StudentT" -}-{-| - Uniform : "Statistics.Distribution.Uniform" -}-{-| - F : "Statistics.Distribution.FDistribution" -}-{-| - Laplace : "Statistics.Distribution.Laplace" -}-{-# INLINE randomDouble #-}-randomDouble :: (- ContGen d- ) => String -- ^ Index name (one character)- -> Int -- ^ Number of elements- -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution")- -> IO (Tensor Double) -- ^ Generated linear functional--randomDouble [i] s = Tensor.randomDouble ([],[]) ([i],[s])-randomDouble _ _ = \_ -> return $ Err invalidIndices--{-| Generate linear functional with random integer components with given probability distribution.-The functional is wrapped in the IO monad. -}-{-| Available probability distributions: -}-{-| - Binomial : "Statistics.Distribution.Binomial" -}-{-| - Poisson : "Statistics.Distribution.Poisson" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -}-{-# INLINE randomInt #-}-randomInt :: (- DiscreteGen d- ) => String -- ^ Index name (one character)- -> Int -- ^ Number of elements- -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution")- -> IO (Tensor Int) -- ^ Generated linear functional--randomInt [i] s = Tensor.randomInt ([],[]) ([i],[s])-randomInt _ _ = \_ -> return $ Err invalidIndices--{-| Generate linear functional with random real components with given probability distribution and given seed.-The functional is wrapped in a monad. -}-{-| Available probability distributions: -}-{-| - Beta : "Statistics.Distribution.BetaDistribution" -}-{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -}-{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -}-{-| - Exponential : "Statistics.Distribution.Exponential" -}-{-| - Gamma : "Statistics.Distribution.Gamma" -}-{-| - Normal : "Statistics.Distribution.Normal" -}-{-| - StudentT : "Statistics.Distribution.StudentT" -}-{-| - Uniform : "Statistics.Distribution.Uniform" -}-{-| - F : "Statistics.Distribution.FDistribution" -}-{-| - Laplace : "Statistics.Distribution.Laplace" -}-{-# INLINE randomDoubleSeed #-}-randomDoubleSeed :: (- ContGen d, PrimMonad m- ) => String -- ^ Index name (one character)- -> Int -- ^ Number of elements- -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution")- -> Int -- ^ Randomness seed- -> m (Tensor Double) -- ^ Generated linear functional--randomDoubleSeed [i] s = Tensor.randomDoubleSeed ([],[]) ([i],[s])-randomDoubleSeed _ _ = \_ _ -> return $ Err invalidIndices--{-| Generate linear functional with random integer components with given probability distribution and given seed.-The functional is wrapped in a monad. -}-{-| Available probability distributions: -}-{-| - Binomial : "Statistics.Distribution.Binomial" -}-{-| - Poisson : "Statistics.Distribution.Poisson" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -}-{-# INLINE randomIntSeed #-}-randomIntSeed :: (- DiscreteGen d, PrimMonad m- ) => String -- ^ Index name (one character)- -> Int -- ^ Number of elements- -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution")- -> Int -- ^ Randomness seed- -> m (Tensor Int) -- ^ Generated linear functional--randomIntSeed [i] s = Tensor.randomIntSeed ([],[]) ([i],[s])-randomIntSeed _ _ = \_ _ -> return $ Err invalidIndices--{-| Generate linear functional as function of indices -}-{-# INLINE fromIndices' #-}-fromIndices' :: (- Num a- ) => String -- ^ Index name (one character)- -> (Int -> a) -- ^ Generator function - returns a linear functional component at index @i@- -> Tensor a -- ^ Generated linear functional--fromIndices' i = case i of- [d] -> \f -> InfiniteTensor (Infinite.Covariant [d]) $ (Scalar . f) <$> [0..]- _ -> \_ -> Err invalidIndices--{-| Generate linear functional with all components equal to some @v@ -}-{-# INLINE Multilinear.Form.const' #-}-const' :: (- Num a- ) => String -- ^ Index name (one character)- -> a -- ^ Value of each element- -> Tensor a -- ^ Generated linear functional--const' i = case i of- [d] -> \v -> InfiniteTensor (Infinite.Covariant [d]) $ (\_ -> Scalar v) <$> ([0..] :: [Int])- _ -> \_ -> Err invalidIndices-+{-| +Module : Multilinear.Form +Description : Linear functional constructors (finitely- or infinitely-dimensional) +Copyright : (c) Artur M. Brodzki, 2018 +License : BSD3 +Maintainer : artur@brodzki.org +Stability : experimental +Portability : Windows/POSIX + +- This module provides convenient constructors that generates a linear functionals +- Finitely-dimensional functionals provide much greater performance that infinitely-dimensional + +-} + +module Multilinear.Form ( + -- * Generators + -- ** Finite functionals + Multilinear.Form.fromIndices, + Multilinear.Form.const, + Multilinear.Form.randomDouble, + Multilinear.Form.randomDoubleSeed, + Multilinear.Form.randomInt, + Multilinear.Form.randomIntSeed, + -- ** Infinite functionals + Multilinear.Form.fromIndices', + Multilinear.Form.const' +) where + +import Control.Monad.Primitive +import Multilinear.Generic +import Multilinear.Index.Infinite as Infinite +import Multilinear.Tensor as Tensor +import Statistics.Distribution + +invalidIndices :: String +invalidIndices = "Indices and its sizes not compatible with structure of linear functional!" + +-- * Finite functional generators + +{-| Generate linear functional as function of indices -} +{-# INLINE fromIndices #-} +fromIndices :: ( + Num a + ) => String -- ^ Index name (one character) + -> Int -- ^ Number of elements + -> (Int -> a) -- ^ Generator function - returns a linear functional component at index @i@ + -> Tensor a -- ^ Generated linear functional + +fromIndices [i] s f = Tensor.fromIndices ([],[]) ([i],[s]) $ \[] [x] -> f x +fromIndices _ _ _ = Err invalidIndices + +{-| Generate linear functional with all components equal to some @v@ -} +{-# INLINE Multilinear.Form.const #-} +const :: ( + Num a + ) => String -- ^ Index name (one character) + -> Int -- ^ Number of elements + -> a -- ^ Value of each element + -> Tensor a -- ^ Generated linear functional + +const [i] s = Tensor.const ([],[]) ([i],[s]) +const _ _ = \_ -> Err invalidIndices + +{-| Generate linear functional with random real components with given probability distribution. +The functional is wrapped in the IO monad. -} +{-| Available probability distributions: -} +{-| - Beta : "Statistics.Distribution.BetaDistribution" -} +{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -} +{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -} +{-| - Exponential : "Statistics.Distribution.Exponential" -} +{-| - Gamma : "Statistics.Distribution.Gamma" -} +{-| - Normal : "Statistics.Distribution.Normal" -} +{-| - StudentT : "Statistics.Distribution.StudentT" -} +{-| - Uniform : "Statistics.Distribution.Uniform" -} +{-| - F : "Statistics.Distribution.FDistribution" -} +{-| - Laplace : "Statistics.Distribution.Laplace" -} +{-# INLINE randomDouble #-} +randomDouble :: ( + ContGen d + ) => String -- ^ Index name (one character) + -> Int -- ^ Number of elements + -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution") + -> IO (Tensor Double) -- ^ Generated linear functional + +randomDouble [i] s = Tensor.randomDouble ([],[]) ([i],[s]) +randomDouble _ _ = \_ -> return $ Err invalidIndices + +{-| Generate linear functional with random integer components with given probability distribution. +The functional is wrapped in the IO monad. -} +{-| Available probability distributions: -} +{-| - Binomial : "Statistics.Distribution.Binomial" -} +{-| - Poisson : "Statistics.Distribution.Poisson" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -} +{-# INLINE randomInt #-} +randomInt :: ( + DiscreteGen d + ) => String -- ^ Index name (one character) + -> Int -- ^ Number of elements + -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution") + -> IO (Tensor Int) -- ^ Generated linear functional + +randomInt [i] s = Tensor.randomInt ([],[]) ([i],[s]) +randomInt _ _ = \_ -> return $ Err invalidIndices + +{-| Generate linear functional with random real components with given probability distribution and given seed. +The functional is wrapped in a monad. -} +{-| Available probability distributions: -} +{-| - Beta : "Statistics.Distribution.BetaDistribution" -} +{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -} +{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -} +{-| - Exponential : "Statistics.Distribution.Exponential" -} +{-| - Gamma : "Statistics.Distribution.Gamma" -} +{-| - Normal : "Statistics.Distribution.Normal" -} +{-| - StudentT : "Statistics.Distribution.StudentT" -} +{-| - Uniform : "Statistics.Distribution.Uniform" -} +{-| - F : "Statistics.Distribution.FDistribution" -} +{-| - Laplace : "Statistics.Distribution.Laplace" -} +{-# INLINE randomDoubleSeed #-} +randomDoubleSeed :: ( + ContGen d, PrimMonad m + ) => String -- ^ Index name (one character) + -> Int -- ^ Number of elements + -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution") + -> Int -- ^ Randomness seed + -> m (Tensor Double) -- ^ Generated linear functional + +randomDoubleSeed [i] s = Tensor.randomDoubleSeed ([],[]) ([i],[s]) +randomDoubleSeed _ _ = \_ _ -> return $ Err invalidIndices + +{-| Generate linear functional with random integer components with given probability distribution and given seed. +The functional is wrapped in a monad. -} +{-| Available probability distributions: -} +{-| - Binomial : "Statistics.Distribution.Binomial" -} +{-| - Poisson : "Statistics.Distribution.Poisson" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -} +{-# INLINE randomIntSeed #-} +randomIntSeed :: ( + DiscreteGen d, PrimMonad m + ) => String -- ^ Index name (one character) + -> Int -- ^ Number of elements + -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution") + -> Int -- ^ Randomness seed + -> m (Tensor Int) -- ^ Generated linear functional + +randomIntSeed [i] s = Tensor.randomIntSeed ([],[]) ([i],[s]) +randomIntSeed _ _ = \_ _ -> return $ Err invalidIndices + +{-| Generate linear functional as function of indices -} +{-# INLINE fromIndices' #-} +fromIndices' :: ( + Num a + ) => String -- ^ Index name (one character) + -> (Int -> a) -- ^ Generator function - returns a linear functional component at index @i@ + -> Tensor a -- ^ Generated linear functional + +fromIndices' i = case i of + [d] -> \f -> InfiniteTensor (Infinite.Covariant [d]) $ (Scalar . f) <$> [0..] + _ -> \_ -> Err invalidIndices + +{-| Generate linear functional with all components equal to some @v@ -} +{-# INLINE Multilinear.Form.const' #-} +const' :: ( + Num a + ) => String -- ^ Index name (one character) + -> a -- ^ Value of each element + -> Tensor a -- ^ Generated linear functional + +const' i = case i of + [d] -> \v -> InfiniteTensor (Infinite.Covariant [d]) $ (\_ -> Scalar v) <$> ([0..] :: [Int]) + _ -> \_ -> Err invalidIndices +
src/Multilinear/Generic.hs view
@@ -1,1070 +1,1030 @@-{-|-Module : Multilinear.Generic.AsArray-Description : Generic array tensor-Copyright : (c) Artur M. Brodzki, 2018-License : BSD3-Maintainer : artur@brodzki.org-Stability : experimental-Portability : Windows/POSIX--- This module contains generic implementation of tensor defined as nested arrays---}--module Multilinear.Generic (- Tensor(..), (!), mergeScalars,- isScalar, isSimple, isFiniteTensor, isInfiniteTensor,- dot, _elemByElem, contractionErr, tensorIndex, _standardize-) where--import Control.DeepSeq-import Data.Bits-import Data.Foldable-import Data.List-import Data.Maybe-import Data.Monoid-import qualified Data.Vector as Boxed-import GHC.Generics-import Multilinear.Class as Multilinear-import qualified Multilinear.Index as Index-import qualified Multilinear.Index.Finite as Finite-import qualified Multilinear.Index.Infinite as Infinite--{-| ERROR MESSAGES -}-incompatibleTypes :: String-incompatibleTypes = "Incompatible tensor types!"--scalarIndices :: String-scalarIndices = "Scalar has no indices!"--differentIndices :: String-differentIndices = "Tensors have different indices!"--infiniteIndex :: String-infiniteIndex = "Index is infinitely-dimensional!"--infiniteTensor :: String-infiniteTensor = "This tensor is infinitely-dimensional and cannot be printed!"--indexNotFound :: String-indexNotFound = "This tensor has not such index!"--{-| Tensor defined recursively as scalar or list of other tensors -}-{-| @c@ is type of a container, @i@ is type of index size and @a@ is type of tensor elements -}-data Tensor a =- {-| Scalar -}- Scalar {- {-| value of scalar -}- scalarVal :: a- } |- {-| Simple, one-dimensional finite tensor -}- SimpleFinite {- tensorFiniteIndex :: Finite.Index,- tensorScalars :: Boxed.Vector a- } |- {-| Finite array of other tensors -}- FiniteTensor {- {-| Finite index "Mutltilinear.Index.Finite" of tensor -}- tensorFiniteIndex :: Finite.Index,- {-| Array of tensors on deeper recursion level -}- tensorsFinite :: Boxed.Vector (Tensor a)- } |- {-| Infinite list of other tensors -}- InfiniteTensor {- {-| Infinite index "Mutltilinear.Index.Infinite" of tensor -}- tensorInfiniteIndex :: Infinite.Index,- {-| Infinite list of tensors on deeper recursion level -}- tensorsInfinite :: [Tensor a]- } |- {-| Operations on tensors may throw an error -}- Err {- {-| Error message -}- errMessage :: String- } deriving (Eq, Generic)--{-| Return true if tensor is a scalar -}-{-# INLINE isScalar #-}-isScalar :: Tensor a -> Bool-isScalar x = case x of- Scalar _ -> True- _ -> False--{-| Return true if tensor is a simple tensor -}-{-# INLINE isSimple #-}-isSimple :: Tensor a -> Bool-isSimple x = case x of- SimpleFinite _ _ -> True- _ -> False--{-| Return True if tensor is a complex tensor -}-{-# INLINE isFiniteTensor #-}-isFiniteTensor :: Tensor a -> Bool-isFiniteTensor x = case x of- FiniteTensor _ _ -> True- _ -> False--{-| Return True if tensor is a infinite tensor -}-{-# INLINE isInfiniteTensor #-}-isInfiniteTensor :: Tensor a -> Bool-isInfiniteTensor x = case x of- InfiniteTensor _ _ -> True- _ -> False--{- Return True if tensor is a error tensor -}-{-# INLINE isErrTensor #-}-isErrTensor :: Tensor a -> Bool-isErrTensor x = case x of- Err _ -> True- _ -> False--{-| Return generic tensor index -}-{-# INLINE tensorIndex #-}-tensorIndex :: Tensor a -> Index.TIndex-tensorIndex x = case x of- Scalar _ -> error scalarIndices- SimpleFinite i _ -> Index.toTIndex i- FiniteTensor i _ -> Index.toTIndex i- InfiniteTensor i _ -> Index.toTIndex i- Err msg -> error msg--{-| Return True if tensor has no elements -}-{-# INLINE isEmptyTensor #-}-isEmptyTensor :: Tensor a -> Bool-isEmptyTensor x = case x of- Scalar _ -> False- SimpleFinite _ ts -> Boxed.null ts- FiniteTensor _ ts -> Boxed.null ts- InfiniteTensor _ ts -> null ts- Err _ -> False--{-| Returns sample element of the tensor. Used to determine some features common for all elements, like bit-qualities. -}-{-# INLINE firstElem #-}-firstElem :: Tensor a -> a-firstElem x = case x of- Scalar val -> val- SimpleFinite _ ts -> Boxed.head ts- FiniteTensor _ ts -> firstElem $ Boxed.head ts- InfiniteTensor _ ts -> firstElem $ head ts- Err msg -> error msg--{-| Returns sample tensor on deeper recursion level.Used to determine some features common for all tensors -}-{-# INLINE firstTensor #-}-firstTensor :: Tensor a -> Tensor a-firstTensor x = case x of- FiniteTensor _ ts -> Boxed.head ts- InfiniteTensor _ ts -> Data.List.head ts- _ -> x--{-| Recursive indexing on list tensor- @t ! i = t[i]@ -}-{-# INLINE (!) #-}-(!) :: Tensor a -- ^ tensor @t@- -> Int -- ^ index @i@- -> Tensor a -- ^ tensor @t[i]@-t ! i = case t of- Scalar _ -> Err scalarIndices- Err msg -> Err msg- SimpleFinite ind ts -> if i >= Finite.indexSize ind then error ("Index + " ++ show ind ++ " out of bonds!") else Scalar $ ts Boxed.! i- FiniteTensor ind ts -> if i >= Finite.indexSize ind then error ("Index + " ++ show ind ++ " out of bonds!") else ts Boxed.! i- InfiniteTensor _ ts -> ts !! i---- NFData instance-instance NFData a => NFData (Tensor a)---- move contravariant indices to lower recursion level-_standardize :: Num a => Tensor a -> Tensor a-_standardize tens = foldr' (\i t -> if Index.isContravariant i then t <<<| Index.indexName i else t) tens $ indices tens---- Print tensor-instance (- Show a, Num a- ) => Show (Tensor a) where-- -- merge errors first and then print whole tensor- show = show' . _standardize . _mergeErr- where- show' x = case x of- -- Scalar is showed simply as its value- Scalar v -> show v- -- SimpleFinite is shown dependent on its index...- SimpleFinite index ts -> show index ++ "S: " ++ case index of- -- If index is contravariant, show tensor components vertically- Finite.Contravariant _ _ -> _showVertical ts- -- If index is covariant or indifferent, show tensor compoments horizontally- _ -> _showHorizontal ts- -- FiniteTensor is shown dependent on its index...- FiniteTensor index ts -> show index ++ "T: " ++ case index of- -- If index is contravariant, show tensor components vertically- Finite.Contravariant _ _ -> _showVertical ts- -- If index is covariant or indifferent, show tensor compoments horizontally- _ -> _showHorizontal ts- -- Infinite tensor print erorr message as it cannot be fully shown- InfiniteTensor _ _ -> show infiniteTensor- -- Error prints its error message- Err msg -> show msg- - -- Merge many errors in tensor to the first one- _mergeErr x = case x of- -- Error tensor is passed further- Err msg -> Err msg- -- FiniteTensor is merged to first error on deeper recursion level- FiniteTensor _ ts ->- -- find first error if present- let err = Data.List.find isErrTensor (_mergeErr <$> ts)- -- and return this error if found, whole tensor otherwise- in fromMaybe x err- -- in other types of tensor cannot be any error- _ -> x-- -- print container elements vertically- -- used to show contravariant components of tensor, which by convention are written vertically- _showVertical :: (Show a, Foldable c) => c a -> String- _showVertical container =- "\n" ++ tail (foldl' (\string e -> string ++ "\n |" ++ show e) "" container)-- -- print container elements horizontally- -- used to show covariant (or indifferent) components of tensor, which by convention are written horizontally- _showHorizontal :: (Show a, Foldable c) => c a -> String- _showHorizontal container =- "[" ++ tail (foldl' (\string e -> string ++ "," ++ show e) "" container) ++ "]"---- Tensor is a functor-instance Functor Tensor where-- {-# INLINE fmap #-}- fmap f x = case x of- -- Mapping scalar simply maps its value- Scalar v -> Scalar $ f v- -- Mapping complex tensor does mapping element by element- SimpleFinite index ts -> SimpleFinite index (f <$> ts)- FiniteTensor index ts -> FiniteTensor index $ fmap (fmap f) ts- InfiniteTensor index ts -> InfiniteTensor index $ fmap (fmap f) ts- -- Mapping errors changes nothing- Err msg -> Err msg---- Tensors can be compared lexigographically--- Allowes to put tensors in typical ordered containers-instance (- Ord a- ) => Ord (Tensor a) where-- {-# INLINE (<=) #-}- -- Error is smaller by other tensors, so when printing ordered containers, all erorrs will be printed first- -- Two errors are compared by they messages lexigographically- Err msg1 <= Err msg2 = msg1 <= msg2- Err _ <= _ = True- _ <= Err _ = False- -- Scalar is smaller than any complex tensor- -- Two scalars are compared by they values- Scalar x1 <= Scalar x2 = x1 <= x2- Scalar _ <= _ = True- _ <= Scalar _ = False- -- Complex tensors are compared lexigographically- SimpleFinite _ ts1 <= SimpleFinite _ ts2 = ts1 <= ts2- FiniteTensor _ ts1 <= FiniteTensor _ ts2 = ts1 <= ts2- InfiniteTensor _ ts1 <= InfiniteTensor _ ts2 = ts1 <= ts2- FiniteTensor _ _ <= SimpleFinite _ _ = False- SimpleFinite _ _ <= FiniteTensor _ _ = True- InfiniteTensor _ _ <= FiniteTensor _ _ = False- FiniteTensor _ _ <= InfiniteTensor _ _ = True- InfiniteTensor _ _ <= SimpleFinite _ _ = False- SimpleFinite _ _ <= InfiniteTensor _ _ = True---- Tensors concatenation makes them a monoid-instance (- Num a- ) => Monoid (Tensor a) where-- {-| Neutral element is a scalar as it has no indices and concatenation is by common inidces -}- {-# INLINE mempty #-}- mempty = Scalar 0-- {-| Tensor concatenation -}- {-# INLINE mappend #-}- mappend t1 t2 = - -- To preserve tensor structure, indices must be the same- if indices t1 == indices t2 - then case (t1,t2) of- -- Concatenation with scalar does nothing - Scalar is a neutral element- (Scalar _, _) -> t2- (_, Scalar _) -> t1- -- Concatenation of two SimpleFiniteTensors- (SimpleFinite i1 ts1, SimpleFinite _ ts2) -> - SimpleFinite i1 $ ts1 <> ts2- -- Concatenation of two FiniteTensors- (FiniteTensor i1 ts1, FiniteTensor _ ts2) ->- FiniteTensor i1 $ ts1 <> ts2- -- Concatenation of other tensors (especially infinite ones) is impossible- _ -> Err differentIndices- -- If tensor indices are different, concatenation is impossible- else Err differentIndices--{-| Merge FiniteTensor of Scalars to SimpleFinite tensor for performance improvement -}-{-# INLINE mergeScalars #-}-mergeScalars :: Tensor a -> Tensor a-mergeScalars x = case x of- (FiniteTensor index1 ts1) -> case ts1 Boxed.! 