diff --git a/CHANGELOG b/CHANGELOG --- a/CHANGELOG +++ b/CHANGELOG @@ -1,3 +1,16 @@ +0.18.0.0 +-------- + + * Many new functions and instances in the Static module + + * meanCov and gaussianSample use Herm type + + * thinQR, thinRQ + + * compactSVDTol + + * unitary changed to normalize, also admits Vector (Complex Double) + 0.17.0.0 -------- @@ -275,4 +288,3 @@ * added NFData instances for Matrix and Vector. * liftVector, liftVector2 replaced by mapVector, zipVector. - diff --git a/THANKS.md b/THANKS.md --- a/THANKS.md +++ b/THANKS.md @@ -160,7 +160,7 @@ - Denis Laxalde separated the gsl tests from the base ones. - Dominic Steinitz (idontgetoutmuch) reported a bug in the static diagonal creation functions and - added Cholesky to Static. + added Cholesky to Static. He also added support for tridiagonal matrix solver and fixed several bugs. - Dylan Thurston reported an error in the glpk documentation and ambiguity in the description of linearSolve. @@ -170,7 +170,8 @@ - Ian Ross reported the max/minIndex bug. -- Niklas Hambüchen improved the documentation. +- Niklas Hambüchen improved the documentation and fixed compilation with GHC-8.2 + adding type signatures. Added disable-default-paths flag. - "erdeszt" optimized "conv" using a direct vector reverse. @@ -192,7 +193,8 @@ - Matt Peddie wrote the interfaces to the interpolation and simulated annealing modules. -- "maxc01" solved uninstallability in FreeBSD and improved urandom +- "maxc01" solved uninstallability in FreeBSD, improved urandom, and fixed a Windows + link error using rand_s. - "ntfrgl" added {take,drop}Last{Rows,Columns} and odeSolveVWith with generalized step control function and fixed link errors related to mod/mod_l. @@ -202,5 +204,33 @@ - Ilan Godik and Douglas McClean helped with Windows support. - Vassil Keremidchiev fixed the cabal options for OpenBlas, fixed several installation - issues, and added support for stack-based build. + issues, and added support for stack-based build. He also added support for LTS 8.15 + under Windows. + +- Greg Nwosu fixed arm compilation + +- Patrik Jansson changed meanCov and gaussianSample to use Herm type. Fixed stack.yaml. + +- Justin Le added NFData instances for Static types, added mapping and outer product + methods to Domain, and many other functions to the Static module. + +- Sidharth Kapur added Normed and numeric instances for several Static types, +fixed the CPP issue in cabal files, and made many other contributions. + +- Matt Renaud improved the documentation. + +- Joshua Moerman fixed cabal/stack flags for windows. + +- Francesco Mazzoli, Niklas Hambüchen, Patrick Chilton, and Andras Slemmer + discovered a serious and subtle bug in the wrapper helpers causing memory corruption. + Andras Slemmer fixed the bug. Thank you all. + +- Kevin Slagle implemented thinQR and thinRQ, much faster than the original qr, + and added compactSVDTol. He also added an optimized reorderVector for hTensor. + +- "fedeinthemix" suggested a better name and a more general type for unitary. + +- Huw Campbell fixed a bug in equal. + +- Hiromi Ishii fixed compilation problems for ghc-8.4 diff --git a/hmatrix.cabal b/hmatrix.cabal --- a/hmatrix.cabal +++ b/hmatrix.cabal @@ -1,11 +1,11 @@ Name: hmatrix -Version: 0.17.0.2 +Version: 0.20.2 License: BSD3 License-file: LICENSE Author: Alberto Ruiz -Maintainer: Alberto Ruiz +Maintainer: Dominic Steinitz Stability: provisional -Homepage: https://github.com/albertoruiz/hmatrix +Homepage: https://github.com/haskell-numerics/hmatrix Synopsis: Numeric Linear Algebra Description: Linear systems, matrix decompositions, and other numerical computations based on BLAS and LAPACK. . @@ -16,9 +16,9 @@ Code examples: Category: Math -tested-with: GHC==8.0 +tested-with: GHC==8.10 -cabal-version: >=1.8 +cabal-version: >=1.18 build-type: Simple @@ -29,10 +29,22 @@ flag openblas description: Link with OpenBLAS (https://github.com/xianyi/OpenBLAS) optimized libraries. default: False - manual: True + manual: True +flag disable-default-paths + description: When enabled, don't add default hardcoded include/link dirs by default. Needed for hermetic builds like in nix. + default: False + manual: True + +flag no-random_r + description: When enabled, don't depend on the random_r() C function. + default: False + manual: True + library + default-language: Haskell2010 + Build-Depends: base >= 4.8 && < 5, binary, array, @@ -40,8 +52,10 @@ random, split, bytestring, + primitive, storable-complex, - vector >= 0.8 + semigroups, + vector >= 0.11 hs-source-dirs: src @@ -55,7 +69,6 @@ Internal.Devel Internal.Vectorized Internal.Matrix - Internal.Foreign Internal.ST Internal.IO Internal.Element @@ -79,13 +92,12 @@ src/Internal/C/vector-aux.c - extensions: ForeignFunctionInterface, - CPP + other-extensions: ForeignFunctionInterface ghc-options: -Wall -fno-warn-missing-signatures -fno-warn-orphans - -fprof-auto + -fno-prof-auto cc-options: -O4 -Wall @@ -94,43 +106,51 @@ if arch(i386) cc-options: -msse2 - cpp-options: -DBINARY + if flag(no-random_r) + cc-options: -DNO_RANDOM_R + if os(OSX) if flag(openblas) - extra-lib-dirs: /opt/local/lib/openblas/lib + if !flag(disable-default-paths) + extra-lib-dirs: /opt/local/lib/openblas/lib extra-libraries: openblas else extra-libraries: blas lapack - extra-lib-dirs: /opt/local/lib/ - include-dirs: /opt/local/include/ - extra-lib-dirs: /usr/local/lib/ - include-dirs: /usr/local/include/ + if !flag(disable-default-paths) + extra-lib-dirs: /opt/local/lib/ + include-dirs: /opt/local/include/ + extra-lib-dirs: /usr/local/lib/ + include-dirs: /usr/local/include/ if arch(i386) cc-options: -arch i386 frameworks: Accelerate if os(freebsd) if flag(openblas) - extra-lib-dirs: /usr/local/lib/openblas/lib + if !flag(disable-default-paths) + extra-lib-dirs: /usr/local/lib/openblas/lib extra-libraries: openblas else extra-libraries: blas lapack - extra-lib-dirs: /usr/local/lib - include-dirs: /usr/local/include - extra-libraries: gfortran + if !flag(disable-default-paths) + extra-lib-dirs: /usr/local/lib + include-dirs: /usr/local/include + extra-libraries: gfortran + extra-lib-dirs: /usr/local/lib/gcc9 /usr/local/lib/gcc8 /usr/local/lib/gcc7 if os(windows) if flag(openblas) - extra-libraries: libopenblas + extra-libraries: openblas else extra-libraries: blas lapack if os(linux) if flag(openblas) - extra-lib-dirs: /usr/lib/openblas/lib + if !flag(disable-default-paths) + extra-lib-dirs: /usr/lib/openblas/lib extra-libraries: openblas else extra-libraries: blas lapack @@ -141,5 +161,4 @@ source-repository head type: git - location: https://github.com/albertoruiz/hmatrix - + location: https://github.com/haskell-numerics/hmatrix diff --git a/src/Internal/Algorithms.hs b/src/Internal/Algorithms.hs --- a/src/Internal/Algorithms.hs +++ b/src/Internal/Algorithms.hs @@ -1,9 +1,10 @@ {-# LANGUAGE FlexibleContexts, FlexibleInstances #-} {-# LANGUAGE CPP #-} {-# LANGUAGE MultiParamTypeClasses #-} -{-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE TypeFamilies #-} +{-# OPTIONS_GHC -fno-warn-missing-signatures #-} + ----------------------------------------------------------------------------- {- | Module : Internal.Algorithms @@ -20,16 +21,24 @@ -} ----------------------------------------------------------------------------- -module Internal.Algorithms where +module Internal.Algorithms ( + module Internal.Algorithms, + UpLo(..) +) where +#if MIN_VERSION_base(4,11,0) +import Prelude hiding ((<>)) +#endif + import Internal.Vector import Internal.Matrix import Internal.Element import Internal.Conversion -import Internal.LAPACK as LAPACK +import Internal.LAPACK import Internal.Numeric import Data.List(foldl1') import qualified Data.Array as A +import qualified Data.Vector.Storable as Vector import Internal.ST import Internal.Vectorized(range) import Control.DeepSeq @@ -57,13 +66,17 @@ mbLinearSolve' :: Matrix t -> Matrix t -> Maybe (Matrix t) linearSolve' :: Matrix t -> Matrix t -> Matrix t cholSolve' :: Matrix t -> Matrix t -> Matrix t + triSolve' :: UpLo -> Matrix t -> Matrix t -> Matrix t + triDiagSolve' :: Vector t -> Vector t -> Vector t -> Matrix t -> Matrix t ldlPacked' :: Matrix t -> (Matrix t, [Int]) ldlSolve' :: (Matrix t, [Int]) -> Matrix t -> Matrix t linearSolveSVD' :: Matrix t -> Matrix t -> Matrix t linearSolveLS' :: Matrix t -> Matrix t -> Matrix t eig' :: Matrix t -> (Vector (Complex Double), Matrix (Complex Double)) + geig' :: Matrix t -> Matrix t -> (Vector (Complex Double), Vector t, Matrix (Complex Double)) eigSH'' :: Matrix t -> (Vector Double, Matrix t) eigOnly :: Matrix t -> Vector (Complex Double) + geigOnly :: Matrix t -> Matrix t -> (Vector (Complex Double), Vector t) eigOnlySH :: Matrix t -> Vector Double cholSH' :: Matrix t -> Matrix t mbCholSH' :: Matrix t -> Maybe (Matrix t) @@ -82,11 +95,15 @@ linearSolve' = linearSolveR -- (luSolve . luPacked) ?? mbLinearSolve' = mbLinearSolveR cholSolve' = cholSolveR + triSolve' = triSolveR + triDiagSolve' = triDiagSolveR linearSolveLS' = linearSolveLSR linearSolveSVD' = linearSolveSVDR Nothing eig' = eigR eigSH'' = eigS + geig' = eigG eigOnly = eigOnlyR + geigOnly = eigOnlyG eigOnlySH = eigOnlyS cholSH' = cholS mbCholSH' = mbCholS @@ -111,10 +128,14 @@ linearSolve' = linearSolveC mbLinearSolve' = mbLinearSolveC cholSolve' = cholSolveC + triSolve' = triSolveC + triDiagSolve' = triDiagSolveC linearSolveLS' = linearSolveLSC linearSolveSVD' = linearSolveSVDC Nothing eig' = eigC + geig' = eigGC eigOnly = eigOnlyC + geigOnly = eigOnlyGC eigSH'' = eigH eigOnlySH = eigOnlyH cholSH' = cholH @@ -158,7 +179,8 @@ -0.690 -0.352 0.433 -0.233 0.398 >>> s -fromList [35.18264833189422,1.4769076999800903,1.089145439970417e-15] +[35.18264833189422,1.4769076999800903,1.089145439970417e-15] +it :: Vector Double >>> disp 3 v 3x3 @@ -212,7 +234,8 @@ -0.690 -0.352 0.433 >>> s -fromList [35.18264833189422,1.4769076999800903,1.089145439970417e-15] +[35.18264833189422,1.4769076999800903,1.089145439970417e-15] +it :: Vector Double >>> disp 3 v 3x3 @@ -271,7 +294,8 @@ -0.690 -0.352 >>> s -fromList [35.18264833189422,1.4769076999800903] +[35.18264833189422,1.476907699980091] +it :: Vector Double >>> disp 3 u 5x2 @@ -291,9 +315,13 @@ -} compactSVD :: Field t => Matrix t -> (Matrix t, Vector Double, Matrix t) -compactSVD m = (u', subVector 0 d s, v') where +compactSVD = compactSVDTol 1 + +-- | @compactSVDTol r@ is similar to 'compactSVD' (for which @r=1@), but uses tolerance @tol=r*g*eps*(max rows cols)@ to distinguish nonzero singular values, where @g@ is the greatest singular value. If @g Double -> Matrix t -> (Matrix t, Vector Double, Matrix t) +compactSVDTol r m = (u', subVector 0 d s, v') where (u,s,v) = thinSVD m - d = rankSVD (1*eps) m s `max` 1 + d = rankSVD (r*eps) m s `max` 1 u' = takeColumns d u v' = takeColumns d v @@ -345,6 +373,79 @@ -> Matrix t -- ^ solution cholSolve = {-# SCC "cholSolve" #-} cholSolve' +-- | Solve a triangular linear system. If `Upper` is specified then +-- all elements below the diagonal are ignored; if `Lower` is +-- specified then all elements above the diagonal are ignored. +triSolve + :: Field t + => UpLo -- ^ `Lower` or `Upper` + -> Matrix t -- ^ coefficient matrix + -> Matrix t -- ^ right hand sides + -> Matrix t -- ^ solution +triSolve = {-# SCC "triSolve" #-} triSolve' + +-- | Solve a tridiagonal linear system. Suppose you wish to solve \(Ax = b\) where +-- +-- \[ +-- A = +-- \begin{bmatrix} +-- 1.0 & 4.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 +-- \\ 3.0 & 1.0 & 4.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 +-- \\ 0.0 & 3.0 & 1.0 & 4.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 +-- \\ 0.0 & 0.0 & 3.0 & 1.0 & 4.0 & 0.0 & 0.0 & 0.0 & 0.0 +-- \\ 0.0 & 0.0 & 0.0 & 3.0 & 1.0 & 4.0 & 0.0 & 0.0 & 0.0 +-- \\ 0.0 & 0.0 & 0.0 & 0.0 & 3.0 & 1.0 & 4.0 & 0.0 & 0.0 +-- \\ 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 3.0 & 1.0 & 4.0 & 0.0 +-- \\ 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 3.0 & 1.0 & 4.0 +-- \\ 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 3.0 & 1.0 +-- \end{bmatrix} +-- \quad +-- b = +-- \begin{bmatrix} +-- 1.0 & 1.0 & 1.0 +-- \\ 1.0 & -1.0 & 2.0 +-- \\ 1.0 & 1.0 & 3.0 +-- \\ 1.0 & -1.0 & 4.0 +-- \\ 1.0 & 1.0 & 5.0 +-- \\ 1.0 & -1.0 & 6.0 +-- \\ 1.0 & 1.0 & 7.0 +-- \\ 1.0 & -1.0 & 8.0 +-- \\ 1.0 & 1.0 & 9.0 +-- \end{bmatrix} +-- \] +-- +-- then +-- +-- @ +-- dL = fromList [3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0] +-- d = fromList [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0] +-- dU = fromList [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0] +-- +-- b = (9><3) +-- [ +-- 1.0, 1.0, 1.0, +-- 1.0, -1.0, 2.0, +-- 1.0, 1.0, 3.0, +-- 1.0, -1.0, 4.0, +-- 1.0, 1.0, 5.0, +-- 1.0, -1.0, 6.0, +-- 1.0, 1.0, 7.0, +-- 1.0, -1.0, 8.0, +-- 1.0, 1.0, 9.0 +-- ] +-- +-- x = triDiagSolve dL d dU b +-- @ +-- +triDiagSolve + :: Field t + => Vector t -- ^ lower diagonal: \(n - 1\) elements + -> Vector t -- ^ diagonal: \(n\) elements + -> Vector t -- ^ upper diagonal: \(n - 1\) elements + -> Matrix t -- ^ right hand sides + -> Matrix t -- ^ solution +triDiagSolve = {-# SCC "triDiagSolve" #-} triDiagSolve' + -- | Minimum norm solution of a general linear least squares problem Ax=B using the SVD. Admits rank-deficient systems but it is slower than 'linearSolveLS'. The effective rank of A is determined by treating as zero those singular valures which are less than 'eps' times the largest singular value. linearSolveSVD :: Field t => Matrix t -> Matrix t -> Matrix t linearSolveSVD = {-# SCC "linearSolveSVD" #-} linearSolveSVD' @@ -420,10 +521,25 @@ eig :: Field t => Matrix t -> (Vector (Complex Double), Matrix (Complex Double)) eig = {-# SCC "eig" #-} eig' +-- | Generalized eigenvalues (not ordered) and eigenvectors (as columns) of a pair of nonsymmetric matrices. +-- Eigenvalues are represented as pairs of alpha, beta, where eigenvalue = alpha / beta. Alpha is always +-- complex, but betas has the same type as the input matrix. +-- +-- If @(alphas, betas, v) = geig a b@, then @a \<> v == b \<> v \<> diag (alphas / betas)@ +-- +-- Note that beta can be 0 and that has reasonable interpretation. +geig :: Field t => Matrix t -> Matrix t -> (Vector (Complex Double), Vector t, Matrix (Complex Double)) +geig = {-# SCC "geig" #-} geig' + -- | Eigenvalues (not ordered) of a general square matrix. eigenvalues :: Field t => Matrix t -> Vector (Complex Double) eigenvalues = {-# SCC "eigenvalues" #-} eigOnly +-- | Generalized eigenvalues of a pair of matrices. Represented as pairs of alpha, beta, +-- where eigenvalue is alpha / beta as in 'geig'. +geigenvalues :: Field t => Matrix t -> Matrix t -> (Vector (Complex Double), Vector t) +geigenvalues = {-# SCC "geigenvalues" #-} geigOnly + -- | Similar to 'eigSH' without checking that the input matrix is hermitian or symmetric. It works with the upper triangular part. eigSH' :: Field t => Matrix t -> (Vector Double, Matrix t) eigSH' = {-# SCC "eigSH'" #-} eigSH'' @@ -446,7 +562,7 @@ >>> let (l, v) = eigSH a >>> l -fromList [11.344814282762075,0.17091518882717918,-0.5157294715892575] +[11.344814282762075,0.17091518882717918,-0.5157294715892575] >>> disp 3 $ v <> diag l <> tr v 3x3 @@ -475,9 +591,14 @@ -- | QR factorization. -- -- If @(q,r) = qr m@ then @m == q \<> r@, where q is unitary and r is upper triangular. +-- Note: the current implementation is very slow for large matrices. 'thinQR' is much faster. qr :: Field t => Matrix t -> (Matrix t, Matrix t) qr = {-# SCC "qr" #-} unpackQR . qr' +-- | A version of 'qr' which returns only the @min (rows m) (cols m)@ columns of @q@ and rows of @r@. +thinQR :: Field t => Matrix t -> (Matrix t, Matrix t) +thinQR = {-# SCC "thinQR" #-} thinUnpackQR . qr' + -- | Compute the QR decomposition of a matrix in compact form. qrRaw :: Field t => Matrix t -> QR t qrRaw m = QR x v @@ -494,9 +615,17 @@ -- | RQ factorization. -- -- If @(r,q) = rq m@ then @m == r \<> q@, where q is unitary and r is upper triangular. +-- Note: the current implementation is very slow for large matrices. 'thinRQ' is much faster. rq :: Field t => Matrix t -> (Matrix t, Matrix t) -rq m = {-# SCC "rq" #-} (r,q) where - (q',r') = qr $ trans $ rev1 m +rq = {-# SCC "rq" #-} rqFromQR qr + +-- | A version of 'rq' which returns only the @min (rows m) (cols m)@ columns of @r@ and rows of @q@. +thinRQ :: Field t => Matrix t -> (Matrix t, Matrix t) +thinRQ = {-# SCC "thinQR" #-} rqFromQR thinQR + +rqFromQR :: Field t => (Matrix t -> (Matrix t, Matrix t)) -> Matrix t -> (Matrix t, Matrix t) +rqFromQR qr0 m = (r,q) where + (q',r') = qr0 $ trans $ rev1 m r = rev2 (trans r') q = rev2 (trans q') rev1 = flipud . fliprl @@ -724,6 +853,12 @@ hs = zipWith haussholder (toList tau) vs q = foldl1' mXm hs +thinUnpackQR :: (Field t) => (Matrix t, Vector t) -> (Matrix t, Matrix t) +thinUnpackQR (pq, tau) = (q, r) + where mn = uncurry min $ size pq + q = qrgr mn $ QR pq tau + r = fromRows $ zipWith (\i v -> Vector.replicate i 0 Vector.