0 of- Scalar _ -> SimpleFinite index1 (scalarVal <$> ts1)- _ -> FiniteTensor index1 $ mergeScalars <$> ts1- _ -> x--{-| Apply a tensor operator (here denoted by (+) ) elem by elem, trying to connect as many common indices as possible -}-{-# INLINE _elemByElem' #-}-_elemByElem' :: Num a - => Tensor a -- ^ First argument of operator- -> Tensor a -- ^ Second argument of operator- -> (a -> a -> a) -- ^ Operator on tensor elements if indices are different- -> (Tensor a -> Tensor a -> Tensor a) -- ^ Tensor operator called if indices are the same- -> Tensor a -- ^ Result tensor---- @Scalar x + Scalar y = Scalar x + y@-_elemByElem' (Scalar x1) (Scalar x2) f _ = Scalar $ f x1 x2--- @Scalar x + Tensor t[i] = Tensor r[i] | r[i] = x + t[i]@-_elemByElem' (Scalar x) t f _ = (x `f`) <$> t--- @Tensor t[i] + Scalar x = Tensor r[i] | r[i] = t[i] + x@-_elemByElem' t (Scalar x) f _ = (`f` x) <$> t---- Two finite tensors case-_elemByElem' t1@(FiniteTensor index1 v1) t2@(FiniteTensor index2 v2) f op- | Index.indexName index1 == Index.indexName index2 = op t1 t2- | Index.indexName index1 `Data.List.elem` indicesNames t2 =- FiniteTensor index2 $ (\x -> _elemByElem' t1 x f op) <$> v2- | otherwise = FiniteTensor index1 $ (\x -> _elemByElem' x t2 f op) <$> v1---- Two infinite tensors case-_elemByElem' t1@(InfiniteTensor index1 v1) t2@(InfiniteTensor index2 v2) f op- | Index.indexName index1 == Index.indexName index2 = op t1 t2- | Index.indexName index1 `Data.List.elem` indicesNames t2 =- InfiniteTensor index2 $ (\x -> _elemByElem' t1 x f op) <$> v2- | otherwise = InfiniteTensor index1 $ (\x -> _elemByElem' x t2 f op) <$> v1---- Two simple tensors case-_elemByElem' t1@(SimpleFinite index1 v1) t2@(SimpleFinite index2 _) f op- | Index.indexName index1 == Index.indexName index2 = op t1 t2- | otherwise = FiniteTensor index1 $ (\x -> f x <$> t2) <$> v1---- Finite and infinite tensor case-_elemByElem' t1@(FiniteTensor index1 v1) t2@(InfiniteTensor index2 v2) f op- | Index.indexName index1 == Index.indexName index2 = op t1 t2- | Index.indexName index1 `Data.List.elem` indicesNames t2 =- InfiniteTensor index2 $ (\x -> _elemByElem' t1 x f op) <$> v2- | otherwise = FiniteTensor index1 $ (\x -> _elemByElem' x t2 f op) <$> v1---- Infinite and finite tensor case-_elemByElem' t1@(InfiniteTensor index1 v1) t2@(FiniteTensor index2 v2) f op- | Index.indexName index1 == Index.indexName index2 = op t1 t2- | Index.indexName index1 `Data.List.elem` indicesNames t2 =- FiniteTensor index2 $ (\x -> _elemByElem' t1 x f op) <$> v2- | otherwise = InfiniteTensor index1 $ (\x -> _elemByElem' x t2 f op) <$> v1---- Simple and finite tensor case-_elemByElem' t1@(SimpleFinite index1 _) t2@(FiniteTensor index2 v2) f op- | Index.indexName index1 == Index.indexName index2 = op t1 t2- | otherwise = FiniteTensor index2 $ (\x -> _elemByElem' t1 x f op) <$> v2---- Finite and simple tensor case-_elemByElem' t1@(FiniteTensor index1 v1) t2@(SimpleFinite index2 _) f op- | Index.indexName index1 == Index.indexName index2 = op t1 t2- | otherwise = FiniteTensor index1 $ (\x -> _elemByElem' x t2 f op) <$> v1---- Simple and infinite tensor case-_elemByElem' t1@(SimpleFinite index1 _) t2@(InfiniteTensor index2 v2) f op- | Index.indexName index1 == Index.indexName index2 = op t1 t2- | otherwise = InfiniteTensor index2 $ (\x -> _elemByElem' t1 x f op) <$> v2---- Infinite and simple tensor case-_elemByElem' t1@(InfiniteTensor index1 v1) t2@(SimpleFinite index2 _) f op- | Index.indexName index1 == Index.indexName index2 = op t1 t2- | otherwise = InfiniteTensor index1 $ (\x -> _elemByElem' x t2 f op) <$> v1---- Appying operator to error tensor simply pushes this error further-_elemByElem' (Err msg) _ _ _ = Err msg-_elemByElem' _ (Err msg) _ _ = Err msg--{-| Apply a tensor operator elem by elem and merge scalars to simple tensor at the and -}-{-# INLINE _elemByElem #-}-_elemByElem :: Num a - => Tensor a -- ^ First argument of operator- -> Tensor a -- ^ Second argument of operator- -> (a -> a -> a) -- ^ Operator on tensor elements if indices are different- -> (Tensor a -> Tensor a -> Tensor a) -- ^ Tensor operator called if indices are the same- -> Tensor a -- ^ Result tensor-_elemByElem t1 t2 f op = - let commonIndices = filter (`Data.List.elem` indicesNames t2) $ indicesNames t1- t1' = foldl' (|>>>) t1 commonIndices- t2' = foldl' (|>>>) t2 commonIndices- in mergeScalars $ _elemByElem' t1' t2' f op---- Zipping two tensors with a combinator, assuming they have the same indices-{-# INLINE zipT #-}-zipT :: Num a- => (Tensor a -> Tensor a -> Tensor a) -- ^ Two tensors combinator- -> (Tensor a -> a -> Tensor a) -- ^ Tensor and scalar combinator- -> (a -> Tensor a -> Tensor a) -- ^ Scalar and tensor combinator- -> (a -> a -> a) -- ^ Two scalars combinator- -> Tensor a -- ^ First tensor to zip- -> Tensor a -- ^ Second tensor to zip- -> Tensor a -- ^ Result tensor---- Two simple tensors case-zipT _ _ _ f (SimpleFinite index1 v1) (SimpleFinite index2 v2) = - if index1 == index2 then SimpleFinite index1 $ Boxed.zipWith f v1 v2 else Err incompatibleTypes----Two finite tensors case-zipT f _ _ _ (FiniteTensor index1 v1) (FiniteTensor index2 v2) = - if index1 == index2 then FiniteTensor index1 $ Boxed.zipWith f v1 v2 else Err incompatibleTypes---- Two infinte tensors case-zipT f _ _ _ (InfiniteTensor index1 v1) (InfiniteTensor index2 v2) = - if index1 == index2 then InfiniteTensor index1 $ Data.List.zipWith f v1 v2 else Err incompatibleTypes---- Infinite and finite tensor case-zipT f _ _ _ (InfiniteTensor _ v1) (FiniteTensor index2 v2) = - FiniteTensor index2 $ Boxed.zipWith f (Boxed.fromList $ take (Boxed.length v2) v1) v2---- Finite and infinite tensor case-zipT f _ _ _ (FiniteTensor index1 v1) (InfiniteTensor _ v2) = - FiniteTensor index1 $ Boxed.zipWith f v1 (Boxed.fromList $ take (Boxed.length v1) v2)---- Finite and simple tensor case-zipT _ f _ _ (FiniteTensor index1 v1) (SimpleFinite index2 v2) = - if index1 == index2 then FiniteTensor index1 $ Boxed.zipWith f v1 v2 else Err incompatibleTypes---- Simple and finite tensor case-zipT _ _ f _ (SimpleFinite index1 v1) (FiniteTensor index2 v2) = - if index1 == index2 then FiniteTensor index1 $ Boxed.zipWith f v1 v2 else Err incompatibleTypes---- Infinite and simple tensor case-zipT _ f _ _ (InfiniteTensor _ v1) (SimpleFinite index2 v2) = - FiniteTensor index2 $ Boxed.zipWith f (Boxed.fromList $ take (Boxed.length v2) v1) v2---- Simple and infinite tensor case-zipT _ _ f _ (SimpleFinite index1 v1) (InfiniteTensor _ v2) = - FiniteTensor index1 $ Boxed.zipWith f v1 (Boxed.fromList $ take (Boxed.length v1) v2)---- Zipping error tensor simply pushes this erorr further-zipT _ _ _ _ (Err msg) _ = Err msg-zipT _ _ _ _ _ (Err msg) = Err msg---- Zipping something with scalar is impossible-zipT _ _ _ _ _ _ = Err scalarIndices---- dot product of two tensors-{-# INLINE dot #-}-dot :: Num a- => Tensor a -- ^ First dot product argument- -> Tensor a -- ^ Second dot product argument- -> Tensor a -- ^ Resulting dot product---- Two simple tensors product-dot (SimpleFinite i1@(Finite.Covariant count1 _) ts1') (SimpleFinite i2@(Finite.Contravariant count2 _) ts2')- | count1 == count2 = - Scalar $ Boxed.sum $ Boxed.zipWith (*) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)-dot (SimpleFinite i1@(Finite.Contravariant count1 _) ts1') (SimpleFinite i2@(Finite.Contravariant count2 _) ts2')- | count1 == count2 = - SimpleFinite i1 $ Boxed.zipWith (*) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)-dot (SimpleFinite i1@(Finite.Covariant count1 _) ts1') (SimpleFinite i2@(Finite.Covariant count2 _) ts2')- | count1 == count2 = - SimpleFinite i1 $ Boxed.zipWith (*) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)---- Two finite tensors product-dot (FiniteTensor i1@(Finite.Covariant count1 _) ts1') (FiniteTensor i2@(Finite.Contravariant count2 _) ts2')- | count1 == count2 = Boxed.sum $ Boxed.zipWith (*) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)-dot (FiniteTensor i1@(Finite.Contravariant count1 _) ts1') (FiniteTensor i2@(Finite.Contravariant count2 _) ts2')- | count1 == count2 = FiniteTensor i1 $ Boxed.zipWith (*) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)-dot (FiniteTensor i1@(Finite.Covariant count1 _) ts1') (FiniteTensor i2@(Finite.Covariant count2 _) ts2')- | count1 == count2 = FiniteTensor i1 $ Boxed.zipWith (*) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)----- Simple tensor and finite tensor product-dot (SimpleFinite i1@(Finite.Covariant count1 _) ts1') (FiniteTensor i2@(Finite.Contravariant count2 _) ts2')- | count1 == count2 = Boxed.sum $ Boxed.zipWith (*.) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)-dot (SimpleFinite i1@(Finite.Contravariant count1 _) ts1') (FiniteTensor i2@(Finite.Contravariant count2 _) ts2')- | count1 == count2 = FiniteTensor i1 $ Boxed.zipWith (*.) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)-dot (SimpleFinite i1@(Finite.Covariant count1 _) ts1') (FiniteTensor i2@(Finite.Covariant count2 _) ts2')- | count1 == count2 = FiniteTensor i1 $ Boxed.zipWith (*.) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)---- Finite tensor and simple tensor product-dot (FiniteTensor i1@(Finite.Covariant count1 _) ts1') (SimpleFinite i2@(Finite.Contravariant count2 _) ts2')- | count1 == count2 = Boxed.sum $ Boxed.zipWith (.*) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)-dot (FiniteTensor i1@(Finite.Contravariant count1 _) ts1') (SimpleFinite i2@(Finite.Contravariant count2 _) ts2')- | count1 == count2 = FiniteTensor i1 $ Boxed.zipWith (.*) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)-dot (FiniteTensor i1@(Finite.Covariant count1 _) ts1') (SimpleFinite i2@(Finite.Covariant count2 _) ts2')- | count1 == count2 = FiniteTensor i1 $ Boxed.zipWith (.*) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)---- Simple tensor and infinite tensor product-dot (SimpleFinite (Finite.Covariant count1 _) ts1') (InfiniteTensor (Infinite.Contravariant _) ts2') = - Boxed.sum $ Boxed.zipWith (*.) ts1' (Boxed.fromList $ take count1 ts2')-dot (SimpleFinite (Finite.Contravariant count1 _) ts1') (InfiniteTensor i2@(Infinite.Contravariant _) ts2') = - InfiniteTensor i2 $ Boxed.toList $ Boxed.zipWith (*.) ts1' (Boxed.fromList $ take count1 ts2')-dot (SimpleFinite (Finite.Covariant count1 _) ts1') (InfiniteTensor i2@(Infinite.Covariant _) ts2') = - InfiniteTensor i2 $ Boxed.toList $ Boxed.zipWith (*.) ts1' (Boxed.fromList $ take count1 ts2')---- Infinite tensor and simple tensor product-dot (InfiniteTensor (Infinite.Covariant _) ts1') (SimpleFinite (Finite.Contravariant count2 _) ts2') = - Boxed.sum $ Boxed.zipWith (.*) (Boxed.fromList $ take count2 ts1') ts2'-dot (InfiniteTensor i1@(Infinite.Contravariant _) ts1') (SimpleFinite (Finite.Contravariant count2 _) ts2') = - InfiniteTensor i1 $ Boxed.toList $ Boxed.zipWith (.*) (Boxed.fromList $ take count2 ts1') ts2'-dot (InfiniteTensor i1@(Infinite.Covariant _) ts1') (SimpleFinite (Finite.Covariant count2 _) ts2') = - InfiniteTensor i1 $ Boxed.toList $ Boxed.zipWith (.*) (Boxed.fromList $ take count2 ts1') ts2'---- Finite tensor and infinite tensor product-dot (FiniteTensor (Finite.Covariant count1 _) ts1') (InfiniteTensor (Infinite.Contravariant _) ts2') = - Boxed.sum $ Boxed.zipWith (*) ts1' (Boxed.fromList $ take count1 ts2')-dot (FiniteTensor (Finite.Contravariant count1 _) ts1') (InfiniteTensor i2@(Infinite.Contravariant _) ts2') = - InfiniteTensor i2 $ Boxed.toList $ Boxed.zipWith (*) ts1' (Boxed.fromList $ take count1 ts2')-dot (FiniteTensor (Finite.Covariant count1 _) ts1') (InfiniteTensor i2@(Infinite.Covariant _) ts2') = - InfiniteTensor i2 $ Boxed.toList $ Boxed.zipWith (*) ts1' (Boxed.fromList $ take count1 ts2')---- Infinite tensor and finite tensor product-dot (InfiniteTensor (Infinite.Covariant _) ts1') (FiniteTensor (Finite.Contravariant count2 _) ts2') = - Boxed.sum $ Boxed.zipWith (*) (Boxed.fromList $ take count2 ts1') ts2'-dot (InfiniteTensor i1@(Infinite.Contravariant _) ts1') (FiniteTensor (Finite.Contravariant count2 _) ts2') = - InfiniteTensor i1 $ Boxed.toList $ Boxed.zipWith (*) (Boxed.fromList $ take count2 ts1') ts2'-dot (InfiniteTensor i1@(Infinite.Covariant _) ts1') (FiniteTensor (Finite.Covariant count2 _) ts2') = - InfiniteTensor i1 $ Boxed.toList $ Boxed.zipWith (*) (Boxed.fromList $ take count2 ts1') ts2'---- In other cases cannot happen!-dot t1' t2' = contractionErr (tensorIndex t1') (tensorIndex t2')---- bit dot product of two tensors-{-# INLINE bitDot #-}-bitDot :: (- Num a, Bits a- ) => Tensor a -- ^ First dot product argument- -> Tensor a -- ^ Second dot product argument- -> Tensor a -- ^ Resulting dot product---- Two finite tensors product-bitDot (FiniteTensor i1@(Finite.Covariant count1 _) ts1') (FiniteTensor i2@(Finite.Contravariant count2 _) ts2')- | count1 == count2 = Data.Foldable.foldl' (.|.) 0 $ Boxed.zipWith (.&.) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)---- Two simple tensors product-bitDot (SimpleFinite i1@(Finite.Covariant count1 _) ts1') (SimpleFinite i2@(Finite.Contravariant count2 _) ts2')- | count1 == count2 = - let dotProduct v1 v2 = Data.Foldable.foldl' (.|.) 0 $ Boxed.zipWith (.&.) v1 v2- in Scalar $ dotProduct ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)---- Simple tensor and finite tensor product-bitDot (SimpleFinite i1@(Finite.Covariant count1 _) ts1') (FiniteTensor i2@(Finite.Contravariant count2 _) ts2')- | count1 == count2 = Data.Foldable.foldl' (.|.) 0 $ Boxed.zipWith (\e t -> (e .&.) <$> t) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)---- Finite tensor and simple tensor product-bitDot (FiniteTensor i1@(Finite.Covariant count1 _) ts1') (SimpleFinite i2@(Finite.Contravariant count2 _) ts2')- | count1 == count2 = Data.Foldable.foldl' (.|.) 0 $ Boxed.zipWith (\t e -> (.&. e) <$> t) ts1' ts2'- | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2)---- Simple tensor and infinite tensor product-bitDot (SimpleFinite (Finite.Covariant count1 _) ts1') (InfiniteTensor (Infinite.Contravariant _) ts2') = - Data.Foldable.foldl' (.|.) 0 $ Boxed.zipWith (\e t -> (e .&.) <$> t) ts1' (Boxed.fromList $ take count1 ts2')---- Infinite tensor and simple tensor product-bitDot (InfiniteTensor (Infinite.Covariant _) ts1') (SimpleFinite (Finite.Contravariant count2 _) ts2') = - Data.Foldable.foldl' (.|.) 0 $ Boxed.zipWith (\t e -> (.&. e) <$> t) (Boxed.fromList $ take count2 ts1') ts2'---- Finite tensor and infinite tensor product-bitDot (FiniteTensor (Finite.Covariant count1 _) ts1') (InfiniteTensor (Infinite.Contravariant _) ts2') = - Boxed.sum $ Boxed.zipWith (*) ts1' (Boxed.fromList $ take count1 ts2')---- Infinite tensor and finite tensor product-bitDot (InfiniteTensor (Infinite.Covariant _) ts1') (FiniteTensor (Finite.Contravariant count2 _) ts2') = - Boxed.sum $ Boxed.zipWith (*) (Boxed.fromList $ take count2 ts1') ts2'---- In other cases cannot happen!-bitDot t1' t2' = contractionErr (tensorIndex t1') (tensorIndex t2')---- contraction error-{-# INLINE contractionErr #-}-contractionErr :: Index.TIndex -- ^ Index of first dot product parameter- -> Index.TIndex -- ^ Index of second dot product parameter- -> Tensor a -- ^ Erorr message--contractionErr i1' i2' = Err $- "Tensor product: " ++ incompatibleTypes ++- " - index1 is " ++ show i1' ++- " and index2 is " ++ show i2'---- Tensors can be added, subtracted and multiplicated-instance Num a => Num (Tensor a) where-- -- Adding - element by element- {-# INLINE (+) #-}- t1 + t2 = _elemByElem t1 t2 (+) $ zipT (+) (.+) (+.) (+)-- -- Subtracting - element by element- {-# INLINE (-) #-}- t1 - t2 = _elemByElem t1 t2 (-) $ zipT (-) (.-) (-.) (-)-- -- Multiplicating is treated as tensor product- -- Tensor product applies Einstein summation convention- {-# INLINE (*) #-}- t1 * t2 = _elemByElem t1 t2 (*) dot-- -- Absolute value - element by element- {-# INLINE abs #-}- abs t = abs <$> t-- -- Signum operation - element by element- {-# INLINE signum #-}- signum t = signum <$> t-- -- Simple integer can be conveted to Scalar- {-# INLINE fromInteger #-}- fromInteger x = Scalar $ fromInteger x---- Bit operations on tensors-instance (- Num a, Bits a- ) => Bits (Tensor a) where-- -- Bit sum - elem by elem- {-# INLINE (.|.) #-}- t1 .|. t2 = _elemByElem t1 t2 (.|.) $ zipT (.|.) (\t e -> (.|. e) <$> t) (\e t -> (e .|.) <$> t) (.|.)-- -- Bit tensor product- -- Summation and multiplication are replaced by its bit equivalents- -- Two scalars are multiplicated by their values- {-# INLINE (.&.) #-}- t1 .&. t2 = _elemByElem t1 t2 (.&.) bitDot-- -- Bit exclusive sum (XOR) - elem by elem- {-# INLINE xor #-}- t1 `xor` t2 = _elemByElem t1 t2 xor $ zipT xor (\t e -> (`xor` e) <$> t) (\e t -> (e `xor`) <$> t) xor-- -- Bit complement- {-# INLINE complement #-}- complement = Multilinear.map complement-- -- Bit shift of all elements- {-# INLINE shift #-}- shift t n = Multilinear.map (`shift` n) t-- -- Bit rotating of all elements- {-# INLINE rotate #-}- rotate t n = Multilinear.map (`rotate` n) t-- -- Returns number of bits of elements of tensor, -1 for elements of undefined size- {-# INLINE bitSize #-}- bitSize (Scalar x) = fromMaybe (-1) $ bitSizeMaybe x- bitSize (Err _) = -1- bitSize t =- if isEmptyTensor t- then (-1)- else fromMaybe (-1) $ bitSizeMaybe $ firstElem t-- -- Returns number of bits of elements of tensor- {-# INLINE bitSizeMaybe #-}- bitSizeMaybe (Scalar x) = bitSizeMaybe x- bitSizeMaybe (Err _) = Nothing- bitSizeMaybe t =- if isEmptyTensor t- then Nothing- else bitSizeMaybe $ firstElem t-- -- Returns true if tensors element are signed- {-# INLINE isSigned #-}- isSigned (Scalar x) = isSigned x- isSigned (Err _) = False- isSigned t =- not (isEmptyTensor t) &&- isSigned (firstElem t)-- -- bit i is a scalar value with the ith bit set and all other bits clear.- {-# INLINE bit #-}- bit i = Scalar (bit i)-- -- Test bit - shoud retur True, if bit n if equal to 1.- -- Tensors are entities with many elements, so this function always returns False.- -- Do not use it, it is implemented only for legacy purposes.- {-# INLINE testBit #-}- testBit _ _ = False-- -- Return the number of set bits in the argument. This number is known as the population count or the Hamming weight.- {-# INLINE popCount #-}- popCount = popCountDefault---- Tensors can be divided by each other-instance Fractional a => Fractional (Tensor a) where-- {-# INLINE (/) #-}- -- Scalar division return result of division of its values- Scalar x1 / Scalar x2 = Scalar $ x1 / x2- -- Tensor and scalar are divided value by value- Scalar x1 / t2 = (x1 /) <$> t2- t1 / Scalar x2 = (/ x2) <$> t1- Err msg / _ = Err msg- _ / Err msg = Err msg- -- Two complex tensors cannot be (for now) simply divided- -- // TODO - tensor division and inversion- _ / _ = Err "TODO"-- -- A scalar can be generated from rational number- {-# INLINE fromRational #-}- fromRational x = Scalar $ fromRational x---- Real-number functions on tensors.--- Function of tensor is tensor of function of its elements--- E.g. exp [1,2,3,4] = [exp 1, exp2, exp3, exp4]-instance Floating a => Floating (Tensor a) where-- {-| PI number -}- {-# INLINE pi #-}- pi = Scalar pi-- {-| Exponential function. (exp t)[i] = exp( t[i] ) -}- {-# INLINE exp #-}- exp t = exp <$> t-- {-| Natural logarithm. (log t)[i] = log( t[i] ) -}- {-# INLINE log #-}- log t = log <$> t-- {-| Sinus. (sin t)[i] = sin( t[i] ) -}- {-# INLINE sin #-}- sin t = sin <$> t-- {-| Cosinus. (cos t)[i] = cos( t[i] ) -}- {-# INLINE cos #-}- cos t = cos <$> t-- {-| Inverse sinus. (asin t)[i] = asin( t[i] ) -}- {-# INLINE asin #-}- asin t = asin <$> t-- {-| Inverse cosinus. (acos t)[i] = acos( t[i] ) -}- {-# INLINE acos #-}- acos t = acos <$> t-- {-| Inverse tangent. (atan t)[i] = atan( t[i] ) -}- {-# INLINE atan #-}- atan t = atan <$> t-- {-| Hyperbolic sinus. (sinh t)[i] = sinh( t[i] ) -}- {-# INLINE sinh #-}- sinh t = sinh <$> t-- {-| Hyperbolic cosinus. (cosh t)[i] = cosh( t[i] ) -}- {-# INLINE cosh #-}- cosh t = cosh <$> t-- {-| Inverse hyperbolic sinus. (asinh t)[i] = asinh( t[i] ) -}- {-# INLINE asinh #-}- asinh t = acosh <$> t-- {-| Inverse hyperbolic cosinus. (acosh t)[i] = acosh (t[i] ) -}- {-# INLINE acosh #-}- acosh t = acosh <$> t-- {-| Inverse hyperbolic tangent. (atanh t)[i] = atanh( t[i] ) -}- {-# INLINE atanh #-}- atanh t = atanh <$> t---- Multilinear operations-instance Num a => Multilinear Tensor a where-- -- Add scalar right- {-# INLINE (.+) #-}- t .+ x = (+x) <$> t-- -- Subtract scalar right- {-# INLINE (.-) #-}- t .- x = (\p -> p - x) <$> t-- -- Multiplicate by scalar right- {-# INLINE (.*) #-}- t .* x = (*x) <$> t-- -- Add scalar left- {-# INLINE (+.) #-}- x +. t = (x+) <$> t-- -- Subtract scalar left- {-# INLINE (-.) #-}- x -. t = (x-) <$> t-- -- Multiplicate by scalar left- {-# INLINE (*.) #-}- x *. t = (x*) <$> t-- -- Two tensors sum- {-# INLINE (.+.) #-}- t1 .+. t2 = _elemByElem t1 t2 (+) $ zipT (+) (.+) (+.) (+)-- -- Two tensors difference- {-# INLINE (.-.) #-}- t1 .-. t2 = _elemByElem t1 t2 (-) $ zipT (+) (.+) (+.) (+)-- -- Tensor product- {-# INLINE (.*.) #-}- t1 .*. t2 = _elemByElem t1 t2 (+) dot-- -- List of all tensor indices- {-# INLINE indices #-}- indices x = case x of- Scalar _ -> []- FiniteTensor i ts -> Index.toTIndex i : indices (head $ toList ts)- InfiniteTensor i ts -> Index.toTIndex i : indices (head ts)- SimpleFinite i _ -> [Index.toTIndex i]- Err _ -> []-- -- Get tensor order [ (contravariant,covariant)-type ]- {-# INLINE order #-}- order x = case x of- Scalar _ -> (0,0)- SimpleFinite index _ -> case index of- Finite.Contravariant _ _ -> (1,0)- Finite.Covariant _ _ -> (0,1)- Finite.Indifferent _ _ -> (0,0)- Err _ -> (-1,-1)- _ -> let (cnvr, covr) = order $ firstTensor x- in case tensorIndex x of- Index.Contravariant _ _ -> (cnvr+1,covr)- Index.Covariant _ _ -> (cnvr,covr+1)- Index.Indifferent _ _ -> (cnvr,covr)-- -- Get size of tensor index or Left if index is infinite or tensor has no such index- {-# INLINE size #-}- size t iname = case t of- Scalar _ -> error scalarIndices- SimpleFinite index _ -> - if Index.indexName index == iname - then Finite.indexSize index - else error indexNotFound- FiniteTensor index _ -> - if Index.indexName index == iname- then Finite.indexSize index- else size (firstTensor t) iname- InfiniteTensor _ _ -> error infiniteIndex- Err msg -> error msg-- -- Rename tensor indices- {-# INLINE ($|) #-}- - Scalar x $| _ = Scalar x- SimpleFinite (Finite.Contravariant isize _) ts $| (u:_, _) = SimpleFinite (Finite.Contravariant isize [u]) ts- SimpleFinite (Finite.Covariant isize _) ts $| (_, d:_) = SimpleFinite (Finite.Covariant isize [d]) ts- FiniteTensor (Finite.Contravariant isize _) ts $| (u:us, ds) = FiniteTensor (Finite.Contravariant isize [u]) $ ($| (us,ds)) <$> ts- FiniteTensor (Finite.Covariant isize _) ts $| (us, d:ds) = FiniteTensor (Finite.Covariant isize [d]) $ ($| (us,ds)) <$> ts- InfiniteTensor (Infinite.Contravariant _) ts $| (u:us, ds) = InfiniteTensor (Infinite.Contravariant [u]) $ ($| (us,ds)) <$> ts- InfiniteTensor (Infinite.Covariant _) ts $| (us, d:ds) = InfiniteTensor (Infinite.Covariant [d]) $ ($| (us,ds)) <$> ts- Err msg $| _ = Err msg- t $| _ = t-- -- Raise an index- {-# INLINE (/\) #-}- Scalar x /\ _ = Scalar x- FiniteTensor index ts /\ n- | Index.indexName index == n =- FiniteTensor (Finite.Contravariant (Finite.indexSize index) n) $ (/\ n) <$> ts- | otherwise =- FiniteTensor index $ (/\ n) <$> ts- InfiniteTensor index ts /\ n- | Index.indexName index == n =- InfiniteTensor (Infinite.Contravariant n) $ (/\ n) <$> ts- | otherwise =- InfiniteTensor index $ (/\ n) <$> ts- t1@(SimpleFinite index ts) /\ n- | Index.indexName index == n =- SimpleFinite (Finite.Contravariant (Finite.indexSize index) n) ts- | otherwise = t1- Err msg /\ _ = Err msg-- -- Lower an index- {-# INLINE (\/) #-}- Scalar x \/ _ = Scalar x- FiniteTensor index ts \/ n- | Index.indexName index == n =- FiniteTensor (Finite.Covariant (Finite.indexSize index) n) $ (\/ n) <$> ts- | otherwise =- FiniteTensor index $ (\/ n) <$> ts- InfiniteTensor index ts \/ n- | Index.indexName index == n =- InfiniteTensor (Infinite.Covariant n) $ (\/ n) <$> ts- | otherwise =- InfiniteTensor index $ (\/ n) <$> ts- t1@(SimpleFinite index ts) \/ n- | Index.indexName index == n =- SimpleFinite (Finite.Covariant (Finite.indexSize index) n) ts- | otherwise = t1- Err msg \/ _ = Err msg-- {-| Transpose a tensor (switch all indices types) -}- {-# INLINE transpose #-}- transpose (Scalar x) = Scalar x-- transpose (FiniteTensor (Finite.Covariant count name) ts) =- FiniteTensor (Finite.Contravariant count name) (Multilinear.transpose <$> ts)- transpose (FiniteTensor (Finite.Contravariant count name) ts) =- FiniteTensor (Finite.Covariant count name) (Multilinear.transpose <$> ts)- transpose (FiniteTensor (Finite.Indifferent count name) ts) =- FiniteTensor (Finite.Indifferent count name) (Multilinear.transpose <$> ts)-- transpose (InfiniteTensor (Infinite.Covariant name) ts) =- InfiniteTensor (Infinite.Contravariant name) (Multilinear.transpose <$> ts)- transpose (InfiniteTensor (Infinite.Contravariant name) ts) =- InfiniteTensor (Infinite.Covariant name) (Multilinear.transpose <$> ts)- transpose (InfiniteTensor (Infinite.Indifferent name) ts) =- InfiniteTensor (Infinite.Indifferent name) (Multilinear.transpose <$> ts)-- transpose (SimpleFinite (Finite.Covariant count name) ts) =- SimpleFinite (Finite.Contravariant count name) ts- transpose (SimpleFinite (Finite.Contravariant count name) ts) =- SimpleFinite (Finite.Covariant count name) ts- transpose (SimpleFinite (Finite.Indifferent count name) ts) =- SimpleFinite (Finite.Indifferent count name) ts-- transpose (Err msg) = Err msg-- {-| Concatenation of two tensor with given index or by creating a new one -}- {-# INLINE augment #-}- augment t1 t2 ind =- let t1' = t1 <<<| ind- t2' = t2 <<<| ind- in t1' <> t2'-- {-| Shift tensor index right -}- {-| Moves given index one level deeper in recursion -}- {-# INLINE shiftRight #-}- -- Error tensor has no indices to shift- Err msg `shiftRight` _ = Err msg- -- Scalar has no indices to shift- Scalar x `shiftRight` _ = Scalar x- -- Simple tensor has only one index which cannot be shifted- t1@(SimpleFinite _ _) `shiftRight` _ = t1- -- Finite tensor is shifted by converting to list and transposing it- t1@(FiniteTensor index1 ts1) `shiftRight` ind- -- We don't shift this index- | Data.List.length (indicesNames t1) > 1 && Index.indexName index1 /= ind =- FiniteTensor index1 $ (|>> ind) <$> ts1- -- We found index to shift- | Data.List.length (indicesNames t1) > 1 && Index.indexName index1 == ind =- -- Next index- let index2 = tensorFiniteIndex (ts1 Boxed.! 0)- -- Elements to transpose- dane = if isSimple (ts1 Boxed.! 0)- then (Scalar <$>) <$> (tensorScalars <$> ts1)- else tensorsFinite <$> ts1- -- Convert to list- daneList = Boxed.toList <$> Boxed.toList dane- -- and transpose tensor data (standard function available only for list)- transposedList = Data.List.transpose daneList- -- then reconvert to vector again- transposed = Boxed.fromList <$> Boxed.fromList transposedList- -- and reconstruct tensor with transposed elements- in mergeScalars $ FiniteTensor index2 $ FiniteTensor index1 <$> transposed- | otherwise = t1-- -- Infinite tensor is shifted by transposing nested lists- t1@(InfiniteTensor index1 ts1) `shiftRight` ind- -- We don't shift this index- | Data.List.length (indicesNames t1) > 1 && Index.indexName index1 /= ind =- InfiniteTensor index1 $ (|>> ind) <$> ts1- -- We found index to shift- | Data.List.length (indicesNames t1) > 1 && Index.indexName index1 == ind =- -- Next index- let index2 = tensorInfiniteIndex (head ts1)- -- Elements to transpose- dane = if isSimple (head ts1)- then (Scalar <$>) <$> (Boxed.toList . tensorScalars <$> ts1)- else tensorsInfinite <$> ts1- -- transpose tensor data (standard function available only for list)- transposed = Data.List.transpose dane- -- and reconstruct tensor with transposed elements- in mergeScalars $ InfiniteTensor index2 $ InfiniteTensor index1 <$> transposed- | otherwise = t1---{-| List allows for random access to tensor elements -}-instance Num a => Accessible Tensor a where-- {-| Accessing tensor elements -}- {-# INLINE el #-}-- -- Scalar has only one element- el (Scalar x) _ = Scalar x-- -- simple tensor case- el t1@(SimpleFinite index1 _) (inds,vals) =- -- zip indices with their given values- let indvals = zip inds vals- -- find value for simple tensor index if given- val = Data.List.find (\(n,_) -> [n] == Index.indexName index1) indvals- -- if value for current index is given- in if isJust val- -- then get it from current tensor- then t1 ! snd (fromJust val)- -- otherwise return whole tensor - no filtering defined- else t1-- -- finite tensor case- el t1@(FiniteTensor index1 v1) (inds,vals) =- -- zip indices with their given values- let indvals = zip inds vals- -- find value for current index if given- val = Data.List.find (\(n,_) -> [n] == Index.indexName index1) indvals- -- and remove used index from indices list- indvals1 = Data.List.filter (\(n,_) -> [n] /= Index.indexName index1) indvals- -- indices unused so far- inds1 = Data.List.map fst indvals1- -- and its corresponding values- vals1 = Data.List.map snd indvals1- -- if value for current index was given- in if isJust val- -- then get it from current tensor and recursively process other indices- then el (t1 ! snd (fromJust val)) (inds1,vals1)- -- otherwise recursively access elements of all child tensors- else FiniteTensor index1 $ (\t -> el t (inds,vals)) <$> v1-- -- infinite tensor case- el t1@(InfiniteTensor index1 v1) (inds,vals) =- -- zip indices with their given values- let indvals = zip inds vals- -- find value for current index if given- val = Data.List.find (\(n,_) -> [n] == Index.indexName index1) indvals- -- and remove used index from indices list- indvals1 = Data.List.filter (\(n,_) -> [n] /= Index.indexName index1) indvals- -- indices unused so far- inds1 = Data.List.map fst indvals1- -- and its corresponding values- vals1 = Data.List.map snd indvals1- -- if value for current index was given- in if isJust val- -- then get it from current tensor and recursively process other indices- then el (t1 ! snd (fromJust val)) (inds1,vals1)- -- otherwise recursively access elements of all child tensors- else InfiniteTensor index1 $ (\t -> el t (inds,vals)) <$> v1-- -- accessing elements of erorr tensor simply pushes this error further- el (Err msg) _ = Err msg-- {-| Mapping with indices. -}- {-# INLINE iMap #-}- iMap f t = iMap' t zeroList- where- zeroList = 0:zeroList-- iMap' (Scalar x) inds =- Scalar $ f inds x- iMap' (SimpleFinite index ts) inds =- SimpleFinite index $ Boxed.imap (\i e -> f (inds ++ [i]) e) ts- iMap' (FiniteTensor index ts) inds =- FiniteTensor index $ Boxed.imap (\i e -> iMap' e (inds ++ [i])) ts- iMap' (InfiniteTensor index ts) inds =- InfiniteTensor index $ (\tind -> iMap' (fst tind) $ inds ++ [snd tind]) <$> zip ts [0..]- iMap' (Err msg) _ =- Err msg+{-| +Module : Multilinear.Generic.AsArray +Description : Generic array tensor +Copyright : (c) Artur M. Brodzki, 2018 +License : BSD3 +Maintainer : artur@brodzki.org +Stability : experimental +Portability : Windows/POSIX + +- This module contains generic implementation of tensor defined as nested arrays + +-} + +module Multilinear.Generic ( + Tensor(..), (!), mergeScalars, + isScalar, isSimple, isFiniteTensor, isInfiniteTensor, + dot, _elemByElem, contractionErr, tensorIndex, _standardize +) where + +import Control.DeepSeq +import Data.Bits +import Data.Foldable +import Data.List +import Data.Maybe +import qualified Data.Vector as Boxed +import GHC.Generics +import Multilinear.Class as Multilinear +import qualified Multilinear.Index as Index +import qualified Multilinear.Index.Finite as Finite +import qualified Multilinear.Index.Infinite as Infinite + +{-| ERROR MESSAGES -} +incompatibleTypes :: String +incompatibleTypes = "Incompatible tensor types!" + +scalarIndices :: String +scalarIndices = "Scalar has no indices!" + +infiniteIndex :: String +infiniteIndex = "Index is infinitely-dimensional!" + +infiniteTensor :: String +infiniteTensor = "This tensor is infinitely-dimensional and cannot be printed!" + +indexNotFound :: String +indexNotFound = "This tensor has not such index!" + +{-| Tensor defined recursively as scalar or list of other tensors -} +{-| @c@ is type of a container, @i@ is type of index size and @a@ is type of tensor elements -} +data Tensor a = + {-| Scalar -} + Scalar { + {-| value of scalar -} + scalarVal :: a + } | + {-| Simple, one-dimensional finite tensor -} + SimpleFinite { + tensorFiniteIndex :: Finite.Index, + tensorScalars :: Boxed.Vector a + } | + {-| Finite array of other tensors -} + FiniteTensor { + {-| Finite index "Mutltilinear.Index.Finite" of tensor -} + tensorFiniteIndex :: Finite.Index, + {-| Array of tensors on deeper recursion level -} + tensorsFinite :: Boxed.Vector (Tensor a) + } | + {-| Infinite list of other tensors -} + InfiniteTensor { + {-| Infinite index "Mutltilinear.Index.Infinite" of tensor -} + tensorInfiniteIndex :: Infinite.Index, + {-| Infinite list of tensors on deeper recursion level -} + tensorsInfinite :: [Tensor a] + } | + {-| Operations on tensors may throw an error -} + Err { + {-| Error message -} + errMessage :: String + } deriving (Eq, Generic) + +{-| Return true if tensor is a scalar -} +{-# INLINE isScalar #-} +isScalar :: Tensor a -> Bool +isScalar x = case x of + Scalar _ -> True + _ -> False + +{-| Return true if tensor is a simple tensor -} +{-# INLINE isSimple #-} +isSimple :: Tensor a -> Bool +isSimple x = case x of + SimpleFinite _ _ -> True + _ -> False + +{-| Return True if tensor is a complex tensor -} +{-# INLINE isFiniteTensor #-} +isFiniteTensor :: Tensor a -> Bool +isFiniteTensor x = case x of + FiniteTensor _ _ -> True + _ -> False + +{-| Return True if tensor is a infinite tensor -} +{-# INLINE isInfiniteTensor #-} +isInfiniteTensor :: Tensor a -> Bool +isInfiniteTensor x = case x of + InfiniteTensor _ _ -> True + _ -> False + +{- Return True if tensor is a error tensor -} +{-# INLINE isErrTensor #-} +isErrTensor :: Tensor a -> Bool +isErrTensor x = case x of + Err _ -> True + _ -> False + +{-| Return generic tensor index -} +{-# INLINE tensorIndex #-} +tensorIndex :: Tensor a -> Index.TIndex +tensorIndex x = case x of + Scalar _ -> error scalarIndices + SimpleFinite i _ -> Index.toTIndex i + FiniteTensor i _ -> Index.toTIndex i + InfiniteTensor i _ -> Index.toTIndex i + Err msg -> error msg + +{-| Return True if tensor has no elements -} +{-# INLINE isEmptyTensor #-} +isEmptyTensor :: Tensor a -> Bool +isEmptyTensor x = case x of + Scalar _ -> False + SimpleFinite _ ts -> Boxed.null ts + FiniteTensor _ ts -> Boxed.null ts + InfiniteTensor _ ts -> null ts + Err _ -> False + +{-| Returns sample element of the tensor. Used to determine some features common for all elements, like bit-qualities. -} +{-# INLINE firstElem #-} +firstElem :: Tensor a -> a +firstElem x = case x of + Scalar val -> val + SimpleFinite _ ts -> Boxed.head ts + FiniteTensor _ ts -> firstElem $ Boxed.head ts + InfiniteTensor _ ts -> firstElem $ head ts + Err msg -> error msg + +{-| Returns sample tensor on deeper recursion level.Used to determine some features common for all tensors -} +{-# INLINE firstTensor #-} +firstTensor :: Tensor a -> Tensor a +firstTensor x = case x of + FiniteTensor _ ts -> Boxed.head ts + InfiniteTensor _ ts -> Data.List.head ts + _ -> x + +{-| Recursive indexing on list tensor + @t ! i = t[i]@ -} +{-# INLINE (!) #-} +(!) :: Tensor a -- ^ tensor @t@ + -> Int -- ^ index @i@ + -> Tensor a -- ^ tensor @t[i]@ +t ! i = case t of + Scalar _ -> Err scalarIndices + Err msg -> Err msg + SimpleFinite ind ts -> if i >= Finite.indexSize ind then error ("Index + " ++ show ind ++ " out of bonds!") else Scalar $ ts Boxed.! i + FiniteTensor ind ts -> if i >= Finite.indexSize ind then error ("Index + " ++ show ind ++ " out of bonds!") else ts Boxed.! i + InfiniteTensor _ ts -> ts !! i + +-- NFData instance +instance NFData a => NFData (Tensor a) + +-- move contravariant indices to lower recursion level +_standardize :: Num a => Tensor a -> Tensor a +_standardize tens = foldr' (\i t -> if Index.isContravariant i then t <<<| Index.indexName i else t) tens $ indices tens + +-- Print tensor +instance ( + Show a, Num a + ) => Show (Tensor a) where + + -- merge errors first and then print whole tensor + show = show' . _standardize . _mergeErr + where + show' x = case x of + -- Scalar is showed simply as its value + Scalar v -> show v + -- SimpleFinite is shown dependent on its index... + SimpleFinite index ts -> show index ++ "S: " ++ case index of + -- If index is contravariant, show tensor components vertically + Finite.Contravariant _ _ -> _showVertical ts + -- If index is covariant or indifferent, show tensor compoments horizontally + _ -> _showHorizontal ts + -- FiniteTensor is shown dependent on its index... + FiniteTensor index ts -> show index ++ "T: " ++ case index of + -- If index is contravariant, show tensor components vertically + Finite.Contravariant _ _ -> _showVertical ts + -- If index is covariant or indifferent, show tensor compoments horizontally + _ -> _showHorizontal ts + -- Infinite tensor print erorr message as it cannot be fully shown + InfiniteTensor _ _ -> show infiniteTensor + -- Error prints its error message + Err msg -> show msg + + -- Merge many errors in tensor to the first one + _mergeErr x = case x of + -- Error tensor is passed further + Err msg -> Err msg + -- FiniteTensor is merged to first error on deeper recursion level + FiniteTensor _ ts -> + -- find first error if present + let err = Data.List.find isErrTensor (_mergeErr <$> ts) + -- and return this error if found, whole tensor otherwise + in fromMaybe x err + -- in other types of tensor cannot be any error + _ -> x + + -- print container elements vertically + -- used to show contravariant components of tensor, which by convention are written vertically + _showVertical :: (Show a, Foldable c) => c a -> String + _showVertical container = + "\n" ++ tail (foldl' (\string e -> string ++ "\n |" ++ show e) "" container) + + -- print container elements horizontally + -- used to show covariant (or indifferent) components of tensor, which by convention are written horizontally + _showHorizontal :: (Show a, Foldable c) => c a -> String + _showHorizontal container = + "[" ++ tail (foldl' (\string e -> string ++ "," ++ show e) "" container) ++ "]" + +-- Tensor is a functor +instance Functor Tensor where + + {-# INLINE fmap #-} + fmap f x = case x of + -- Mapping scalar simply maps its value + Scalar v -> Scalar $ f v + -- Mapping complex tensor does mapping element by element + SimpleFinite index ts -> SimpleFinite index (f <$> ts) + FiniteTensor index ts -> FiniteTensor index $ fmap (fmap f) ts + InfiniteTensor index ts -> InfiniteTensor index $ fmap (fmap f) ts + -- Mapping errors changes nothing + Err msg -> Err msg + +-- Tensors can be compared lexigographically +-- Allowes to put tensors in typical ordered containers +instance ( + Ord a + ) => Ord (Tensor a) where + + {-# INLINE (<=) #-} + -- Error is smaller by other tensors, so when printing ordered containers, all erorrs will be printed first + -- Two errors are compared by they messages lexigographically + Err msg1 <= Err msg2 = msg1 <= msg2 + Err _ <= _ = True + _ <= Err _ = False + -- Scalar is smaller than any complex tensor + -- Two scalars are compared by they values + Scalar x1 <= Scalar x2 = x1 <= x2 + Scalar _ <= _ = True + _ <= Scalar _ = False + -- Complex tensors are compared lexigographically + SimpleFinite _ ts1 <= SimpleFinite _ ts2 = ts1 <= ts2 + FiniteTensor _ ts1 <= FiniteTensor _ ts2 = ts1 <= ts2 + InfiniteTensor _ ts1 <= InfiniteTensor _ ts2 = ts1 <= ts2 + FiniteTensor _ _ <= SimpleFinite _ _ = False + SimpleFinite _ _ <= FiniteTensor _ _ = True + InfiniteTensor _ _ <= FiniteTensor _ _ = False + FiniteTensor _ _ <= InfiniteTensor _ _ = True + InfiniteTensor _ _ <= SimpleFinite _ _ = False + SimpleFinite _ _ <= InfiniteTensor _ _ = True + +{-| Merge FiniteTensor of Scalars to SimpleFinite tensor for performance improvement -} +{-# INLINE mergeScalars #-} +mergeScalars :: Tensor a -> Tensor a +mergeScalars x = case x of + (FiniteTensor index1 ts1) -> case ts1 Boxed.! 0 of + Scalar _ -> SimpleFinite index1 (scalarVal <$> ts1) + _ -> FiniteTensor index1 $ mergeScalars <$> ts1 + _ -> x + +{-| Apply a tensor operator (here denoted by (+) ) elem by elem, trying to connect as many common indices as possible -} +{-# INLINE _elemByElem' #-} +_elemByElem' :: Num a + => Tensor a -- ^ First argument of operator + -> Tensor a -- ^ Second argument of operator + -> (a -> a -> a) -- ^ Operator on tensor elements if indices are different + -> (Tensor a -> Tensor a -> Tensor a) -- ^ Tensor operator called if indices are the same + -> Tensor a -- ^ Result tensor + +-- @Scalar x + Scalar y = Scalar x + y@ +_elemByElem' (Scalar x1) (Scalar x2) f _ = Scalar $ f x1 x2 +-- @Scalar x + Tensor t[i] = Tensor r[i] | r[i] = x + t[i]@ +_elemByElem' (Scalar x) t f _ = (x `f`) <$> t +-- @Tensor t[i] + Scalar x = Tensor r[i] | r[i] = t[i] + x@ +_elemByElem' t (Scalar x) f _ = (`f` x) <$> t + +-- Two finite tensors case +_elemByElem' t1@(FiniteTensor index1 v1) t2@(FiniteTensor index2 v2) f op + | Index.indexName index1 == Index.indexName index2 = op t1 t2 + | Index.indexName index1 `Data.List.elem` indicesNames t2 = + FiniteTensor index2 $ (\x -> _elemByElem' t1 x f op) <$> v2 + | otherwise = FiniteTensor index1 $ (\x -> _elemByElem' x t2 f op) <$> v1 + +-- Two infinite tensors case +_elemByElem' t1@(InfiniteTensor index1 v1) t2@(InfiniteTensor index2 v2) f op + | Index.indexName index1 == Index.indexName index2 = op t1 t2 + | Index.indexName index1 `Data.List.elem` indicesNames t2 = + InfiniteTensor index2 $ (\x -> _elemByElem' t1 x f op) <$> v2 + | otherwise = InfiniteTensor index1 $ (\x -> _elemByElem' x t2 f op) <$> v1 + +-- Two simple tensors case +_elemByElem' t1@(SimpleFinite index1 v1) t2@(SimpleFinite index2 _) f op + | Index.indexName index1 == Index.indexName index2 = op t1 t2 + | otherwise = FiniteTensor index1 $ (\x -> f x <$> t2) <$> v1 + +-- Finite and infinite tensor case +_elemByElem' t1@(FiniteTensor index1 v1) t2@(InfiniteTensor index2 v2) f op + | Index.indexName index1 == Index.indexName index2 = op t1 t2 + | Index.indexName index1 `Data.List.elem` indicesNames t2 = + InfiniteTensor index2 $ (\x -> _elemByElem' t1 x f op) <$> v2 + | otherwise = FiniteTensor index1 $ (\x -> _elemByElem' x t2 f op) <$> v1 + +-- Infinite and finite tensor case +_elemByElem' t1@(InfiniteTensor index1 v1) t2@(FiniteTensor index2 v2) f op + | Index.indexName index1 == Index.indexName index2 = op t1 t2 + | Index.indexName index1 `Data.List.elem` indicesNames t2 = + FiniteTensor index2 $ (\x -> _elemByElem' t1 x f op) <$> v2 + | otherwise = InfiniteTensor index1 $ (\x -> _elemByElem' x t2 f op) <$> v1 + +-- Simple and finite tensor case +_elemByElem' t1@(SimpleFinite index1 _) t2@(FiniteTensor index2 v2) f op + | Index.indexName index1 == Index.indexName index2 = op t1 t2 + | otherwise = FiniteTensor index2 $ (\x -> _elemByElem' t1 x f op) <$> v2 + +-- Finite and simple tensor case +_elemByElem' t1@(FiniteTensor index1 v1) t2@(SimpleFinite index2 _) f op + | Index.indexName index1 == Index.indexName index2 = op t1 t2 + | otherwise = FiniteTensor index1 $ (\x -> _elemByElem' x t2 f op) <$> v1 + +-- Simple and infinite tensor case +_elemByElem' t1@(SimpleFinite index1 _) t2@(InfiniteTensor index2 v2) f op + | Index.indexName index1 == Index.indexName index2 = op t1 t2 + | otherwise = InfiniteTensor index2 $ (\x -> _elemByElem' t1 x f op) <$> v2 + +-- Infinite and simple tensor case +_elemByElem' t1@(InfiniteTensor index1 v1) t2@(SimpleFinite index2 _) f op + | Index.indexName index1 == Index.indexName index2 = op t1 t2 + | otherwise = InfiniteTensor index1 $ (\x -> _elemByElem' x t2 f op) <$> v1 + +-- Appying operator to error tensor simply pushes this error further +_elemByElem' (Err msg) _ _ _ = Err msg +_elemByElem' _ (Err msg) _ _ = Err msg + +{-| Apply a tensor operator elem by elem and merge scalars to simple tensor at the and -} +{-# INLINE _elemByElem #-} +_elemByElem :: Num a + => Tensor a -- ^ First argument of operator + -> Tensor a -- ^ Second argument of operator + -> (a -> a -> a) -- ^ Operator on tensor elements if indices are different + -> (Tensor a -> Tensor a -> Tensor a) -- ^ Tensor operator called if indices are the same + -> Tensor a -- ^ Result tensor +_elemByElem t1 t2 f op = + let commonIndices = filter (`Data.List.elem` indicesNames t2) $ indicesNames t1 + t1' = foldl' (|>>>) t1 commonIndices + t2' = foldl' (|>>>) t2 commonIndices + in mergeScalars $ _elemByElem' t1' t2' f op + +-- Zipping two tensors with a combinator, assuming they have the same indices +{-# INLINE zipT #-} +zipT :: Num a + => (Tensor a -> Tensor a -> Tensor a) -- ^ Two tensors combinator + -> (Tensor a -> a -> Tensor a) -- ^ Tensor and scalar combinator + -> (a -> Tensor a -> Tensor a) -- ^ Scalar and tensor combinator + -> (a -> a -> a) -- ^ Two scalars combinator + -> Tensor a -- ^ First tensor to zip + -> Tensor a -- ^ Second tensor to zip + -> Tensor a -- ^ Result tensor + +-- Two simple tensors case +zipT _ _ _ f (SimpleFinite index1 v1) (SimpleFinite index2 v2) = + if index1 == index2 then SimpleFinite index1 $ Boxed.zipWith f v1 v2 else Err incompatibleTypes + +--Two finite tensors case +zipT f _ _ _ (FiniteTensor index1 v1) (FiniteTensor index2 v2) = + if index1 == index2 then FiniteTensor index1 $ Boxed.zipWith f v1 v2 else Err incompatibleTypes + +-- Two infinte tensors case +zipT f _ _ _ (InfiniteTensor index1 v1) (InfiniteTensor index2 v2) = + if index1 == index2 then InfiniteTensor index1 $ Data.List.zipWith f v1 v2 else Err incompatibleTypes + +-- Infinite and finite tensor case +zipT f _ _ _ (InfiniteTensor _ v1) (FiniteTensor index2 v2) = + FiniteTensor index2 $ Boxed.zipWith f (Boxed.fromList $ take (Boxed.length v2) v1) v2 + +-- Finite and infinite tensor case +zipT f _ _ _ (FiniteTensor index1 v1) (InfiniteTensor _ v2) = + FiniteTensor index1 $ Boxed.zipWith f v1 (Boxed.fromList $ take (Boxed.length v1) v2) + +-- Finite and simple tensor case +zipT _ f _ _ (FiniteTensor index1 v1) (SimpleFinite index2 v2) = + if index1 == index2 then FiniteTensor index1 $ Boxed.zipWith f v1 v2 else Err incompatibleTypes + +-- Simple and finite tensor case +zipT _ _ f _ (SimpleFinite index1 v1) (FiniteTensor index2 v2) = + if index1 == index2 then FiniteTensor index1 $ Boxed.zipWith f v1 v2 else Err incompatibleTypes + +-- Infinite and simple tensor case +zipT _ f _ _ (InfiniteTensor _ v1) (SimpleFinite index2 v2) = + FiniteTensor index2 $ Boxed.zipWith f (Boxed.fromList $ take (Boxed.length v2) v1) v2 + +-- Simple and infinite tensor case +zipT _ _ f _ (SimpleFinite index1 v1) (InfiniteTensor _ v2) = + FiniteTensor index1 $ Boxed.zipWith f v1 (Boxed.fromList $ take (Boxed.length v1) v2) + +-- Zipping error tensor simply pushes this erorr further +zipT _ _ _ _ (Err msg) _ = Err msg +zipT _ _ _ _ _ (Err msg) = Err msg + +-- Zipping something with scalar is impossible +zipT _ _ _ _ _ _ = Err scalarIndices + +-- dot product of two tensors +{-# INLINE dot #-} +dot :: Num a + => Tensor a -- ^ First dot product argument + -> Tensor a -- ^ Second dot product argument + -> Tensor a -- ^ Resulting dot product + +-- Two simple tensors product +dot (SimpleFinite i1@(Finite.Covariant count1 _) ts1') (SimpleFinite i2@(Finite.Contravariant count2 _) ts2') + | count1 == count2 = + Scalar $ Boxed.sum $ Boxed.zipWith (*) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) +dot (SimpleFinite i1@(Finite.Contravariant count1 _) ts1') (SimpleFinite i2@(Finite.Contravariant count2 _) ts2') + | count1 == count2 = + SimpleFinite i1 $ Boxed.zipWith (*) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) +dot (SimpleFinite i1@(Finite.Covariant count1 _) ts1') (SimpleFinite i2@(Finite.Covariant count2 _) ts2') + | count1 == count2 = + SimpleFinite i1 $ Boxed.zipWith (*) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) + +-- Two finite tensors product +dot (FiniteTensor i1@(Finite.Covariant count1 _) ts1') (FiniteTensor i2@(Finite.Contravariant count2 _) ts2') + | count1 == count2 = Boxed.sum $ Boxed.zipWith (*) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) +dot (FiniteTensor i1@(Finite.Contravariant count1 _) ts1') (FiniteTensor i2@(Finite.Contravariant count2 _) ts2') + | count1 == count2 = FiniteTensor i1 $ Boxed.zipWith (*) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) +dot (FiniteTensor i1@(Finite.Covariant count1 _) ts1') (FiniteTensor i2@(Finite.Covariant count2 _) ts2') + | count1 == count2 = FiniteTensor i1 $ Boxed.zipWith (*) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) + + +-- Simple tensor and finite tensor product +dot (SimpleFinite i1@(Finite.Covariant count1 _) ts1') (FiniteTensor i2@(Finite.Contravariant count2 _) ts2') + | count1 == count2 = Boxed.sum $ Boxed.zipWith (*.) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) +dot (SimpleFinite i1@(Finite.Contravariant count1 _) ts1') (FiniteTensor i2@(Finite.Contravariant count2 _) ts2') + | count1 == count2 = FiniteTensor i1 $ Boxed.zipWith (*.) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) +dot (SimpleFinite i1@(Finite.Covariant count1 _) ts1') (FiniteTensor i2@(Finite.Covariant count2 _) ts2') + | count1 == count2 = FiniteTensor i1 $ Boxed.zipWith (*.) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) + +-- Finite tensor and simple tensor product +dot (FiniteTensor i1@(Finite.Covariant count1 _) ts1') (SimpleFinite i2@(Finite.Contravariant count2 _) ts2') + | count1 == count2 = Boxed.sum $ Boxed.zipWith (.*) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) +dot (FiniteTensor i1@(Finite.Contravariant count1 _) ts1') (SimpleFinite i2@(Finite.Contravariant count2 _) ts2') + | count1 == count2 = FiniteTensor i1 $ Boxed.zipWith (.*) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) +dot (FiniteTensor i1@(Finite.Covariant count1 _) ts1') (SimpleFinite i2@(Finite.Covariant count2 _) ts2') + | count1 == count2 = FiniteTensor i1 $ Boxed.zipWith (.*) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) + +-- Simple tensor and infinite tensor product +dot (SimpleFinite (Finite.Covariant count1 _) ts1') (InfiniteTensor (Infinite.Contravariant _) ts2') = + Boxed.sum $ Boxed.zipWith (*.) ts1' (Boxed.fromList $ take count1 ts2') +dot (SimpleFinite (Finite.Contravariant count1 _) ts1') (InfiniteTensor i2@(Infinite.Contravariant _) ts2') = + InfiniteTensor i2 $ Boxed.toList $ Boxed.zipWith (*.) ts1' (Boxed.fromList $ take count1 ts2') +dot (SimpleFinite (Finite.Covariant count1 _) ts1') (InfiniteTensor i2@(Infinite.Covariant _) ts2') = + InfiniteTensor i2 $ Boxed.toList $ Boxed.zipWith (*.) ts1' (Boxed.fromList $ take count1 ts2') + +-- Infinite tensor and simple tensor product +dot (InfiniteTensor (Infinite.Covariant _) ts1') (SimpleFinite (Finite.Contravariant count2 _) ts2') = + Boxed.sum $ Boxed.zipWith (.*) (Boxed.fromList $ take count2 ts1') ts2' +dot (InfiniteTensor i1@(Infinite.Contravariant _) ts1') (SimpleFinite (Finite.Contravariant count2 _) ts2') = + InfiniteTensor i1 $ Boxed.toList $ Boxed.zipWith (.*) (Boxed.fromList $ take count2 ts1') ts2' +dot (InfiniteTensor i1@(Infinite.Covariant _) ts1') (SimpleFinite (Finite.Covariant count2 _) ts2') = + InfiniteTensor i1 $ Boxed.toList $ Boxed.zipWith (.*) (Boxed.fromList $ take count2 ts1') ts2' + +-- Finite tensor and infinite tensor product +dot (FiniteTensor (Finite.Covariant count1 _) ts1') (InfiniteTensor (Infinite.Contravariant _) ts2') = + Boxed.sum $ Boxed.zipWith (*) ts1' (Boxed.fromList $ take count1 ts2') +dot (FiniteTensor (Finite.Contravariant count1 _) ts1') (InfiniteTensor i2@(Infinite.Contravariant _) ts2') = + InfiniteTensor i2 $ Boxed.toList $ Boxed.zipWith (*) ts1' (Boxed.fromList $ take count1 ts2') +dot (FiniteTensor (Finite.Covariant count1 _) ts1') (InfiniteTensor i2@(Infinite.Covariant _) ts2') = + InfiniteTensor i2 $ Boxed.toList $ Boxed.zipWith (*) ts1' (Boxed.fromList $ take count1 ts2') + +-- Infinite tensor and finite tensor product +dot (InfiniteTensor (Infinite.Covariant _) ts1') (FiniteTensor (Finite.Contravariant count2 _) ts2') = + Boxed.sum $ Boxed.zipWith (*) (Boxed.fromList $ take count2 ts1') ts2' +dot (InfiniteTensor i1@(Infinite.Contravariant _) ts1') (FiniteTensor (Finite.Contravariant count2 _) ts2') = + InfiniteTensor i1 $ Boxed.toList $ Boxed.zipWith (*) (Boxed.fromList $ take count2 ts1') ts2' +dot (InfiniteTensor i1@(Infinite.Covariant _) ts1') (FiniteTensor (Finite.Covariant count2 _) ts2') = + InfiniteTensor i1 $ Boxed.toList $ Boxed.zipWith (*) (Boxed.fromList $ take count2 ts1') ts2' + +-- In other cases cannot happen! +dot t1' t2' = contractionErr (tensorIndex t1') (tensorIndex t2') + +-- bit dot product of two tensors +{-# INLINE bitDot #-} +bitDot :: ( + Num a, Bits a + ) => Tensor a -- ^ First dot product argument + -> Tensor a -- ^ Second dot product argument + -> Tensor a -- ^ Resulting dot product + +-- Two finite tensors product +bitDot (FiniteTensor i1@(Finite.Covariant count1 _) ts1') (FiniteTensor i2@(Finite.Contravariant count2 _) ts2') + | count1 == count2 = Data.Foldable.foldl' (.|.) 0 $ Boxed.zipWith (.&.) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) + +-- Two simple tensors product +bitDot (SimpleFinite i1@(Finite.Covariant count1 _) ts1') (SimpleFinite i2@(Finite.Contravariant count2 _) ts2') + | count1 == count2 = + let dotProduct v1 v2 = Data.Foldable.foldl' (.|.) 0 $ Boxed.zipWith (.&.) v1 v2 + in Scalar $ dotProduct ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) + +-- Simple tensor and finite tensor product +bitDot (SimpleFinite i1@(Finite.Covariant count1 _) ts1') (FiniteTensor i2@(Finite.Contravariant count2 _) ts2') + | count1 == count2 = Data.Foldable.foldl' (.|.) 0 $ Boxed.zipWith (\e t -> (e .&.) <$> t) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) + +-- Finite tensor and simple tensor product +bitDot (FiniteTensor i1@(Finite.Covariant count1 _) ts1') (SimpleFinite i2@(Finite.Contravariant count2 _) ts2') + | count1 == count2 = Data.Foldable.foldl' (.|.) 0 $ Boxed.zipWith (\t e -> (.&. e) <$> t) ts1' ts2' + | otherwise = contractionErr (Index.toTIndex i1) (Index.toTIndex i2) + +-- Simple tensor and infinite tensor product +bitDot (SimpleFinite (Finite.Covariant count1 _) ts1') (InfiniteTensor (Infinite.Contravariant _) ts2') = + Data.Foldable.foldl' (.|.) 0 $ Boxed.zipWith (\e t -> (e .&.) <$> t) ts1' (Boxed.fromList $ take count1 ts2') + +-- Infinite tensor and simple tensor product +bitDot (InfiniteTensor (Infinite.Covariant _) ts1') (SimpleFinite (Finite.Contravariant count2 _) ts2') = + Data.Foldable.foldl' (.|.) 0 $ Boxed.zipWith (\t e -> (.&. e) <$> t) (Boxed.fromList $ take count2 ts1') ts2' + +-- Finite tensor and infinite tensor product +bitDot (FiniteTensor (Finite.Covariant count1 _) ts1') (InfiniteTensor (Infinite.Contravariant _) ts2') = + Boxed.sum $ Boxed.zipWith (*) ts1' (Boxed.fromList $ take count1 ts2') + +-- Infinite tensor and finite tensor product +bitDot (InfiniteTensor (Infinite.Covariant _) ts1') (FiniteTensor (Finite.Contravariant count2 _) ts2') = + Boxed.sum $ Boxed.zipWith (*) (Boxed.fromList $ take count2 ts1') ts2' + +-- In other cases cannot happen! +bitDot t1' t2' = contractionErr (tensorIndex t1') (tensorIndex t2') + +-- contraction error +{-# INLINE contractionErr #-} +contractionErr :: Index.TIndex -- ^ Index of first dot product parameter + -> Index.TIndex -- ^ Index of second dot product parameter + -> Tensor a -- ^ Erorr message + +contractionErr i1' i2' = Err $ + "Tensor product: " ++ incompatibleTypes ++ + " - index1 is " ++ show i1' ++ + " and index2 is " ++ show i2' + +-- Tensors can be added, subtracted and multiplicated +instance Num a => Num (Tensor a) where + + -- Adding - element by element + {-# INLINE (+) #-} + t1 + t2 = _elemByElem t1 t2 (+) $ zipT (+) (.+) (+.) (+) + + -- Subtracting - element by element + {-# INLINE (-) #-} + t1 - t2 = _elemByElem t1 t2 (-) $ zipT (-) (.-) (-.) (-) + + -- Multiplicating is treated as tensor product + -- Tensor product applies Einstein summation convention + {-# INLINE (*) #-} + t1 * t2 = _elemByElem t1 t2 (*) dot + + -- Absolute value - element by element + {-# INLINE abs #-} + abs t = abs <$> t + + -- Signum operation - element by element + {-# INLINE signum #-} + signum t = signum <$> t + + -- Simple integer can be conveted to Scalar + {-# INLINE fromInteger #-} + fromInteger x = Scalar $ fromInteger x + +-- Bit operations on tensors +instance ( + Num a, Bits a + ) => Bits (Tensor a) where + + -- Bit sum - elem by elem + {-# INLINE (.|.) #-} + t1 .|. t2 = _elemByElem t1 t2 (.|.) $ zipT (.|.) (\t e -> (.|. e) <$> t) (\e t -> (e .|.) <$> t) (.|.) + + -- Bit tensor product + -- Summation and multiplication are replaced by its bit equivalents + -- Two scalars are multiplicated by their values + {-# INLINE (.&.) #-} + t1 .&. t2 = _elemByElem t1 t2 (.&.) bitDot + + -- Bit exclusive sum (XOR) - elem by elem + {-# INLINE xor #-} + t1 `xor` t2 = _elemByElem t1 t2 xor $ zipT xor (\t e -> (`xor` e) <$> t) (\e t -> (e `xor`) <$> t) xor + + -- Bit complement + {-# INLINE complement #-} + complement = Multilinear.map complement + + -- Bit shift of all elements + {-# INLINE shift #-} + shift t n = Multilinear.map (`shift` n) t + + -- Bit rotating of all elements + {-# INLINE rotate #-} + rotate t n = Multilinear.map (`rotate` n) t + + -- Returns number of bits of elements of tensor, -1 for elements of undefined size + {-# INLINE bitSize #-} + bitSize (Scalar x) = fromMaybe (-1) $ bitSizeMaybe x + bitSize (Err _) = -1 + bitSize t = + if isEmptyTensor t + then (-1) + else fromMaybe (-1) $ bitSizeMaybe $ firstElem t + + -- Returns number of bits of elements of tensor + {-# INLINE bitSizeMaybe #-} + bitSizeMaybe (Scalar x) = bitSizeMaybe x + bitSizeMaybe (Err _) = Nothing + bitSizeMaybe t = + if isEmptyTensor t + then Nothing + else bitSizeMaybe $ firstElem t + + -- Returns true if tensors element are signed + {-# INLINE isSigned #-} + isSigned (Scalar x) = isSigned x + isSigned (Err _) = False + isSigned t = + not (isEmptyTensor t) && + isSigned (firstElem t) + + -- bit i is a scalar value with the ith bit set and all other bits clear. + {-# INLINE bit #-} + bit i = Scalar (bit i) + + -- Test bit - shoud retur True, if bit n if equal to 1. + -- Tensors are entities with many elements, so this function always returns False. + -- Do not use it, it is implemented only for legacy purposes. + {-# INLINE testBit #-} + testBit _ _ = False + + -- Return the number of set bits in the argument. This number is known as the population count or the Hamming weight. + {-# INLINE popCount #-} + popCount = popCountDefault + +-- Tensors can be divided by each other +instance Fractional a => Fractional (Tensor a) where + + {-# INLINE (/) #-} + -- Scalar division return result of division of its values + Scalar x1 / Scalar x2 = Scalar $ x1 / x2 + -- Tensor and scalar are divided value by value + Scalar x1 / t2 = (x1 /) <$> t2 + t1 / Scalar x2 = (/ x2) <$> t1 + Err msg / _ = Err msg + _ / Err msg = Err msg + -- Two complex tensors cannot be (for now) simply divided + -- // TODO - tensor division and inversion + _ / _ = Err "TODO" + + -- A scalar can be generated from rational number + {-# INLINE fromRational #-} + fromRational x = Scalar $ fromRational x + +-- Real-number functions on tensors. +-- Function of tensor is tensor of function of its elements +-- E.g. exp [1,2,3,4] = [exp 1, exp2, exp3, exp4] +instance Floating a => Floating (Tensor a) where + + {-| PI number -} + {-# INLINE pi #-} + pi = Scalar pi + + {-| Exponential function. (exp t)[i] = exp( t[i] ) -} + {-# INLINE exp #-} + exp t = exp <$> t + + {-| Natural logarithm. (log t)[i] = log( t[i] ) -} + {-# INLINE log #-} + log t = log <$> t + + {-| Sinus. (sin t)[i] = sin( t[i] ) -} + {-# INLINE sin #-} + sin t = sin <$> t + + {-| Cosinus. (cos t)[i] = cos( t[i] ) -} + {-# INLINE cos #-} + cos t = cos <$> t + + {-| Inverse sinus. (asin t)[i] = asin( t[i] ) -} + {-# INLINE asin #-} + asin t = asin <$> t + + {-| Inverse cosinus. (acos t)[i] = acos( t[i] ) -} + {-# INLINE acos #-} + acos t = acos <$> t + + {-| Inverse tangent. (atan t)[i] = atan( t[i] ) -} + {-# INLINE atan #-} + atan t = atan <$> t + + {-| Hyperbolic sinus. (sinh t)[i] = sinh( t[i] ) -} + {-# INLINE sinh #-} + sinh t = sinh <$> t + + {-| Hyperbolic cosinus. (cosh t)[i] = cosh( t[i] ) -} + {-# INLINE cosh #-} + cosh t = cosh <$> t + + {-| Inverse hyperbolic sinus. (asinh t)[i] = asinh( t[i] ) -} + {-# INLINE asinh #-} + asinh t = acosh <$> t + + {-| Inverse hyperbolic cosinus. (acosh t)[i] = acosh (t[i] ) -} + {-# INLINE acosh #-} + acosh t = acosh <$> t + + {-| Inverse hyperbolic tangent. (atanh t)[i] = atanh( t[i] ) -} + {-# INLINE atanh #-} + atanh t = atanh <$> t + +-- Multilinear operations +instance Num a => Multilinear Tensor a where + + -- Add scalar right + {-# INLINE (.+) #-} + t .+ x = (+x) <$> t + + -- Subtract scalar right + {-# INLINE (.-) #-} + t .- x = (\p -> p - x) <$> t + + -- Multiplicate by scalar right + {-# INLINE (.*) #-} + t .* x = (*x) <$> t + + -- Add scalar left + {-# INLINE (+.) #-} + x +. t = (x+) <$> t + + -- Subtract scalar left + {-# INLINE (-.) #-} + x -. t = (x-) <$> t + + -- Multiplicate by scalar left + {-# INLINE (*.) #-} + x *. t = (x*) <$> t + + -- Two tensors sum + {-# INLINE (.+.) #-} + t1 .+. t2 = _elemByElem t1 t2 (+) $ zipT (+) (.+) (+.) (+) + + -- Two tensors difference + {-# INLINE (.-.) #-} + t1 .-. t2 = _elemByElem t1 t2 (-) $ zipT (+) (.+) (+.) (+) + + -- Tensor product + {-# INLINE (.*.) #-} + t1 .*. t2 = _elemByElem t1 t2 (+) dot + + -- List of all tensor indices + {-# INLINE indices #-} + indices x = case x of + Scalar _ -> [] + FiniteTensor i ts -> Index.toTIndex i : indices (head $ toList ts) + InfiniteTensor i ts -> Index.toTIndex i : indices (head ts) + SimpleFinite i _ -> [Index.toTIndex i] + Err _ -> [] + + -- Get tensor order [ (contravariant,covariant)-type ] + {-# INLINE order #-} + order x = case x of + Scalar _ -> (0,0) + SimpleFinite index _ -> case index of + Finite.Contravariant _ _ -> (1,0) + Finite.Covariant _ _ -> (0,1) + Finite.Indifferent _ _ -> (0,0) + Err _ -> (-1,-1) + _ -> let (cnvr, covr) = order $ firstTensor x + in case tensorIndex x of + Index.Contravariant _ _ -> (cnvr+1,covr) + Index.Covariant _ _ -> (cnvr,covr+1) + Index.Indifferent _ _ -> (cnvr,covr) + + -- Get size of tensor index or Left if index is infinite or tensor has no such index + {-# INLINE size #-} + size t iname = case t of + Scalar _ -> error scalarIndices + SimpleFinite index _ -> + if Index.indexName index == iname + then Finite.indexSize index + else error indexNotFound + FiniteTensor index _ -> + if Index.indexName index == iname + then Finite.indexSize index + else size (firstTensor t) iname + InfiniteTensor _ _ -> error infiniteIndex + Err msg -> error msg + + -- Rename tensor indices + {-# INLINE ($|) #-} + + Scalar x $| _ = Scalar x + SimpleFinite (Finite.Contravariant isize _) ts $| (u:_, _) = SimpleFinite (Finite.Contravariant isize [u]) ts + SimpleFinite (Finite.Covariant isize _) ts $| (_, d:_) = SimpleFinite (Finite.Covariant isize [d]) ts + FiniteTensor (Finite.Contravariant isize _) ts $| (u:us, ds) = FiniteTensor (Finite.Contravariant isize [u]) $ ($| (us,ds)) <$> ts + FiniteTensor (Finite.Covariant isize _) ts $| (us, d:ds) = FiniteTensor (Finite.Covariant isize [d]) $ ($| (us,ds)) <$> ts + InfiniteTensor (Infinite.Contravariant _) ts $| (u:us, ds) = InfiniteTensor (Infinite.Contravariant [u]) $ ($| (us,ds)) <$> ts + InfiniteTensor (Infinite.Covariant _) ts $| (us, d:ds) = InfiniteTensor (Infinite.Covariant [d]) $ ($| (us,ds)) <$> ts + Err msg $| _ = Err msg + t $| _ = t + + -- Raise an index + {-# INLINE (/\) #-} + Scalar x /\ _ = Scalar x + FiniteTensor index ts /\ n + | Index.indexName index == n = + FiniteTensor (Finite.Contravariant (Finite.indexSize index) n) $ (/\ n) <$> ts + | otherwise = + FiniteTensor index $ (/\ n) <$> ts + InfiniteTensor index ts /\ n + | Index.indexName index == n = + InfiniteTensor (Infinite.Contravariant n) $ (/\ n) <$> ts + | otherwise = + InfiniteTensor index $ (/\ n) <$> ts + t1@(SimpleFinite index ts) /\ n + | Index.indexName index == n = + SimpleFinite (Finite.Contravariant (Finite.indexSize index) n) ts + | otherwise = t1 + Err msg /\ _ = Err msg + + -- Lower an index + {-# INLINE (\/) #-} + Scalar x \/ _ = Scalar x + FiniteTensor index ts \/ n + | Index.indexName index == n = + FiniteTensor (Finite.Covariant (Finite.indexSize index) n) $ (\/ n) <$> ts + | otherwise = + FiniteTensor index $ (\/ n) <$> ts + InfiniteTensor index ts \/ n + | Index.indexName index == n = + InfiniteTensor (Infinite.Covariant n) $ (\/ n) <$> ts + | otherwise = + InfiniteTensor index $ (\/ n) <$> ts + t1@(SimpleFinite index ts) \/ n + | Index.indexName index == n = + SimpleFinite (Finite.Covariant (Finite.indexSize index) n) ts + | otherwise = t1 + Err msg \/ _ = Err msg + + {-| Transpose a tensor (switch all indices types) -} + {-# INLINE transpose #-} + transpose (Scalar x) = Scalar x + + transpose (FiniteTensor (Finite.Covariant count name) ts) = + FiniteTensor (Finite.Contravariant count name) (Multilinear.transpose <$> ts) + transpose (FiniteTensor (Finite.Contravariant count name) ts) = + FiniteTensor (Finite.Covariant count name) (Multilinear.transpose <$> ts) + transpose (FiniteTensor (Finite.Indifferent count name) ts) = + FiniteTensor (Finite.Indifferent count name) (Multilinear.transpose <$> ts) + + transpose (InfiniteTensor (Infinite.Covariant name) ts) = + InfiniteTensor (Infinite.Contravariant name) (Multilinear.transpose <$> ts) + transpose (InfiniteTensor (Infinite.Contravariant name) ts) = + InfiniteTensor (Infinite.Covariant name) (Multilinear.transpose <$> ts) + transpose (InfiniteTensor (Infinite.Indifferent name) ts) = + InfiniteTensor (Infinite.Indifferent name) (Multilinear.transpose <$> ts) + + transpose (SimpleFinite (Finite.Covariant count name) ts) = + SimpleFinite (Finite.Contravariant count name) ts + transpose (SimpleFinite (Finite.Contravariant count name) ts) = + SimpleFinite (Finite.Covariant count name) ts + transpose (SimpleFinite (Finite.Indifferent count name) ts) = + SimpleFinite (Finite.Indifferent count name) ts + + transpose (Err msg) = Err msg + + {-| Shift tensor index right -} + {-| Moves given index one level deeper in recursion -} + {-# INLINE shiftRight #-} + -- Error tensor has no indices to shift + Err msg `shiftRight` _ = Err msg + -- Scalar has no indices to shift + Scalar x `shiftRight` _ = Scalar x + -- Simple tensor has only one index which cannot be shifted + t1@(SimpleFinite _ _) `shiftRight` _ = t1 + -- Finite tensor is shifted by converting to list and transposing it + t1@(FiniteTensor index1 ts1) `shiftRight` ind + -- We don't shift this index + | Data.List.length (indicesNames t1) > 1 && Index.indexName index1 /= ind = + FiniteTensor index1 $ (|>> ind) <$> ts1 + -- We found index to shift + | Data.List.length (indicesNames t1) > 1 && Index.indexName index1 == ind = + -- Next index + let index2 = tensorFiniteIndex (ts1 Boxed.! 0) + -- Elements to transpose + dane = if isSimple (ts1 Boxed.! 0) + then (Scalar <$>) <$> (tensorScalars <$> ts1) + else tensorsFinite <$> ts1 + -- Convert to list + daneList = Boxed.toList <$> Boxed.toList dane + -- and transpose tensor data (standard function available only for list) + transposedList = Data.List.transpose daneList + -- then reconvert to vector again + transposed = Boxed.fromList <$> Boxed.fromList transposedList + -- and reconstruct tensor with transposed elements + in mergeScalars $ FiniteTensor index2 $ FiniteTensor index1 <$> transposed + | otherwise = t1 + + -- Infinite tensor is shifted by transposing nested lists + t1@(InfiniteTensor index1 ts1) `shiftRight` ind + -- We don't shift this index + | Data.List.length (indicesNames t1) > 1 && Index.indexName index1 /= ind = + InfiniteTensor index1 $ (|>> ind) <$> ts1 + -- We found index to shift + | Data.List.length (indicesNames t1) > 1 && Index.indexName index1 == ind = + -- Next index + let index2 = tensorInfiniteIndex (head ts1) + -- Elements to transpose + dane = if isSimple (head ts1) + then (Scalar <$>) <$> (Boxed.toList . tensorScalars <$> ts1) + else tensorsInfinite <$> ts1 + -- transpose tensor data (standard function available only for list) + transposed = Data.List.transpose dane + -- and reconstruct tensor with transposed elements + in mergeScalars $ InfiniteTensor index2 $ InfiniteTensor index1 <$> transposed + | otherwise = t1 + + +{-| List allows for random access to tensor elements -} +instance Num a => Accessible Tensor a where + + {-| Accessing tensor elements -} + {-# INLINE el #-} + + -- Scalar has only one element + el (Scalar x) _ = Scalar x + + -- simple tensor case + el t1@(SimpleFinite index1 _) (inds,vals) = + -- zip indices with their given values + let indvals = zip inds vals + -- find value for simple tensor index if given + val = Data.List.find (\(n,_) -> [n] == Index.indexName index1) indvals + -- if value for current index is given + in if isJust val + -- then get it from current tensor + then t1 ! snd (fromJust val) + -- otherwise return whole tensor - no filtering defined + else t1 + + -- finite tensor case + el t1@(FiniteTensor index1 v1) (inds,vals) = + -- zip indices with their given values + let indvals = zip inds vals + -- find value for current index if given + val = Data.List.find (\(n,_) -> [n] == Index.indexName index1) indvals + -- and remove used index from indices list + indvals1 = Data.List.filter (\(n,_) -> [n] /= Index.indexName index1) indvals + -- indices unused so far + inds1 = Data.List.map fst indvals1 + -- and its corresponding values + vals1 = Data.List.map snd indvals1 + -- if value for current index was given + in if isJust val + -- then get it from current tensor and recursively process other indices + then el (t1 ! snd (fromJust val)) (inds1,vals1) + -- otherwise recursively access elements of all child tensors + else FiniteTensor index1 $ (\t -> el t (inds,vals)) <$> v1 + + -- infinite tensor case + el t1@(InfiniteTensor index1 v1) (inds,vals) = + -- zip indices with their given values + let indvals = zip inds vals + -- find value for current index if given + val = Data.List.find (\(n,_) -> [n] == Index.indexName index1) indvals + -- and remove used index from indices list + indvals1 = Data.List.filter (\(n,_) -> [n] /= Index.indexName index1) indvals + -- indices unused so far + inds1 = Data.List.map fst indvals1 + -- and its corresponding values + vals1 = Data.List.map snd indvals1 + -- if value for current index was given + in if isJust val + -- then get it from current tensor and recursively process other indices + then el (t1 ! snd (fromJust val)) (inds1,vals1) + -- otherwise recursively access elements of all child tensors + else InfiniteTensor index1 $ (\t -> el t (inds,vals)) <$> v1 + + -- accessing elements of erorr tensor simply pushes this error further + el (Err msg) _ = Err msg + + {-| Mapping with indices. -} + {-# INLINE iMap #-} + iMap f t = iMap' t zeroList + where + zeroList = 0:zeroList + + iMap' (Scalar x) inds = + Scalar $ f inds x + iMap' (SimpleFinite index ts) inds = + SimpleFinite index $ Boxed.imap (\i e -> f (inds ++ [i]) e) ts + iMap' (FiniteTensor index ts) inds = + FiniteTensor index $ Boxed.imap (\i e -> iMap' e (inds ++ [i])) ts + iMap' (InfiniteTensor index ts) inds = + InfiniteTensor index $ (\tind -> iMap' (fst tind) $ inds ++ [snd tind]) <$> zip ts [0..] + iMap' (Err msg) _ = + Err msg