++ Vector.drop i v) [0..mn-1] (toRows pq) + unpackHess :: (Field t) => (Matrix t -> (Matrix t,Vector t)) -> Matrix t -> (Matrix t, Matrix t) unpackHess hf m | rows m == 1 = ((1><1)[1],m) @@ -1027,4 +1162,3 @@ -- for usage in 'chol', 'eigSH', etc. Only a triangular part of the matrix will be used. trustSym :: Matrix t -> Herm t trustSym x = (Herm x) - diff --git a/src/Internal/C/lapack-aux.c b/src/Internal/C/lapack-aux.c --- a/src/Internal/C/lapack-aux.c +++ b/src/Internal/C/lapack-aux.c @@ -45,6 +45,9 @@ for(q=0;q 0) { ret = CODE; } else if(RES < 0) { ret = RES; }) +#define UNWIND(RES,CODE,LABEL) MACRO(if(RES) { ret = CODE; goto LABEL; }) #define BAD_SIZE 2000 #define BAD_CODE 2001 @@ -116,6 +119,7 @@ integer *info); int svd_l_R(ODMAT(a),ODMAT(u), DVEC(s),ODMAT(v)) { + integer ret = 0; integer m = ar; integer n = ac; integer q = MIN(m,n); @@ -152,9 +156,12 @@ vp,&ldvt, &ans, &lwork, &res); + CHECK(res,res); + lwork = ceil(ans); double * work = (double*)malloc(lwork*sizeof(double)); CHECK(!work,MEM); + dgesvd_ (jobu,jobvt, &m,&n,ap,&m, sp, @@ -162,9 +169,10 @@ vp,&ldvt, work, &lwork, &res); - CHECK(res,res); + + MARK(res, res); free(work); - OK + return ret; } // (alternative version) @@ -175,9 +183,10 @@ integer *iwork, integer *info); int svd_l_Rdd(ODMAT(a),ODMAT(u), DVEC(s),ODMAT(v)) { - integer m = ar; - integer n = ac; - integer q = MIN(m,n); + integer ret = 0; + integer m = ar; + integer n = ac; + integer q = MIN(m,n); REQUIRES(sn==q,BAD_SIZE); REQUIRES((up == NULL && vp == NULL) || (ur==m && vc==n @@ -195,20 +204,27 @@ } DEBUGMSG("svd_l_Rdd"); integer* iwk = (integer*) malloc(8*q*sizeof(integer)); - CHECK(!iwk,MEM); + UNWIND(!iwk,MEM,cleanup0); integer lwk = -1; integer res; // ask for optimal lwk double ans; dgesdd_ (jobz,&m,&n,ap,&m,sp,up,&m,vp,&ldvt,&ans,&lwk,iwk,&res); + UNWIND(res,res,cleanup1); + lwk = ans; double * workv = (double*)malloc(lwk*sizeof(double)); - CHECK(!workv,MEM); + UNWIND(!workv,MEM,cleanup1); + dgesdd_ (jobz,&m,&n,ap,&m,sp,up,&m,vp,&ldvt,workv,&lwk,iwk,&res); - CHECK(res,res); - free(iwk); + UNWIND(res,res,cleanup2); + +cleanup2: free(workv); - OK +cleanup1: + free(iwk); +cleanup0: + return ret; } //////////////////// complex svd //////////////////////////////////// @@ -219,11 +235,14 @@ integer *lwork, doublereal *rwork, integer *info); int svd_l_C(OCMAT(a),OCMAT(u), DVEC(s),OCMAT(v)) { - integer m = ar; - integer n = ac; - integer q = MIN(m,n); + integer ret = 0; + integer m = ar; + integer n = ac; + integer q = MIN(m,n); REQUIRES(sn==q,BAD_SIZE); REQUIRES(up==NULL || (ur==m && (uc==m || uc==q)),BAD_SIZE); + REQUIRES(vp==NULL || (vc==n && (vr==n || vr==q)),BAD_SIZE); + char* jobu = "A"; if (up==NULL) { jobu = "N"; @@ -232,7 +251,6 @@ jobu = "S"; } } - REQUIRES(vp==NULL || (vc==n && (vr==n || vr==q)),BAD_SIZE); char* jobvt = "A"; integer ldvt = n; if (vp==NULL) { @@ -245,7 +263,8 @@ }DEBUGMSG("svd_l_C"); double *rwork = (double*) malloc(5*q*sizeof(double)); - CHECK(!rwork,MEM); + UNWIND(!rwork,MEM,cleanup0); + integer lwork = -1; integer res; // ask for optimal lwork @@ -258,9 +277,12 @@ &ans, &lwork, rwork, &res); + UNWIND(res,res,cleanup1); + lwork = ceil(ans.r); doublecomplex * work = (doublecomplex*)malloc(lwork*sizeof(doublecomplex)); - CHECK(!work,MEM); + UNWIND(!work,MEM,cleanup1); + zgesvd_ (jobu,jobvt, &m,&n,ap,&m, sp, @@ -269,10 +291,14 @@ work, &lwork, rwork, &res); - CHECK(res,res); + UNWIND(res,res,cleanup2); + +cleanup2: free(work); +cleanup1: free(rwork); - OK +cleanup0: + return ret; } int zgesdd_ (char *jobz, integer *m, integer *n, @@ -281,49 +307,68 @@ integer *lwork, doublereal *rwork, integer* iwork, integer *info); int svd_l_Cdd(OCMAT(a),OCMAT(u), DVEC(s),OCMAT(v)) { - integer m = ar; - integer n = ac; - integer q = MIN(m,n); - REQUIRES(sn==q,BAD_SIZE); + integer ret = 0; + integer m = ar; + integer n = ac; + integer mx = MAX(m,n); + integer mn = MIN(m,n); + REQUIRES(sn==mn,BAD_SIZE); REQUIRES((up == NULL && vp == NULL) || (ur==m && vc==n - && ((uc == q && vr == q) + && ((uc == mn && vr == mn) || (uc == m && vc==n))),BAD_SIZE); char* jobz = "A"; integer ldvt = n; if (up==NULL) { jobz = "N"; } else { - if (uc==q && vr == q) { + if (uc==mn && vr == mn) { jobz = "S"; - ldvt = q; + ldvt = mn; } } DEBUGMSG("svd_l_Cdd"); - integer* iwk = (integer*) malloc(8*q*sizeof(integer)); - CHECK(!iwk,MEM); + integer* iwk = (integer*) malloc(8*mn*sizeof(integer)); + UNWIND(!iwk,MEM,cleanup0); + + // Docs: http://www.netlib.org/lapack/explore-html/d8/d54/zgesdd_8f_source.html + // RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) + // Let mx = max(M,N) and mn = min(M,N). + // If JOBZ = 'N', LRWORK >= 5*mn (LAPACK <= 3.6 needs 7*mn); + // else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn; + // else LRWORK >= max( 5*mn*mn + 5*mn, + // 2*mx*mn + 2*mn*mn + mn ). int lrwk; - if (0 && *jobz == 'N') { - lrwk = 5*q; // does not work, crash at free below + if (*jobz == 'N') { + lrwk = 7*mn; } else { - lrwk = 5*q*q + 7*q; + lrwk = MAX(5*mn*mn + 7*mn, 2*mx*mn + 2*mn*mn + mn); } - double *rwk = (double*)malloc(lrwk*sizeof(double));; - CHECK(!rwk,MEM); + double *rwk = (double*)malloc(MAX(1, lrwk)*sizeof(double));; + UNWIND(!rwk,MEM,cleanup1); + integer lwk = -1; integer res; // ask for optimal lwk doublecomplex ans; zgesdd_ (jobz,&m,&n,ap,&m,sp,up,&m,vp,&ldvt,&ans,&lwk,rwk,iwk,&res); + UNWIND(res,res,cleanup2); + lwk = ans.r; doublecomplex * workv = (doublecomplex*)malloc(lwk*sizeof(doublecomplex)); - CHECK(!workv,MEM); + UNWIND(!workv,MEM,cleanup2); + zgesdd_ (jobz,&m,&n,ap,&m,sp,up,&m,vp,&ldvt,workv,&lwk,rwk,iwk,&res); - CHECK(res,res); + UNWIND(res,res,cleanup3); + +cleanup3: free(workv); +cleanup2: free(rwk); +cleanup1: free(iwk); - OK +cleanup0: + return ret; } //////////////////// general complex eigensystem //////////// @@ -334,15 +379,18 @@ integer *lwork, doublereal *rwork, integer *info); int eig_l_C(OCMAT(a), OCMAT(u), CVEC(s),OCMAT(v)) { - integer n = ar; + integer ret = 0; + integer n = ar; REQUIRES(ac==n && sn==n, BAD_SIZE); REQUIRES(up==NULL || (ur==n && uc==n), BAD_SIZE); char jobvl = up==NULL?'N':'V'; REQUIRES(vp==NULL || (vr==n && vc==n), BAD_SIZE); char jobvr = vp==NULL?'N':'V'; DEBUGMSG("eig_l_C"); + double *rwork = (double*) malloc(2*n*sizeof(double)); - CHECK(!rwork,MEM); + UNWIND(!rwork,MEM,cleanup0); + integer lwork = -1; integer res; // ask for optimal lwork @@ -355,9 +403,13 @@ &ans, &lwork, rwork, &res); + + UNWIND(res,res,cleanup1); + lwork = ceil(ans.r); doublecomplex * work = (doublecomplex*)malloc(lwork*sizeof(doublecomplex)); - CHECK(!work,MEM); + UNWIND(!work,MEM,cleanup1); + zgeev_ (&jobvl,&jobvr, &n,ap,&n, sp, @@ -366,10 +418,15 @@ work, &lwork, rwork, &res); - CHECK(res,res); + + UNWIND(res,res,cleanup2); + +cleanup2: free(work); +cleanup1: free(rwork); - OK +cleanup0: + return ret; } @@ -382,7 +439,8 @@ integer *lwork, integer *info); int eig_l_R(ODMAT(a),ODMAT(u), CVEC(s),ODMAT(v)) { - integer n = ar; + integer ret = 0; + integer n = ar; REQUIRES(ac==n && sn==n, BAD_SIZE); REQUIRES(up==NULL || (ur==n && uc==n), BAD_SIZE); char jobvl = up==NULL?'N':'V'; @@ -400,6 +458,8 @@ vp,&n, &ans, &lwork, &res); + CHECK(res,res); + lwork = ceil(ans); double * work = (double*)malloc(lwork*sizeof(double)); CHECK(!work,MEM); @@ -410,12 +470,115 @@ vp,&n, work, &lwork, &res); + MARK(res,res); + + free(work); + return ret; +} + +//////////////////// generalized real eigensystem //////////// + +int dggev_(char *jobvl, char *jobvr, integer *n, + doublereal *a, integer *lda, doublereal *b, integer *ldb, + doublereal *alphar, doublereal *alphai, doublereal *beta, + doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, + doublereal *work, + integer *lwork, integer *info); + +int eig_l_G(ODMAT(a), ODMAT(b), CVEC(alpha), DVEC(beta), ODMAT(vl), ODMAT(vr)) { + integer ret = 0; + integer n = ar; + REQUIRES(ac == n && br == n && bc == n && alphan == n && betan == n, BAD_SIZE); + REQUIRES(vlp==NULL || (vlr==n && vlc==n), BAD_SIZE); + char jobvl = vlp==NULL?'N':'V'; + REQUIRES(vrp==NULL || (vrr==n && vrc==n), BAD_SIZE); + char jobvr = vrp==NULL?'N':'V'; + DEBUGMSG("eig_l_G"); + integer lwork = -1; + integer res; + // ask for optimal lwork + double ans; + dggev_ (&jobvl,&jobvr, + &n, + ap,&n,bp,&n, + (double*)alphap, (double*)alphap+n, betap, + vlp, &n, vrp, &n, + &ans, &lwork, + &res); CHECK(res,res); + + lwork = ceil(ans); + double * work = (double*)malloc(lwork*sizeof(double)); + CHECK(!work,MEM); + + dggev_ (&jobvl,&jobvr, + &n, + ap,&n,bp,&n, + (double*)alphap, (double*)alphap+n, betap, + vlp, &n, vrp, &n, + work, &lwork, + &res); + MARK(res,res); + free(work); - OK + return ret; } +//////////////////// generalized complex eigensystem //////////// +int zggev_(char *jobvl, char *jobvr, integer *n, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + doublecomplex *alphar, doublecomplex *beta, + doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr, + doublecomplex *work, integer *lwork, + doublereal *rwork, integer *info); + +int eig_l_GC(OCMAT(a), OCMAT(b), CVEC(alpha), CVEC(beta), OCMAT(vl), OCMAT(vr)) { + integer ret = 0; + integer n = ar; + REQUIRES(ac == n && br == n && bc == n && alphan == n && betan == n, BAD_SIZE); + REQUIRES(vlp==NULL || (vlr==n && vlc==n), BAD_SIZE); + char jobvl = vlp==NULL?'N':'V'; + REQUIRES(vrp==NULL || (vrr==n && vrc==n), BAD_SIZE); + char jobvr = vrp==NULL?'N':'V'; + DEBUGMSG("eig_l_GC"); + double *rwork = (double*) malloc(8*n*sizeof(double)); + UNWIND(!rwork,MEM,cleanup0); + + integer lwork = -1; + integer res; + // ask for optimal lwork + doublecomplex ans; + zggev_ (&jobvl,&jobvr, + &n, + ap,&n,bp,&n, + alphap, betap, + vlp, &n, vrp, &n, + &ans, &lwork, + rwork, &res); + UNWIND(res,res,cleanup1); + + lwork = ceil(ans.r); + doublecomplex * work = (doublecomplex*)malloc(lwork*sizeof(doublecomplex)); + UNWIND(!work,MEM,cleanup1); + + zggev_ (&jobvl,&jobvr, + &n, + ap,&n,bp,&n, + alphap, betap, + vlp, &n, vrp, &n, + work, &lwork, + rwork, &res); + UNWIND(res,res,cleanup2); + +cleanup2: + free(work); +cleanup1: + free(rwork); +cleanup0: + return ret; +} + //////////////////// symmetric real eigensystem //////////// int dsyev_(char *jobz, char *uplo, integer *n, doublereal *a, @@ -423,7 +586,8 @@ integer *info); int eig_l_S(int wantV,DVEC(s),ODMAT(v)) { - integer n = sn; + integer ret = 0; + integer n = sn; REQUIRES(vr==n && vc==n, BAD_SIZE); char jobz = wantV?'V':'N'; DEBUGMSG("eig_l_S"); @@ -437,17 +601,21 @@ sp, &ans, &lwork, &res); + CHECK(res,res); + lwork = ceil(ans); double * work = (double*)malloc(lwork*sizeof(double)); CHECK(!work,MEM); + dsyev_ (&jobz,&uplo, &n,vp,&n, sp, work, &lwork, &res); - CHECK(res,res); + MARK(res,res); + free(work); - OK + return ret; } //////////////////// hermitian complex eigensystem //////////// @@ -457,12 +625,15 @@ doublereal *rwork, integer *info); int eig_l_H(int wantV,DVEC(s),OCMAT(v)) { - integer n = sn; + integer ret = 0; + integer n = sn; + REQUIRES(vr==n && vc==n, BAD_SIZE); char jobz = wantV?'V':'N'; DEBUGMSG("eig_l_H"); double *rwork = (double*) malloc((3*n-2)*sizeof(double)); - CHECK(!rwork,MEM); + UNWIND(!rwork,MEM,cleanup0); + integer lwork = -1; char uplo = 'U'; integer res; @@ -474,19 +645,26 @@ &ans, &lwork, rwork, &res); + UNWIND(res,res,cleanup1); + lwork = ceil(ans.r); doublecomplex * work = (doublecomplex*)malloc(lwork*sizeof(doublecomplex)); - CHECK(!work,MEM); + UNWIND(!work,MEM,cleanup1); + zheev_ (&jobz,&uplo, &n,vp,&n, sp, work, &lwork, rwork, &res); - CHECK(res,res); + UNWIND(res,res,cleanup2); + +cleanup2: free(work); +cleanup1: free(rwork); - OK +cleanup0: + return ret; } //////////////////// general real linear system //////////// @@ -495,23 +673,25 @@ *lda, integer *ipiv, doublereal *b, integer *ldb, integer *info); int linearSolveR_l(ODMAT(a),ODMAT(b)) { - integer n = ar; + integer ret = 0; + integer n = ar; integer nhrs = bc; + REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE); DEBUGMSG("linearSolveR_l"); integer * ipiv = (integer*)malloc(n*sizeof(integer)); + CHECK(!ipiv,MEM); + integer res; dgesv_ (&n,&nhrs, ap, &n, ipiv, bp, &n, &res); - if(res>0) { - return SINGULAR; - } - CHECK(res,res); + CONVERGED(res,SINGULAR); + free(ipiv); - OK + return ret; } //////////////////// general complex linear system //////////// @@ -521,23 +701,25 @@ info); int linearSolveC_l(OCMAT(a),OCMAT(b)) { - integer n = ar; + integer ret = 0; + integer n = ar; integer nhrs = bc; + REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE); DEBUGMSG("linearSolveC_l"); integer * ipiv = (integer*)malloc(n*sizeof(integer)); + CHECK(!ipiv,MEM); + integer res; zgesv_ (&n,&nhrs, ap, &n, ipiv, bp, &n, &res); - if(res>0) { - return SINGULAR; - } - CHECK(res,res); + CONVERGED(res,SINGULAR); + free(ipiv); - OK + return ret; } //////// symmetric positive definite real linear system using Cholesky //////////// @@ -584,6 +766,182 @@ OK } +//////// triangular real linear system //////////// + +int dtrtrs_(char *uplo, char *trans, char *diag, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * + info); + +int triSolveR_l_u(KODMAT(a),ODMAT(b)) { + integer n = ar; + integer lda = aXc; + integer nhrs = bc; + REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE); + DEBUGMSG("triSolveR_l_u"); + integer res; + dtrtrs_ ("U", + "N", + "N", + &n,&nhrs, + (double*)ap, &lda, + bp, &n, + &res); + CHECK(res,res); + OK +} + +int triSolveR_l_l(KODMAT(a),ODMAT(b)) { + integer n = ar; + integer lda = aXc; + integer nhrs = bc; + REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE); + DEBUGMSG("triSolveR_l_l"); + integer res; + dtrtrs_ ("L", + "N", + "N", + &n,&nhrs, + (double*)ap, &lda, + bp, &n, + &res); + CHECK(res,res); + OK +} + +//////// triangular complex linear system //////////// + +int ztrtrs_(char *uplo, char *trans, char *diag, integer *n, integer *nrhs, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + integer *info); + +int triSolveC_l_u(KOCMAT(a),OCMAT(b)) { + integer n = ar; + integer lda = aXc; + integer nhrs = bc; + REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE); + DEBUGMSG("triSolveC_l_u"); + integer res; + ztrtrs_ ("U", + "N", + "N", + &n,&nhrs, + (doublecomplex*)ap, &lda, + bp, &n, + &res); + CHECK(res,res); + OK +} + +int triSolveC_l_l(KOCMAT(a),OCMAT(b)) { + integer n = ar; + integer lda = aXc; + integer nhrs = bc; + REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE); + DEBUGMSG("triSolveC_l_u"); + integer res; + ztrtrs_ ("L", + "N", + "N", + &n,&nhrs, + (doublecomplex*)ap, &lda, + bp, &n, + &res); + CHECK(res,res); + OK +} + +//////// tridiagonal real linear system //////////// + +int dgttrf_(integer *n, + doublereal *dl, doublereal *d, doublereal *du, doublereal *du2, + integer *ipiv, + integer *info); + +int dgttrs_(char *trans, integer *n, integer *nrhs, + doublereal *dl, doublereal *d, doublereal *du, doublereal *du2, + integer *ipiv, doublereal *b, integer *ldb, + integer *info); + +int triDiagSolveR_l(DVEC(dl), DVEC(d), DVEC(du), ODMAT(b)) { + integer ret = 0; + integer n = dn; + integer nhrs = bc; + REQUIRES(n >= 1 && dln == dn - 1 && dun == dn - 1 && br == n, BAD_SIZE); + DEBUGMSG("triDiagSolveR_l"); + integer res; + integer* ipiv = (integer*)malloc(n*sizeof(integer)); + UNWIND(!ipiv,MEM,cleanup0); + + double* du2 = (double*)malloc((n - 2)*sizeof(double)); + UNWIND(!du2,MEM,cleanup1); + + dgttrf_ (&n, + dlp, dp, dup, du2, + ipiv, + &res); + UNWIND(res,res,cleanup2); + + dgttrs_ ("N", + &n,&nhrs, + dlp, dp, dup, du2, + ipiv, bp, &n, + &res); + UNWIND(res,res,cleanup2); + +cleanup2: + free(du2); +cleanup1: + free(ipiv); +cleanup0: + return ret; +} + +//////// tridiagonal complex linear system //////////// + +int zgttrf_(integer *n, + doublecomplex *dl, doublecomplex *d, doublecomplex *du, doublecomplex *du2, + integer *ipiv, + integer *info); + +int zgttrs_(char *trans, integer *n, integer *nrhs, + doublecomplex *dl, doublecomplex *d, doublecomplex *du, doublecomplex *du2, + integer *ipiv, doublecomplex *b, integer *ldb, + integer *info); + +int triDiagSolveC_l(CVEC(dl), CVEC(d), CVEC(du), OCMAT(b)) { + integer ret = 0; + integer n = dn; + integer nhrs = bc; + REQUIRES(n >= 1 && dln == dn - 1 && dun == dn - 1 && br == n, BAD_SIZE); + DEBUGMSG("triDiagSolveC_l"); + integer res; + integer* ipiv = (integer*)malloc(n*sizeof(integer)); + UNWIND(!ipiv,MEM,cleanup0); + + doublecomplex* du2 = (doublecomplex*)malloc((n - 2)*sizeof(doublecomplex)); + UNWIND(!du2,MEM,cleanup1); + + zgttrf_ (&n, + dlp, dp, dup, du2, + ipiv, + &res); + UNWIND(res,res,cleanup2); + + zgttrs_ ("N", + &n,&nhrs, + dlp, dp, dup, du2, + ipiv, bp, &n, + &res); + UNWIND(res,res,cleanup2); + +cleanup2: + free(du2); +cleanup1: + free(ipiv); +cleanup0: + return ret; +} + //////////////////// least squares real linear system //////////// int dgels_(char *trans, integer *m, integer *n, integer * @@ -591,10 +949,11 @@ doublereal *work, integer *lwork, integer *info); int linearSolveLSR_l(ODMAT(a),ODMAT(b)) { - integer m = ar; - integer n = ac; + integer ret = 0; + integer m = ar; + integer n = ac; integer nrhs = bc; - integer ldb = bXc; + integer ldb = bXc; REQUIRES(m>=1 && n>=1 && br==MAX(m,n), BAD_SIZE); DEBUGMSG("linearSolveLSR_l"); integer res; @@ -605,19 +964,21 @@ bp,&ldb, &ans,&lwork, &res); + CHECK(res,res); + lwork = ceil(ans); double * work = (double*)malloc(lwork*sizeof(double)); + CHECK(!work,MEM); + dgels_ ("N",&m,&n,&nrhs, ap,&m, bp,&ldb, work,&lwork, &res); - if(res>0) { - return SINGULAR; - } - CHECK(res,res); + CONVERGED(res,SINGULAR); + free(work); - OK + return ret; } //////////////////// least squares complex linear system //////////// @@ -627,10 +988,11 @@ doublecomplex *work, integer *lwork, integer *info); int linearSolveLSC_l(OCMAT(a),OCMAT(b)) { - integer m = ar; - integer n = ac; + integer ret = 0; + integer m = ar; + integer n = ac; integer nrhs = bc; - integer ldb = bXc; + integer ldb = bXc; REQUIRES(m>=1 && n>=1 && br==MAX(m,n), BAD_SIZE); DEBUGMSG("linearSolveLSC_l"); integer res; @@ -641,19 +1003,21 @@ bp,&ldb, &ans,&lwork, &res); + CHECK(res,res); + lwork = ceil(ans.r); doublecomplex * work = (doublecomplex*)malloc(lwork*sizeof(doublecomplex)); + CHECK(!work,MEM); + zgels_ ("N",&m,&n,&nrhs, ap,&m, bp,&ldb, work,&lwork, &res); - if(res>0) { - return SINGULAR; - } - CHECK(res,res); + CONVERGED(res,SINGULAR); + free(work); - OK + return ret; } //////////////////// least squares real linear system using SVD //////////// @@ -664,13 +1028,17 @@ integer *info); int linearSolveSVDR_l(double rcond,ODMAT(a),ODMAT(b)) { - integer m = ar; - integer n = ac; + integer ret = 0; + integer m = ar; + integer n = ac; integer nrhs = bc; - integer ldb = bXc; + integer ldb = bXc; REQUIRES(m>=1 && n>=1 && br==MAX(m,n), BAD_SIZE); DEBUGMSG("linearSolveSVDR_l"); - double*S = (double*)malloc(MIN(m,n)*sizeof(double)); + + double * S = (double*)malloc(MIN(m,n)*sizeof(double)); + UNWIND(!S,MEM,cleanup0); + integer res; integer lwork = -1; integer rank; @@ -682,8 +1050,12 @@ &rcond,&rank, &ans,&lwork, &res); + UNWIND(res,res,cleanup1); + lwork = ceil(ans); double * work = (double*)malloc(lwork*sizeof(double)); + UNWIND(!work,MEM,cleanup1); + dgelss_ (&m,&n,&nrhs, ap,&m, bp,&ldb, @@ -691,13 +1063,15 @@ &rcond,&rank, work,&lwork, &res); - if(res>0) { - return NOCONVER; - } - CHECK(res,res); + + CONVERGED(res,NOCONVER); + free(work); +cleanup1: free(S); - OK +cleanup0: + return ret; + } //////////////////// least squares complex linear system using SVD //////////// @@ -709,14 +1083,20 @@ integer *info); int linearSolveSVDC_l(double rcond, OCMAT(a),OCMAT(b)) { - integer m = ar; - integer n = ac; + integer ret = 0; + integer m = ar; + integer n = ac; integer nrhs = bc; - integer ldb = bXc; + integer ldb = bXc; REQUIRES(m>=1 && n>=1 && br==MAX(m,n), BAD_SIZE); DEBUGMSG("linearSolveSVDC_l"); + double*S = (double*)malloc(MIN(m,n)*sizeof(double)); + UNWIND(!S,MEM,cleanup0); + double*RWORK = (double*)malloc(5*MIN(m,n)*sizeof(double)); + UNWIND(!S,MEM,cleanup1); + integer res; integer lwork = -1; integer rank; @@ -729,8 +1109,12 @@ &ans,&lwork, RWORK, &res); + UNWIND(res,res,cleanup2); + lwork = ceil(ans.r); doublecomplex * work = (doublecomplex*)malloc(lwork*sizeof(doublecomplex)); + UNWIND(!work,MEM,cleanup2); + zgelss_ (&m,&n,&nrhs, ap,&m, bp,&ldb, @@ -739,14 +1123,16 @@ work,&lwork, RWORK, &res); - if(res>0) { - return NOCONVER; - } - CHECK(res,res); + CONVERGED(res,NOCONVER); + free(work); +cleanup2: free(RWORK); +cleanup1: free(S); - OK +cleanup0: + return ret; + } //////////////////// Cholesky factorization ///////////////////////// @@ -799,36 +1185,43 @@ lda, doublereal *tau, doublereal *work, integer *info); int qr_l_R(DVEC(tau), ODMAT(r)) { - integer m = rr; - integer n = rc; - integer mn = MIN(m,n); + integer ret = 0; + integer m = rr; + integer n = rc; + integer mn = MIN(m,n); REQUIRES(m>=1 && n >=1 && taun == mn, BAD_SIZE); DEBUGMSG("qr_l_R"); double *WORK = (double*)malloc(n*sizeof(double)); CHECK(!WORK,MEM); + integer res; dgeqr2_ (&m,&n,rp,&m,taup,WORK,&res); - CHECK(res,res); + MARK(res,res); + free(WORK); - OK + return ret; } int zgeqr2_(integer *m, integer *n, doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *work, integer *info); int qr_l_C(CVEC(tau), OCMAT(r)) { - integer m = rr; - integer n = rc; - integer mn = MIN(m,n); + integer ret = 0; + integer m = rr; + integer n = rc; + integer mn = MIN(m,n); REQUIRES(m>=1 && n >=1 && taun == mn, BAD_SIZE); DEBUGMSG("qr_l_C"); + doublecomplex *WORK = (doublecomplex*)malloc(n*sizeof(doublecomplex)); CHECK(!WORK,MEM); + integer res; zgeqr2_ (&m,&n,rp,&m,taup,WORK,&res); - CHECK(res,res); + MARK(res,res); + free(WORK); - OK + return ret; } int dorgqr_(integer *m, integer *n, integer *k, doublereal * @@ -836,18 +1229,21 @@ integer *info); int c_dorgqr(KDVEC(tau), ODMAT(r)) { - integer m = rr; - integer n = MIN(rc,rr); - integer k = taun; + integer ret = 0; + integer m = rr; + integer n = MIN(rc,rr); + integer k = taun; DEBUGMSG("c_dorgqr"); integer lwork = 8*n; // FIXME double *WORK = (double*)malloc(lwork*sizeof(double)); CHECK(!WORK,MEM); + integer res; dorgqr_ (&m,&n,&k,rp,&m,(double*)taup,WORK,&lwork,&res); - CHECK(res,res); + MARK(res,res); + free(WORK); - OK + return ret; } int zungqr_(integer *m, integer *n, integer *k, @@ -855,18 +1251,21 @@ work, integer *lwork, integer *info); int c_zungqr(KCVEC(tau), OCMAT(r)) { - integer m = rr; - integer n = MIN(rc,rr); - integer k = taun; + integer ret = 0; + integer m = rr; + integer n = MIN(rc,rr); + integer k = taun; DEBUGMSG("z_ungqr"); integer lwork = 8*n; // FIXME doublecomplex *WORK = (doublecomplex*)malloc(lwork*sizeof(doublecomplex)); CHECK(!WORK,MEM); + integer res; zungqr_ (&m,&n,&k,rp,&m,(doublecomplex*)taup,WORK,&lwork,&res); - CHECK(res,res); + MARK(res,res); + free(WORK); - OK + return ret; } @@ -877,20 +1276,23 @@ integer *lwork, integer *info); int hess_l_R(DVEC(tau), ODMAT(r)) { - integer m = rr; - integer n = rc; - integer mn = MIN(m,n); + integer ret = 0; + integer m = rr; + integer n = rc; + integer mn = MIN(m,n); REQUIRES(m>=1 && n == m && taun == mn-1, BAD_SIZE); DEBUGMSG("hess_l_R"); integer lwork = 5*n; // FIXME double *WORK = (double*)malloc(lwork*sizeof(double)); CHECK(!WORK,MEM); + integer res; integer one = 1; dgehrd_ (&n,&one,&n,rp,&n,taup,WORK,&lwork,&res); - CHECK(res,res); + MARK(res,res); + free(WORK); - OK + return ret; } @@ -899,20 +1301,23 @@ work, integer *lwork, integer *info); int hess_l_C(CVEC(tau), OCMAT(r)) { - integer m = rr; - integer n = rc; - integer mn = MIN(m,n); + integer ret = 0; + integer m = rr; + integer n = rc; + integer mn = MIN(m,n); REQUIRES(m>=1 && n == m && taun == mn-1, BAD_SIZE); DEBUGMSG("hess_l_C"); integer lwork = 5*n; // FIXME doublecomplex *WORK = (doublecomplex*)malloc(lwork*sizeof(doublecomplex)); CHECK(!WORK,MEM); + integer res; integer one = 1; zgehrd_ (&n,&one,&n,rp,&n,taup,WORK,&lwork,&res); - CHECK(res,res); + MARK(res,res); + free(WORK); - OK + return ret; } //////////////////// Schur factorization ///////////////////////// @@ -923,28 +1328,35 @@ integer *lwork, logical *bwork, integer *info); int schur_l_R(ODMAT(u), ODMAT(s)) { - integer m = sr; - integer n = sc; + integer ret = 0; + integer m = sr; + integer n = sc; REQUIRES(m>=1 && n==m && ur==n && uc==n, BAD_SIZE); DEBUGMSG("schur_l_R"); integer lwork = 6*n; // FIXME double *WORK = (double*)malloc(lwork*sizeof(double)); - double *WR = (double*)malloc(n*sizeof(double)); - double *WI = (double*)malloc(n*sizeof(double)); + UNWIND(!WORK,MEM,cleanup0); + double *WR = (double*)malloc(n*sizeof(double)); + UNWIND(!WORK,MEM,cleanup1); + double *WI = (double*)malloc(n*sizeof(double)); + UNWIND(!WORK,MEM,cleanup2); // WR and WI not really required in this call logical *BWORK = (logical*)malloc(n*sizeof(logical)); + UNWIND(!BWORK,MEM,cleanup3); integer res; integer sdim; dgees_ ("V","N",NULL,&n,sp,&n,&sdim,WR,WI,up,&n,WORK,&lwork,BWORK,&res); - if(res>0) { - return NOCONVER; - } - CHECK(res,res); - free(WR); - free(WI); + CONVERGED(res,NOCONVER); + free(BWORK); +cleanup3: + free(WI); +cleanup2: + free(WR); +cleanup1: free(WORK); - OK +cleanup0: + return ret; } @@ -954,29 +1366,40 @@ doublereal *rwork, logical *bwork, integer *info); int schur_l_C(OCMAT(u), OCMAT(s)) { - integer m = sr; - integer n = sc; + integer ret = 0; + integer m = sr; + integer n = sc; REQUIRES(m>=1 && n==m && ur==n && uc==n, BAD_SIZE); DEBUGMSG("schur_l_C"); integer lwork = 6*n; // FIXME doublecomplex *WORK = (doublecomplex*)malloc(lwork*sizeof(doublecomplex)); - doublecomplex *W = (doublecomplex*)malloc(n*sizeof(doublecomplex)); + UNWIND(!WORK,MEM,cleanup0); + + doublecomplex *W = (doublecomplex*)malloc(n*sizeof(doublecomplex)); + UNWIND(!W,MEM,cleanup1); + // W not really required in this call logical *BWORK = (logical*)malloc(n*sizeof(logical)); - double *RWORK = (double*)malloc(n*sizeof(double)); + UNWIND(!BWORK,MEM,cleanup2); + + double *RWORK = (double*)malloc(n*sizeof(double)); + UNWIND(!RWORK,MEM,cleanup3); integer res; integer sdim; zgees_ ("V","N",NULL,&n,sp,&n,&sdim,W, up,&n, WORK,&lwork,RWORK,BWORK,&res); - if(res>0) { - return NOCONVER; - } - CHECK(res,res); - free(W); + CONVERGED(res,NOCONVER); + + free(RWORK); +cleanup3: free(BWORK); +cleanup2: + free(W); +cleanup1: free(WORK); - OK +cleanup0: + return ret; } //////////////////// LU factorization ///////////////////////// @@ -985,24 +1408,30 @@ lda, integer *ipiv, integer *info); int lu_l_R(DVEC(ipiv), ODMAT(r)) { - integer m = rr; - integer n = rc; - integer mn = MIN(m,n); + integer ret = 0; + integer m = rr; + integer n = rc; + integer mn = MIN(m,n); REQUIRES(m>=1 && n >=1 && ipivn == mn, BAD_SIZE); DEBUGMSG("lu_l_R"); integer* auxipiv = (integer*)malloc(mn*sizeof(integer)); + UNWIND(!auxipiv,MEM,cleanup0); + integer res; dgetrf_ (&m,&n,rp,&m,auxipiv,&res); if(res>0) { res = 0; // FIXME } - CHECK(res,res); - int k; - for (k=0; k=1 && n >=1 && ipivn == mn, BAD_SIZE); DEBUGMSG("lu_l_C"); integer* auxipiv = (integer*)malloc(mn*sizeof(integer)); + UNWIND(!auxipiv,MEM,cleanup0); + integer res; zgetrf_ (&m,&n,rp,&m,auxipiv,&res); if(res>0) { res = 0; // FIXME } - CHECK(res,res); - int k; - for (k=0; k=1 && rc==n && ipivn == n, BAD_SIZE); DEBUGMSG("ldl_R"); + integer* auxipiv = (integer*)malloc(n*sizeof(integer)); + UNWIND(!auxipiv,MEM,cleanup0); + integer res; integer lda = rXc; integer lwork = -1; @@ -1100,15 +1547,22 @@ dsytrf_ ("L",&n,rp,&lda,auxipiv,&ans,&lwork,&res); lwork = ceil(ans); doublereal* work = (doublereal*)malloc(lwork*sizeof(doublereal)); + UNWIND(!work,MEM,cleanup1); + dsytrf_ ("L",&n,rp,&lda,auxipiv,work,&lwork,&res); - CHECK(res,res); + UNWIND(res,res,cleanup2); + int k; for (k=0; k=1 && rc==n && ipivn == n, BAD_SIZE); DEBUGMSG("ldl_R"); integer* auxipiv = (integer*)malloc(n*sizeof(integer)); + UNWIND(!auxipiv,MEM,cleanup0); + integer res; integer lda = rXc; integer lwork = -1; @@ -1127,15 +1585,21 @@ zhetrf_ ("L",&n,rp,&lda,auxipiv,&ans,&lwork,&res); lwork = ceil(ans.r); doublecomplex* work = (doublecomplex*)malloc(lwork*sizeof(doublecomplex)); + UNWIND(!work,MEM,cleanup1); + zhetrf_ ("L",&n,rp,&lda,auxipiv,work,&lwork,&res); - CHECK(res,res); + UNWIND(res,res,cleanup2); int k; for (k=0; k)) +#endif ------------------------------------------------------------------ {- | Creates a real vector containing a range of values: >>> linspace 5 (-3,7::Double) -fromList [-3.0,-0.5,2.0,4.5,7.0]@ +[-3.0,-0.5,2.0,4.5,7.0] +it :: Vector Double ->>> linspace 5 (8,2+i) :: Vector (Complex Double) -fromList [8.0 :+ 0.0,6.5 :+ 0.25,5.0 :+ 0.5,3.5 :+ 0.75,2.0 :+ 1.0] +>>> linspace 5 (8,3:+2) :: Vector (Complex Double) +[8.0 :+ 0.0,6.75 :+ 0.5,5.5 :+ 1.0,4.25 :+ 1.5,3.0 :+ 2.0] +it :: Vector (Complex Double) Logarithmic spacing can be defined as follows: @@ -82,7 +86,8 @@ >>> let v = vector [10,20,30] >>> m #> v -fromList [140.0,320.0] +[140.0,320.0] +it :: Vector Numeric.LinearAlgebra.Data.R -} infixr 8 #> @@ -131,10 +136,12 @@ >>> let x = a <\> v >>> x -fromList [3.0799999999999996,5.159999999999999] +[3.0799999999999996,5.159999999999999] +it :: Vector Numeric.LinearAlgebra.Data.R >>> a #> x -fromList [13.399999999999999,26.799999999999997,1.0] +[13.399999999999999,26.799999999999997,0.9999999999999991] +it :: Vector Numeric.LinearAlgebra.Data.R It also admits multiple right-hand sides stored as columns in a matrix. @@ -162,7 +169,8 @@ where -- | -- >>> build 5 (**2) :: Vector Double - -- fromList [0.0,1.0,4.0,9.0,16.0] + -- [0.0,1.0,4.0,9.0,16.0] + -- it :: Vector Double -- -- Hilbert matrix of order N: -- @@ -179,7 +187,7 @@ where build = build' -instance Container Matrix e => Build (Int,Int) (e -> e -> e) Matrix e +instance (Num e, Container Vector e) => Build (Int,Int) (e -> e -> e) Matrix e where build = build' @@ -199,21 +207,20 @@ {- | Compute mean vector and covariance matrix of the rows of a matrix. ->>> meanCov $ gaussianSample 666 1000 (fromList[4,5]) (diagl[2,3]) -(fromList [4.010341078059521,5.0197204699640405], -(2><2) - [ 1.9862461923890056, -1.0127225830525157e-2 - , -1.0127225830525157e-2, 3.0373954915729318 ]) - +>>> meanCov $ gaussianSample 666 1000 (fromList[4,5]) (trustSym $ diagl [2,3]) +([3.9933155655086696,5.061409102770331],Herm (2><2) + [ 1.9963242906624408, -4.227815571404954e-2 + , -4.227815571404954e-2, 3.2003833097832857 ]) +it :: (Vector Double, Herm Double) -} -meanCov :: Matrix Double -> (Vector Double, Matrix Double) +meanCov :: Matrix Double -> (Vector Double, Herm Double) meanCov x = (med,cov) where r = rows x k = 1 / fromIntegral r med = konst k r `vXm` x meds = konst 1 r `outer` med xc = x `sub` meds - cov = scale (recip (fromIntegral (r-1))) (trans xc `mXm` xc) + cov = scale (recip (fromIntegral (r-1))) (mTm xc) -------------------------------------------------------------------------------- @@ -293,5 +300,3 @@ | otherwise = error $ "out of range index in remap" where [i',j'] = conformMs [i,j] - - diff --git a/src/Internal/Conversion.hs b/src/Internal/Conversion.hs --- a/src/Internal/Conversion.hs +++ b/src/Internal/Conversion.hs @@ -3,7 +3,6 @@ {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE FunctionalDependencies #-} -{-# LANGUAGE UndecidableInstances #-} ----------------------------------------------------------------------------- -- | diff --git a/src/Internal/Convolution.hs b/src/Internal/Convolution.hs --- a/src/Internal/Convolution.hs +++ b/src/Internal/Convolution.hs @@ -1,3 +1,4 @@ +{-# LANGUAGE CPP #-} {-# LANGUAGE FlexibleContexts #-} ----------------------------------------------------------------------------- {- | @@ -23,6 +24,9 @@ import Internal.Element import Internal.Conversion import Internal.Container +#if MIN_VERSION_base(4,11,0) +import Prelude hiding ((<>)) +#endif vectSS :: Element t => Int -> Vector t -> Matrix t @@ -37,7 +41,8 @@ {- ^ correlation >>> corr (fromList[1,2,3]) (fromList [1..10]) -fromList [14.0,20.0,26.0,32.0,38.0,44.0,50.0,56.0] +[14.0,20.0,26.0,32.0,38.0,44.0,50.0,56.0] +it :: (Enum t, Product t, Container Vector t) => Vector t -} corr ker v @@ -50,7 +55,8 @@ {- ^ convolution ('corr' with reversed kernel and padded input, equivalent to polynomial product) >>> conv (fromList[1,1]) (fromList [-1,1]) -fromList [-1.0,0.0,1.0] +[-1.0,0.0,1.0] +it :: (Product t, Container Vector t) => Vector t -} conv ker v diff --git a/src/Internal/Devel.hs b/src/Internal/Devel.hs --- a/src/Internal/Devel.hs +++ b/src/Internal/Devel.hs @@ -16,7 +16,8 @@ import Foreign.C.Types ( CInt ) --import Foreign.Storable.Complex () import Foreign.Ptr(Ptr) -import Control.Exception as E ( SomeException, catch ) +import Control.Exception (SomeException, SomeAsyncException (..)) +import qualified Control.Exception as Exception import Internal.Vector(Vector,avec) import Foreign.Storable(Storable) @@ -54,14 +55,27 @@ -- | postfix error code check infixl 0 #| +(#|) :: IO CInt -> String -> IO () (#|) = flip check -- | Error capture and conversion to Maybe mbCatch :: IO x -> IO (Maybe x) -mbCatch act = E.catch (Just `fmap` act) f - where f :: SomeException -> IO (Maybe x) - f _ = return Nothing +mbCatch act = + hush <$> + Exception.tryJust + (\e -> if isSyncException e then Just e else Nothing) + act + where + hush :: Either a b -> Maybe b + hush = either (const Nothing) Just + + isSyncException :: SomeException -> Bool + isSyncException e = + case Exception.fromException e of + Just (SomeAsyncException _) -> False + Nothing -> True + -------------------------------------------------------------------------------- type CM b r = CInt -> CInt -> Ptr b -> r @@ -80,8 +94,8 @@ where type Trans c b type TransRaw c b - apply :: (Trans c b) -> c -> b - applyRaw :: (TransRaw c b) -> c -> b + apply :: c -> (b -> IO r) -> (Trans c b) -> IO r + applyRaw :: c -> (b -> IO r) -> (TransRaw c b) -> IO r infixl 1 `apply`, `applyRaw` instance Storable t => TransArray (Vector t) @@ -92,4 +106,3 @@ {-# INLINE apply #-} applyRaw = avec {-# INLINE applyRaw #-} - diff --git a/src/Internal/Element.hs b/src/Internal/Element.hs --- a/src/Internal/Element.hs +++ b/src/Internal/Element.hs @@ -1,10 +1,10 @@ {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE FlexibleInstances #-} -{-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} -{-# LANGUAGE CPP #-} +{-# OPTIONS_GHC -fno-warn-orphans #-} + ----------------------------------------------------------------------------- -- | -- Module : Data.Packed.Matrix @@ -32,14 +32,14 @@ import Foreign.Storable(Storable) import System.IO.Unsafe(unsafePerformIO) import Control.Monad(liftM) +import Foreign.C.Types(CInt) ------------------------------------------------------------------- -#ifdef BINARY import Data.Binary -instance (Binary (Vector a), Element a) => Binary (Matrix a) where +instance (Binary a, Element a) => Binary (Matrix a) where put m = do put (cols m) put (flatten m) @@ -48,7 +48,6 @@ v <- get return (reshape c v) -#endif ------------------------------------------------------------------- @@ -56,8 +55,10 @@ show m | rows m == 0 || cols m == 0 = sizes m ++" []" show m = (sizes m++) . dsp . map (map show) . toLists $ m +sizes :: Matrix t -> [Char] sizes m = "("++show (rows m)++"><"++show (cols m)++")\n" +dsp :: [[[Char]]] -> [Char] dsp as = (++" ]") . (" ["++) . init . drop 2 . unlines . map (" , "++) . map unwords' $ transpose mtp where mt = transpose as @@ -76,6 +77,7 @@ rs = read . snd . breakAt '(' .init . fst . breakAt '>' $ dims +breakAt :: Eq a => a -> [a] -> ([a], [a]) breakAt c l = (a++[c],tail b) where (a,b) = break (==c) l @@ -91,7 +93,8 @@ | Drop Int | DropLast Int deriving Show - + +ppext :: Extractor -> [Char] ppext All = ":" ppext (Range a 1 c) = printf "%d:%d" a c ppext (Range a b c) = printf "%d:%d:%d" a b c @@ -131,10 +134,14 @@ infixl 9 ?? (??) :: Element t => Matrix t -> (Extractor,Extractor) -> Matrix t +minEl :: Vector CInt -> CInt minEl = toScalarI Min +maxEl :: Vector CInt -> CInt maxEl = toScalarI Max +cmodi :: Foreign.C.Types.CInt -> Vector Foreign.C.Types.CInt -> Vector Foreign.C.Types.CInt cmodi = vectorMapValI ModVS +extractError :: Matrix t1 -> (Extractor, Extractor) -> t extractError m (e1,e2)= error $ printf "can't extract (%s,%s) from matrix %dx%d" (ppext e1::String) (ppext e2::String) (rows m) (cols m) m ?? (Range a s b,e) | s /= 1 = m ?? (Pos (idxs [a,a+s .. b]), e) @@ -235,8 +242,10 @@ fromBlocks :: Element t => [[Matrix t]] -> Matrix t fromBlocks = fromBlocksRaw . adaptBlocks +fromBlocksRaw :: Element t => [[Matrix t]] -> Matrix t fromBlocksRaw mms = joinVert . map joinHoriz $ mms +adaptBlocks :: Element t => [[Matrix t]] -> [[Matrix t]] adaptBlocks ms = ms' where bc = case common length ms of Just c -> c @@ -489,6 +498,9 @@ m2' = conformMTo (r,c) m2 -- FIXME do not flatten if equal order +lM :: (Storable t, Element t1, Element t2) + => (Vector t1 -> Vector t2 -> Vector t) + -> Matrix t1 -> Matrix t2 -> Matrix t lM f m1 m2 = matrixFromVector RowMajor (max' (rows m1) (rows m2)) @@ -507,6 +519,7 @@ ------------------------------------------------------------ +toBlockRows :: Element t => [Int] -> Matrix t -> [Matrix t] toBlockRows [r] m | r == rows m = [m] toBlockRows rs m @@ -516,6 +529,7 @@ szs = map (* cols m) rs g k = (k><0)[] +toBlockCols :: Element t => [Int] -> Matrix t -> [Matrix t] toBlockCols [c] m | c == cols m = [m] toBlockCols cs m = map trans . toBlockRows cs . trans $ m @@ -579,7 +593,7 @@ mapMatrixWithIndexM :: (Element a, Storable b, Monad m) => ((Int, Int) -> a -> m b) -> Matrix a -> m (Matrix b) -mapMatrixWithIndexM g m = liftM (reshape c) . mapVectorWithIndexM (mk c g) . flatten $ m +mapMatrixWithIndexM g m = liftM (reshape c) . mapVectorWithIndexM (mk c g) . flatten $ m where c = cols m @@ -601,4 +615,3 @@ mapMatrix :: (Element a, Element b) => (a -> b) -> Matrix a -> Matrix b mapMatrix f = liftMatrix (mapVector f) - diff --git a/src/Internal/Foreign.hs b/src/Internal/Foreign.hs deleted file mode 100644 --- a/src/Internal/Foreign.hs +++ /dev/null @@ -1,102 +0,0 @@ -{-# LANGUAGE MagicHash, UnboxedTuples #-} --- | FFI and hmatrix helpers. --- --- Sample usage, to upload a perspective matrix to a shader. --- --- @ glUniformMatrix4fv 0 1 (fromIntegral gl_TRUE) \`appMatrix\` perspective 0.01 100 (pi\/2) (4\/3) --- @ --- - -module Internal.Foreign - ( app - , appVector, appVectorLen - , appMatrix, appMatrixLen, appMatrixRaw, appMatrixRawLen - , unsafeMatrixToVector, unsafeMatrixToForeignPtr - ) where - -import Foreign.C.Types(CInt) -import Internal.Vector -import Internal.Matrix -import qualified Data.Vector.Storable as S -import Foreign (Ptr, ForeignPtr, Storable) -import GHC.Base (IO(..), realWorld#) - -{-# INLINE unsafeInlinePerformIO #-} --- | If we use unsafePerformIO, it may not get inlined, so in a function that returns IO (which are all safe uses of app* in this module), there would be --- unecessary calls to unsafePerformIO or its internals. -unsafeInlinePerformIO :: IO a -> a -unsafeInlinePerformIO (IO f) = case f realWorld# of - (# _, x #) -> x - -{-# INLINE app #-} --- | Only useful since it is left associated with a precedence of 1, unlike 'Prelude.$', which is right associative. --- e.g. --- --- @ --- someFunction --- \`appMatrixLen\` m --- \`appVectorLen\` v --- \`app\` other --- \`app\` arguments --- \`app\` go here --- @ --- --- One could also write: --- --- @ --- (someFunction --- \`appMatrixLen\` m --- \`appVectorLen\` v) --- other --- arguments --- (go here) --- @ --- -app :: (a -> b) -> a -> b -app f = f - -{-# INLINE appVector #-} -appVector :: Storable a => (Ptr a -> b) -> Vector a -> b -appVector f x = unsafeInlinePerformIO (S.unsafeWith x (return . f)) - -{-# INLINE appVectorLen #-} -appVectorLen :: Storable a => (CInt -> Ptr a -> b) -> Vector a -> b -appVectorLen f x = unsafeInlinePerformIO (S.unsafeWith x (return . f (fromIntegral (S.length x)))) - -{-# INLINE appMatrix #-} -appMatrix :: Element a => (Ptr a -> b) -> Matrix a -> b -appMatrix f x = unsafeInlinePerformIO (S.unsafeWith (flatten x) (return . f)) - -{-# INLINE appMatrixLen #-} -appMatrixLen :: Element a => (CInt -> CInt -> Ptr a -> b) -> Matrix a -> b -appMatrixLen f x = unsafeInlinePerformIO (S.unsafeWith (flatten x) (return . f r c)) - where - r = fromIntegral (rows x) - c = fromIntegral (cols x) - -{-# INLINE appMatrixRaw #-} -appMatrixRaw :: Storable a => (Ptr a -> b) -> Matrix a -> b -appMatrixRaw f x = unsafeInlinePerformIO (S.unsafeWith (xdat x) (return . f)) - -{-# INLINE appMatrixRawLen #-} -appMatrixRawLen :: Element a => (CInt -> CInt -> Ptr a -> b) -> Matrix a -> b -appMatrixRawLen f x = unsafeInlinePerformIO (S.unsafeWith (xdat x) (return . f r c)) - where - r = fromIntegral (rows x) - c = fromIntegral (cols x) - -infixl 1 `app` -infixl 1 `appVector` -infixl 1 `appMatrix` -infixl 1 `appMatrixRaw` - -{-# INLINE unsafeMatrixToVector #-} --- | This will disregard the order of the matrix, and simply return it as-is. --- If the order of the matrix is RowMajor, this function is identical to 'flatten'. -unsafeMatrixToVector :: Matrix a -> Vector a -unsafeMatrixToVector = xdat - -{-# INLINE unsafeMatrixToForeignPtr #-} -unsafeMatrixToForeignPtr :: Storable a => Matrix a -> (ForeignPtr a, Int) -unsafeMatrixToForeignPtr m = S.unsafeToForeignPtr0 (xdat m) - diff --git a/src/Internal/IO.hs b/src/Internal/IO.hs --- a/src/Internal/IO.hs +++ b/src/Internal/IO.hs @@ -20,7 +20,7 @@ import Internal.Vector import Internal.Matrix import Internal.Vectorized -import Text.Printf(printf) +import Text.Printf(printf, PrintfArg, PrintfType) import Data.List(intersperse,transpose) import Data.Complex @@ -78,12 +78,18 @@ dispf :: Int -> Matrix Double -> String dispf d x = sdims x ++ "\n" ++ formatFixed (if isInt x then 0 else d) x +sdims :: Matrix t -> [Char] sdims x = show (rows x) ++ "x" ++ show (cols x) +formatFixed :: (Show a, Text.Printf.PrintfArg t, Element t) + => a -> Matrix t -> String formatFixed d x = format " " (printf ("%."++show d++"f")) $ x +isInt :: Matrix Double -> Bool isInt = all lookslikeInt . toList . flatten +formatScaled :: (Text.Printf.PrintfArg b, RealFrac b, Floating b, Num t, Element b, Show t) + => t -> Matrix b -> [Char] formatScaled dec t = "E"++show o++"\n" ++ ss where ss = format " " (printf fmt. g) t g x | o >= 0 = x/10^(o::Int) @@ -133,14 +139,18 @@ s2 = if b<0 then "-" else "" s3 = if b<0 then "-" else "+" +shcr :: (Show a, Show t1, Text.Printf.PrintfType t, Text.Printf.PrintfArg t1, RealFrac t1) + => a -> t1 -> t shcr d a | lookslikeInt a = printf "%.0f" a | otherwise = printf ("%."++show d++"f") a - +lookslikeInt :: (Show a, RealFrac a) => a -> Bool lookslikeInt x = show (round x :: Int) ++".0" == shx || "-0.0" == shx where shx = show x +isZero :: Show a => a -> Bool isZero x = show x `elem` ["0.0","-0.0"] +isOne :: Show a => a -> Bool isOne x = show x `elem` ["1.0","-1.0"] -- | Pretty print a complex matrix with at most n decimal digits. @@ -168,6 +178,6 @@ else return (reshape c v) - +loadMatrix' :: FilePath -> IO (Maybe (Matrix Double)) loadMatrix' name = mbCatch (loadMatrix name) diff --git a/src/Internal/LAPACK.hs b/src/Internal/LAPACK.hs --- a/src/Internal/LAPACK.hs +++ b/src/Internal/LAPACK.hs @@ -1,6 +1,8 @@ {-# LANGUAGE TypeOperators #-} {-# LANGUAGE ViewPatterns #-} +{-# OPTIONS_GHC -fno-warn-missing-signatures #-} + ----------------------------------------------------------------------------- -- | -- Module : Numeric.LinearAlgebra.LAPACK @@ -16,9 +18,11 @@ module Internal.LAPACK where +import Data.Bifunctor (first) + import Internal.Devel import Internal.Vector -import Internal.Matrix hiding ((#)) +import Internal.Matrix hiding ((#), (#!)) import Internal.Conversion import Internal.Element import Foreign.Ptr(nullPtr) @@ -28,10 +32,13 @@ ----------------------------------------------------------------------------------- -infixl 1 # +infixr 1 # a # b = apply a b {-# INLINE (#) #-} +a #! b = a # b # id +{-# INLINE (#!) #-} + ----------------------------------------------------------------------------------- type TMMM t = t ::> t ::> t ::> Ok @@ -56,7 +63,7 @@ when (cols a /= rows b) $ error $ "inconsistent dimensions in matrix product "++ show (rows a,cols a) ++ " x " ++ show (rows b, cols b) s <- createMatrix ColumnMajor (rows a) (cols b) - f (isT a) (isT b) # (tt a) # (tt b) # s #| st + ((tt a) # (tt b) #! s) (f (isT a) (isT b)) #| st return s -- | Matrix product based on BLAS's /dgemm/. @@ -80,7 +87,7 @@ when (cols a /= rows b) $ error $ "inconsistent dimensions in matrix product "++ shSize a ++ " x " ++ shSize b s <- createMatrix ColumnMajor (rows a) (cols b) - c_multiplyI m # a # b # s #|"c_multiplyI" + (a # b #! s) (c_multiplyI m) #|"c_multiplyI" return s multiplyL :: Z -> Matrix Z -> Matrix Z -> Matrix Z @@ -88,7 +95,7 @@ when (cols a /= rows b) $ error $ "inconsistent dimensions in matrix product "++ shSize a ++ " x " ++ shSize b s <- createMatrix ColumnMajor (rows a) (cols b) - c_multiplyL m # a # b # s #|"c_multiplyL" + (a # b #! s) (c_multiplyL m) #|"c_multiplyL" return s ----------------------------------------------------------------------------- @@ -121,7 +128,7 @@ u <- createMatrix ColumnMajor r r s <- createVector (min r c) v <- createMatrix ColumnMajor c c - f # a # u # s # v #| st + (a # u # s #! v) f #| st return (u,s,v) where r = rows x @@ -149,7 +156,7 @@ u <- createMatrix ColumnMajor r q s <- createVector q v <- createMatrix ColumnMajor q c - f # a # u # s # v #| st + (a # u # s #! v) f #| st return (u,s,v) where r = rows x @@ -176,7 +183,7 @@ svAux f st x = unsafePerformIO $ do a <- copy ColumnMajor x s <- createVector q - g # a # s #| st + (a #! s) g #| st return s where r = rows x @@ -197,7 +204,7 @@ a <- copy ColumnMajor x s <- createVector q v <- createMatrix ColumnMajor c c - g # a # s # v #| st + (a # s #! v) g #| st return (s,v) where r = rows x @@ -218,7 +225,7 @@ a <- copy ColumnMajor x u <- createMatrix ColumnMajor r r s <- createVector q - g # a # u # s #| st + (a # u #! s) g #| st return (u,s) where r = rows x @@ -229,7 +236,9 @@ ----------------------------------------------------------------------------- foreign import ccall unsafe "eig_l_R" dgeev :: R ::> R ::> C :> R ::> Ok +foreign import ccall unsafe "eig_l_G" dggev :: R ::> R ::> C :> R :> R ::> R ::> Ok foreign import ccall unsafe "eig_l_C" zgeev :: C ::> C ::> C :> C ::> Ok +foreign import ccall unsafe "eig_l_GC" zggev :: C ::> C ::> C :> C :> C ::> C ::> Ok foreign import ccall unsafe "eig_l_S" dsyev :: CInt -> R :> R ::> Ok foreign import ccall unsafe "eig_l_H" zheev :: CInt -> R :> C ::> Ok @@ -237,7 +246,7 @@ a <- copy ColumnMajor m l <- createVector r v <- createMatrix ColumnMajor r r - g # a # l # v #| st + (a # l #! v) g #| st return (l,v) where r = rows m @@ -252,7 +261,7 @@ eigOnlyAux f st m = unsafePerformIO $ do a <- copy ColumnMajor m l <- createVector r - g # a # l #| st + (a #! l) g #| st return l where r = rows m @@ -277,7 +286,7 @@ a <- copy ColumnMajor m l <- createVector r v <- createMatrix ColumnMajor r r - g # a # l # v #| "eigR" + (a # l #! v) g #| "eigR" return (l,v) where r = rows m @@ -293,19 +302,75 @@ | otherwise = comp' v1 : fixeig ((r2:+i2):r) (v2:vs) fixeig _ _ = error "fixeig with impossible inputs" +-- For dggev alpha(i) / beta(i), alpha(i+1) / beta(i+1) form a complex conjugate pair when Im alpha(i) != 0. +-- However, this does not lead to Re alpha(i) == Re alpha(i+1), since beta(i) and beta(i+1) +-- can be different. Therefore old 'fixeig' would fail for 'eigG'. +fixeigG [] _ = [] +fixeigG [_] [v] = [comp' v] +fixeigG ((_:+ai1) : an : as) (v1:v2:vs) + | abs ai1 > 1e-13 = toComplex' (v1, v2) : toComplex' (v1, mapVector negate v2) : fixeigG as vs + | otherwise = comp' v1 : fixeigG (an:as) (v2:vs) +fixeigG _ _ = error "fixeigG with impossible inputs" -- | Eigenvalues of a general real matrix, using LAPACK's /dgeev/ with jobz == \'N\'. -- The eigenvalues are not sorted. eigOnlyR :: Matrix Double -> Vector (Complex Double) eigOnlyR = fixeig1 . eigOnlyAux dgeev "eigOnlyR" +-- | Generalized eigenvalues and right eigenvectors of a pair of real matrices, using LAPACK's /dggev/. +-- The eigenvectors are the columns of v. The eigenvalues are represented as alphas / betas and not sorted. +eigG :: Matrix Double -> Matrix Double -> (Vector (Complex Double), Vector Double, Matrix (Complex Double)) +eigG a b = (alpha', beta, v'') + where + (alpha, beta, v) = eigGaux dggev a b "eigG" + alpha' = fixeig1 alpha + v' = toRows $ trans v + v'' = fromColumns $ fixeigG (toList alpha') v' +eigGaux f ma mb st = unsafePerformIO $ do + a <- copy ColumnMajor ma + b <- copy ColumnMajor mb + alpha <- createVector r + beta <- createVector r + vr <- createMatrix ColumnMajor r r + + (a # b # alpha # beta #! vr) g #| st + + return (alpha, beta, vr) + where + r = rows ma + g ar ac xra xca pa br bc xrb xcb pb alphan palpha betan pbeta = f ar ac xra xca pa br bc xrb xcb pb alphan palpha betan pbeta 0 0 0 0 nullPtr + +eigGOnlyAux f ma mb st = unsafePerformIO $ do + a <- copy ColumnMajor ma + b <- copy ColumnMajor mb + alpha <- createVector r + beta <- createVector r + + (a # b # alpha #! beta) g #| st + + return (alpha, beta) + where + r = rows ma + g ar ac xra xca pa br bc xrb xcb pb alphan palpha betan pbeta = f ar ac xra xca pa br bc xrb xcb pb alphan palpha betan pbeta 0 0 0 0 nullPtr 0 0 0 0 nullPtr + +-- | Generalized eigenvalues and right eigenvectors of a pair of complex matrices, using LAPACK's /zggev/. +-- The eigenvectors are the columns of v. The eigenvalues are represented as alphas / betas and not sorted. +eigGC :: Matrix (Complex Double) -> Matrix (Complex Double) -> (Vector (Complex Double), Vector (Complex Double), Matrix (Complex Double)) +eigGC a b = eigGaux zggev a b "eigGC" + +eigOnlyG :: Matrix Double -> Matrix Double -> (Vector (Complex Double), Vector Double) +eigOnlyG a b = first fixeig1 $ eigGOnlyAux dggev a b "eigOnlyG" + +eigOnlyGC :: Matrix (Complex Double) -> Matrix (Complex Double) -> (Vector (Complex Double), Vector (Complex Double)) +eigOnlyGC a b = eigGOnlyAux zggev a b "eigOnlyGC" + ----------------------------------------------------------------------------- eigSHAux f st m = unsafePerformIO $ do l <- createVector r v <- copy ColumnMajor m - f # l # v #| st + (l #! v) f #| st return (l,v) where r = rows m @@ -356,7 +421,7 @@ | n1==n2 && n1==r = unsafePerformIO . g $ do a' <- copy ColumnMajor a s <- copy ColumnMajor b - f # a' # s #| st + (a' #! s) f #| st return s | otherwise = error $ st ++ " of nonsquare matrix" where @@ -387,7 +452,7 @@ linearSolveSQAux2 g f st a b | n1==n2 && n1==r = unsafePerformIO . g $ do s <- copy ColumnMajor b - f # a # s #| st + (a #! s) f #| st return s | otherwise = error $ st ++ " of nonsquare matrix" where @@ -403,6 +468,60 @@ cholSolveC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double) cholSolveC a b = linearSolveSQAux2 id zpotrs "cholSolveC" (fmat a) b +-------------------------------------------------------------------------------- +foreign import ccall unsafe "triSolveR_l_u" dtrtrs_u :: R ::> R ::> Ok +foreign import ccall unsafe "triSolveC_l_u" ztrtrs_u :: C ::> C ::> Ok +foreign import ccall unsafe "triSolveR_l_l" dtrtrs_l :: R ::> R ::> Ok +foreign import ccall unsafe "triSolveC_l_l" ztrtrs_l :: C ::> C ::> Ok + + +linearSolveTRAux2 g f st a b + | n1==n2 && n1==r = unsafePerformIO . g $ do + s <- copy ColumnMajor b + (a #! s) f #| st + return s + | otherwise = error $ st ++ " of nonsquare matrix" + where + n1 = rows a + n2 = cols a + r = rows b + +data UpLo = Lower | Upper + +-- | Solves a triangular system of linear equations. +triSolveR :: UpLo -> Matrix Double -> Matrix Double -> Matrix Double +triSolveR Lower a b = linearSolveTRAux2 id dtrtrs_l "triSolveR" (fmat a) b +triSolveR Upper a b = linearSolveTRAux2 id dtrtrs_u "triSolveR" (fmat a) b + +-- | Solves a triangular system of linear equations. +triSolveC :: UpLo -> Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double) +triSolveC Lower a b = linearSolveTRAux2 id ztrtrs_l "triSolveC" (fmat a) b +triSolveC Upper a b = linearSolveTRAux2 id ztrtrs_u "triSolveC" (fmat a) b + +-------------------------------------------------------------------------------- +foreign import ccall unsafe "triDiagSolveR_l" dgttrs :: R :> R :> R :> R ::> Ok +foreign import ccall unsafe "triDiagSolveC_l" zgttrs :: C :> C :> C :> C ::> Ok + +linearSolveGTAux2 g f st dl d du b + | ndl == nd - 1 && + ndu == nd - 1 && + nd == r = unsafePerformIO . g $ do + dl' <- head . toRows <$> copy ColumnMajor (fromRows [dl]) + du' <- head . toRows <$> copy ColumnMajor (fromRows [du]) + s <- copy ColumnMajor b + (dl' # d # du' #! s) f #| st + return s + | otherwise = error $ st ++ " of nonsquare matrix" + where + ndl = dim dl + nd = dim d + ndu = dim du + r = rows b + +-- | Solves a tridiagonal system of linear equations. +triDiagSolveR dl d du b = linearSolveGTAux2 id dgttrs "triDiagSolveR" dl d du b +triDiagSolveC dl d du b = linearSolveGTAux2 id zgttrs "triDiagSolveC" dl d du b + ----------------------------------------------------------------------------------- foreign import ccall unsafe "linearSolveLSR_l" dgels :: R ::> R ::> Ok @@ -415,7 +534,7 @@ a' <- copy ColumnMajor a r <- createMatrix ColumnMajor (max m n) nrhs setRect 0 0 b r - f # a' # r #| st + (a' #! r) f #| st return r | otherwise = error $ "different number of rows in linearSolve ("++st++")" where @@ -458,7 +577,7 @@ cholAux f st a = do r <- copy ColumnMajor a - f # r #| st + (r # id) f #| st return r -- | Cholesky factorization of a complex Hermitian positive definite matrix, using LAPACK's /zpotrf/. @@ -495,7 +614,7 @@ qrAux f st a = unsafePerformIO $ do r <- copy ColumnMajor a tau <- createVector mn - f # tau # r #| st + (tau #! r) f #| st return (r,tau) where m = rows a @@ -514,7 +633,7 @@ qrgrAux f st n (a, tau) = unsafePerformIO $ do res <- copy ColumnMajor (subMatrix (0,0) (rows a,n) a) - f # (subVector 0 n tau') # res #| st + ((subVector 0 n tau') #! res) f #| st return res where tau' = vjoin [tau, constantD 0 n] @@ -534,7 +653,7 @@ hessAux f st a = unsafePerformIO $ do r <- copy ColumnMajor a tau <- createVector (mn-1) - f # tau # r #| st + (tau #! r) f #| st return (r,tau) where m = rows a @@ -556,7 +675,7 @@ schurAux f st a = unsafePerformIO $ do u <- createMatrix ColumnMajor n n s <- copy ColumnMajor a - f # u # s #| st + (u #! s) f #| st return (u,s) where n = rows a @@ -576,7 +695,7 @@ luAux f st a = unsafePerformIO $ do lu <- copy ColumnMajor a piv <- createVector (min n m) - f # piv # lu #| st + (piv #! lu) f #| st return (lu, map (pred.round) (toList piv)) where n = rows a @@ -598,7 +717,7 @@ lusAux f st a piv b | n1==n2 && n2==n =unsafePerformIO $ do x <- copy ColumnMajor b - f # a # piv' # x #| st + (a # piv' #! x) f #| st return x | otherwise = error st where @@ -622,7 +741,7 @@ ldlAux f st a = unsafePerformIO $ do ldl <- copy ColumnMajor a piv <- createVector (rows a) - f # piv # ldl #| st + (piv #! ldl) f #| st return (ldl, map (pred.round) (toList piv)) ----------------------------------------------------------------------------------- @@ -637,4 +756,3 @@ -- | Solve a complex linear system from a precomputed LDL decomposition ('ldlC'), using LAPACK's /zsytrs/. ldlsC :: Matrix (Complex Double) -> [Int] -> Matrix (Complex Double) -> Matrix (Complex Double) ldlsC a piv b = lusAux zsytrs "ldlsC" (fmat a) piv b - diff --git a/src/Internal/Matrix.hs b/src/Internal/Matrix.hs --- a/src/Internal/Matrix.hs +++ b/src/Internal/Matrix.hs @@ -5,10 +5,9 @@ {-# LANGUAGE TypeOperators #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE ViewPatterns #-} +{-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE ConstrainedClassMethods #-} - - -- | -- Module : Internal.Matrix -- Copyright : (c) Alberto Ruiz 2007-15 @@ -23,7 +22,7 @@ import Internal.Vector import Internal.Devel -import Internal.Vectorized hiding ((#)) +import Internal.Vectorized hiding ((#), (#!)) import Foreign.Marshal.Alloc ( free ) import Foreign.Marshal.Array(newArray) import Foreign.Ptr ( Ptr ) @@ -58,19 +57,24 @@ cols = icols {-# INLINE cols #-} +size :: Matrix t -> (Int, Int) size m = (irows m, icols m) {-# INLINE size #-} +rowOrder :: Matrix t -> Bool rowOrder m = xCol m == 1 || cols m == 1 {-# INLINE rowOrder #-} +colOrder :: Matrix t -> Bool colOrder m = xRow m == 1 || rows m == 1 {-# INLINE colOrder #-} +is1d :: Matrix t -> Bool is1d (size->(r,c)) = r==1 || c==1 {-# INLINE is1d #-} -- data is not contiguous +isSlice :: Storable t => Matrix t -> Bool isSlice m@(size->(r,c)) = r*c < dim (xdat m) {-# INLINE isSlice #-} @@ -111,15 +115,15 @@ -- C-Haskell matrix adapters {-# INLINE amatr #-} -amatr :: Storable a => (CInt -> CInt -> Ptr a -> b) -> Matrix a -> b -amatr f x = inlinePerformIO (unsafeWith (xdat x) (return . f r c)) +amatr :: Storable a => Matrix a -> (f -> IO r) -> (CInt -> CInt -> Ptr a -> f) -> IO r +amatr x f g = unsafeWith (xdat x) (f . g r c) where r = fi (rows x) c = fi (cols x) {-# INLINE amat #-} -amat :: Storable a => (CInt -> CInt -> CInt -> CInt -> Ptr a -> b) -> Matrix a -> b -amat f x = inlinePerformIO (unsafeWith (xdat x) (return . f r c sr sc)) +amat :: Storable a => Matrix a -> (f -> IO r) -> (CInt -> CInt -> CInt -> CInt -> Ptr a -> f) -> IO r +amat x f g = unsafeWith (xdat x) (f . g r c sr sc) where r = fi (rows x) c = fi (cols x) @@ -136,20 +140,28 @@ applyRaw = amatr {-# INLINE applyRaw #-} -infixl 1 # +infixr 1 # +(#) :: TransArray c => c -> (b -> IO r) -> Trans c b -> IO r a # b = apply a b {-# INLINE (#) #-} +(#!) :: (TransArray c, TransArray c1) => c1 -> c -> Trans c1 (Trans c (IO r)) -> IO r +a #! b = a # b # id +{-# INLINE (#!) #-} + -------------------------------------------------------------------------------- +copy :: Element t => MatrixOrder -> Matrix t -> IO (Matrix t) copy ord m = extractR ord m 0 (idxs[0,rows m-1]) 0 (idxs[0,cols m-1]) +extractAll :: Element t => MatrixOrder -> Matrix t -> Matrix t extractAll ord m = unsafePerformIO (copy ord m) {- | Creates a vector by concatenation of rows. If the matrix is ColumnMajor, this operation requires a transpose. >>> flatten (ident 3) -fromList [1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0] +[1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0] +it :: (Num t, Element t) => Vector t -} flatten :: Element t => Matrix t -> Vector t @@ -221,11 +233,13 @@ {-# INLINE (@@>) #-} -- Unsafe matrix access without range checking +atM' :: Storable t => Matrix t -> Int -> Int -> t atM' m i j = xdat m `at'` (i * (xRow m) + j * (xCol m)) {-# INLINE atM' #-} ------------------------------------------------------------------ +matrixFromVector :: Storable t => MatrixOrder -> Int -> Int -> Vector t -> Matrix t matrixFromVector _ 1 _ v@(dim->d) = Matrix { irows = 1, icols = d, xdat = v, xRow = d, xCol = 1 } matrixFromVector _ _ 1 v@(dim->d) = Matrix { irows = d, icols = 1, xdat = v, xRow = 1, xCol = d } matrixFromVector o r c v @@ -283,6 +297,7 @@ remapM :: Matrix CInt -> Matrix CInt -> Matrix a -> Matrix a rowOp :: Int -> a -> Int -> Int -> Int -> Int -> Matrix a -> IO () gemm :: Vector a -> Matrix a -> Matrix a -> Matrix a -> IO () + reorderV :: Vector CInt-> Vector CInt-> Vector a -> Vector a -- see reorderVector for documentation instance Element Float where @@ -296,6 +311,7 @@ remapM = remapF rowOp = rowOpAux c_rowOpF gemm = gemmg c_gemmF + reorderV = reorderAux c_reorderF instance Element Double where constantD = constantAux cconstantR @@ -308,6 +324,7 @@ remapM = remapD rowOp = rowOpAux c_rowOpD gemm = gemmg c_gemmD + reorderV = reorderAux c_reorderD instance Element (Complex Float) where constantD = constantAux cconstantQ @@ -320,6 +337,7 @@ remapM = remapQ rowOp = rowOpAux c_rowOpQ gemm = gemmg c_gemmQ + reorderV = reorderAux c_reorderQ instance Element (Complex Double) where constantD = constantAux cconstantC @@ -332,6 +350,7 @@ remapM = remapC rowOp = rowOpAux c_rowOpC gemm = gemmg c_gemmC + reorderV = reorderAux c_reorderC instance Element (CInt) where constantD = constantAux cconstantI @@ -344,6 +363,7 @@ remapM = remapI rowOp = rowOpAux c_rowOpI gemm = gemmg c_gemmI + reorderV = reorderAux c_reorderI instance Element Z where constantD = constantAux cconstantL @@ -356,6 +376,7 @@ remapM = remapL rowOp = rowOpAux c_rowOpL gemm = gemmg c_gemmL + reorderV = reorderAux c_reorderL ------------------------------------------------------------------- @@ -378,18 +399,21 @@ -------------------------------------------------------------------------- +maxZ :: (Num t1, Ord t1, Foldable t) => t t1 -> t1 maxZ xs = if minimum xs == 0 then 0 else maximum xs +conformMs :: Element t => [Matrix t] -> [Matrix t] conformMs ms = map (conformMTo (r,c)) ms where r = maxZ (map rows ms) c = maxZ (map cols ms) - +conformVs :: Element t => [Vector t] -> [Vector t] conformVs vs = map (conformVTo n) vs where n = maxZ (map dim vs) +conformMTo :: Element t => (Int, Int) -> Matrix t -> Matrix t conformMTo (r,c) m | size m == (r,c) = m | size m == (1,1) = matrixFromVector RowMajor r c (constantD (m@@>(0,0)) (r*c)) @@ -397,18 +421,24 @@ | size m == (1,c) = repRows r m | otherwise = error $ "matrix " ++ shSize m ++ " cannot be expanded to " ++ shDim (r,c) +conformVTo :: Element t => Int -> Vector t -> Vector t conformVTo n v | dim v == n = v | dim v == 1 = constantD (v@>0) n | otherwise = error $ "vector of dim=" ++ show (dim v) ++ " cannot be expanded to dim=" ++ show n +repRows :: Element t => Int -> Matrix t -> Matrix t repRows n x = fromRows (replicate n (flatten x)) +repCols :: Element t => Int -> Matrix t -> Matrix t repCols n x = fromColumns (replicate n (flatten x)) +shSize :: Matrix t -> [Char] shSize = shDim . size +shDim :: (Show a, Show a1) => (a1, a) -> [Char] shDim (r,c) = "(" ++ show r ++"x"++ show c ++")" +emptyM :: Storable t => Int -> Int -> Matrix t emptyM r c = matrixFromVector RowMajor r c (fromList[]) ---------------------------------------------------------------------- @@ -423,11 +453,17 @@ --------------------------------------------------------------- +extractAux :: (Eq t3, Eq t2, TransArray c, Storable a, Storable t1, + Storable t, Num t3, Num t2, Integral t1, Integral t) + => (t3 -> t2 -> CInt -> Ptr t1 -> CInt -> Ptr t + -> Trans c (CInt -> CInt -> CInt -> CInt -> Ptr a -> IO CInt)) + -> MatrixOrder -> c -> t3 -> Vector t1 -> t2 -> Vector t -> IO (Matrix a) extractAux f ord m moder vr modec vc = do let nr = if moder == 0 then fromIntegral $ vr@>1 - vr@>0 + 1 else dim vr nc = if modec == 0 then fromIntegral $ vc@>1 - vc@>0 + 1 else dim vc r <- createMatrix ord nr nc - f moder modec # vr # vc # m # r #|"extract" + (vr # vc # m #! r) (f moder modec) #|"extract" + return r type Extr x = CInt -> CInt -> CIdxs (CIdxs (OM x (OM x (IO CInt)))) @@ -441,7 +477,10 @@ --------------------------------------------------------------- -setRectAux f i j m r = f (fi i) (fi j) # m # r #|"setRect" +setRectAux :: (TransArray c1, TransArray c) + => (CInt -> CInt -> Trans c1 (Trans c (IO CInt))) + -> Int -> Int -> c1 -> c -> IO () +setRectAux f i j m r = (m #! r) (f (fi i) (fi j)) #|"setRect" type SetRect x = I -> I -> x ::> x::> Ok @@ -454,19 +493,29 @@ -------------------------------------------------------------------------------- +sortG :: (Storable t, Storable a) + => (CInt -> Ptr t -> CInt -> Ptr a -> IO CInt) -> Vector t -> Vector a sortG f v = unsafePerformIO $ do r <- createVector (dim v) - f # v # r #|"sortG" + (v #! r) f #|"sortG" return r +sortIdxD :: Vector Double -> Vector CInt sortIdxD = sortG c_sort_indexD +sortIdxF :: Vector Float -> Vector CInt sortIdxF = sortG c_sort_indexF +sortIdxI :: Vector CInt -> Vector CInt sortIdxI = sortG c_sort_indexI +sortIdxL :: Vector Z -> Vector I sortIdxL = sortG c_sort_indexL +sortValD :: Vector Double -> Vector Double sortValD = sortG c_sort_valD +sortValF :: Vector Float -> Vector Float sortValF = sortG c_sort_valF +sortValI :: Vector CInt -> Vector CInt sortValI = sortG c_sort_valI +sortValL :: Vector Z -> Vector Z sortValL = sortG c_sort_valL foreign import ccall unsafe "sort_indexD" c_sort_indexD :: CV Double (CV CInt (IO CInt)) @@ -481,14 +530,21 @@ -------------------------------------------------------------------------------- +compareG :: (TransArray c, Storable t, Storable a) + => Trans c (CInt -> Ptr t -> CInt -> Ptr a -> IO CInt) + -> c -> Vector t -> Vector a compareG f u v = unsafePerformIO $ do r <- createVector (dim v) - f # u # v # r #|"compareG" + (u # v #! r) f #|"compareG" return r +compareD :: Vector Double -> Vector Double -> Vector CInt compareD = compareG c_compareD +compareF :: Vector Float -> Vector Float -> Vector CInt compareF = compareG c_compareF +compareI :: Vector CInt -> Vector CInt -> Vector CInt compareI = compareG c_compareI +compareL :: Vector Z -> Vector Z -> Vector CInt compareL = compareG c_compareL foreign import ccall unsafe "compareD" c_compareD :: CV Double (CV Double (CV CInt (IO CInt))) @@ -498,16 +554,33 @@ -------------------------------------------------------------------------------- +selectG :: (TransArray c, TransArray c1, TransArray c2, Storable t, Storable a) + => Trans c2 (Trans c1 (CInt -> Ptr t -> Trans c (CInt -> Ptr a -> IO CInt))) + -> c2 -> c1 -> Vector t -> c -> Vector a selectG f c u v w = unsafePerformIO $ do r <- createVector (dim v) - f # c # u # v # w # r #|"selectG" + (c # u # v # w #! r) f #|"selectG" return r +selectD :: Vector CInt -> Vector Double -> Vector Double -> Vector Double -> Vector Double selectD = selectG c_selectD +selectF :: Vector CInt -> Vector Float -> Vector Float -> Vector Float -> Vector Float selectF = selectG c_selectF +selectI :: Vector CInt -> Vector CInt -> Vector CInt -> Vector CInt -> Vector CInt selectI = selectG c_selectI +selectL :: Vector CInt -> Vector Z -> Vector Z -> Vector Z -> Vector Z selectL = selectG c_selectL +selectC :: Vector CInt + -> Vector (Complex Double) + -> Vector (Complex Double) + -> Vector (Complex Double) + -> Vector (Complex Double) selectC = selectG c_selectC +selectQ :: Vector CInt + -> Vector (Complex Float) + -> Vector (Complex Float) + -> Vector (Complex Float) + -> Vector (Complex Float) selectQ = selectG c_selectQ type Sel x = CV CInt (CV x (CV x (CV x (CV x (IO CInt))))) @@ -521,16 +594,29 @@ --------------------------------------------------------------------------- +remapG :: (TransArray c, TransArray c1, Storable t, Storable a) + => (CInt -> CInt -> CInt -> CInt -> Ptr t + -> Trans c1 (Trans c (CInt -> CInt -> CInt -> CInt -> Ptr a -> IO CInt))) + -> Matrix t -> c1 -> c -> Matrix a remapG f i j m = unsafePerformIO $ do r <- createMatrix RowMajor (rows i) (cols i) - f # i # j # m # r #|"remapG" + (i # j # m #! r) f #|"remapG" return r +remapD :: Matrix CInt -> Matrix CInt -> Matrix Double -> Matrix Double remapD = remapG c_remapD +remapF :: Matrix CInt -> Matrix CInt -> Matrix Float -> Matrix Float remapF = remapG c_remapF +remapI :: Matrix CInt -> Matrix CInt -> Matrix CInt -> Matrix CInt remapI = remapG c_remapI +remapL :: Matrix CInt -> Matrix CInt -> Matrix Z -> Matrix Z remapL = remapG c_remapL +remapC :: Matrix CInt + -> Matrix CInt + -> Matrix (Complex Double) + -> Matrix (Complex Double) remapC = remapG c_remapC +remapQ :: Matrix CInt -> Matrix CInt -> Matrix (Complex Float) -> Matrix (Complex Float) remapQ = remapG c_remapQ type Rem x = OM CInt (OM CInt (OM x (OM x (IO CInt)))) @@ -544,9 +630,12 @@ -------------------------------------------------------------------------------- +rowOpAux :: (TransArray c, Storable a) => + (CInt -> Ptr a -> CInt -> CInt -> CInt -> CInt -> Trans c (IO CInt)) + -> Int -> a -> Int -> Int -> Int -> Int -> c -> IO () rowOpAux f c x i1 i2 j1 j2 m = do px <- newArray [x] - f (fi c) px (fi i1) (fi i2) (fi j1) (fi j2) # m #|"rowOp" + (m # id) (f (fi c) px (fi i1) (fi i2) (fi j1) (fi j2)) #|"rowOp" free px type RowOp x = CInt -> Ptr x -> CInt -> CInt -> CInt -> CInt -> x ::> Ok @@ -562,7 +651,10 @@ -------------------------------------------------------------------------------- -gemmg f v m1 m2 m3 = f # v # m1 # m2 # m3 #|"gemmg" +gemmg :: (TransArray c1, TransArray c, TransArray c2, TransArray c3) + => Trans c3 (Trans c2 (Trans c1 (Trans c (IO CInt)))) + -> c3 -> c2 -> c1 -> c -> IO () +gemmg f v m1 m2 m3 = (v # m1 # m2 #! m3) f #|"gemmg" type Tgemm x = x :> x ::> x ::> x ::> Ok @@ -577,6 +669,37 @@ -------------------------------------------------------------------------------- +reorderAux :: (TransArray c, Storable t, Storable a1, Storable t1, Storable a) => + (CInt -> Ptr a -> CInt -> Ptr t1 + -> Trans c (CInt -> Ptr t -> CInt -> Ptr a1 -> IO CInt)) + -> Vector t1 -> c -> Vector t -> Vector a1 +reorderAux f s d v = unsafePerformIO $ do + k <- createVector (dim s) + r <- createVector (dim v) + (k # s # d # v #! r) f #| "reorderV" + return r + +type Reorder x = CV CInt (CV CInt (CV CInt (CV x (CV x (IO CInt))))) + +foreign import ccall unsafe "reorderD" c_reorderD :: Reorder Double +foreign import ccall unsafe "reorderF" c_reorderF :: Reorder Float +foreign import ccall unsafe "reorderI" c_reorderI :: Reorder CInt +foreign import ccall unsafe "reorderC" c_reorderC :: Reorder (Complex Double) +foreign import ccall unsafe "reorderQ" c_reorderQ :: Reorder (Complex Float) +foreign import ccall unsafe "reorderL" c_reorderL :: Reorder Z + +-- | Transpose an array with dimensions @dims@ by making a copy using @strides@. For example, for an array with 3 indices, +-- @(reorderVector strides dims v) ! ((i * dims ! 1 + j) * dims ! 2 + k) == v ! (i * strides ! 0 + j * strides ! 1 + k * strides ! 