src/Multilinear/Index.hs view
@@ -1,105 +1,105 @@-{-|-Module : Index-Description : Implements tensor index.-Copyright : (c) Artur M. Brodzki, 2018-License : BSD3-Maintainer : artur@brodzki.org-Stability : experimental-Portability : Windows/POSIX--Generic tensor index which may be finitely- or infinitely-dimensional. ---}--module Multilinear.Index (- Index(..),- TIndex(..)-) where--{-| Tensor index class which may be lower (covariant), upper (contravariant) or indifferent. -}-class Index i where-- {-| Index name -}- indexName :: i -> String-- {-| Returns True if index is lower (covariant), False otherwise. -}- isCovariant :: i -> Bool-- {-| Returns True if index is upper (contravariant), False otherwise. -}- isContravariant :: i -> Bool-- {-| Returns True if index if indifferent, False otherwise. -}- isIndifferent :: i -> Bool-- {-| Returns True if two indices are equivalent, thus differs only by name, but share same size and type. -}- equivI :: i -> i -> Bool-- {-| Infix equivalent for 'equiv'. Has low priority equal to 2. -}- infixl 2 !=!- (!=!) :: i -> i -> Bool- i1 !=! i2 = equivI i1 i2-- {-| Convert to generic index type -}- toTIndex :: i -> TIndex--{-| Generic index type finitely- or infinitely-dimensional -}-data TIndex =- Covariant {- indexSize :: Maybe Int,- tIndexName :: String- } |- Contravariant {- indexSize :: Maybe Int,- tIndexName :: String- } |- Indifferent {- indexSize :: Maybe Int,- tIndexName :: String- }- deriving Eq--{-| Show tensor index -}-instance Show TIndex where- show (Covariant c n) = "[" ++ n ++ ":" ++ show c ++ "]"- show (Contravariant c n) = "<" ++ n ++ ":" ++ show c ++ ">"- show (Indifferent c n) = "(" ++ n ++ ":" ++ show c ++ ")"--{-| Finite index is a Multilinear.Index instance -}-instance Index TIndex where-- {-| Index name -}- indexName = tIndexName-- {-| Return true if index is covariant |-}- isCovariant (Covariant _ _) = True- isCovariant _ = False-- {-| Return true if index is contravariant |-}- isContravariant (Contravariant _ _) = True- isContravariant _ = False-- {-| Return true if index is indifferent |-}- isIndifferent (Indifferent _ _) = True- isIndifferent _ = False-- {-| Returns true if two indices are quivalent, i.e. differs only by name, but share same type and size. -}- equivI (Covariant count1 _) (Covariant count2 _)- | count1 == count2 = True- | otherwise = False- equivI (Contravariant count1 _) (Contravariant count2 _)- | count1 == count2 = True- | otherwise = False- equivI (Indifferent count1 _) (Indifferent count2 _)- | count1 == count2 = True- | otherwise = False- equivI _ _ = False-- {-| TIndex must not be converted to TIndex -}- toTIndex = id--{-| Indices can be compared by its size |-}-{-| Used to allow to put tensors to typical ordered containers |-}-instance Ord TIndex where- ind1 <= ind2 = indexSize ind1 <= indexSize ind2--+{-| +Module : Index +Description : Implements tensor index. +Copyright : (c) Artur M. Brodzki, 2018 +License : BSD3 +Maintainer : artur@brodzki.org +Stability : experimental +Portability : Windows/POSIX + +Generic tensor index which may be finitely- or infinitely-dimensional. + +-} + +module Multilinear.Index ( + Index(..), + TIndex(..) +) where + +{-| Tensor index class which may be lower (covariant), upper (contravariant) or indifferent. -} +class Index i where + + {-| Index name -} + indexName :: i -> String + + {-| Returns True if index is lower (covariant), False otherwise. -} + isCovariant :: i -> Bool + + {-| Returns True if index is upper (contravariant), False otherwise. -} + isContravariant :: i -> Bool + + {-| Returns True if index if indifferent, False otherwise. -} + isIndifferent :: i -> Bool + + {-| Returns True if two indices are equivalent, thus differs only by name, but share same size and type. -} + equivI :: i -> i -> Bool + + {-| Infix equivalent for 'equiv'. Has low priority equal to 2. -} + infixl 2 !=! + (!=!) :: i -> i -> Bool + i1 !=! i2 = equivI i1 i2 + + {-| Convert to generic index type -} + toTIndex :: i -> TIndex + +{-| Generic index type finitely- or infinitely-dimensional -} +data TIndex = + Covariant { + indexSize :: Maybe Int, + tIndexName :: String + } | + Contravariant { + indexSize :: Maybe Int, + tIndexName :: String + } | + Indifferent { + indexSize :: Maybe Int, + tIndexName :: String + } + deriving Eq + +{-| Show tensor index -} +instance Show TIndex where + show (Covariant c n) = "[" ++ n ++ ":" ++ show c ++ "]" + show (Contravariant c n) = "<" ++ n ++ ":" ++ show c ++ ">" + show (Indifferent c n) = "(" ++ n ++ ":" ++ show c ++ ")" + +{-| Finite index is a Multilinear.Index instance -} +instance Index TIndex where + + {-| Index name -} + indexName = tIndexName + + {-| Return true if index is covariant |-} + isCovariant (Covariant _ _) = True + isCovariant _ = False + + {-| Return true if index is contravariant |-} + isContravariant (Contravariant _ _) = True + isContravariant _ = False + + {-| Return true if index is indifferent |-} + isIndifferent (Indifferent _ _) = True + isIndifferent _ = False + + {-| Returns true if two indices are quivalent, i.e. differs only by name, but share same type and size. -} + equivI (Covariant count1 _) (Covariant count2 _) + | count1 == count2 = True + | otherwise = False + equivI (Contravariant count1 _) (Contravariant count2 _) + | count1 == count2 = True + | otherwise = False + equivI (Indifferent count1 _) (Indifferent count2 _) + | count1 == count2 = True + | otherwise = False + equivI _ _ = False + + {-| TIndex must not be converted to TIndex -} + toTIndex = id + +{-| Indices can be compared by its size |-} +{-| Used to allow to put tensors to typical ordered containers |-} +instance Ord TIndex where + ind1 <= ind2 = indexSize ind1 <= indexSize ind2 + +
src/Multilinear/Index/Finite.hs view
@@ -1,85 +1,85 @@-{-|-Module : Multilinear.Index.Finite-Description : Finite-dimensional tensor index.-Copyright : (c) Artur M. Brodzki, 2018-License : BSD3-Maintainer : artur@brodzki.org-Stability : experimental-Portability : Windows/POSIX--Finite-dimensional tensor index.---}--module Multilinear.Index.Finite (- Index(..),-) where--import Control.DeepSeq-import GHC.Generics-import qualified Multilinear.Index as TIndex--{-| Index of finite-dimensional tensor with specified size -}-data Index =- Covariant {- indexSize :: Int,- indexName' :: String- } |- Contravariant {- indexSize :: Int,- indexName' :: String- } |- Indifferent {- indexSize :: Int,- indexName' :: String- }- deriving (Eq, Generic)--{-| Show instance of Finite index -}-instance Show Index where- show (Covariant c n) = "[" ++ n ++ ":" ++ show c ++ "]"- show (Contravariant c n) = "<" ++ n ++ ":" ++ show c ++ ">"- show (Indifferent c n) = "(" ++ n ++ ":" ++ show c ++ ")"--{-| Finite index is a Multilinear.Index instance -}-instance TIndex.Index Index where-- {-| Index name -}- indexName = indexName'-- {-| Return true if index is covariant |-}- isCovariant (Covariant _ _) = True- isCovariant _ = False-- {-| Return true if index is contravariant |-}- isContravariant (Contravariant _ _) = True- isContravariant _ = False-- {-| Return true if index is indifferent |-}- isIndifferent (Indifferent _ _) = True- isIndifferent _ = False-- {-| Returns true if two indices are quivalent, i.e. differs only by name, but share same type and size. -}- equivI (Covariant count1 _) (Covariant count2 _)- | count1 == count2 = True- | otherwise = False- equivI (Contravariant count1 _) (Contravariant count2 _)- | count1 == count2 = True- | otherwise = False- equivI (Indifferent count1 _) (Indifferent count2 _)- | count1 == count2 = True- | otherwise = False- equivI _ _ = False-- {-| Convert to TIndex type -}- toTIndex (Covariant size name) = TIndex.Covariant (Just size) name- toTIndex (Contravariant size name) = TIndex.Contravariant (Just size) name- toTIndex (Indifferent size name) = TIndex.Indifferent (Just size) name--{-| Indices can be compared by its size |-}-{-| Used to allow to put tensors to typical ordered containers |-}-instance Ord Index where- ind1 <= ind2 = indexSize ind1 <= indexSize ind2---- NFData instance-instance NFData Index+{-| +Module : Multilinear.Index.Finite +Description : Finite-dimensional tensor index. +Copyright : (c) Artur M. Brodzki, 2018 +License : BSD3 +Maintainer : artur@brodzki.org +Stability : experimental +Portability : Windows/POSIX + +Finite-dimensional tensor index. + +-} + +module Multilinear.Index.Finite ( + Index(..), +) where + +import Control.DeepSeq +import GHC.Generics +import qualified Multilinear.Index as TIndex + +{-| Index of finite-dimensional tensor with specified size -} +data Index = + Covariant { + indexSize :: Int, + indexName' :: String + } | + Contravariant { + indexSize :: Int, + indexName' :: String + } | + Indifferent { + indexSize :: Int, + indexName' :: String + } + deriving (Eq, Generic) + +{-| Show instance of Finite index -} +instance Show Index where + show (Covariant c n) = "[" ++ n ++ ":" ++ show c ++ "]" + show (Contravariant c n) = "<" ++ n ++ ":" ++ show c ++ ">" + show (Indifferent c n) = "(" ++ n ++ ":" ++ show c ++ ")" + +{-| Finite index is a Multilinear.Index instance -} +instance TIndex.Index Index where + + {-| Index name -} + indexName = indexName' + + {-| Return true if index is covariant |-} + isCovariant (Covariant _ _) = True + isCovariant _ = False + + {-| Return true if index is contravariant |-} + isContravariant (Contravariant _ _) = True + isContravariant _ = False + + {-| Return true if index is indifferent |-} + isIndifferent (Indifferent _ _) = True + isIndifferent _ = False + + {-| Returns true if two indices are quivalent, i.e. differs only by name, but share same type and size. -} + equivI (Covariant count1 _) (Covariant count2 _) + | count1 == count2 = True + | otherwise = False + equivI (Contravariant count1 _) (Contravariant count2 _) + | count1 == count2 = True + | otherwise = False + equivI (Indifferent count1 _) (Indifferent count2 _) + | count1 == count2 = True + | otherwise = False + equivI _ _ = False + + {-| Convert to TIndex type -} + toTIndex (Covariant size name) = TIndex.Covariant (Just size) name + toTIndex (Contravariant size name) = TIndex.Contravariant (Just size) name + toTIndex (Indifferent size name) = TIndex.Indifferent (Just size) name + +{-| Indices can be compared by its size |-} +{-| Used to allow to put tensors to typical ordered containers |-} +instance Ord Index where + ind1 <= ind2 = indexSize ind1 <= indexSize ind2 + +-- NFData instance +instance NFData Index
src/Multilinear/Index/Infinite.hs view
@@ -1,71 +1,71 @@-{-|-Module : Multilinear.Index.Infinite-Description : Infinite-dimensional tensor index.-Copyright : (c) Artur M. Brodzki, 2018-License : BSD3-Maintainer : artur@brodzki.org-Stability : experimental-Portability : Windows/POSIX--Infinite-dimensional tensor index.---}--module Multilinear.Index.Infinite (- Index(..)-) where--import Control.DeepSeq-import GHC.Generics-import qualified Multilinear.Index as TIndex--{-| Index of infinite-dimensional tensor -}-data Index =- Covariant {- indexName' :: String- } |- Contravariant {- indexName' :: String- } |- Indifferent {- indexName' :: String- }- deriving (Eq, Generic)--{-| Show instance of Infinite index -}-instance Show Index where- show (Covariant n) = "[" ++ n ++ "]"- show (Contravariant n) = "<" ++ n ++ ">"- show (Indifferent n) = "(" ++ n ++ ")"--{-| Infinite index is a Multilinear.Index instance -}-instance TIndex.Index Index where-- {-| Index name -}- indexName = indexName'-- {-| Return true if index is covariant |-}- isCovariant (Covariant _) = True- isCovariant _ = False-- {-| Return true if index is contravariant |-}- isContravariant (Contravariant _) = True- isContravariant _ = False-- {-| Return true if index is indifferent |-}- isIndifferent (Indifferent _) = True- isIndifferent _ = False-- {-| Returns true if two indices are quivalent, i.e. differs only by name, but share same type. -}- equivI (Covariant _) (Covariant _) = True- equivI (Contravariant _) (Contravariant _) = True- equivI (Indifferent _) (Indifferent _) = True- equivI _ _ = False-- {-| Convert to TIndex -}- toTIndex (Covariant name) = TIndex.Covariant Nothing name- toTIndex (Contravariant name) = TIndex.Contravariant Nothing name- toTIndex (Indifferent name) = TIndex.Indifferent Nothing name---- NFData instance-instance NFData Index+{-| +Module : Multilinear.Index.Infinite +Description : Infinite-dimensional tensor index. +Copyright : (c) Artur M. Brodzki, 2018 +License : BSD3 +Maintainer : artur@brodzki.org +Stability : experimental +Portability : Windows/POSIX + +Infinite-dimensional tensor index. + +-} + +module Multilinear.Index.Infinite ( + Index(..) +) where + +import Control.DeepSeq +import GHC.Generics +import qualified Multilinear.Index as TIndex + +{-| Index of infinite-dimensional tensor -} +data Index = + Covariant { + indexName' :: String + } | + Contravariant { + indexName' :: String + } | + Indifferent { + indexName' :: String + } + deriving (Eq, Generic) + +{-| Show instance of Infinite index -} +instance Show Index where + show (Covariant n) = "[" ++ n ++ "]" + show (Contravariant n) = "<" ++ n ++ ">" + show (Indifferent n) = "(" ++ n ++ ")" + +{-| Infinite index is a Multilinear.Index instance -} +instance TIndex.Index Index where + + {-| Index name -} + indexName = indexName' + + {-| Return true if index is covariant |-} + isCovariant (Covariant _) = True + isCovariant _ = False + + {-| Return true if index is contravariant |-} + isContravariant (Contravariant _) = True + isContravariant _ = False + + {-| Return true if index is indifferent |-} + isIndifferent (Indifferent _) = True + isIndifferent _ = False + + {-| Returns true if two indices are quivalent, i.e. differs only by name, but share same type. -} + equivI (Covariant _) (Covariant _) = True + equivI (Contravariant _) (Contravariant _) = True + equivI (Indifferent _) (Indifferent _) = True + equivI _ _ = False + + {-| Convert to TIndex -} + toTIndex (Covariant name) = TIndex.Covariant Nothing name + toTIndex (Contravariant name) = TIndex.Contravariant Nothing name + toTIndex (Indifferent name) = TIndex.Indifferent Nothing name + +-- NFData instance +instance NFData Index
src/Multilinear/Matrix.hs view
@@ -1,147 +1,147 @@-{-|-Module : Multilinear.Matrix-Description : Matrix constructors (finitely- or infinitely dimensional)-Copyright : (c) Artur M. Brodzki, 2018-License : BSD3-Maintainer : artur@brodzki.org-Stability : experimental-Portability : Windows/POSIX--- This module provides convenient constructors that generates a matrix (finitely- or infinite-dimensional)-- Finitely-dimensional matrices provide much greater performance than infinitely-dimensional---}--module Multilinear.Matrix (- -- * Generators- Multilinear.Matrix.fromIndices, - Multilinear.Matrix.const,- Multilinear.Matrix.randomDouble, - Multilinear.Matrix.randomDoubleSeed,- Multilinear.Matrix.randomInt, - Multilinear.Matrix.randomIntSeed,-) where--import Control.Monad.Primitive-import Multilinear.Generic-import qualified Multilinear.Tensor as Tensor-import Statistics.Distribution--invalidIndices :: String-invalidIndices = "Indices and its sizes not compatible with structure of matrix!"--{-| Generate matrix as function of its indices -}-{-# INLINE fromIndices #-}-fromIndices :: (- Num a- ) => String -- ^ Indices names (one character per index, first character: rows index, second character: columns index)- -> Int -- ^ Number of matrix rows- -> Int -- ^ Number of matrix columns- -> (Int -> Int -> a) -- ^ Generator function - returns a matrix component at @i,j@- -> Tensor a -- ^ Generated matrix--fromIndices [u,d] us ds f = Tensor.fromIndices ([u],[us]) ([d],[ds]) $ \[ui] [di] -> f ui di-fromIndices _ _ _ _ = Err invalidIndices--{-| Generate matrix with all components equal to @v@ -}-{-# INLINE Multilinear.Matrix.const #-}-const :: (- Num a- ) => String -- ^ Indices names (one character per index, first character: rows index, second character: columns index)- -> Int -- ^ Number of matrix rows- -> Int -- ^ Number of matrix columns- -> a -- ^ Value of matrix components- -> Tensor a -- ^ Generated matrix--const [u,d] us ds = Tensor.const ([u],[us]) ([d],[ds])-const _ _ _ = \_ -> Err invalidIndices--{-| Generate matrix with random real components with given probability distribution.-The matrix is wrapped in the IO monad. -}-{-| Available probability distributions: -}-{-| - Beta : "Statistics.Distribution.BetaDistribution" -}-{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -}-{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -}-{-| - Exponential : "Statistics.Distribution.Exponential" -}-{-| - Gamma : "Statistics.Distribution.Gamma" -}-{-| - Normal : "Statistics.Distribution.Normal" -}-{-| - StudentT : "Statistics.Distribution.StudentT" -}-{-| - Uniform : "Statistics.Distribution.Uniform" -}-{-| - F : "Statistics.Distribution.FDistribution" -}-{-| - Laplace : "Statistics.Distribution.Laplace" -}-{-# INLINE randomDouble #-}-randomDouble :: (- ContGen d- ) => String -- ^ Indices names (one character per index, first character: rows index, second character: columns index)- -> Int -- ^ Number of matrix rows- -> Int -- ^ Number of matrix columns- -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution")- -> IO (Tensor Double) -- ^ Generated matrix--randomDouble [u,d] us ds = Tensor.randomDouble ([u],[us]) ([d],[ds])-randomDouble _ _ _ = \_ -> return $ Err invalidIndices--{-| Generate matrix with random integer components with given probability distribution.-The matrix is wrapped in the IO monad. -}-{-| Available probability distributions: -}-{-| - Binomial : "Statistics.Distribution.Binomial" -}-{-| - Poisson : "Statistics.Distribution.Poisson" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -}-{-# INLINE randomInt #-}-randomInt :: (- DiscreteGen d- ) => String -- ^ Indices names (one character per index, first character: rows index, second character: columns index)- -> Int -- ^ Number of matrix rows- -> Int -- ^ Number of matrix columns- -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution")- -> IO (Tensor Int) -- ^ Generated matrix--randomInt [u,d] us ds = Tensor.randomInt ([u],[us]) ([d],[ds])-randomInt _ _ _ = \_ -> return $ Err invalidIndices--{-| Generate matrix with random real components with given probability distribution and given seed.-The matrix is wrapped in the a monad. -}-{-| Available probability distributions: -}-{-| - Beta : "Statistics.Distribution.BetaDistribution" -}-{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -}-{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -}-{-| - Exponential : "Statistics.Distribution.Exponential" -}-{-| - Gamma : "Statistics.Distribution.Gamma" -}-{-| - Normal : "Statistics.Distribution.Normal" -}-{-| - StudentT : "Statistics.Distribution.StudentT" -}-{-| - Uniform : "Statistics.Distribution.Uniform" -}-{-| - F : "Statistics.Distribution.FDistribution" -}-{-| - Laplace : "Statistics.Distribution.Laplace" -}-{-# INLINE randomDoubleSeed #-}-randomDoubleSeed :: (- ContGen d, PrimMonad m- ) => String -- ^ Indices names (one character per index, first character: rows index, second character: columns index)- -> Int -- ^ Number of matrix rows- -> Int -- ^ Number of matrix columns- -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution")- -> Int -- ^ Randomness seed- -> m (Tensor Double) -- ^ Generated matrix--randomDoubleSeed [u,d] us ds = Tensor.randomDoubleSeed ([u],[us]) ([d],[ds])-randomDoubleSeed _ _ _ = \_ _ -> return $ Err invalidIndices--{-| Generate matrix with random integer components with given probability distribution. and given seed.-The matrix is wrapped in a monad. -}-{-| Available probability distributions: -}-{-| - Binomial : "Statistics.Distribution.Binomial" -}-{-| - Poisson : "Statistics.Distribution.Poisson" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -}-{-# INLINE randomIntSeed #-}-randomIntSeed :: (- DiscreteGen d, PrimMonad m- ) => String -- ^ Indices names (one character per index, first character: rows index, second character: columns index)- -> Int -- ^ Number of matrix rows- -> Int -- ^ Number of matrix columns- -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution")- -> Int -- ^ Randomness seed- -> m (Tensor Int) -- ^ Generated matrix--randomIntSeed [u,d] us ds = Tensor.randomIntSeed ([u],[us]) ([d],[ds])-randomIntSeed _ _ _ = \_ _ -> return $ Err invalidIndices+{-| +Module : Multilinear.Matrix +Description : Matrix constructors (finitely- or infinitely dimensional) +Copyright : (c) Artur M. Brodzki, 2018 +License : BSD3 +Maintainer : artur@brodzki.org +Stability : experimental +Portability : Windows/POSIX + +- This module provides convenient constructors that generates a matrix (finitely- or infinite-dimensional) +- Finitely-dimensional matrices provide much greater performance than infinitely-dimensional + +-} + +module Multilinear.Matrix ( + -- * Generators + Multilinear.Matrix.fromIndices, + Multilinear.Matrix.const, + Multilinear.Matrix.randomDouble, + Multilinear.Matrix.randomDoubleSeed, + Multilinear.Matrix.randomInt, + Multilinear.Matrix.randomIntSeed, +) where + +import Control.Monad.Primitive +import Multilinear.Generic +import qualified Multilinear.Tensor as Tensor +import Statistics.Distribution + +invalidIndices :: String +invalidIndices = "Indices and its sizes not compatible with structure of matrix!" + +{-| Generate matrix as function of its indices -} +{-# INLINE fromIndices #-} +fromIndices :: ( + Num a + ) => String -- ^ Indices names (one character per index, first character: rows index, second character: columns index) + -> Int -- ^ Number of matrix rows + -> Int -- ^ Number of matrix columns + -> (Int -> Int -> a) -- ^ Generator function - returns a matrix component at @i,j@ + -> Tensor a -- ^ Generated matrix + +fromIndices [u,d] us ds f = Tensor.fromIndices ([u],[us]) ([d],[ds]) $ \[ui] [di] -> f ui di +fromIndices _ _ _ _ = Err invalidIndices + +{-| Generate matrix with all components equal to @v@ -} +{-# INLINE Multilinear.Matrix.const #-} +const :: ( + Num a + ) => String -- ^ Indices names (one character per index, first character: rows index, second character: columns index) + -> Int -- ^ Number of matrix rows + -> Int -- ^ Number of matrix columns + -> a -- ^ Value of matrix components + -> Tensor a -- ^ Generated matrix + +const [u,d] us ds = Tensor.const ([u],[us]) ([d],[ds]) +const _ _ _ = \_ -> Err invalidIndices + +{-| Generate matrix with random real components with given probability distribution. +The matrix is wrapped in the IO monad. -} +{-| Available probability distributions: -} +{-| - Beta : "Statistics.Distribution.BetaDistribution" -} +{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -} +{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -} +{-| - Exponential : "Statistics.Distribution.Exponential" -} +{-| - Gamma : "Statistics.Distribution.Gamma" -} +{-| - Normal : "Statistics.Distribution.Normal" -} +{-| - StudentT : "Statistics.Distribution.StudentT" -} +{-| - Uniform : "Statistics.Distribution.Uniform" -} +{-| - F : "Statistics.Distribution.FDistribution" -} +{-| - Laplace : "Statistics.Distribution.Laplace" -} +{-# INLINE randomDouble #-} +randomDouble :: ( + ContGen d + ) => String -- ^ Indices names (one character per index, first character: rows index, second character: columns index) + -> Int -- ^ Number of matrix rows + -> Int -- ^ Number of matrix columns + -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution") + -> IO (Tensor Double) -- ^ Generated matrix + +randomDouble [u,d] us ds = Tensor.randomDouble ([u],[us]) ([d],[ds]) +randomDouble _ _ _ = \_ -> return $ Err invalidIndices + +{-| Generate matrix with random integer components with given probability distribution. +The matrix is wrapped in the IO monad. -} +{-| Available probability distributions: -} +{-| - Binomial : "Statistics.Distribution.Binomial" -} +{-| - Poisson : "Statistics.Distribution.Poisson" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -} +{-# INLINE randomInt #-} +randomInt :: ( + DiscreteGen d + ) => String -- ^ Indices names (one character per index, first character: rows index, second character: columns index) + -> Int -- ^ Number of matrix rows + -> Int -- ^ Number of matrix columns + -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution") + -> IO (Tensor Int) -- ^ Generated matrix + +randomInt [u,d] us ds = Tensor.randomInt ([u],[us]) ([d],[ds]) +randomInt _ _ _ = \_ -> return $ Err invalidIndices + +{-| Generate matrix with random real components with given probability distribution and given seed. +The matrix is wrapped in the a monad. -} +{-| Available probability distributions: -} +{-| - Beta : "Statistics.Distribution.BetaDistribution" -} +{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -} +{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -} +{-| - Exponential : "Statistics.Distribution.Exponential" -} +{-| - Gamma : "Statistics.Distribution.Gamma" -} +{-| - Normal : "Statistics.Distribution.Normal" -} +{-| - StudentT : "Statistics.Distribution.StudentT" -} +{-| - Uniform : "Statistics.Distribution.Uniform" -} +{-| - F : "Statistics.Distribution.FDistribution" -} +{-| - Laplace : "Statistics.Distribution.Laplace" -} +{-# INLINE randomDoubleSeed #-} +randomDoubleSeed :: ( + ContGen d, PrimMonad m + ) => String -- ^ Indices names (one character per index, first character: rows index, second character: columns index) + -> Int -- ^ Number of matrix rows + -> Int -- ^ Number of matrix columns + -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution") + -> Int -- ^ Randomness seed + -> m (Tensor Double) -- ^ Generated matrix + +randomDoubleSeed [u,d] us ds = Tensor.randomDoubleSeed ([u],[us]) ([d],[ds]) +randomDoubleSeed _ _ _ = \_ _ -> return $ Err invalidIndices + +{-| Generate matrix with random integer components with given probability distribution. and given seed. +The matrix is wrapped in a monad. -} +{-| Available probability distributions: -} +{-| - Binomial : "Statistics.Distribution.Binomial" -} +{-| - Poisson : "Statistics.Distribution.Poisson" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -} +{-# INLINE randomIntSeed #-} +randomIntSeed :: ( + DiscreteGen d, PrimMonad m + ) => String -- ^ Indices names (one character per index, first character: rows index, second character: columns index) + -> Int -- ^ Number of matrix rows + -> Int -- ^ Number of matrix columns + -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution") + -> Int -- ^ Randomness seed + -> m (Tensor Int) -- ^ Generated matrix + +randomIntSeed [u,d] us ds = Tensor.randomIntSeed ([u],[us]) ([d],[ds]) +randomIntSeed _ _ _ = \_ _ -> return $ Err invalidIndices
src/Multilinear/NForm.hs view
@@ -1,168 +1,168 @@-{-|-Module : Multilinear.NForm-Description : N-Forms, dot and cross product and determinant-Copyright : (c) Artur M. Brodzki, 2018-License : GLP-3-Maintainer : artur@brodzki.org-Stability : experimental-Portability : Windows/POSIX--- This module provides convenient constructors that generates n-forms (tensors with n lower indices with finite or infinite size). -- Finitely-dimensional n-forms provide much greater performance than infinitely-dimensional---}--module Multilinear.NForm (- -- * Generators- Multilinear.NForm.fromIndices, - Multilinear.NForm.const,- Multilinear.NForm.randomDouble, - Multilinear.NForm.randomDoubleSeed,- Multilinear.NForm.randomInt, - Multilinear.NForm.randomIntSeed,- -- * Common cases- Multilinear.NForm.dot, - Multilinear.NForm.cross-) where--import Control.Monad.Primitive-import Multilinear.Generic-import qualified Multilinear.Tensor as Tensor-import Statistics.Distribution--invalidIndices :: String-invalidIndices = "Indices and its sizes incompatible with n-form structure!"--invalidCrossProductIndices :: String-invalidCrossProductIndices = "Indices and its sizes incompatible with cross product structure!"--{-| Generate N-form as function of its indices -}-{-# INLINE fromIndices #-}-fromIndices :: (- Num a- ) => String -- ^ Indices names (one characted per index)- -> [Int] -- ^ Indices sizes- -> ([Int] -> a) -- ^ Generator function- -> Tensor a -- ^ Generated N-form--fromIndices d ds f = Tensor.fromIndices ([],[]) (d,ds) $ \[] -> f--{-| Generate N-form with all components equal to @v@ -}-{-# INLINE Multilinear.NForm.const #-}-const :: (- Num a- ) => String -- ^ Indices names (one characted per index)- -> [Int] -- ^ Indices sizes- -> a -- ^ N-form elements value- -> Tensor a -- ^ Generated N-form--const d ds = Tensor.const ([],[]) (d,ds)--{-| Generate n-vector with random real components with given probability distribution.-The n-vector is wrapped in the IO monad. -}-{-| Available probability distributions: -}-{-| - Beta : "Statistics.Distribution.BetaDistribution" -}-{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -}-{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -}-{-| - Exponential : "Statistics.Distribution.Exponential" -}-{-| - Gamma : "Statistics.Distribution.Gamma" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Normal : "Statistics.Distribution.Normal" -}-{-| - StudentT : "Statistics.Distribution.StudentT" -}-{-| - Uniform : "Statistics.Distribution.Uniform" -}-{-| - F : "Statistics.Distribution.FDistribution" -}-{-| - Laplace : "Statistics.Distribution.Laplace" -}-{-# INLINE randomDouble #-}-randomDouble :: (- ContGen d- ) => String -- ^ Indices names (one character per index)- -> [Int] -- ^ Indices sizes- -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution")- -> IO (Tensor Double) -- ^ Generated linear functional--randomDouble d ds = Tensor.randomDouble ([],[]) (d,ds)--{-| Generate n-vector with random integer components with given probability distribution.-The n-vector is wrapped in the IO monad. -}-{-| Available probability distributions: -}-{-| - Binomial : "Statistics.Distribution.Binomial" -}-{-| - Poisson : "Statistics.Distribution.Poisson" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -}-{-# INLINE randomInt #-}-randomInt :: (- DiscreteGen d- ) => String -- ^ Indices names (one character per index)- -> [Int] -- ^ Indices sizes- -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution")- -> IO (Tensor Int) -- ^ Generated n-vector--randomInt d ds = Tensor.randomInt ([],[]) (d,ds)--{-| Generate n-vector with random real components with given probability distribution and given seed.-The form is wrapped in a monad. -}-{-| Available probability distributions: -}-{-| - Beta : "Statistics.Distribution.BetaDistribution" -}-{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -}-{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -}-{-| - Exponential : "Statistics.Distribution.Exponential" -}-{-| - Gamma : "Statistics.Distribution.Gamma" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Normal : "Statistics.Distribution.Normal" -}-{-| - StudentT : "Statistics.Distribution.StudentT" -}-{-| - Uniform : "Statistics.Distribution.Uniform" -}-{-| - F : "Statistics.Distribution.FDistribution" -}-{-| - Laplace : "Statistics.Distribution.Laplace" -}-{-# INLINE randomDoubleSeed #-}-randomDoubleSeed :: (- ContGen d, PrimMonad m- ) => String -- ^ Index name (one character)- -> [Int] -- ^ Number of elements- -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution")- -> Int -- ^ Randomness seed- -> m (Tensor Double) -- ^ Generated n-vector--randomDoubleSeed d ds = Tensor.randomDoubleSeed ([],[]) (d,ds)--{-| Generate n-vector with random integer components with given probability distribution and given seed.-The form is wrapped in a monad. -}-{-| Available probability distributions: -}-{-| - Binomial : "Statistics.Distribution.Binomial" -}-{-| - Poisson : "Statistics.Distribution.Poisson" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -}-{-# INLINE randomIntSeed #-}-randomIntSeed :: (- DiscreteGen d, PrimMonad m- ) => String -- ^ Index name (one character)- -> [Int] -- ^ Number of elements- -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution")- -> Int -- ^ Randomness seed- -> m (Tensor Int) -- ^ Generated n-vector--randomIntSeed d ds = Tensor.randomIntSeed ([],[]) (d,ds)--{-| 2-form representing a dot product -}-{-# INLINE dot #-}-dot :: (- Num a- ) => String -- ^ Indices names (one characted per index)- -> Int -- ^ Size of tensor (dot product is a square tensor)- -> Tensor a -- ^ Generated dot product--dot [i1,i2] size = fromIndices [i1,i2] [size,size] (\[i,j] -> if i == j then 1 else 0)-dot _ _ = Err invalidIndices--{-| Tensor representing a cross product (Levi - Civita symbol). It also allows to compute a determinant of square matrix - determinant of matrix @M@ is a equal to length of cross product of all columns of @M@ -}--- // TODO-{-# INLINE cross #-}-cross :: (- Num a- ) => String -- ^ Indices names (one characted per index)- -> Int -- ^ Size of tensor (dot product is a square tensor)- -> Tensor a -- ^ Generated dot product--cross [i,j,k] size =- Tensor.fromIndices ([i],[size]) ([j,k],[size,size])- (\[_] [_,_] -> 0)-cross _ _ = Err invalidCrossProductIndices+{-| +Module : Multilinear.NForm +Description : N-Forms, dot and cross product and determinant +Copyright : (c) Artur M. Brodzki, 2018 +License : GLP-3 +Maintainer : artur@brodzki.org +Stability : experimental +Portability : Windows/POSIX + +- This module provides convenient constructors that generates n-forms (tensors with n lower indices with finite or infinite size). +- Finitely-dimensional n-forms provide much greater performance than infinitely-dimensional + +-} + +module Multilinear.NForm ( + -- * Generators + Multilinear.NForm.fromIndices, + Multilinear.NForm.const, + Multilinear.NForm.randomDouble, + Multilinear.NForm.randomDoubleSeed, + Multilinear.NForm.randomInt, + Multilinear.NForm.randomIntSeed, + -- * Common cases + Multilinear.NForm.dot, + Multilinear.NForm.cross +) where + +import Control.Monad.Primitive +import Multilinear.Generic +import qualified Multilinear.Tensor as Tensor +import Statistics.Distribution + +invalidIndices :: String +invalidIndices = "Indices and its sizes incompatible with n-form structure!" + +invalidCrossProductIndices :: String +invalidCrossProductIndices = "Indices and its sizes incompatible with cross product structure!" + +{-| Generate N-form as function of its indices -} +{-# INLINE fromIndices #-} +fromIndices :: ( + Num a + ) => String -- ^ Indices names (one characted per index) + -> [Int] -- ^ Indices sizes + -> ([Int] -> a) -- ^ Generator function + -> Tensor a -- ^ Generated N-form + +fromIndices d ds f = Tensor.fromIndices ([],[]) (d,ds) $ \[] -> f + +{-| Generate N-form with all components equal to @v@ -} +{-# INLINE Multilinear.NForm.const #-} +const :: ( + Num a + ) => String -- ^ Indices names (one characted per index) + -> [Int] -- ^ Indices sizes + -> a -- ^ N-form elements value + -> Tensor a -- ^ Generated N-form + +const d ds = Tensor.const ([],[]) (d,ds) + +{-| Generate n-vector with random real components with given probability distribution. +The n-vector is wrapped in the IO monad. -} +{-| Available probability distributions: -} +{-| - Beta : "Statistics.Distribution.BetaDistribution" -} +{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -} +{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -} +{-| - Exponential : "Statistics.Distribution.Exponential" -} +{-| - Gamma : "Statistics.Distribution.Gamma" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Normal : "Statistics.Distribution.Normal" -} +{-| - StudentT : "Statistics.Distribution.StudentT" -} +{-| - Uniform : "Statistics.Distribution.Uniform" -} +{-| - F : "Statistics.Distribution.FDistribution" -} +{-| - Laplace : "Statistics.Distribution.Laplace" -} +{-# INLINE randomDouble #-} +randomDouble :: ( + ContGen d + ) => String -- ^ Indices names (one character per index) + -> [Int] -- ^ Indices sizes + -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution") + -> IO (Tensor Double) -- ^ Generated linear functional + +randomDouble d ds = Tensor.randomDouble ([],[]) (d,ds) + +{-| Generate n-vector with random integer components with given probability distribution. +The n-vector is wrapped in the IO monad. -} +{-| Available probability distributions: -} +{-| - Binomial : "Statistics.Distribution.Binomial" -} +{-| - Poisson : "Statistics.Distribution.Poisson" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -} +{-# INLINE randomInt #-} +randomInt :: ( + DiscreteGen d + ) => String -- ^ Indices names (one character per index) + -> [Int] -- ^ Indices sizes + -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution") + -> IO (Tensor Int) -- ^ Generated n-vector + +randomInt d ds = Tensor.randomInt ([],[]) (d,ds) + +{-| Generate n-vector with random real components with given probability distribution and given seed. +The form is wrapped in a monad. -} +{-| Available probability distributions: -} +{-| - Beta : "Statistics.Distribution.BetaDistribution" -} +{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -} +{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -} +{-| - Exponential : "Statistics.Distribution.Exponential" -} +{-| - Gamma : "Statistics.Distribution.Gamma" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Normal : "Statistics.Distribution.Normal" -} +{-| - StudentT : "Statistics.Distribution.StudentT" -} +{-| - Uniform : "Statistics.Distribution.Uniform" -} +{-| - F : "Statistics.Distribution.FDistribution" -} +{-| - Laplace : "Statistics.Distribution.Laplace" -} +{-# INLINE randomDoubleSeed #-} +randomDoubleSeed :: ( + ContGen d, PrimMonad m + ) => String -- ^ Index name (one character) + -> [Int] -- ^ Number of elements + -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution") + -> Int -- ^ Randomness seed + -> m (Tensor Double) -- ^ Generated n-vector + +randomDoubleSeed d ds = Tensor.randomDoubleSeed ([],[]) (d,ds) + +{-| Generate n-vector with random integer components with given probability distribution and given seed. +The form is wrapped in a monad. -} +{-| Available probability distributions: -} +{-| - Binomial : "Statistics.Distribution.Binomial" -} +{-| - Poisson : "Statistics.Distribution.Poisson" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -} +{-# INLINE randomIntSeed #-} +randomIntSeed :: ( + DiscreteGen d, PrimMonad m + ) => String -- ^ Index name (one character) + -> [Int] -- ^ Number of elements + -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution") + -> Int -- ^ Randomness seed + -> m (Tensor Int) -- ^ Generated n-vector + +randomIntSeed d ds = Tensor.randomIntSeed ([],[]) (d,ds) + +{-| 2-form representing a dot product -} +{-# INLINE dot #-} +dot :: ( + Num a + ) => String -- ^ Indices names (one characted per index) + -> Int -- ^ Size of tensor (dot product is a square tensor) + -> Tensor a -- ^ Generated dot product + +dot [i1,i2] size = fromIndices [i1,i2] [size,size] (\[i,j] -> if i == j then 1 else 0) +dot _ _ = Err invalidIndices + +{-| Tensor representing a cross product (Levi - Civita symbol). It also allows to compute a determinant of square matrix - determinant of matrix @M@ is a equal to length of cross product of all columns of @M@ -} +-- // TODO +{-# INLINE cross #-} +cross :: ( + Num a + ) => String -- ^ Indices names (one characted per index) + -> Int -- ^ Size of tensor (dot product is a square tensor) + -> Tensor a -- ^ Generated dot product + +cross [i,j,k] size = + Tensor.fromIndices ([i],[size]) ([j,k],[size,size]) + (\[_] [_,_] -> 0) +cross _ _ = Err invalidCrossProductIndices
src/Multilinear/NVector.hs view
@@ -1,134 +1,134 @@-{-|-Module : Multilinear.NVector-Description : N-Vectors constructors (finitely- or infinitely-dimensional)-Copyright : (c) Artur M. Brodzki, 2018-License : BSD3-Maintainer : artur@brodzki.org-Stability : experimental-Portability : Windows/POSIX--- This module provides convenient constructors that generate a n-vector (tensor with n upper indices with finite or infinite size). -- Finitely-dimensional n-vectors provide much greater performance than infinitely-dimensional---}--module Multilinear.NVector (- -- * Generators- Multilinear.NVector.fromIndices, - Multilinear.NVector.const,- Multilinear.NVector.randomDouble, - Multilinear.NVector.randomDoubleSeed,- Multilinear.NVector.randomInt, - Multilinear.NVector.randomIntSeed,-) where--import Control.Monad.Primitive-import Multilinear.Generic-import Multilinear.Tensor as Tensor-import Statistics.Distribution--{-| Generate n-vector as function of its indices -}-{-# INLINE fromIndices #-}-fromIndices :: (- Num a- ) => String -- ^ Indices names (one characted per index)- -> [Int] -- ^ Indices sizes- -> ([Int] -> a) -- ^ Generator function- -> Tensor a -- ^ Generated n-vector--fromIndices u us f = Tensor.fromIndices (u,us) ([],[]) $ \uis [] -> f uis--{-| Generate n-vector with all components equal to @v@ -}-{-# INLINE Multilinear.NForm.const #-}-const :: (- Num a- ) => String -- ^ Indices names (one characted per index)- -> [Int] -- ^ Indices sizes- -> a -- ^ n-vector elements value- -> Tensor a -- ^ Generated n-vector--const u us = Tensor.const (u,us) ([],[])--{-| Generate n-vector with random real components with given probability distribution.-The n-vector is wrapped in the IO monad. -}-{-| Available probability distributions: -}-{-| - Beta : "Statistics.Distribution.BetaDistribution" -}-{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -}-{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -}-{-| - Exponential : "Statistics.Distribution.Exponential" -}-{-| - Gamma : "Statistics.Distribution.Gamma" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Normal : "Statistics.Distribution.Normal" -}-{-| - StudentT : "Statistics.Distribution.StudentT" -}-{-| - Uniform : "Statistics.Distribution.Uniform" -}-{-| - F : "Statistics.Distribution.FDistribution" -}-{-| - Laplace : "Statistics.Distribution.Laplace" -}-{-# INLINE randomDouble #-}-randomDouble :: (- ContGen d- ) => String -- ^ Indices names (one character per index)- -> [Int] -- ^ Indices sizes- -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution")- -> IO (Tensor Double) -- ^ Generated linear functional--randomDouble u us = Tensor.randomDouble (u,us) ([],[])--{-| Generate n-vector with random integer components with given probability distribution.-The n-vector is wrapped in the IO monad. -}-{-| Available probability distributions: -}-{-| - Binomial : "Statistics.Distribution.Binomial" -}-{-| - Poisson : "Statistics.Distribution.Poisson" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -}-{-# INLINE randomInt #-}-randomInt :: (- DiscreteGen d- ) => String -- ^ Indices names (one character per index)- -> [Int] -- ^ Indices sizes- -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution")- -> IO (Tensor Int) -- ^ Generated n-vector--randomInt u us = Tensor.randomInt (u,us) ([],[])--{-| Generate n-vector with random real components with given probability distribution and given seed.-The form is wrapped in a monad. -}-{-| Available probability distributions: -}-{-| - Beta : "Statistics.Distribution.BetaDistribution" -}-{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -}-{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -}-{-| - Exponential : "Statistics.Distribution.Exponential" -}-{-| - Gamma : "Statistics.Distribution.Gamma" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Normal : "Statistics.Distribution.Normal" -}-{-| - StudentT : "Statistics.Distribution.StudentT" -}-{-| - Uniform : "Statistics.Distribution.Uniform" -}-{-| - F : "Statistics.Distribution.FDistribution" -}-{-| - Laplace : "Statistics.Distribution.Laplace" -}-{-# INLINE randomDoubleSeed #-}-randomDoubleSeed :: (- ContGen d, PrimMonad m- ) => String -- ^ Index name (one character)- -> [Int] -- ^ Number of elements- -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution")- -> Int -- ^ Randomness seed- -> m (Tensor Double) -- ^ Generated n-vector--randomDoubleSeed u us = Tensor.randomDoubleSeed (u,us) ([],[])--{-| Generate n-vector with random integer components with given probability distribution and given seed.