2)@ +-- This function is intended to be used internally by tensor libraries. +reorderVector :: Element a + => Vector CInt -- ^ @strides@: array strides + -> Vector CInt -- ^ @dims@: array dimensions of new array @v@ + -> Vector a -- ^ @v@: flattened input array + -> Vector a -- ^ @v'@: flattened output array +reorderVector = reorderV + +-------------------------------------------------------------------------------- + foreign import ccall unsafe "saveMatrix" c_saveMatrix :: CString -> CString -> Double ::> Ok @@ -590,10 +713,9 @@ saveMatrix name format m = do cname <- newCString name cformat <- newCString format - c_saveMatrix cname cformat # m #|"saveMatrix" + (m # id) (c_saveMatrix cname cformat) #|"saveMatrix" free cname free cformat return () -------------------------------------------------------------------------------- - diff --git a/src/Internal/Modular.hs b/src/Internal/Modular.hs --- a/src/Internal/Modular.hs +++ b/src/Internal/Modular.hs @@ -1,17 +1,15 @@ +{-# LANGUAGE CPP #-} {-# LANGUAGE DataKinds #-} -{-# LANGUAGE KindSignatures #-} {-# LANGUAGE GeneralizedNewtypeDeriving #-} -{-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE FunctionalDependencies #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE ScopedTypeVariables #-} -{-# LANGUAGE Rank2Types #-} {-# LANGUAGE FlexibleInstances #-} -{-# LANGUAGE UndecidableInstances #-} -{-# LANGUAGE GADTs #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE TypeOperators #-} +{-# OPTIONS_GHC -fno-warn-missing-signatures #-} + {- | Module : Internal.Modular Copyright : (c) Alberto Ruiz 2015 @@ -38,13 +36,20 @@ gaussElim, gaussElim_1, gaussElim_2, luST, luSolve', luPacked', magnit, invershur) import Internal.ST(mutable) +#if MIN_VERSION_base(4,11,0) +import GHC.TypeLits hiding (Mod) +#else import GHC.TypeLits +#endif import Data.Proxy(Proxy) import Foreign.ForeignPtr(castForeignPtr) import Foreign.Storable import Data.Ratio import Data.Complex import Control.DeepSeq ( NFData(..) ) +#if MIN_VERSION_base(4,11,0) +import Prelude hiding ((<>)) +#endif @@ -72,11 +77,11 @@ where compare a b = compare (unMod a) (unMod b) -instance (Integral t, KnownNat m, Integral (Mod m t)) => Real (Mod m t) +instance (Integral t, Real t, KnownNat m) => Real (Mod m t) where toRational x = toInteger x % 1 -instance (Integral t, KnownNat m, Num (Mod m t)) => Integral (Mod m t) +instance (Integral t, KnownNat m) => Integral (Mod m t) where toInteger = toInteger . unMod quotRem a b = (Mod q, Mod r) @@ -84,7 +89,7 @@ (q,r) = quotRem (unMod a) (unMod b) -- | this instance is only valid for prime m -instance (Show (Mod m t), Num (Mod m t), Eq t, KnownNat m) => Fractional (Mod m t) +instance (Integral t, Show t, Eq t, KnownNat m) => Fractional (Mod m t) where recip x | x*r == 1 = r @@ -114,7 +119,7 @@ where show = show . unMod -instance forall n t . (Integral t, KnownNat n) => Num (Mod n t) +instance (Integral t, KnownNat n) => Num (Mod n t) where (+) = l2 (\m a b -> (a + b) `mod` (fromIntegral m)) (*) = l2 (\m a b -> (a * b) `mod` (fromIntegral m)) @@ -140,6 +145,7 @@ gemm u a b c = gemmg (c_gemmMI m') (f2i u) (f2iM a) (f2iM b) (f2iM c) where m' = fromIntegral . natVal $ (undefined :: Proxy m) + reorderV strides dims = i2f . reorderAux c_reorderI strides dims . f2i instance KnownNat m => Element (Mod m Z) where @@ -157,13 +163,14 @@ gemm u a b c = gemmg (c_gemmML m') (f2i u) (f2iM a) (f2iM b) (f2iM c) where m' = fromIntegral . natVal $ (undefined :: Proxy m) + reorderV strides dims = i2f . reorderAux c_reorderL strides dims . f2i -instance forall m . KnownNat m => CTrans (Mod m I) -instance forall m . KnownNat m => CTrans (Mod m Z) +instance KnownNat m => CTrans (Mod m I) +instance KnownNat m => CTrans (Mod m Z) -instance forall m . KnownNat m => Container Vector (Mod m I) +instance KnownNat m => Container Vector (Mod m I) where conj' = id size' = dim @@ -203,7 +210,7 @@ fromZ' = vmod . fromZ' toZ' = toZ' . f2i -instance forall m . KnownNat m => Container Vector (Mod m Z) +instance KnownNat m => Container Vector (Mod m Z) where conj' = id size' = dim @@ -311,7 +318,7 @@ lift2m f a b = liftMatrix vmod (f (f2iM a) (f2iM b)) -instance forall m . KnownNat m => Num (Vector (Mod m I)) +instance KnownNat m => Num (Vector (Mod m I)) where (+) = lift2 (+) (*) = lift2 (*) @@ -321,7 +328,7 @@ negate = lift1 negate fromInteger x = fromInt (fromInteger x) -instance forall m . KnownNat m => Num (Vector (Mod m Z)) +instance KnownNat m => Num (Vector (Mod m Z)) where (+) = lift2 (+) (*) = lift2 (*) diff --git a/src/Internal/Numeric.hs b/src/Internal/Numeric.hs --- a/src/Internal/Numeric.hs +++ b/src/Internal/Numeric.hs @@ -1,4 +1,3 @@ -{-# LANGUAGE CPP #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE FlexibleInstances #-} @@ -6,6 +5,8 @@ {-# LANGUAGE FunctionalDependencies #-} {-# LANGUAGE UndecidableInstances #-} +{-# OPTIONS_GHC -fno-warn-missing-signatures #-} + ----------------------------------------------------------------------------- -- | -- Module : Data.Packed.Internal.Numeric @@ -26,6 +27,7 @@ import Internal.Vectorized import Internal.LAPACK(multiplyR,multiplyC,multiplyF,multiplyQ,multiplyI,multiplyL) import Data.List.Split(chunksOf) +import qualified Data.Vector.Storable as V -------------------------------------------------------------------------------- @@ -103,8 +105,8 @@ add' = vectorZipI Add sub = vectorZipI Sub mul = vectorZipI Mul - equal u v = dim u == dim v && maxElement' (vectorMapI Abs (sub u v)) == 0 - scalar' x = fromList [x] + equal = (==) + scalar' = V.singleton konst' = constantD build' = buildV cmap' = mapVector @@ -142,8 +144,8 @@ add' = vectorZipL Add sub = vectorZipL Sub mul = vectorZipL Mul - equal u v = dim u == dim v && maxElement' (vectorMapL Abs (sub u v)) == 0 - scalar' x = fromList [x] + equal = (==) + scalar' = V.singleton konst' = constantD build' = buildV cmap' = mapVector @@ -182,8 +184,8 @@ add' = vectorZipF Add sub = vectorZipF Sub mul = vectorZipF Mul - equal u v = dim u == dim v && maxElement (vectorMapF Abs (sub u v)) == 0.0 - scalar' x = fromList [x] + equal = (==) + scalar' = V.singleton konst' = constantD build' = buildV cmap' = mapVector @@ -219,8 +221,8 @@ add' = vectorZipR Add sub = vectorZipR Sub mul = vectorZipR Mul - equal u v = dim u == dim v && maxElement (vectorMapR Abs (sub u v)) == 0.0 - scalar' x = fromList [x] + equal = (==) + scalar' = V.singleton konst' = constantD build' = buildV cmap' = mapVector @@ -256,8 +258,8 @@ add' = vectorZipC Add sub = vectorZipC Sub mul = vectorZipC Mul - equal u v = dim u == dim v && maxElement (mapVector magnitude (sub u v)) == 0.0 - scalar' x = fromList [x] + equal = (==) + scalar' = V.singleton konst' = constantD build' = buildV cmap' = mapVector @@ -292,8 +294,8 @@ add' = vectorZipQ Add sub = vectorZipQ Sub mul = vectorZipQ Mul - equal u v = dim u == dim v && maxElement (mapVector magnitude (sub u v)) == 0.0 - scalar' x = fromList [x] + equal = (==) + scalar' = V.singleton konst' = constantD build' = buildV cmap' = mapVector @@ -788,13 +790,7 @@ type instance RealOf I = I type instance RealOf Z = Z -type family ComplexOf x - -type instance ComplexOf Double = Complex Double -type instance ComplexOf (Complex Double) = Complex Double - -type instance ComplexOf Float = Complex Float -type instance ComplexOf (Complex Float) = Complex Float +type ComplexOf x = Complex (RealOf x) type family SingleOf x diff --git a/src/Internal/Random.hs b/src/Internal/Random.hs --- a/src/Internal/Random.hs +++ b/src/Internal/Random.hs @@ -31,13 +31,13 @@ gaussianSample :: Seed -> Int -- ^ number of rows -> Vector Double -- ^ mean vector - -> Matrix Double -- ^ covariance matrix + -> Herm Double -- ^ covariance matrix -> Matrix Double -- ^ result gaussianSample seed n med cov = m where c = dim med meds = konst' 1 n `outer` med rs = reshape c $ randomVector seed Gaussian (c * n) - m = rs `mXm` cholSH cov `add` meds + m = rs `mXm` chol cov `add` meds -- | Obtains a matrix whose rows are pseudorandom samples from a multivariate -- uniform distribution. diff --git a/src/Internal/ST.hs b/src/Internal/ST.hs --- a/src/Internal/ST.hs +++ b/src/Internal/ST.hs @@ -81,6 +81,8 @@ unsafeFreezeVector (STVector x) = unsafeIOToST . return $ x {-# INLINE safeIndexV #-} +safeIndexV :: Storable t2 + => (STVector s t2 -> Int -> t) -> STVector t1 t2 -> Int -> t safeIndexV f (STVector v) k | k < 0 || k>= dim v = error $ "out of range error in vector (dim=" ++show (dim v)++", pos="++show k++")" @@ -150,9 +152,12 @@ freezeMatrix :: (Element t) => STMatrix s t -> ST s (Matrix t) freezeMatrix m = liftSTMatrix id m +cloneMatrix :: Element t => Matrix t -> IO (Matrix t) cloneMatrix m = copy (orderOf m) m {-# INLINE safeIndexM #-} +safeIndexM :: (STMatrix s t2 -> Int -> Int -> t) + -> STMatrix t1 t2 -> Int -> Int -> t safeIndexM f (STMatrix m) r c | r<0 || r>=rows m || c<0 || c>=cols m = error $ "out of range error in matrix (size=" @@ -184,6 +189,7 @@ | Col Int | FromCol Int +getColRange :: Int -> ColRange -> (Int, Int) getColRange c AllCols = (0,c-1) getColRange c (ColRange a b) = (a `mod` c, b `mod` c) getColRange c (Col a) = (a `mod` c, a `mod` c) @@ -194,6 +200,7 @@ | Row Int | FromRow Int +getRowRange :: Int -> RowRange -> (Int, Int) getRowRange r AllRows = (0,r-1) getRowRange r (RowRange a b) = (a `mod` r, b `mod` r) getRowRange r (Row a) = (a `mod` r, a `mod` r) @@ -223,6 +230,7 @@ i2' = i2 `mod` (rows m) +extractMatrix :: Element a => STMatrix t a -> RowRange -> ColRange -> ST s (Matrix a) extractMatrix (STMatrix m) rr rc = unsafeIOToST (extractR (orderOf m) m 0 (idxs[i1,i2]) 0 (idxs[j1,j2])) where (i1,i2) = getRowRange (rows m) rr @@ -231,6 +239,7 @@ -- | r0 c0 height width data Slice s t = Slice (STMatrix s t) Int Int Int Int +slice :: Element a => Slice t a -> Matrix a slice (Slice (STMatrix m) r0 c0 nr nc) = subMatrix (r0,c0) (nr,nc) m gemmm :: Element t => t -> Slice s t -> t -> Slice s t -> Slice s t -> ST s () @@ -238,12 +247,11 @@ where res = unsafeIOToST (gemm v a b r) v = fromList [alpha,beta] - + mutable :: Element t => (forall s . (Int, Int) -> STMatrix s t -> ST s u) -> Matrix t -> (Matrix t,u) mutable f a = runST $ do x <- thawMatrix a info <- f (rows a, cols a) x r <- unsafeFreezeMatrix x return (r,info) - diff --git a/src/Internal/Sparse.hs b/src/Internal/Sparse.hs --- a/src/Internal/Sparse.hs +++ b/src/Internal/Sparse.hs @@ -1,9 +1,11 @@ -{-# LANGUAGE RecordWildCards #-} -{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE BangPatterns #-} {-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE RecordWildCards #-} module Internal.Sparse( - GMatrix(..), CSR(..), mkCSR, fromCSR, + GMatrix(..), CSR(..), mkCSR, fromCSR, impureCSR, mkSparse, mkDiagR, mkDense, AssocMatrix, toDense, @@ -14,10 +16,12 @@ import Internal.Matrix import Internal.Numeric import qualified Data.Vector.Storable as V -import Data.Function(on) +import qualified Data.Vector.Storable.Mutable as M import Control.Arrow((***)) -import Control.Monad(when) -import Data.List(groupBy, sort) +import Control.Monad(when, foldM) +import Control.Monad.ST (runST) +import Control.Monad.Primitive (PrimMonad) +import Data.List(sort) import Foreign.C.Types(CInt(..)) import Internal.Devel @@ -25,10 +29,7 @@ import Foreign(Ptr) import Text.Printf(printf) -infixl 0 ~!~ -c ~!~ msg = when c (error msg) - -type AssocMatrix = [((Int,Int),Double)] +type AssocMatrix = [(IndexOf Matrix, Double)] data CSR = CSR { csrVals :: Vector Double @@ -47,23 +48,79 @@ } deriving Show +-- | Produce a CSR sparse matrix from a association matrix. mkCSR :: AssocMatrix -> CSR -mkCSR sm' = CSR{..} +mkCSR ms = + runST $ impureCSR runFold $ sort ms + where + runFold next initialise xtract as0 = do + i0 <- initialise + acc <- foldM next i0 as0 + xtract acc + +-- | Produce a CSR sparse matrix by applying a generic folding function. +-- +-- This allows one to build a CSR from an effectful streaming source +-- when combined with libraries like pipes, io-streams, or streaming. +-- +-- For example +-- +-- > impureCSR Pipes.Prelude.foldM :: PrimMonad m => Producer AssocEntry m () -> m CSR +-- > impureCSR Streaming.Prelude.foldM :: PrimMonad m => Stream (Of AssocEntry) m r -> m (Of CSR r) +-- +impureCSR + :: PrimMonad m + => (forall x . (x -> (IndexOf Matrix, Double) -> m x) -> m x -> (x -> m CSR) -> r) + -> r +impureCSR f = f next begin done where - sm = sort sm' - rws = map ((fromList *** fromList) - . unzip - . map ((succ.fi.snd) *** id) - ) - . groupBy ((==) `on` (fst.fst)) - $ sm - rszs = map (fi . dim . fst) rws - csrRows = fromList (scanl (+) 1 rszs) - csrVals = vjoin (map snd rws) - csrCols = vjoin (map fst rws) - csrNRows = dim csrRows - 1 - csrNCols = fromIntegral (V.maximum csrCols) + sfi = succ . fi + begin = do + mv <- M.unsafeNew 64 + mr <- M.unsafeNew 64 + mc <- M.unsafeNew 64 + return (mv, mr, mc, 0, 0, 0, -1) + next (!mv, !mr, !mc, !idxVC, !idxR, !maxC, !curRow) ((r,c),d) = do + when (r < curRow) $ + error (printf "impureCSR: row %i specified after %i" r curRow) + + let lenVC = M.length mv + lenR = M.length mr + maxC' = max maxC c + + (mv', mc') <- + if idxVC >= lenVC then do + mv' <- M.unsafeGrow mv lenVC + mc' <- M.unsafeGrow mc lenVC + return (mv', mc') + else + return (mv, mc) + + mr' <- + if idxR >= lenR - 1 then + M.unsafeGrow mr lenR + else + return mr + + M.unsafeWrite mc' idxVC (sfi c) + M.unsafeWrite mv' idxVC d + + idxR' <- + foldM + (\idxR' _ -> idxR' + 1 <$ M.unsafeWrite mr' idxR' (sfi idxVC)) + idxR [1 .. (r-curRow)] + + return (mv', mr', mc', idxVC + 1, idxR', maxC', r) + + done (!mv, !mr, !mc, !idxVC, !idxR, !maxC, !curR) = do + M.unsafeWrite mr idxR (sfi idxVC) + vv <- V.unsafeFreeze (M.unsafeTake idxVC mv) + vc <- V.unsafeFreeze (M.unsafeTake idxVC mc) + vr <- V.unsafeFreeze (M.unsafeTake (idxR + 1) mr) + return $ CSR vv vc vr (succ curR) (succ maxC) + + {- | General matrix with specialized internal representations for dense, sparse, diagonal, banded, and constant elements. @@ -122,11 +179,12 @@ fromCSR :: CSR -> GMatrix fromCSR csr = SparseR {..} where - gmCSR @ CSR {..} = csr + gmCSR@CSR {..} = csr nRows = csrNRows nCols = csrNCols +mkDiagR :: Int -> Int -> Vector Double -> GMatrix mkDiagR r c v | dim v <= min r c = Diag{..} | otherwise = error $ printf "mkDiagR: incorrect sizes (%d,%d) [%d]" r c (dim v) @@ -142,15 +200,19 @@ gmXv :: GMatrix -> Vector Double -> Vector Double gmXv SparseR { gmCSR = CSR{..}, .. } v = unsafePerformIO $ do - dim v /= nCols ~!~ printf "gmXv (CSR): incorrect sizes: (%d,%d) x %d" nRows nCols (dim v) + when (dim v /= nCols) $ + error (printf "gmXv (CSR): incorrect sizes: (%d,%d) x %d" nRows nCols (dim v)) + r <- createVector nRows - c_smXv # csrVals # csrCols # csrRows # v # r #|"CSRXv" + (csrVals # csrCols # csrRows # v #! r) c_smXv #|"CSRXv" return r gmXv SparseC { gmCSC = CSC{..}, .. } v = unsafePerformIO $ do - dim v /= nCols ~!~ printf "gmXv (CSC): incorrect sizes: (%d,%d) x %d" nRows nCols (dim v) + when (dim v /= nCols) $ + error (printf "gmXv (CSC): incorrect sizes: (%d,%d) x %d" nRows nCols (dim v)) + r <- createVector nRows - c_smTXv # cscVals # cscRows # cscCols # v # r #|"CSCXv" + (cscVals # cscRows # cscCols # v #! r) c_smTXv #|"CSCXv" return r gmXv Diag{..} v @@ -170,8 +232,10 @@ {- | general matrix - vector product >>> let m = mkSparse [((0,999),1.0),((1,1999),2.0)] +m :: GMatrix >>> m !#> vector [1..2000] -fromList [1000.0,4000.0] +[1000.0,4000.0] +it :: Vector Double -} infixr 8 !#> @@ -211,4 +275,3 @@ tr (Diag v n m) = Diag v m n tr (Dense a n m) = Dense (tr a) m n tr' = tr - diff --git a/src/Internal/Static.hs b/src/Internal/Static.hs --- a/src/Internal/Static.hs +++ b/src/Internal/Static.hs @@ -1,3 +1,4 @@ +{-# LANGUAGE CPP #-} #if __GLASGOW_HASKELL__ >= 708 {-# LANGUAGE DataKinds #-} @@ -11,7 +12,11 @@ {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE ViewPatterns #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE DeriveGeneric #-} +{-# OPTIONS_GHC -fno-warn-missing-signatures #-} + {- | Module : Internal.Static Copyright : (c) Alberto Ruiz 2006-14 @@ -28,18 +33,35 @@ import Numeric.LinearAlgebra hiding (konst,size,R,C) import Internal.Vector as D hiding (R,C) import Internal.ST +import Control.DeepSeq import Data.Proxy(Proxy) import Foreign.Storable(Storable) import Text.Printf +import Data.Binary +import GHC.Generics (Generic) +import Data.Proxy (Proxy(..)) + -------------------------------------------------------------------------------- type ℝ = Double type ℂ = Complex Double newtype Dim (n :: Nat) t = Dim t - deriving Show + deriving (Show, Generic) +instance (KnownNat n, Binary a) => Binary (Dim n a) where + get = do + k <- get + let n = natVal (Proxy :: Proxy n) + if n == k + then Dim <$> get + else fail ("Expected dimension " ++ (show n) ++ ", but found dimension " ++ (show k)) + + put (Dim x) = do + put (natVal (Proxy :: Proxy n)) + put x + lift1F :: (c t -> c t) -> Dim n (c t) -> Dim n (c t) @@ -50,18 +72,22 @@ -> Dim n (c t) -> Dim n (c t) -> Dim n (c t) lift2F f (Dim u) (Dim v) = Dim (f u v) +instance NFData t => NFData (Dim n t) where + rnf (Dim (force -> !_)) = () + -------------------------------------------------------------------------------- newtype R n = R (Dim n (Vector ℝ)) - deriving (Num,Fractional,Floating) + deriving (Num,Fractional,Floating,Generic,Binary) newtype C n = C (Dim n (Vector ℂ)) - deriving (Num,Fractional,Floating) + deriving (Num,Fractional,Floating,Generic) newtype L m n = L (Dim m (Dim n (Matrix ℝ))) - -newtype M m n = M (Dim m (Dim n (Matrix ℂ))) + deriving (Generic, Binary) +newtype M m n = M (Dim m (Dim n (Matrix ℂ))) + deriving (Generic) mkR :: Vector ℝ -> R n mkR = R . Dim @@ -75,6 +101,18 @@ mkM :: Matrix ℂ -> M m n mkM x = M (Dim (Dim x)) +instance NFData (R n) where + rnf (R (force -> !_)) = () + +instance NFData (C n) where + rnf (C (force -> !_)) = () + +instance NFData (L n m) where + rnf (L (force -> !_)) = () + +instance NFData (M n m) where + rnf (M (force -> !_)) = () + -------------------------------------------------------------------------------- type V n t = Dim n (Vector t) @@ -92,9 +130,9 @@ where du = fromIntegral . natVal $ (undefined :: Proxy n) dv = fromIntegral . natVal $ (undefined :: Proxy m) - u' | du > 1 && LA.size u == 1 = LA.konst (u D.@> 0) du + u' | du /= 1 && LA.size u == 1 = LA.konst (u D.@> 0) du | otherwise = u - v' | dv > 1 && LA.size v == 1 = LA.konst (v D.@> 0) dv + v' | dv /= 1 && LA.size v == 1 = LA.konst (v D.