-The form is wrapped in a monad. -}-{-| Available probability distributions: -}-{-| - Binomial : "Statistics.Distribution.Binomial" -}-{-| - Poisson : "Statistics.Distribution.Poisson" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -}-{-# INLINE randomIntSeed #-}-randomIntSeed :: (- DiscreteGen d, PrimMonad m- ) => String -- ^ Index name (one character)- -> [Int] -- ^ Number of elements- -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution")- -> Int -- ^ Randomness seed- -> m (Tensor Int) -- ^ Generated n-vector--randomIntSeed u us = Tensor.randomIntSeed (u,us) ([],[])+{-| +Module : Multilinear.NVector +Description : N-Vectors constructors (finitely- or infinitely-dimensional) +Copyright : (c) Artur M. Brodzki, 2018 +License : BSD3 +Maintainer : artur@brodzki.org +Stability : experimental +Portability : Windows/POSIX + +- This module provides convenient constructors that generate a n-vector (tensor with n upper indices with finite or infinite size). +- Finitely-dimensional n-vectors provide much greater performance than infinitely-dimensional + +-} + +module Multilinear.NVector ( + -- * Generators + Multilinear.NVector.fromIndices, + Multilinear.NVector.const, + Multilinear.NVector.randomDouble, + Multilinear.NVector.randomDoubleSeed, + Multilinear.NVector.randomInt, + Multilinear.NVector.randomIntSeed, +) where + +import Control.Monad.Primitive +import Multilinear.Generic +import Multilinear.Tensor as Tensor +import Statistics.Distribution + +{-| Generate n-vector as function of its indices -} +{-# INLINE fromIndices #-} +fromIndices :: ( + Num a + ) => String -- ^ Indices names (one characted per index) + -> [Int] -- ^ Indices sizes + -> ([Int] -> a) -- ^ Generator function + -> Tensor a -- ^ Generated n-vector + +fromIndices u us f = Tensor.fromIndices (u,us) ([],[]) $ \uis [] -> f uis + +{-| Generate n-vector with all components equal to @v@ -} +{-# INLINE Multilinear.NForm.const #-} +const :: ( + Num a + ) => String -- ^ Indices names (one characted per index) + -> [Int] -- ^ Indices sizes + -> a -- ^ n-vector elements value + -> Tensor a -- ^ Generated n-vector + +const u us = Tensor.const (u,us) ([],[]) + +{-| Generate n-vector with random real components with given probability distribution. +The n-vector is wrapped in the IO monad. -} +{-| Available probability distributions: -} +{-| - Beta : "Statistics.Distribution.BetaDistribution" -} +{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -} +{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -} +{-| - Exponential : "Statistics.Distribution.Exponential" -} +{-| - Gamma : "Statistics.Distribution.Gamma" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Normal : "Statistics.Distribution.Normal" -} +{-| - StudentT : "Statistics.Distribution.StudentT" -} +{-| - Uniform : "Statistics.Distribution.Uniform" -} +{-| - F : "Statistics.Distribution.FDistribution" -} +{-| - Laplace : "Statistics.Distribution.Laplace" -} +{-# INLINE randomDouble #-} +randomDouble :: ( + ContGen d + ) => String -- ^ Indices names (one character per index) + -> [Int] -- ^ Indices sizes + -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution") + -> IO (Tensor Double) -- ^ Generated linear functional + +randomDouble u us = Tensor.randomDouble (u,us) ([],[]) + +{-| Generate n-vector with random integer components with given probability distribution. +The n-vector is wrapped in the IO monad. -} +{-| Available probability distributions: -} +{-| - Binomial : "Statistics.Distribution.Binomial" -} +{-| - Poisson : "Statistics.Distribution.Poisson" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -} +{-# INLINE randomInt #-} +randomInt :: ( + DiscreteGen d + ) => String -- ^ Indices names (one character per index) + -> [Int] -- ^ Indices sizes + -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution") + -> IO (Tensor Int) -- ^ Generated n-vector + +randomInt u us = Tensor.randomInt (u,us) ([],[]) + +{-| Generate n-vector with random real components with given probability distribution and given seed. +The form is wrapped in a monad. -} +{-| Available probability distributions: -} +{-| - Beta : "Statistics.Distribution.BetaDistribution" -} +{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -} +{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -} +{-| - Exponential : "Statistics.Distribution.Exponential" -} +{-| - Gamma : "Statistics.Distribution.Gamma" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Normal : "Statistics.Distribution.Normal" -} +{-| - StudentT : "Statistics.Distribution.StudentT" -} +{-| - Uniform : "Statistics.Distribution.Uniform" -} +{-| - F : "Statistics.Distribution.FDistribution" -} +{-| - Laplace : "Statistics.Distribution.Laplace" -} +{-# INLINE randomDoubleSeed #-} +randomDoubleSeed :: ( + ContGen d, PrimMonad m + ) => String -- ^ Index name (one character) + -> [Int] -- ^ Number of elements + -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution") + -> Int -- ^ Randomness seed + -> m (Tensor Double) -- ^ Generated n-vector + +randomDoubleSeed u us = Tensor.randomDoubleSeed (u,us) ([],[]) + +{-| Generate n-vector with random integer components with given probability distribution and given seed. +The form is wrapped in a monad. -} +{-| Available probability distributions: -} +{-| - Binomial : "Statistics.Distribution.Binomial" -} +{-| - Poisson : "Statistics.Distribution.Poisson" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -} +{-# INLINE randomIntSeed #-} +randomIntSeed :: ( + DiscreteGen d, PrimMonad m + ) => String -- ^ Index name (one character) + -> [Int] -- ^ Number of elements + -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution") + -> Int -- ^ Randomness seed + -> m (Tensor Int) -- ^ Generated n-vector + +randomIntSeed u us = Tensor.randomIntSeed (u,us) ([],[])
src/Multilinear/Tensor.hs view
@@ -1,289 +1,289 @@-{-|-Module : Multilinear.Tensor-Description : Tensors constructors (finitely- or infinitely-dimensional)-Copyright : (c) Artur M. Brodzki, 2018-License : BSD3-Maintainer : artur@brodzki.org-Stability : experimental-Portability : Windows/POSIX--- This module provides convenient constructors that generate a arbitrary finitely- or infinitely-dimensional tensors. -- Finitely-dimensional tensors provide much greater performance than inifitely-dimensional---}--module Multilinear.Tensor (- -- * Generators- Multilinear.Tensor.fromIndices, - Multilinear.Tensor.generate,- Multilinear.Tensor.const,- Multilinear.Tensor.randomDouble, - Multilinear.Tensor.randomDoubleSeed,- Multilinear.Tensor.randomInt, - Multilinear.Tensor.randomIntSeed-) where--import Control.Monad.Primitive-import qualified Data.Vector as Boxed-import Multilinear.Generic-import Multilinear.Index.Finite as Finite-import Statistics.Distribution-import qualified System.Random.MWC as MWC--invalidIndices :: (String, [Int]) -> (String, [Int]) -> String-invalidIndices us ds = "Indices and its sizes incompatible, upper indices: " ++ show us ++", lower indices: " ++ show ds--{-| Generate tensor as functions of its indices -}-{-# INLINE fromIndices #-}-fromIndices :: (- Num a- ) => (String,[Int]) -- ^ Upper indices names (one character per index) and its sizes- -> (String,[Int]) -- ^ Lower indices names (one character per index) and its sizes- -> ([Int] -> [Int] -> a) -- ^ Generator function (f [u1,u2,...] [d1,d2,...] returns a tensor element at t [u1,u2,...] [d1,d2,...])- -> Tensor a -- ^ Generated tensor---- If only one upper index is given, generate a SimpleFinite tensor with upper index-fromIndices ([u],[s]) ([],[]) f = - SimpleFinite (Contravariant s [u]) $ Boxed.generate s $ \x -> f [x] []---- If only one lower index is given, generate a SimpleFinite tensor with lower index-fromIndices ([],[]) ([d],[s]) f = - SimpleFinite (Covariant s [d]) $ Boxed.generate s $ \x -> f [] [x]---- If many indices are given, first generate upper indices recursively from indices list-fromIndices (u:us,s:size) d f =- FiniteTensor (Contravariant s [u]) $ Boxed.generate s (\x -> fromIndices (us,size) d (\uss dss -> f (x:uss) dss) )---- After upper indices, generate lower indices recursively from indices list-fromIndices u (d:ds,s:size) f =- FiniteTensor (Covariant s [d]) $ Boxed.generate s (\x -> fromIndices u (ds,size) (\uss dss -> f uss (x:dss)) )---- If there are indices without size or sizes without names, throw an error-fromIndices us ds _ = Err $ invalidIndices us ds--{-| Generate tensor composed of other tensors -}-{-# INLINE generate #-}-generate :: (- Num a- ) => (String,[Int]) -- ^ Upper indices names (one character per index) and its sizes- -> (String,[Int]) -- ^ Lower indices names (one character per index) and its sizes- -> ([Int] -> [Int] -> Tensor a) -- ^ Generator function (f [u1,u2,...] [d1,d2,...] returns a tensor element at t [u1,u2,...] [d1,d2,...])- -> Tensor a -- ^ Generated tensor---- If no indices are given, generate a tensor by using generator function-generate ([],[]) ([],[]) f = f [] []---- If many indices are given, first generate upper indices recursively from indices list-generate (u:us,s:size) d f =- FiniteTensor (Contravariant s [u]) $ Boxed.generate s (\x -> generate (us,size) d (\uss dss -> f (x:uss) dss) )---- After upper indices, generate lower indices recursively from indices list-generate u (d:ds,s:size) f =- FiniteTensor (Covariant s [d]) $ Boxed.generate s (\x -> generate u (ds,size) (\uss dss -> f uss (x:dss)) )---- If there are indices without size or sizes without names, throw an error-generate us ds _ = Err $ invalidIndices us ds--{-| Generate tensor with all components equal to @v@ -}-{-# INLINE Multilinear.Tensor.const #-}-const :: (- Num a- ) => (String,[Int]) -- ^ Upper indices names (one character per index) and its sizes- -> (String,[Int]) -- ^ Lower indices names (one character per index) and its sizes- -> a -- ^ Tensor elements value- -> Tensor a -- ^ Generated tensor---- If only one upper index is given, generate a SimpleFinite tensor with upper index-const ([u],[s]) ([],[]) v =- SimpleFinite (Contravariant s [u]) $ Boxed.replicate s v---- If only ine lower index is given, generate a SimpleFinite tensor with lower index-const ([],[]) ([d],[s]) v =- SimpleFinite (Covariant s [d]) $ Boxed.replicate s v---- If many indices are given, first generate upper indices recursively from indices list-const (u:us,s:size) d v =- FiniteTensor (Contravariant s [u]) $ Boxed.replicate (fromIntegral s) $ Multilinear.Tensor.const (us,size) d v---- After upper indices, generate lower indices recursively from indices list-const u (d:ds,s:size) v =- FiniteTensor (Covariant s [d]) $ Boxed.replicate (fromIntegral s) $ Multilinear.Tensor.const u (ds,size) v---- If there are indices without size or sizes without names, throw an error-const us ds _ = Err $ invalidIndices us ds--{-| Generate tensor with random real components with given probability distribution.-The tensor is wrapped in the IO monad. -}-{-| Available probability distributions: -}-{-| - Beta : "Statistics.Distribution.BetaDistribution" -}-{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -}-{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -}-{-| - Exponential : "Statistics.Distribution.Exponential" -}-{-| - Gamma : "Statistics.Distribution.Gamma" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Normal : "Statistics.Distribution.Normal" -}-{-| - StudentT : "Statistics.Distribution.StudentT" -}-{-| - Uniform : "Statistics.Distribution.Uniform" -}-{-| - F : "Statistics.Distribution.FDistribution" -}-{-| - Laplace : "Statistics.Distribution.Laplace" -}-{-# INLINE randomDouble #-}-randomDouble :: (- ContGen d- ) => (String,[Int]) -- ^ Upper indices names (one character per index) and its sizes- -> (String,[Int]) -- ^ Lower indices names (one character per index) and its sizes- -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution")- -> IO (Tensor Double) -- ^ Generated tensor---- If only one upper index is given, generate a SimpleFinite tensor with upper index-randomDouble ([u],[s]) ([],[]) distr = do- gen <- MWC.createSystemRandom- component <- sequence $ Boxed.generate s $ \_ -> genContVar distr gen- return $ SimpleFinite (Contravariant s [u]) component---- If only one lower index is given, generate a SimpleFinite tensor with lower index-randomDouble ([],[]) ([d],[s]) distr = do- gen <- MWC.createSystemRandom- component <- sequence $ Boxed.generate s $ \_ -> genContVar distr gen- return $ SimpleFinite (Covariant s [d]) component---- If many indices are given, first generate upper indices recursively from indices list-randomDouble (u:us,s:size) d distr = do- tensors <- sequence $ Boxed.generate s $ \_ -> randomDouble (us,size) d distr- return $ FiniteTensor (Contravariant s [u]) tensors---- After upper indices, generate lower indices recursively from indices list-randomDouble u (d:ds,s:size) distr = do- tensors <- sequence $ Boxed.generate s $ \_ -> randomDouble u (ds,size) distr- return $ FiniteTensor (Covariant s [d]) tensors---- If there are indices without size or sizes without names, throw an error-randomDouble us ds _ = return $ Err $ invalidIndices us ds--{-| Generate tensor with random integer components with given probability distribution.-The tensor is wrapped in the IO monad. -}-{-| Available probability distributions: -}-{-| - Binomial : "Statistics.Distribution.Binomial" -}-{-| - Poisson : "Statistics.Distribution.Poisson" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -}-{-# INLINE randomInt #-}-randomInt :: (- DiscreteGen d- ) => (String,[Int]) -- ^ Upper indices names (one character per index) and its sizes- -> (String,[Int]) -- ^ Lower indices names (one character per index) and its sizes- -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution")- -> IO (Tensor Int) -- ^ Generated tensor---- If only one upper index is given, generate a SimpleFinite tensor with upper index-randomInt ([u],[s]) ([],[]) distr = do- gen <- MWC.createSystemRandom- component <- sequence $ Boxed.generate s $ \_ -> genDiscreteVar distr gen- return $ SimpleFinite (Contravariant s [u]) component---- If only one lower index is given, generate a SimpleFinite tensor with lower index-randomInt ([],[]) ([d],[s]) distr = do- gen <- MWC.createSystemRandom- component <- sequence $ Boxed.generate s $ \_ -> genDiscreteVar distr gen- return $ SimpleFinite (Covariant s [d]) component---- If many indices are given, first generate upper indices recursively from indices list-randomInt (u:us,s:size) d distr = do- tensors <- sequence $ Boxed.generate s $ \_ -> randomInt (us,size) d distr- return $ FiniteTensor (Contravariant s [u]) tensors---- After upper indices, generate lower indices recursively from indices list-randomInt u (d:ds,s:size) distr = do- tensors <- sequence $ Boxed.generate s $ \_ -> randomInt u (ds,size) distr- return $ FiniteTensor (Covariant s [d]) tensors---- If there are indices without size or sizes without names, throw an error-randomInt us ds _ = return $ Err $ invalidIndices us ds--{-| Generate tensor with random real components with given probability distribution and given seed.-The tensor is wrapped in a monad. -}-{-| Available probability distributions: -}-{-| - Beta : "Statistics.Distribution.BetaDistribution" -}-{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -}-{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -}-{-| - Exponential : "Statistics.Distribution.Exponential" -}-{-| - Gamma : "Statistics.Distribution.Gamma" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Normal : "Statistics.Distribution.Normal" -}-{-| - StudentT : "Statistics.Distribution.StudentT" -}-{-| - Uniform : "Statistics.Distribution.Uniform" -}-{-| - F : "Statistics.Distribution.FDistribution" -}-{-| - Laplace : "Statistics.Distribution.Laplace" -}-{-# INLINE randomDoubleSeed #-}-randomDoubleSeed :: (- ContGen d, PrimMonad m- ) => (String,[Int]) -- ^ Upper indices names (one character per index) and its sizes- -> (String,[Int]) -- ^ Lower indices names (one character per index) and its sizes- -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution")- -> Int -- ^ Randomness seed- -> m (Tensor Double) -- ^ Generated tensor---- If only one upper index is given, generate a SimpleFinite tensor with upper index-randomDoubleSeed ([u],[s]) ([],[]) distr seed = do- gen <- MWC.initialize (Boxed.singleton $ fromIntegral seed)- component <- sequence $ Boxed.generate s $ \_ -> genContVar distr gen- return $ SimpleFinite (Contravariant s [u]) component---- If only one lower index is given, generate a SimpleFinite tensor with lower index-randomDoubleSeed ([],[]) ([d],[s]) distr seed = do- gen <- MWC.initialize (Boxed.singleton $ fromIntegral seed)- component <- sequence $ Boxed.generate s $ \_ -> genContVar distr gen- return $ SimpleFinite (Covariant s [d]) component---- If many indices are given, first generate upper indices recursively from indices list-randomDoubleSeed (u:us,s:size) d distr seed = do- tensors <- sequence $ Boxed.generate s $ \_ -> randomDoubleSeed (us,size) d distr seed- return $ FiniteTensor (Contravariant s [u]) tensors---- After upper indices, generate lower indices recursively from indices list-randomDoubleSeed u (d:ds,s:size) distr seed = do- tensors <- sequence $ Boxed.generate s $ \_ -> randomDoubleSeed u (ds,size) distr seed- return $ FiniteTensor (Covariant s [d]) tensors---- If there are indices without size or sizes without names, throw an error-randomDoubleSeed us ds _ _ = return $ Err $ invalidIndices us ds--{-| Generate tensor with random integer components with given probability distribution and given seed.-The tensor is wrapped in a monad. -}-{-| Available probability distributions: -}-{-| - Binomial : "Statistics.Distribution.Binomial" -}-{-| - Poisson : "Statistics.Distribution.Poisson" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -}-{-# INLINE randomIntSeed #-}-randomIntSeed :: (- DiscreteGen d, PrimMonad m- ) => (String,[Int]) -- ^ Index name (one character)- -> (String,[Int]) -- ^ Number of elements- -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution")- -> Int -- ^ Randomness seed- -> m (Tensor Int) -- ^ Generated tensor---- If only one upper index is given, generate a SimpleFinite tensor with upper index-randomIntSeed ([u],[s]) ([],[]) distr seed = do- gen <- MWC.initialize (Boxed.singleton $ fromIntegral seed)- component <- sequence $ Boxed.generate s $ \_ -> genDiscreteVar distr gen- return $ SimpleFinite (Contravariant s [u]) component---- If only one lower index is given, generate a SimpleFinite tensor with lower index-randomIntSeed ([],[]) ([d],[s]) distr seed = do- gen <- MWC.initialize (Boxed.singleton $ fromIntegral seed)- component <- sequence $ Boxed.generate s $ \_ -> genDiscreteVar distr gen- return $ SimpleFinite (Covariant s [d]) component---- If many indices are given, first generate upper indices recursively from indices list-randomIntSeed (u:us,s:size) d distr seed = do- tensors <- sequence $ Boxed.generate s $ \_ -> randomIntSeed (us,size) d distr seed- return $ FiniteTensor (Contravariant s [u]) tensors---- After upper indices, generate lower indices recursively from indices list-randomIntSeed u (d:ds,s:size) distr seed = do- tensors <- sequence $ Boxed.generate s $ \_ -> randomIntSeed u (ds,size) distr seed- return $ FiniteTensor (Covariant s [d]) tensors---- If there are indices without size or sizes without names, throw an error-randomIntSeed us ds _ _ = return $ Err $ invalidIndices us ds+{-| +Module : Multilinear.Tensor +Description : Tensors constructors (finitely- or infinitely-dimensional) +Copyright : (c) Artur M. Brodzki, 2018 +License : BSD3 +Maintainer : artur@brodzki.org +Stability : experimental +Portability : Windows/POSIX + +- This module provides convenient constructors that generate a arbitrary finitely- or infinitely-dimensional tensors. +- Finitely-dimensional tensors provide much greater performance than inifitely-dimensional + +-} + +module Multilinear.Tensor ( + -- * Generators + Multilinear.Tensor.fromIndices, + Multilinear.Tensor.generate, + Multilinear.Tensor.const, + Multilinear.Tensor.randomDouble, + Multilinear.Tensor.randomDoubleSeed, + Multilinear.Tensor.randomInt, + Multilinear.Tensor.randomIntSeed +) where + +import Control.Monad.Primitive +import qualified Data.Vector as Boxed +import Multilinear.Generic +import Multilinear.Index.Finite as Finite +import Statistics.Distribution +import qualified System.Random.MWC as MWC + +invalidIndices :: (String, [Int]) -> (String, [Int]) -> String +invalidIndices us ds = "Indices and its sizes incompatible, upper indices: " ++ show us ++", lower indices: " ++ show ds + +{-| Generate tensor as functions of its indices -} +{-# INLINE fromIndices #-} +fromIndices :: ( + Num a + ) => (String,[Int]) -- ^ Upper indices names (one character per index) and its sizes + -> (String,[Int]) -- ^ Lower indices names (one character per index) and its sizes + -> ([Int] -> [Int] -> a) -- ^ Generator function (f [u1,u2,...] [d1,d2,...] returns a tensor element at t [u1,u2,...] [d1,d2,...]) + -> Tensor a -- ^ Generated tensor + +-- If only one upper index is given, generate a SimpleFinite tensor with upper index +fromIndices ([u],[s]) ([],[]) f = + SimpleFinite (Contravariant s [u]) $ Boxed.generate s $ \x -> f [x] [] + +-- If only one lower index is given, generate a SimpleFinite tensor with lower index +fromIndices ([],[]) ([d],[s]) f = + SimpleFinite (Covariant s [d]) $ Boxed.generate s $ \x -> f [] [x] + +-- If many indices are given, first generate upper indices recursively from indices list +fromIndices (u:us,s:size) d f = + FiniteTensor (Contravariant s [u]) $ Boxed.generate s (\x -> fromIndices (us,size) d (\uss dss -> f (x:uss) dss) ) + +-- After upper indices, generate lower indices recursively from indices list +fromIndices u (d:ds,s:size) f = + FiniteTensor (Covariant s [d]) $ Boxed.generate s (\x -> fromIndices u (ds,size) (\uss dss -> f uss (x:dss)) ) + +-- If there are indices without size or sizes without names, throw an error +fromIndices us ds _ = Err $ invalidIndices us ds + +{-| Generate tensor composed of other tensors -} +{-# INLINE generate #-} +generate :: ( + Num a + ) => (String,[Int]) -- ^ Upper indices names (one character per index) and its sizes + -> (String,[Int]) -- ^ Lower indices names (one character per index) and its sizes + -> ([Int] -> [Int] -> Tensor a) -- ^ Generator function (f [u1,u2,...] [d1,d2,...] returns a tensor element at t [u1,u2,...] [d1,d2,...]) + -> Tensor a -- ^ Generated tensor + +-- If no indices are given, generate a tensor by using generator function +generate ([],[]) ([],[]) f = f [] [] + +-- If many indices are given, first generate upper indices recursively from indices list +generate (u:us,s:size) d f = + FiniteTensor (Contravariant s [u]) $ Boxed.generate s (\x -> generate (us,size) d (\uss dss -> f (x:uss) dss) ) + +-- After upper indices, generate lower indices recursively from indices list +generate u (d:ds,s:size) f = + FiniteTensor (Covariant s [d]) $ Boxed.generate s (\x -> generate u (ds,size) (\uss dss -> f uss (x:dss)) ) + +-- If there are indices without size or sizes without names, throw an error +generate us ds _ = Err $ invalidIndices us ds + +{-| Generate tensor with all components equal to @v@ -} +{-# INLINE Multilinear.Tensor.const #-} +const :: ( + Num a + ) => (String,[Int]) -- ^ Upper indices names (one character per index) and its sizes + -> (String,[Int]) -- ^ Lower indices names (one character per index) and its sizes + -> a -- ^ Tensor elements value + -> Tensor a -- ^ Generated tensor + +-- If only one upper index is given, generate a SimpleFinite tensor with upper index +const ([u],[s]) ([],[]) v = + SimpleFinite (Contravariant s [u]) $ Boxed.replicate s v + +-- If only ine lower index is given, generate a SimpleFinite tensor with lower index +const ([],[]) ([d],[s]) v = + SimpleFinite (Covariant s [d]) $ Boxed.replicate s v + +-- If many indices are given, first generate upper indices recursively from indices list +const (u:us,s:size) d v = + FiniteTensor (Contravariant s [u]) $ Boxed.replicate (fromIntegral s) $ Multilinear.Tensor.const (us,size) d v + +-- After upper indices, generate lower indices recursively from indices list +const u (d:ds,s:size) v = + FiniteTensor (Covariant s [d]) $ Boxed.replicate (fromIntegral s) $ Multilinear.Tensor.const u (ds,size) v + +-- If there are indices without size or sizes without names, throw an error +const us ds _ = Err $ invalidIndices us ds + +{-| Generate tensor with random real components with given probability distribution. +The tensor is wrapped in the IO monad. -} +{-| Available probability distributions: -} +{-| - Beta : "Statistics.Distribution.BetaDistribution" -} +{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -} +{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -} +{-| - Exponential : "Statistics.Distribution.Exponential" -} +{-| - Gamma : "Statistics.Distribution.Gamma" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Normal : "Statistics.Distribution.Normal" -} +{-| - StudentT : "Statistics.Distribution.StudentT" -} +{-| - Uniform : "Statistics.Distribution.Uniform" -} +{-| - F : "Statistics.Distribution.FDistribution" -} +{-| - Laplace : "Statistics.Distribution.Laplace" -} +{-# INLINE randomDouble #-} +randomDouble :: ( + ContGen d + ) => (String,[Int]) -- ^ Upper indices names (one character per index) and its sizes + -> (String,[Int]) -- ^ Lower indices names (one character per index) and its sizes + -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution") + -> IO (Tensor Double) -- ^ Generated tensor + +-- If only one upper index is given, generate a SimpleFinite tensor with upper index +randomDouble ([u],[s]) ([],[]) distr = do + gen <- MWC.createSystemRandom + component <- sequence $ Boxed.generate s $ \_ -> genContVar distr gen + return $ SimpleFinite (Contravariant s [u]) component + +-- If only one lower index is given, generate a SimpleFinite tensor with lower index +randomDouble ([],[]) ([d],[s]) distr = do + gen <- MWC.createSystemRandom + component <- sequence $ Boxed.generate s $ \_ -> genContVar distr gen + return $ SimpleFinite (Covariant s [d]) component + +-- If many indices are given, first generate upper indices recursively from indices list +randomDouble (u:us,s:size) d distr = do + tensors <- sequence $ Boxed.generate s $ \_ -> randomDouble (us,size) d distr + return $ FiniteTensor (Contravariant s [u]) tensors + +-- After upper indices, generate lower indices recursively from indices list +randomDouble u (d:ds,s:size) distr = do + tensors <- sequence $ Boxed.generate s $ \_ -> randomDouble u (ds,size) distr + return $ FiniteTensor (Covariant s [d]) tensors + +-- If there are indices without size or sizes without names, throw an error +randomDouble us ds _ = return $ Err $ invalidIndices us ds + +{-| Generate tensor with random integer components with given probability distribution. +The tensor is wrapped in the IO monad. -} +{-| Available probability distributions: -} +{-| - Binomial : "Statistics.Distribution.Binomial" -} +{-| - Poisson : "Statistics.Distribution.Poisson" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -} +{-# INLINE randomInt #-} +randomInt :: ( + DiscreteGen d + ) => (String,[Int]) -- ^ Upper indices names (one character per index) and its sizes + -> (String,[Int]) -- ^ Lower indices names (one character per index) and its sizes + -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution") + -> IO (Tensor Int) -- ^ Generated tensor + +-- If only one upper index is given, generate a SimpleFinite tensor with upper index +randomInt ([u],[s]) ([],[]) distr = do + gen <- MWC.createSystemRandom + component <- sequence $ Boxed.generate s $ \_ -> genDiscreteVar distr gen + return $ SimpleFinite (Contravariant s [u]) component + +-- If only one lower index is given, generate a SimpleFinite tensor with lower index +randomInt ([],[]) ([d],[s]) distr = do + gen <- MWC.createSystemRandom + component <- sequence $ Boxed.generate s $ \_ -> genDiscreteVar distr gen + return $ SimpleFinite (Covariant s [d]) component + +-- If many indices are given, first generate upper indices recursively from indices list +randomInt (u:us,s:size) d distr = do + tensors <- sequence $ Boxed.generate s $ \_ -> randomInt (us,size) d distr + return $ FiniteTensor (Contravariant s [u]) tensors + +-- After upper indices, generate lower indices recursively from indices list +randomInt u (d:ds,s:size) distr = do + tensors <- sequence $ Boxed.generate s $ \_ -> randomInt u (ds,size) distr + return $ FiniteTensor (Covariant s [d]) tensors + +-- If there are indices without size or sizes without names, throw an error +randomInt us ds _ = return $ Err $ invalidIndices us ds + +{-| Generate tensor with random real components with given probability distribution and given seed. +The tensor is wrapped in a monad. -} +{-| Available probability distributions: -} +{-| - Beta : "Statistics.Distribution.BetaDistribution" -} +{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -} +{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -} +{-| - Exponential : "Statistics.Distribution.Exponential" -} +{-| - Gamma : "Statistics.Distribution.Gamma" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Normal : "Statistics.Distribution.Normal" -} +{-| - StudentT : "Statistics.Distribution.StudentT" -} +{-| - Uniform : "Statistics.Distribution.Uniform" -} +{-| - F : "Statistics.Distribution.FDistribution" -} +{-| - Laplace : "Statistics.Distribution.Laplace" -} +{-# INLINE randomDoubleSeed #-} +randomDoubleSeed :: ( + ContGen d, PrimMonad m + ) => (String,[Int]) -- ^ Upper indices names (one character per index) and its sizes + -> (String,[Int]) -- ^ Lower indices names (one character per index) and its sizes + -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution") + -> Int -- ^ Randomness seed + -> m (Tensor Double) -- ^ Generated tensor + +-- If only one upper index is given, generate a SimpleFinite tensor with upper index +randomDoubleSeed ([u],[s]) ([],[]) distr seed = do + gen <- MWC.initialize (Boxed.singleton $ fromIntegral seed) + component <- sequence $ Boxed.generate s $ \_ -> genContVar distr gen + return $ SimpleFinite (Contravariant s [u]) component + +-- If only one lower index is given, generate a SimpleFinite tensor with lower index +randomDoubleSeed ([],[]) ([d],[s]) distr seed = do + gen <- MWC.initialize (Boxed.singleton $ fromIntegral seed) + component <- sequence $ Boxed.generate s $ \_ -> genContVar distr gen + return $ SimpleFinite (Covariant s [d]) component + +-- If many indices are given, first generate upper indices recursively from indices list +randomDoubleSeed (u:us,s:size) d distr seed = do + tensors <- sequence $ Boxed.generate s $ \_ -> randomDoubleSeed (us,size) d distr seed + return $ FiniteTensor (Contravariant s [u]) tensors + +-- After upper indices, generate lower indices recursively from indices list +randomDoubleSeed u (d:ds,s:size) distr seed = do + tensors <- sequence $ Boxed.generate s $ \_ -> randomDoubleSeed u (ds,size) distr seed + return $ FiniteTensor (Covariant s [d]) tensors + +-- If there are indices without size or sizes without names, throw an error +randomDoubleSeed us ds _ _ = return $ Err $ invalidIndices us ds + +{-| Generate tensor with random integer components with given probability distribution and given seed. +The tensor is wrapped in a monad. -} +{-| Available probability distributions: -} +{-| - Binomial : "Statistics.Distribution.Binomial" -} +{-| - Poisson : "Statistics.Distribution.Poisson" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -} +{-# INLINE randomIntSeed #-} +randomIntSeed :: ( + DiscreteGen d, PrimMonad m + ) => (String,[Int]) -- ^ Index name (one character) + -> (String,[Int]) -- ^ Number of elements + -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution") + -> Int -- ^ Randomness seed + -> m (Tensor Int) -- ^ Generated tensor + +-- If only one upper index is given, generate a SimpleFinite tensor with upper index +randomIntSeed ([u],[s]) ([],[]) distr seed = do + gen <- MWC.initialize (Boxed.singleton $ fromIntegral seed) + component <- sequence $ Boxed.generate s $ \_ -> genDiscreteVar distr gen + return $ SimpleFinite (Contravariant s [u]) component + +-- If only one lower index is given, generate a SimpleFinite tensor with lower index +randomIntSeed ([],[]) ([d],[s]) distr seed = do + gen <- MWC.initialize (Boxed.singleton $ fromIntegral seed) + component <- sequence $ Boxed.generate s $ \_ -> genDiscreteVar distr gen + return $ SimpleFinite (Covariant s [d]) component + +-- If many indices are given, first generate upper indices recursively from indices list +randomIntSeed (u:us,s:size) d distr seed = do + tensors <- sequence $ Boxed.generate s $ \_ -> randomIntSeed (us,size) d distr seed + return $ FiniteTensor (Contravariant s [u]) tensors + +-- After upper indices, generate lower indices recursively from indices list +randomIntSeed u (d:ds,s:size) distr seed = do + tensors <- sequence $ Boxed.generate s $ \_ -> randomIntSeed u (ds,size) distr seed + return $ FiniteTensor (Covariant s [d]) tensors + +-- If there are indices without size or sizes without names, throw an error +randomIntSeed us ds _ _ = return $ Err $ invalidIndices us ds
src/Multilinear/Vector.hs view
@@ -1,142 +1,142 @@-{-|-Module : Multilinear.Vector-Description : Vector constructors (finitely- or infinitely-dimensional)-Copyright : (c) Artur M. Brodzki, 2018-License : BSD3-Maintainer : artur@brodzki.org-Stability : experimental-Portability : Windows/POSIX--- This module provides convenient constructors that generates a vector (tensor with one upper index) of finite or infinite size. -- Finitely-dimensional vectors provide much greater performance than infinitely-dimensional ---}--module Multilinear.Vector (- -- * Generators- Multilinear.Vector.fromIndices, - Multilinear.Vector.const,- Multilinear.Vector.randomDouble, - Multilinear.Vector.randomDoubleSeed,- Multilinear.Vector.randomInt, - Multilinear.Vector.randomIntSeed-) where--import Control.Monad.Primitive-import Multilinear.Generic-import Multilinear.Tensor as Tensor-import Statistics.Distribution--invalidIndices :: String-invalidIndices = "Indices and its sizes not compatible with structure of vector!"--{-| Generate vector as function of indices -}-{-# INLINE fromIndices #-}-fromIndices :: (- Num a- ) => String -- ^ Index name (one character)- -> Int -- ^ Number of elements- -> (Int -> a) -- ^ Generator function - returns a vector component at index @i@- -> Tensor a -- ^ Generated vector--fromIndices [i] s f = Tensor.fromIndices ([i],[s]) ([],[]) $ \[x] [] -> f x-fromIndices _ _ _ = Err invalidIndices--{-| Generate vector with all components equal to some @v@ -}-{-# INLINE Multilinear.Vector.const #-}-const :: (- Num a- ) => String -- ^ Index name (one character)- -> Int -- ^ Number of elements- -> a -- ^ Value of each element- -> Tensor a -- ^ Generated vector--const [i] s = Tensor.const ([i],[s]) ([],[])-const _ _ = \_ -> Err invalidIndices--{-| Generate vector with random real components with given probability distribution.-The vector is wrapped in the IO monad. -}-{-| Available probability distributions: -}-{-| - Beta : "Statistics.Distribution.BetaDistribution" -}-{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -}-{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -}-{-| - Exponential : "Statistics.Distribution.Exponential" -}-{-| - Gamma : "Statistics.Distribution.Gamma" -}-{-| - Normal : "Statistics.Distribution.Normal" -}-{-| - StudentT : "Statistics.Distribution.StudentT" -}-{-| - Uniform : "Statistics.Distribution.Uniform" -}-{-| - F : "Statistics.Distribution.FDistribution" -}-{-| - Laplace : "Statistics.Distribution.Laplace" -}-{-# INLINE randomDouble #-}-randomDouble :: (- ContGen d- ) => String -- ^ Index name (one character)- -> Int -- ^ Number of elements- -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution")- -> IO (Tensor Double) -- ^ Generated vector--randomDouble [i] s = Tensor.randomDouble ([i],[s]) ([],[])-randomDouble _ _ = \_ -> return $ Err invalidIndices--{-| Generate vector with random integer components with given probability distribution.-The vector is wrapped in the IO monad. -}-{-| Available probability distributions: -}-{-| - Binomial : "Statistics.Distribution.Binomial" -}-{-| - Poisson : "Statistics.Distribution.Poisson" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -}-{-# INLINE randomInt #-}-randomInt :: (- DiscreteGen d- ) => String -- ^ Index name (one character)- -> Int -- ^ Number of elements- -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution")- -> IO (Tensor Int) -- ^ Generated vector--randomInt [i] s = Tensor.randomInt ([i],[s]) ([],[])-randomInt _ _ = \_ -> return $ Err invalidIndices--{-| Generate vector with random real components with given probability distribution and given seed.-The vector is wrapped in a monad. -}-{-| Available probability distributions: -}-{-| - Beta : "Statistics.Distribution.BetaDistribution" -}-{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -}-{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -}-{-| - Exponential : "Statistics.Distribution.Exponential" -}-{-| - Gamma : "Statistics.Distribution.Gamma" -}-{-| - Normal : "Statistics.Distribution.Normal" -}-{-| - StudentT : "Statistics.Distribution.StudentT" -}-{-| - Uniform : "Statistics.Distribution.Uniform" -}-{-| - F : "Statistics.Distribution.FDistribution" -}-{-| - Laplace : "Statistics.Distribution.Laplace" -}-{-# INLINE randomDoubleSeed #-}-randomDoubleSeed :: (- ContGen d, PrimMonad m- ) => String -- ^ Index name (one character)- -> Int -- ^ Number of elements- -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution")- -> Int -- ^ Randomness seed- -> m (Tensor Double) -- ^ Generated vector--randomDoubleSeed [i] s = Tensor.randomDoubleSeed ([i],[s]) ([],[])-randomDoubleSeed _ _ = \_ _ -> return $ Err invalidIndices--{-| Generate vector with random integer components with given probability distribution and given seed.-The vector is wrapped in a monad. -}-{-| Available probability distributions: -}-{-| - Binomial : "Statistics.Distribution.Binomial" -}-{-| - Poisson : "Statistics.Distribution.Poisson" -}-{-| - Geometric : "Statistics.Distribution.Geometric" -}-{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -}-{-# INLINE randomIntSeed #-}-randomIntSeed :: (- DiscreteGen d, PrimMonad m- ) => String -- ^ Index name (one character)- -> Int -- ^ Number of elements- -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution")- -> Int -- ^ Randomness seed- -> m (Tensor Int) -- ^ Generated vector--randomIntSeed [i] s = Tensor.randomIntSeed ([i],[s]) ([],[])-randomIntSeed _ _ = \_ _ -> return $ Err invalidIndices-+{-| +Module : Multilinear.Vector +Description : Vector constructors (finitely- or infinitely-dimensional) +Copyright : (c) Artur M. Brodzki, 2018 +License : BSD3 +Maintainer : artur@brodzki.org +Stability : experimental +Portability : Windows/POSIX + +- This module provides convenient constructors that generates a vector (tensor with one upper index) of finite or infinite size. +- Finitely-dimensional vectors provide much greater performance than infinitely-dimensional + +-} + +module Multilinear.Vector ( + -- * Generators + Multilinear.Vector.fromIndices, + Multilinear.Vector.const, + Multilinear.Vector.randomDouble, + Multilinear.Vector.randomDoubleSeed, + Multilinear.Vector.randomInt, + Multilinear.Vector.randomIntSeed +) where + +import Control.Monad.Primitive +import Multilinear.Generic +import Multilinear.Tensor as Tensor +import Statistics.Distribution + +invalidIndices :: String +invalidIndices = "Indices and its sizes not compatible with structure of vector!" + +{-| Generate vector as function of indices -} +{-# INLINE fromIndices #-} +fromIndices :: ( + Num a + ) => String -- ^ Index name (one character) + -> Int -- ^ Number of elements + -> (Int -> a) -- ^ Generator function - returns a vector component at index @i@ + -> Tensor a -- ^ Generated vector + +fromIndices [i] s f = Tensor.fromIndices ([i],[s]) ([],[]) $ \[x] [] -> f x +fromIndices _ _ _ = Err invalidIndices + +{-| Generate vector with all components equal to some @v@ -} +{-# INLINE Multilinear.Vector.const #-} +const :: ( + Num a + ) => String -- ^ Index name (one character) + -> Int -- ^ Number of elements + -> a -- ^ Value of each element + -> Tensor a -- ^ Generated vector + +const [i] s = Tensor.const ([i],[s]) ([],[]) +const _ _ = \_ -> Err invalidIndices + +{-| Generate vector with random real components with given probability distribution. +The vector is wrapped in the IO monad. -} +{-| Available probability distributions: -} +{-| - Beta : "Statistics.Distribution.BetaDistribution" -} +{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -} +{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -} +{-| - Exponential : "Statistics.Distribution.Exponential" -} +{-| - Gamma : "Statistics.Distribution.Gamma" -} +{-| - Normal : "Statistics.Distribution.Normal" -} +{-| - StudentT : "Statistics.Distribution.StudentT" -} +{-| - Uniform : "Statistics.Distribution.Uniform" -} +{-| - F : "Statistics.Distribution.FDistribution" -} +{-| - Laplace : "Statistics.Distribution.Laplace" -} +{-# INLINE randomDouble #-} +randomDouble :: ( + ContGen d + ) => String -- ^ Index name (one character) + -> Int -- ^ Number of elements + -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution") + -> IO (Tensor Double) -- ^ Generated vector + +randomDouble [i] s = Tensor.randomDouble ([i],[s]) ([],[]) +randomDouble _ _ = \_ -> return $ Err invalidIndices + +{-| Generate vector with random integer components with given probability distribution. +The vector is wrapped in the IO monad. -} +{-| Available probability distributions: -} +{-| - Binomial : "Statistics.Distribution.Binomial" -} +{-| - Poisson : "Statistics.Distribution.Poisson" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -} +{-# INLINE randomInt #-} +randomInt :: ( + DiscreteGen d + ) => String -- ^ Index name (one character) + -> Int -- ^ Number of elements + -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution") + -> IO (Tensor Int) -- ^ Generated vector + +randomInt [i] s = Tensor.randomInt ([i],[s]) ([],[]) +randomInt _ _ = \_ -> return $ Err invalidIndices + +{-| Generate vector with random real components with given probability distribution and given seed. +The vector is wrapped in a monad. -} +{-| Available probability distributions: -} +{-| - Beta : "Statistics.Distribution.BetaDistribution" -} +{-| - Cauchy : "Statistics.Distribution.CauchyLorentz" -} +{-| - Chi-squared : "Statistics.Distribution.ChiSquared" -} +{-| - Exponential : "Statistics.Distribution.Exponential" -} +{-| - Gamma : "Statistics.Distribution.Gamma" -} +{-| - Normal : "Statistics.Distribution.Normal" -} +{-| - StudentT : "Statistics.Distribution.StudentT" -} +{-| - Uniform : "Statistics.Distribution.Uniform" -} +{-| - F : "Statistics.Distribution.FDistribution" -} +{-| - Laplace : "Statistics.Distribution.Laplace" -} +{-# INLINE randomDoubleSeed #-} +randomDoubleSeed :: ( + ContGen d, PrimMonad m + ) => String -- ^ Index name (one character) + -> Int -- ^ Number of elements + -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution") + -> Int -- ^ Randomness seed + -> m (Tensor Double) -- ^ Generated vector + +randomDoubleSeed [i] s = Tensor.randomDoubleSeed ([i],[s]) ([],[]) +randomDoubleSeed _ _ = \_ _ -> return $ Err invalidIndices + +{-| Generate vector with random integer components with given probability distribution and given seed. +The vector is wrapped in a monad. -} +{-| Available probability distributions: -} +{-| - Binomial : "Statistics.Distribution.Binomial" -} +{-| - Poisson : "Statistics.Distribution.Poisson" -} +{-| - Geometric : "Statistics.Distribution.Geometric" -} +{-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -} +{-# INLINE randomIntSeed #-} +randomIntSeed :: ( + DiscreteGen d, PrimMonad m + ) => String -- ^ Index name (one character) + -> Int -- ^ Number of elements + -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution") + -> Int -- ^ Randomness seed + -> m (Tensor Int) -- ^ Generated vector + +randomIntSeed [i] s = Tensor.randomIntSeed ([i],[s]) ([],[]) +randomIntSeed _ _ = \_ _ -> return $ Err invalidIndices +
test/Spec.hs view
@@ -1,35 +1,35 @@-{-|-Module : Main (Spec.hs)-Description : Tests of Multilinear library-Copyright : (c) Artur M. Brodzki, 2018-License : BSD3-Maintainer : artur@brodzki.org-Stability : experimental-Portability : Windows/POSIX---}--module Main (- main-) where--import Control.DeepSeq-import Criterion.Main-import Criterion.Measurement as Meas-import Criterion.Types-import Multilinear.Generic-import qualified Multilinear.Matrix as Matrix--m1 :: Tensor Double-m1 = Matrix.fromIndices "ij" 100 100 $ \i j -> fromIntegral (2*i) - exp (fromIntegral j)--m2 :: Tensor Double-m2 = Matrix.fromIndices "jk" 100 100 $ \i j -> sin (fromIntegral i) + cos (fromIntegral j)--main :: IO ()-main = do- putStrLn "Two matrices 1000x1000 multiplying..."- (meas,_) <- Meas.measure ( nfIO $ (m1 * m2) `deepseq` putStrLn "End!" ) 1- putStrLn $ "Measured time: " ++ show (measCpuTime meas) ++ " s."- return ()-+{-| +Module : Main (Spec.hs) +Description : Tests of Multilinear library +Copyright : (c) Artur M. Brodzki, 2018 +License : BSD3 +Maintainer : artur@brodzki.org +Stability : experimental +Portability : Windows/POSIX + +-} + +module Main ( + main +) where + +import Control.DeepSeq +import Criterion.Main +import Criterion.Measurement as Meas +import Criterion.Types +import Multilinear.Generic +import qualified Multilinear.Matrix as Matrix + +m1 :: Tensor Double +m1 = Matrix.fromIndices "ij" 100 100 $ \i j -> fromIntegral (2*i) - exp (fromIntegral j) + +m2 :: Tensor Double +m2 = Matrix.fromIndices "jk" 100 100 $ \i j -> sin (fromIntegral i) + cos (fromIntegral j) + +main :: IO () +main = do + putStrLn "Two matrices 1000x1000 multiplying..." + (meas,_) <- Meas.measure ( nfIO $ (m1 * m2) `deepseq` putStrLn "End!" ) 1 + putStrLn $ "Measured time: " ++ show (measCpuTime meas) ++ " s." + return () +