@> 0) dv | otherwise = v @@ -173,7 +211,7 @@ singleM m = rows m == 1 && cols m == 1 -instance forall n. KnownNat n => Sized ℂ (C n) Vector +instance KnownNat n => Sized ℂ (C n) Vector where size _ = fromIntegral . natVal $ (undefined :: Proxy n) konst x = mkC (LA.scalar x) @@ -189,7 +227,7 @@ r = mkC v :: C n -instance forall n. KnownNat n => Sized ℝ (R n) Vector +instance KnownNat n => Sized ℝ (R n) Vector where size _ = fromIntegral . natVal $ (undefined :: Proxy n) konst x = mkR (LA.scalar x) @@ -206,7 +244,7 @@ -instance forall m n . (KnownNat m, KnownNat n) => Sized ℝ (L m n) Matrix +instance (KnownNat m, KnownNat n) => Sized ℝ (L m n) Matrix where size _ = ((fromIntegral . natVal) (undefined :: Proxy m) ,(fromIntegral . natVal) (undefined :: Proxy n)) @@ -224,7 +262,7 @@ r = mkL x :: L m n -instance forall m n . (KnownNat m, KnownNat n) => Sized ℂ (M m n) Matrix +instance (KnownNat m, KnownNat n) => Sized ℂ (M m n) Matrix where size _ = ((fromIntegral . natVal) (undefined :: Proxy m) ,(fromIntegral . natVal) (undefined :: Proxy n)) @@ -282,43 +320,43 @@ -------------------------------------------------------------------------------- -instance forall n . KnownNat n => Show (R n) +instance KnownNat n => Show (R n) where show s@(R (Dim v)) - | singleV v = "("++show (v!0)++" :: R "++show d++")" - | otherwise = "(vector"++ drop 8 (show v)++" :: R "++show d++")" + | singleV v = "(" ++ show (v!0) ++ " :: R " ++ show d ++ ")" + | otherwise = "(vector " ++ show v ++ " :: R " ++ show d ++")" where d = size s -instance forall n . KnownNat n => Show (C n) +instance KnownNat n => Show (C n) where show s@(C (Dim v)) - | singleV v = "("++show (v!0)++" :: C "++show d++")" - | otherwise = "(vector"++ drop 8 (show v)++" :: C "++show d++")" + | singleV v = "(" ++ show (v!0) ++ " :: C " ++ show d ++ ")" + | otherwise = "(vector " ++ show v ++ " :: C " ++ show d ++")" where d = size s -instance forall m n . (KnownNat m, KnownNat n) => Show (L m n) +instance (KnownNat m, KnownNat n) => Show (L m n) where - show (isDiag -> Just (z,y,(m',n'))) = printf "(diag %s %s :: L %d %d)" (show z) (drop 9 $ show y) m' n' + show (isDiag -> Just (z,y,(m',n'))) = printf "(diag %s %s :: L %d %d)" (show z) (show y) m' n' show s@(L (Dim (Dim x))) | singleM x = printf "(%s :: L %d %d)" (show (x `atIndex` (0,0))) m' n' - | otherwise = "(matrix"++ dropWhile (/='\n') (show x)++" :: L "++show m'++" "++show n'++")" + | otherwise = "(matrix" ++ dropWhile (/='\n') (show x) ++ " :: L " ++ show m' ++ " " ++ show n' ++ ")" where (m',n') = size s -instance forall m n . (KnownNat m, KnownNat n) => Show (M m n) +instance (KnownNat m, KnownNat n) => Show (M m n) where - show (isDiagC -> Just (z,y,(m',n'))) = printf "(diag %s %s :: M %d %d)" (show z) (drop 9 $ show y) m' n' + show (isDiagC -> Just (z,y,(m',n'))) = printf "(diag %s %s :: M %d %d)" (show z) (show y) m' n' show s@(M (Dim (Dim x))) | singleM x = printf "(%s :: M %d %d)" (show (x `atIndex` (0,0))) m' n' - | otherwise = "(matrix"++ dropWhile (/='\n') (show x)++" :: M "++show m'++" "++show n'++")" + | otherwise = "(matrix" ++ dropWhile (/='\n') (show x) ++ " :: M " ++ show m' ++ " " ++ show n' ++ ")" where (m',n') = size s -------------------------------------------------------------------------------- -instance forall n t . (Num (Vector t), Numeric t )=> Num (Dim n (Vector t)) +instance (Num (Vector t), Numeric t )=> Num (Dim n (Vector t)) where (+) = lift2F (+) (*) = lift2F (*) @@ -328,7 +366,7 @@ negate = lift1F negate fromInteger x = Dim (fromInteger x) -instance (Num (Vector t), Num (Matrix t), Fractional t, Numeric t) => Fractional (Dim n (Vector t)) +instance (Num (Vector t), Fractional t, Numeric t) => Fractional (Dim n (Vector t)) where fromRational x = Dim (fromRational x) (/) = lift2F (/) @@ -353,7 +391,7 @@ pi = Dim pi -instance (Num (Matrix t), Numeric t) => Num (Dim m (Dim n (Matrix t))) +instance (Num (Vector t), Numeric t) => Num (Dim m (Dim n (Matrix t))) where (+) = (lift2F . lift2F) (+) (*) = (lift2F . lift2F) (*) @@ -363,12 +401,12 @@ negate = (lift1F . lift1F) negate fromInteger x = Dim (Dim (fromInteger x)) -instance (Num (Vector t), Num (Matrix t), Fractional t, Numeric t) => Fractional (Dim m (Dim n (Matrix t))) +instance (Num (Vector t), Fractional t, Numeric t) => Fractional (Dim m (Dim n (Matrix t))) where fromRational x = Dim (Dim (fromRational x)) (/) = (lift2F.lift2F) (/) -instance (Num (Vector t), Floating (Matrix t), Fractional t, Numeric t) => Floating (Dim m (Dim n (Matrix t))) where +instance (Floating (Vector t), Floating t, Numeric t) => Floating (Dim m (Dim n (Matrix t))) where sin = (lift1F . lift1F) sin cos = (lift1F . lift1F) cos tan = (lift1F . lift1F) tan @@ -482,6 +520,18 @@ (**) = lift2MD (**) pi = M pi +instance Additive (R n) where + add = (+) + +instance Additive (C n) where + add = (+) + +instance (KnownNat m, KnownNat n) => Additive (L m n) where + add = (+) + +instance (KnownNat m, KnownNat n) => Additive (M m n) where + add = (+) + -------------------------------------------------------------------------------- @@ -518,6 +568,17 @@ putStr "C " >> putStr (tail . dropWhile (/='x') $ su) -------------------------------------------------------------------------------- + +overMatL' :: (KnownNat m, KnownNat n) + => (LA.Matrix ℝ -> LA.Matrix ℝ) -> L m n -> L m n +overMatL' f = mkL . f . unwrap +{-# INLINE overMatL' #-} + +overMatM' :: (KnownNat m, KnownNat n) + => (LA.Matrix ℂ -> LA.Matrix ℂ) -> M m n -> M m n +overMatM' f = mkM . f . unwrap +{-# INLINE overMatM' #-} + #else diff --git a/src/Internal/Util.hs b/src/Internal/Util.hs --- a/src/Internal/Util.hs +++ b/src/Internal/Util.hs @@ -1,9 +1,13 @@ +{-# LANGUAGE CPP #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE FunctionalDependencies #-} +{-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE ViewPatterns #-} +{-# OPTIONS_GHC -fno-warn-missing-signatures #-} +{-# OPTIONS_GHC -fno-warn-orphans #-} ----------------------------------------------------------------------------- {- | @@ -41,7 +45,7 @@ ℕ,ℤ,ℝ,ℂ,iC, Normed(..), norm_Frob, norm_nuclear, magnit, - unitary, + normalize, mt, (~!~), pairwiseD2, @@ -79,6 +83,9 @@ import Data.Complex import Data.Function(on) import Internal.ST +#if MIN_VERSION_base(4,11,0) +import Prelude hiding ((<>)) +#endif type ℝ = Double type ℕ = Int @@ -92,7 +99,8 @@ {- | Create a real vector. >>> vector [1..5] -fromList [1.0,2.0,3.0,4.0,5.0] +[1.0,2.0,3.0,4.0,5.0] +it :: Vector R -} vector :: [R] -> Vector R @@ -255,6 +263,7 @@ -- ^ 2-norm of real vector norm = pnorm PNorm2 +-- | p-norm for vectors, operator norm for matrices class Normed a where norm_0 :: a -> R @@ -319,10 +328,11 @@ norm_2 = norm_2 . double norm_Inf = norm_Inf . double - +-- | Frobenius norm (Schatten p-norm with p=2) norm_Frob :: (Normed (Vector t), Element t) => Matrix t -> R norm_Frob = norm_2 . flatten +-- | Sum of singular values (Schatten p-norm with p=1) norm_nuclear :: Field t => Matrix t -> R norm_nuclear = sumElements . singularValues @@ -341,8 +351,8 @@ -- | Obtains a vector in the same direction with 2-norm=1 -unitary :: Vector Double -> Vector Double -unitary v = v / scalar (norm v) +normalize :: (Normed (Vector t), Num (Vector t), Field t) => Vector t -> Vector t +normalize v = v / real (scalar (norm_2 v)) -- | trans . inv @@ -369,7 +379,8 @@ On a matrix it gets the k-th row as a vector: >>> matrix 5 [1..15] ! 1 -fromList [6.0,7.0,8.0,9.0,10.0] +[6.0,7.0,8.0,9.0,10.0] +it :: Vector Double >>> matrix 5 [1..15] ! 1 ! 3 9.0 @@ -406,7 +417,7 @@ instance Element t => Indexable (Matrix t) (Vector t) where - m!j = subVector (j*c) c (flatten m) + m ! j = subVector (j*c) c (flatten m) where c = cols m @@ -611,6 +622,9 @@ s1 = fromRows $ pivotDown (rows x) 0 rs -- interesting s2 = pivotUp (rows x-1) (toRows $ flipud s1) +pivotDown + :: forall t . (Fractional t, Num (Vector t), Ord t, Indexable (Vector t) t, Numeric t) + => Int -> Int -> [Vector t] -> [Vector t] pivotDown t n xs | t == n = [] | otherwise = y : pivotDown t (n+1) ys @@ -618,8 +632,9 @@ y:ys = redu (pivot n xs) pivot k = (const k &&& id) - . sortBy (flip compare `on` (abs. (!k))) + . sortBy (flip compare `on` (abs. (! k))) + redu :: (Int, [Vector t]) -> [Vector t] redu (k,x:zs) | p == 0 = error "gauss: singular!" -- FIXME | otherwise = u : map f zs @@ -630,12 +645,16 @@ redu (_,[]) = [] +pivotUp + :: forall t . (Fractional t, Num (Vector t), Ord t, Indexable (Vector t) t, Numeric t) + => Int -> [Vector t] -> [Vector t] pivotUp n xs | n == -1 = [] | otherwise = y : pivotUp (n-1) ys where y:ys = redu' (n,xs) + redu' :: (Int, [Vector t]) -> [Vector t] redu' (k,x:zs) = u : map f zs where u = x @@ -893,4 +912,3 @@ , remap r (tr c) p == ep , tr p ?? (PosCyc (idxs[-5,13]), Pos (idxs[3,7,1])) == (2><3) [35,75,15,33,73,13] ] - diff --git a/src/Internal/Vector.hs b/src/Internal/Vector.hs --- a/src/Internal/Vector.hs +++ b/src/Internal/Vector.hs @@ -1,6 +1,7 @@ -{-# LANGUAGE MagicHash, CPP, UnboxedTuples, BangPatterns, FlexibleContexts #-} +{-# LANGUAGE MagicHash, UnboxedTuples, BangPatterns, FlexibleContexts #-} {-# LANGUAGE TypeSynonymInstances #-} +{-# OPTIONS_GHC -fno-warn-orphans #-} -- | -- Module : Internal.Vector @@ -39,12 +40,11 @@ import qualified Data.Vector.Storable as Vector import Data.Vector.Storable(Vector, fromList, unsafeToForeignPtr, unsafeFromForeignPtr, unsafeWith) -#ifdef BINARY import Data.Binary +import Data.Binary.Put import Control.Monad(replicateM) import qualified Data.ByteString.Internal as BS import Data.Vector.Storable.Internal(updPtr) -#endif type I = CInt type Z = Int64 @@ -64,13 +64,13 @@ -- | Number of elements dim :: (Storable t) => Vector t -> Int dim = Vector.length +{-# INLINE dim #-} -- C-Haskell vector adapter {-# INLINE avec #-} -avec :: Storable a => (CInt -> Ptr a -> b) -> Vector a -> b -avec f v = inlinePerformIO (unsafeWith v (return . f (fromIntegral (Vector.length v)))) -infixl 1 `avec` +avec :: Storable a => Vector a -> (f -> IO r) -> ((CInt -> Ptr a -> f) -> IO r) +avec v f g = unsafeWith v $ \ptr -> f (g (fromIntegral (Vector.length v)) ptr) -- allocates memory for a new vector createVector :: Storable a => Int -> IO (Vector a) @@ -94,6 +94,7 @@ -} +safeRead :: Storable a => Vector a -> (Ptr a -> IO c) -> c safeRead v = inlinePerformIO . unsafeWith v {-# INLINE safeRead #-} @@ -115,7 +116,8 @@ be used, for instance, with infinite lists. >>> 5 |> [1..] -fromList [1.0,2.0,3.0,4.0,5.0] +[1.0,2.0,3.0,4.0,5.0] +it :: (Enum a, Num a, Foreign.Storable.Storable a) => Vector a -} (|>) :: (Storable a) => Int -> [a] -> Vector a @@ -134,7 +136,8 @@ {- | takes a number of consecutive elements from a Vector >>> subVector 2 3 (fromList [1..10]) -fromList [3.0,4.0,5.0] +[3.0,4.0,5.0] +it :: (Enum t, Num t, Foreign.Storable.Storable t) => Vector t -} subVector :: Storable t => Int -- ^ index of the starting element @@ -142,6 +145,7 @@ -> Vector t -- ^ source -> Vector t -- ^ result subVector = Vector.slice +{-# INLINE subVector #-} @@ -167,7 +171,8 @@ {- | concatenate a list of vectors >>> vjoin [fromList [1..5::Double], konst 1 3] -fromList [1.0,2.0,3.0,4.0,5.0,1.0,1.0,1.0] +[1.0,2.0,3.0,4.0,5.0,1.0,1.0,1.0] +it :: Vector Double -} vjoin :: Storable t => [Vector t] -> Vector t @@ -189,7 +194,8 @@ {- | Extract consecutive subvectors of the given sizes. >>> takesV [3,4] (linspace 10 (1,10::Double)) -[fromList [1.0,2.0,3.0],fromList [4.0,5.0,6.0,7.0]] +[[1.0,2.0,3.0],[4.0,5.0,6.0,7.0]] +it :: [Vector Double] -} takesV :: Storable t => [Int] -> Vector t -> [Vector t] @@ -201,7 +207,7 @@ --------------------------------------------------------------- --- | transforms a complex vector into a real vector with alternating real and imaginary parts +-- | transforms a complex vector into a real vector with alternating real and imaginary parts asReal :: (RealFloat a, Storable a) => Vector (Complex a) -> Vector a asReal v = unsafeFromForeignPtr (castForeignPtr fp) (2*i) (2*n) where (fp,i,n) = unsafeToForeignPtr v @@ -246,7 +252,7 @@ {-# INLINE zipVectorWith #-} -- | unzipWith for Vectors -unzipVectorWith :: (Storable (a,b), Storable c, Storable d) +unzipVectorWith :: (Storable (a,b), Storable c, Storable d) => ((a,b) -> (c,d)) -> Vector (a,b) -> (Vector c,Vector d) unzipVectorWith f u = unsafePerformIO $ do let n = dim u @@ -257,7 +263,7 @@ unsafeWith w $ \pw -> do let go (-1) = return () go !k = do z <- peekElemOff pu k - let (x,y) = f z + let (x,y) = f z pokeElemOff pv k x pokeElemOff pw k y go (k-1) @@ -284,11 +290,13 @@ go (dim v -1) x {-# INLINE foldVectorWithIndex #-} +foldLoop :: (Int -> t -> t) -> t -> Int -> t foldLoop f s0 d = go (d - 1) s0 where go 0 s = f (0::Int) s go !j !s = go (j - 1) (f j s) +foldVectorG :: Storable t1 => (Int -> (Int -> t1) -> t -> t) -> t -> Vector t1 -> t foldVectorG f s0 v = foldLoop g s0 (dim v) where g !k !s = f k (safeRead v . flip peekElemOff) s {-# INLINE g #-} -- Thanks to Ryan Ingram (http://permalink.gmane.org/gmane.comp.lang.haskell.cafe/46479) @@ -305,11 +313,11 @@ return w where mapVectorM' w' !k !t | k == t = do - x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k + x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k y <- f x return $! inlinePerformIO $! unsafeWith w' $! \q -> pokeElemOff q k y | otherwise = do - x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k + x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k y <- f x _ <- return $! inlinePerformIO $! unsafeWith w' $! \q -> pokeElemOff q k y mapVectorM' w' (k+1) t @@ -324,7 +332,7 @@ x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k f x | otherwise = do - x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k + x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k _ <- f x mapVectorM' (k+1) t {-# INLINE mapVectorM_ #-} @@ -338,11 +346,11 @@ return w where mapVectorM' w' !k !t | k == t = do - x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k + x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k y <- f k x return $! inlinePerformIO $! unsafeWith w' $! \q -> pokeElemOff q k y | otherwise = do - x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k + x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k y <- f k x _ <- return $! inlinePerformIO $! unsafeWith w' $! \q -> pokeElemOff q k y mapVectorM' w' (k+1) t @@ -357,7 +365,7 @@ x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k f k x | otherwise = do - x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k + x <- return $! inlinePerformIO $! unsafeWith v $! \p -> peekElemOff p k _ <- f k x mapVectorM' (k+1) t {-# INLINE mapVectorWithIndexM_ #-} @@ -380,7 +388,6 @@ -------------------------------------------------------------------------------- -#ifdef BINARY -- a 64K cache, with a Double taking 13 bytes in Bytestring, -- implies a chunk size of 5041 @@ -392,8 +399,10 @@ m = d `mod` chunk in if m /= 0 then reverse (m:(replicate c chunk)) else (replicate c chunk) +putVector :: (Storable t, Binary t) => Vector t -> Data.Binary.Put.PutM () putVector v = mapM_ put $! toList v +getVector :: (Storable a, Binary a) => Int -> Get (Vector a) getVector d = do xs <- replicateM d get return $! fromList xs @@ -432,7 +441,6 @@ -- get = fmap bs2v get -#endif ------------------------------------------------------------------- @@ -458,4 +466,3 @@ unzipVector = unzipVectorWith id ------------------------------------------------------------------- - diff --git a/src/Internal/Vectorized.hs b/src/Internal/Vectorized.hs --- a/src/Internal/Vectorized.hs +++ b/src/Internal/Vectorized.hs @@ -27,10 +27,16 @@ import System.IO.Unsafe(unsafePerformIO) import Control.Monad(when) -infixl 1 # +infixr 1 # +(#) :: TransArray c => c -> (b -> IO r) -> TransRaw c b -> IO r a # b = applyRaw a b {-# INLINE (#) #-} +(#!) :: (TransArray c, TransArray c1) => c1 -> c -> TransRaw c1 (TransRaw c (IO r)) -> IO r +a #! b = a # b # id +{-# INLINE (#!) #-} + +fromei :: Enum a => a -> CInt fromei x = fromIntegral (fromEnum x) :: CInt data FunCodeV = Sin @@ -97,13 +103,23 @@ sumC :: Vector (Complex Double) -> Complex Double sumC = sumg c_sumC +sumI :: ( TransRaw c (CInt -> Ptr a -> IO CInt) ~ (CInt -> Ptr I -> I :> Ok) + , TransArray c + , Storable a + ) + => I -> c -> a sumI m = sumg (c_sumI m) +sumL :: ( TransRaw c (CInt -> Ptr a -> IO CInt) ~ (CInt -> Ptr Z -> Z :> Ok) + , TransArray c + , Storable a + ) => Z -> c -> a sumL m = sumg (c_sumL m) +sumg :: (TransArray c, Storable a) => TransRaw c (CInt -> Ptr a -> IO CInt) -> c -> a sumg f x = unsafePerformIO $ do r <- createVector 1 - f # x # r #| "sum" + (x #! r) f #| "sum" return $ r @> 0 type TVV t = t :> t :> Ok @@ -137,9 +153,11 @@ prodL :: Z-> Vector Z -> Z prodL = prodg . c_prodL +prodg :: (TransArray c, Storable a) + => TransRaw c (CInt -> Ptr a -> IO CInt) -> c -> a prodg f x = unsafePerformIO $ do r <- createVector 1 - f # x # r #| "prod" + (x #! r) f #| "prod" return $ r @> 0 @@ -152,26 +170,38 @@ ------------------------------------------------------------------ +toScalarAux :: (Enum a, TransArray c, Storable a1) + => (CInt -> TransRaw c (CInt -> Ptr a1 -> IO CInt)) -> a -> c -> a1 toScalarAux fun code v = unsafePerformIO $ do r <- createVector 1 - fun (fromei code) # v # r #|"toScalarAux" + (v #! r) (fun (fromei code)) #|"toScalarAux" return (r @> 0) + +vectorMapAux :: (Enum a, Storable t, Storable a1) + => (CInt -> CInt -> Ptr t -> CInt -> Ptr a1 -> IO CInt) + -> a -> Vector t -> Vector a1 vectorMapAux fun code v = unsafePerformIO $ do r <- createVector (dim v) - fun (fromei code) # v # r #|"vectorMapAux" + (v #! r) (fun (fromei code)) #|"vectorMapAux" return r +vectorMapValAux :: (Enum a, Storable a2, Storable t, Storable a1) + => (CInt -> Ptr a2 -> CInt -> Ptr t -> CInt -> Ptr a1 -> IO CInt) + -> a -> a2 -> Vector t -> Vector a1 vectorMapValAux fun code val v = unsafePerformIO $ do r <- createVector (dim v) pval <- newArray [val] - fun (fromei code) pval # v # r #|"vectorMapValAux" + (v #! r) (fun (fromei code) pval) #|"vectorMapValAux" free pval return r +vectorZipAux :: (Enum a, TransArray c, Storable t, Storable a1) + => (CInt -> CInt -> Ptr t -> TransRaw c (CInt -> Ptr a1 -> IO CInt)) + -> a -> Vector t -> c -> Vector a1 vectorZipAux fun code u v = unsafePerformIO $ do r <- createVector (dim u) - fun (fromei code) # u # v # r #|"vectorZipAux" + (u # v #! r) (fun (fromei code)) #|"vectorZipAux" return r --------------------------------------------------------------------- @@ -368,16 +398,17 @@ -> Vector Double randomVector seed dist n = unsafePerformIO $ do r <- createVector n - c_random_vector (fi seed) ((fi.fromEnum) dist) # r #|"randomVector" + (r # id) (c_random_vector (fi seed) ((fi.fromEnum) dist)) #|"randomVector" return r foreign import ccall unsafe "random_vector" c_random_vector :: CInt -> CInt -> Double :> Ok -------------------------------------------------------------------------------- +roundVector :: Vector Double -> Vector Double roundVector v = unsafePerformIO $ do r <- createVector (dim v) - c_round_vector # v # r #|"roundVector" + (v #! r) c_round_vector #|"roundVector" return r foreign import ccall unsafe "round_vector" c_round_vector :: TVV Double @@ -386,12 +417,13 @@ -- | -- >>> range 5 --- fromList [0,1,2,3,4] +-- [0,1,2,3,4] +-- it :: Vector I -- range :: Int -> Vector I range n = unsafePerformIO $ do r <- createVector n - c_range_vector # r #|"range" + (r # id) c_range_vector #|"range" return r foreign import ccall unsafe "range_vector" c_range_vector :: CInt :> Ok @@ -429,9 +461,11 @@ long2intV = tog c_long2int +tog :: (Storable t, Storable a) + => (CInt -> Ptr t -> CInt -> Ptr a -> IO CInt) -> Vector t -> Vector a tog f v = unsafePerformIO $ do r <- createVector (dim v) - f # v # r #|"tog" + (v #! r) f #|"tog" return r foreign import ccall unsafe "float2double" c_float2double :: Float :> Double :> Ok @@ -448,9 +482,11 @@ --------------------------------------------------------------- +stepg :: (Storable t, Storable a) + => (CInt -> Ptr t -> CInt -> Ptr a -> IO CInt) -> Vector t -> Vector a stepg f v = unsafePerformIO $ do r <- createVector (dim v) - f # v # r #|"step" + (v #! r) f #|"step" return r stepD :: Vector Double -> Vector Double @@ -473,9 +509,11 @@ -------------------------------------------------------------------------------- +conjugateAux :: (Storable t, Storable a) + => (CInt -> Ptr t -> CInt -> Ptr a -> IO CInt) -> Vector t -> Vector a conjugateAux fun x = unsafePerformIO $ do v <- createVector (dim x) - fun # x # v #|"conjugateAux" + (x #! v) fun #|"conjugateAux" return v conjugateQ :: Vector (Complex Float) -> Vector (Complex Float) @@ -493,15 +531,17 @@ let n = dim v r <- createVector n let f _ s _ d = copyArray d s n >> return 0 - f # v # r #|"cloneVector" + (v #! r) f #|"cloneVector" return r -------------------------------------------------------------------------------- +constantAux :: (Storable a1, Storable a) + => (Ptr a1 -> CInt -> Ptr a -> IO CInt) -> a1 -> Int -> Vector a constantAux fun x n = unsafePerformIO $ do v <- createVector n px <- newArray [x] - fun px # v #|"constantAux" + (v # id) (fun px) #|"constantAux" free px return v @@ -515,4 +555,3 @@ foreign import ccall unsafe "constantL" cconstantL :: TConst Z ---------------------------------------------------------------------- - diff --git a/src/Numeric/LinearAlgebra.hs b/src/Numeric/LinearAlgebra.hs --- a/src/Numeric/LinearAlgebra.hs +++ b/src/Numeric/LinearAlgebra.hs @@ -1,5 +1,8 @@ +{-# LANGUAGE CPP #-} {-# LANGUAGE FlexibleContexts #-} +{-# OPTIONS_GHC -fno-warn-missing-signatures #-} + ----------------------------------------------------------------------------- {- | Module : Numeric.LinearAlgebra @@ -22,10 +25,12 @@ -- * Numeric classes -- | - -- The standard numeric classes are defined elementwise: + -- The standard numeric classes are defined elementwise (commonly referred to + -- as the Hadamard product or the Schur product): -- -- >>> vector [1,2,3] * vector [3,0,-2] - -- fromList [3.0,0.0,-6.0] + -- [3.0,0.0,-6.0] + -- it :: Vector R -- -- >>> matrix 3 [1..9] * ident 3 -- (3><3) @@ -93,6 +98,11 @@ ldlSolve, ldlPacked, -- ** Positive definite cholSolve, + -- ** Triangular + UpLo(..), + triSolve, + -- ** Tridiagonal + triDiagSolve, -- ** Sparse cgSolve, cgSolve', @@ -116,16 +126,17 @@ svd, thinSVD, compactSVD, + compactSVDTol, singularValues, leftSV, rightSV, -- * Eigendecomposition - eig, eigSH, - eigenvalues, eigenvaluesSH, + eig, geig, eigSH, + eigenvalues, geigenvalues, eigenvaluesSH, geigSH, -- * QR - qr, rq, qrRaw, qrgr, + qr, thinQR, rq, thinRQ, qrRaw, qrgr, -- * Cholesky chol, mbChol, @@ -152,7 +163,7 @@ Seed, RandDist(..), randomVector, rand, randn, gaussianSample, uniformSample, -- * Misc - meanCov, rowOuters, pairwiseD2, unitary, peps, relativeError, magnit, + meanCov, rowOuters, pairwiseD2, normalize, peps, relativeError, magnit, haussholder, optimiseMult, udot, nullspaceSVD, orthSVD, ranksv, iC, sym, mTm, trustSym, unSym, -- * Auxiliary classes @@ -183,6 +194,9 @@ import Internal.Sparse((!#>)) import Internal.CG import Internal.Conversion +#if MIN_VERSION_base(4,11,0) +import Prelude hiding ((<>)) +#endif {- | dense matrix product diff --git a/src/Numeric/LinearAlgebra/Devel.hs b/src/Numeric/LinearAlgebra/Devel.hs --- a/src/Numeric/LinearAlgebra/Devel.hs +++ b/src/Numeric/LinearAlgebra/Devel.hs @@ -12,16 +12,9 @@ -------------------------------------------------------------------------------- module Numeric.LinearAlgebra.Devel( - -- * FFI helpers - -- | Sample usage, to upload a perspective matrix to a shader. - -- - -- @ glUniformMatrix4fv 0 1 (fromIntegral gl_TRUE) \`appMatrix\` perspective 0.01 100 (pi\/2) (4\/3) - -- @ - module Internal.Foreign, - -- * FFI tools -- | See @examples/devel@ in the repository. - + createVector, createMatrix, TransArray(..), MatrixOrder(..), orderOf, cmat, fmat, @@ -34,7 +27,7 @@ -- * ST -- | In-place manipulation inside the ST monad. -- See @examples/inplace.hs@ in the repository. - + -- ** Mutable Vectors STVector, newVector, thawVector, freezeVector, runSTVector, readVector, writeVector, modifyVector, liftSTVector, @@ -58,15 +51,14 @@ liftMatrix, liftMatrix2, liftMatrix2Auto, -- * Sparse representation - CSR(..), fromCSR, mkCSR, + CSR(..), fromCSR, mkCSR, impureCSR, GMatrix(..), -- * Misc - toByteString, fromByteString, showInternal + toByteString, fromByteString, showInternal, reorderVector ) where -import Internal.Foreign import Internal.Devel import Internal.ST import Internal.Vector diff --git a/src/Numeric/LinearAlgebra/HMatrix.hs b/src/Numeric/LinearAlgebra/HMatrix.hs --- a/src/Numeric/LinearAlgebra/HMatrix.hs +++ b/src/Numeric/LinearAlgebra/HMatrix.hs @@ -1,3 +1,4 @@ +{-# LANGUAGE CPP #-} -------------------------------------------------------------------------------- {- | Module : Numeric.LinearAlgebra.HMatrix @@ -19,12 +20,17 @@ import Numeric.LinearAlgebra import Internal.Util import Internal.Algorithms(cholSH, mbCholSH, eigSH', eigenvaluesSH', geigSH') +#if MIN_VERSION_base(4,11,0) +import Prelude hiding ((<>)) +#endif infixr 8 <·> (<·>) :: Numeric t => Vector t -> Vector t -> t (<·>) = dot +app :: Numeric t => Matrix t -> Vector t -> Vector t app m v = m #> v +mul :: Numeric t => Matrix t -> Matrix t -> Matrix t mul a b = a <> b diff --git a/src/Numeric/LinearAlgebra/Static.hs b/src/Numeric/LinearAlgebra/Static.hs --- a/src/Numeric/LinearAlgebra/Static.hs +++ b/src/Numeric/LinearAlgebra/Static.hs @@ -1,3 +1,4 @@ +{-# LANGUAGE CPP #-} {-# LANGUAGE DataKinds #-} {-# LANGUAGE KindSignatures #-} {-# LANGUAGE GeneralizedNewtypeDeriving #-} @@ -13,6 +14,8 @@ {-# LANGUAGE GADTs #-} {-# LANGUAGE TypeFamilies #-} +{-# OPTIONS_GHC -fno-warn-missing-signatures #-} +{-# OPTIONS_GHC -fno-warn-orphans #-} {- | Module : Numeric.LinearAlgebra.Static @@ -42,19 +45,31 @@ blockAt, matrix, -- * Complex - C, M, Her, her, 𝑖, + ℂ, C, M, Her, her, 𝑖, + toComplex, + fromComplex, + complex, + real, + imag, + sqMagnitude, + magnitude, -- * Products (<>),(#>),(<.>), -- * Linear Systems linSolve, (<\>), -- * Factorizations svd, withCompactSVD, svdTall, svdFlat, Eigen(..), - withNullspace, qr, chol, + withNullspace, withOrth, qr, chol, + -- * Norms + Normed(..), + -- * Random arrays + Seed, RandDist(..), + randomVector, rand, randn, gaussianSample, uniformSample, -- * Misc - mean, + mean, meanCov, Disp(..), Domain(..), - withVector, withMatrix, - toRows, toColumns, + withVector, withMatrix, exactLength, exactDims, + toRows, toColumns, withRows, withColumns, Sized(..), Diag(..), Sym, sym, mTm, unSym, (<·>) ) where @@ -65,18 +80,28 @@ row,col,vector,matrix,linspace,toRows,toColumns, (<\>),fromList,takeDiag,svd,eig,eigSH, eigenvalues,eigenvaluesSH,build, - qr,size,dot,chol,range,R,C,sym,mTm,unSym) + qr,size,dot,chol,range,R,C,sym,mTm,unSym, + randomVector,rand,randn,gaussianSample,uniformSample,meanCov, + toComplex, fromComplex, complex, real, magnitude + ) import qualified Numeric.LinearAlgebra as LA -import Data.Proxy(Proxy) +import qualified Numeric.LinearAlgebra.Devel as LA +import Data.Proxy(Proxy(..)) import Internal.Static import Control.Arrow((***)) +import Text.Printf +import Data.Type.Equality ((:~:)(Refl)) +import qualified Data.Bifunctor as BF (first) +#if MIN_VERSION_base(4,11,0) +import Prelude hiding ((<>)) +#endif ud1 :: R n -> Vector ℝ ud1 (R (Dim v)) = v infixl 4 & -(&) :: forall n . (KnownNat n, 1 <= n) +(&) :: forall n . KnownNat n => R n -> ℝ -> R (n+1) u & x = u # (konst x :: R 1) @@ -204,11 +229,11 @@ infixr 8 <·> -(<·>) :: R n -> R n -> ℝ +(<·>) :: KnownNat n => R n -> R n -> ℝ (<·>) = dotR infixr 8 <.> -(<.>) :: R n -> R n -> ℝ +(<.>) :: KnownNat n => R n -> R n -> ℝ (<.>) = dotR -------------------------------------------------------------------------------- @@ -218,21 +243,39 @@ takeDiag :: m -> d -instance forall n . (KnownNat n) => Diag (L n n) (R n) +instance KnownNat n => Diag (L n n) (R n) where - takeDiag m = mkR (LA.takeDiag (extract m)) + takeDiag x = mkR (LA.takeDiag (extract x)) -instance forall m n . (KnownNat m, KnownNat n, m <= n+1) => Diag (L m n) (R m) +instance KnownNat n => Diag (M n n) (C n) where - takeDiag m = mkR (LA.takeDiag (extract m)) + takeDiag x = mkC (LA.takeDiag (extract x)) +-------------------------------------------------------------------------------- -instance forall m n . (KnownNat m, KnownNat n, n <= m+1) => Diag (L m n) (R n) - where - takeDiag m = mkR (LA.takeDiag (extract m)) +toComplex :: KnownNat n => (R n, R n) -> C n +toComplex (r,i) = mkC $ LA.toComplex (ud1 r, ud1 i) +fromComplex :: KnownNat n => C n -> (R n, R n) +fromComplex (C (Dim v)) = let (r,i) = LA.fromComplex v in (mkR r, mkR i) + +complex :: KnownNat n => R n -> C n +complex r = mkC $ LA.toComplex (ud1 r, LA.konst 0 (size r)) + +real :: KnownNat n => C n -> R n +real = fst . fromComplex + +imag :: KnownNat n => C n -> R n +imag = snd . fromComplex + +sqMagnitude :: KnownNat n => C n -> R n +sqMagnitude c = let (r,i) = fromComplex c in r**2 + i**2 + +magnitude :: KnownNat n => C n -> R n +magnitude = sqrt . sqMagnitude + -------------------------------------------------------------------------------- linSolve :: (KnownNat m, KnownNat n) => L m m -> L m n -> Maybe (L m n) @@ -289,7 +332,21 @@ her m = Her $ (m + LA.tr m)/2 +instance (KnownNat n) => Disp (Sym n) + where + disp n (Sym x) = do + let a = extract x + let su = LA.dispf n a + printf "Sym %d" (cols a) >> putStr (dropWhile (/='\n') $ su) +instance (KnownNat n) => Disp (Her n) + where + disp n (Her x) = do + let a = extract x + let su = LA.dispcf n a + printf "Her %d" (cols a) >> putStr (dropWhile (/='\n') $ su) + + instance KnownNat n => Eigen (Sym n) (R n) (L n n) where eigenvalues (Sym (extract -> m)) = mkR . LA.eigenvaluesSH . LA.trustSym $ m @@ -319,6 +376,15 @@ Nothing -> error "static/dynamic mismatch" Just (SomeNat (_ :: Proxy k)) -> f (mkL a :: L n k) +withOrth + :: forall m n z . (KnownNat m, KnownNat n) + => L m n + -> (forall k. (KnownNat k) => L n k -> z) + -> z +withOrth (LA.orth . extract -> a) f = + case someNatVal $ fromIntegral $ cols a of + Nothing -> error "static/dynamic mismatch" + Just (SomeNat (_ :: Proxy k)) -> f (mkL a :: L n k) withCompactSVD :: forall m n z . (KnownNat m, KnownNat n) @@ -349,7 +415,7 @@ headTail :: (KnownNat n, 1<=n) => R n -> (ℝ, R (n-1)) -headTail = ((!0) . extract *** id) . split +headTail = ((! 0) . extract *** id) . split splitRows :: forall p m n . (KnownNat p, KnownNat m, KnownNat n, p<=m) => L m n -> (L p n, L (m-p) n) @@ -365,11 +431,31 @@ toRows :: forall m n . (KnownNat m, KnownNat n) => L m n -> [R n] toRows (LA.toRows . extract -> vs) = map mkR vs +withRows + :: forall n z . KnownNat n + => [R n] + -> (forall m . KnownNat m => L m n -> z) + -> z +withRows (LA.fromRows . map extract -> m) f = + case someNatVal $ fromIntegral $ LA.rows m of + Nothing -> error "static/dynamic mismatch" + Just (SomeNat (_ :: Proxy m)) -> f (mkL m :: L m n) toColumns :: forall m n . (KnownNat m, KnownNat n) => L m n -> [R m] toColumns (LA.toColumns . extract -> vs) = map mkR vs +withColumns + :: forall m z . KnownNat m + => [R m] + -> (forall n . KnownNat n => L m n -> z) + -> z +withColumns (LA.fromColumns . map extract -> m) f = + case someNatVal $ fromIntegral $ LA.cols m of + Nothing -> error "static/dynamic mismatch" + Just (SomeNat (_ :: Proxy n)) -> f (mkL m :: L m n) + + -------------------------------------------------------------------------------- build @@ -392,6 +478,15 @@ Nothing -> error "static/dynamic mismatch" Just (SomeNat (_ :: Proxy m)) -> f (mkR v :: R m) +-- | Useful for constraining two dependently typed vectors to match each +-- other in length when they are unknown at compile-time. +exactLength + :: forall n m . (KnownNat n, KnownNat m) + => R m + -> Maybe (R n) +exactLength v = do + Refl <- sameNat (Proxy :: Proxy n) (Proxy :: Proxy m) + return $ mkR (unwrap v) withMatrix :: forall z @@ -407,6 +502,64 @@ Just (SomeNat (_ :: Proxy n)) -> f (mkL a :: L m n) +-- | Useful for constraining two dependently typed matrices to match each +-- other in dimensions when they are unknown at compile-time. +exactDims + :: forall n m j k . (KnownNat n, KnownNat m, KnownNat j, KnownNat k) + => L m n + -> Maybe (L j k) +exactDims m = do + Refl <- sameNat (Proxy :: Proxy m) (Proxy :: Proxy j) + Refl <- sameNat (Proxy :: Proxy n) (Proxy :: Proxy k) + return $ mkL (unwrap m) + +randomVector + :: forall n . KnownNat n + => Seed + -> RandDist + -> R n +randomVector s d = mkR (LA.randomVector s d + (fromInteger (natVal (Proxy :: Proxy n))) + ) + +rand + :: forall m n . (KnownNat m, KnownNat n) + => IO (L m n) +rand = mkL <$> LA.rand (fromInteger (natVal (Proxy :: Proxy m))) + (fromInteger (natVal (Proxy :: Proxy n))) + +randn + :: forall m n . (KnownNat m, KnownNat n) + => IO (L m n) +randn = mkL <$> LA.randn (fromInteger (natVal (Proxy :: Proxy m))) + (fromInteger (natVal (Proxy :: Proxy n))) + +gaussianSample + :: forall m n . (KnownNat m, KnownNat n) + => Seed + -> R n + -> Sym n + -> L m n +gaussianSample s (extract -> mu) (Sym (extract -> sigma)) = + mkL $ LA.gaussianSample s (fromInteger (natVal (Proxy :: Proxy m))) + mu (LA.trustSym sigma) + +uniformSample + :: forall m n . (KnownNat m, KnownNat n) + => Seed + -> R n -- ^ minimums of each row + -> R n -- ^ maximums of each row + -> L m n +uniformSample s (extract -> mins) (extract -> maxs) = + mkL $ LA.uniformSample s (fromInteger (natVal (Proxy :: Proxy m))) + (zip (LA.toList mins) (LA.toList maxs)) + +meanCov + :: forall m n . (KnownNat m, KnownNat n, 1 <= m) + => L m n + -> (R n, Sym n) +meanCov (extract -> vs) = mkR *** (Sym . mkL . LA.unSym) $ LA.meanCov vs + -------------------------------------------------------------------------------- class Domain field vec mat | mat -> vec field, vec -> mat field, field -> mat vec @@ -416,6 +569,15 @@ dot :: forall n . (KnownNat n) => vec n -> vec n -> field cross :: vec 3 -> vec 3 -> vec 3 diagR :: forall m n k . (KnownNat m, KnownNat n, KnownNat k) => field -> vec k -> mat m n + dvmap :: forall n. KnownNat n => (field -> field) -> vec n -> vec n + dmmap :: forall n m. (KnownNat m, KnownNat n) => (field -> field) -> mat n m -> mat n m + outer :: forall n m. (KnownNat m, KnownNat n) => vec n -> vec m -> mat n m + zipWithVector :: forall n. KnownNat n => (field -> field -> field) -> vec n -> vec n -> vec n + det :: forall n. KnownNat n => mat n n -> field + invlndet :: forall n. KnownNat n => mat n n -> (mat n n, (field, field)) + expm :: forall n. KnownNat n => mat n n -> mat n n + sqrtm :: forall n. KnownNat n => mat n n -> mat n n + inv :: forall n. KnownNat n => mat n n -> mat n n instance Domain ℝ R L @@ -425,6 +587,15 @@ dot = dotR cross = crossR diagR = diagRectR + dvmap = mapR + dmmap = mapL + outer = outerR + zipWithVector = zipWithR + det = detL + invlndet = invlndetL + expm = expmL + sqrtm = sqrtmL + inv = invL instance Domain ℂ C M where @@ -433,6 +604,15 @@ dot = dotC cross = crossC diagR = diagRectC + dvmap = mapC + dmmap = mapM' + outer = outerC + zipWithVector = zipWithC + det = detM + invlndet = invlndetM + expm = expmM + sqrtm = sqrtmM + inv = invM -------------------------------------------------------------------------------- @@ -447,9 +627,9 @@ a' = subVector 0 n a b' = subVector 0 n b -mulR (isDiag -> Just (0,a,_)) (extract -> b) = mkL (asColumn a * takeRows (LA.size a) b) +-- mulR (isDiag -> Just (0,a,_)) (extract -> b) = mkL (asColumn a * takeRows (LA.size a) b) -mulR (extract -> a) (isDiag -> Just (0,b,_)) = mkL (takeColumns (LA.size b) a * asRow b) +-- mulR (extract -> a) (isDiag -> Just (0,b,_)) = mkL (takeColumns (LA.size b) a * asRow b) mulR a b = mkL (extract a LA.<> extract b) @@ -459,10 +639,8 @@ appR m v = mkR (extract m LA.#> extract v) -dotR :: R n -> R n -> ℝ -dotR (ud1 -> u) (ud1 -> v) - | singleV u || singleV v = sumElements (u * v) - | otherwise = udot u v +dotR :: KnownNat n => R n -> R n -> ℝ +dotR (extract -> u) (extract -> v) = LA.dot u v crossR :: R 3 -> R 3 -> R 3 @@ -472,6 +650,33 @@ z2 = x!2*y!0-x!0*y!2 z3 = x!0*y!1-x!1*y!0 +outerR :: (KnownNat m, KnownNat n) => R n -> R m -> L n m +outerR (extract -> x) (extract -> y) = mkL (LA.outer x y) + +mapR :: KnownNat n => (ℝ -> ℝ) -> R n -> R n +mapR f (unwrap -> v) = mkR (LA.cmap f v) + +zipWithR :: KnownNat n => (ℝ -> ℝ -> ℝ) -> R n -> R n -> R n +zipWithR f (extract -> x) (extract -> y) = mkR (LA.zipVectorWith f x y) + +mapL :: (KnownNat n, KnownNat m) => (ℝ -> ℝ) -> L n m -> L n m +mapL f = overMatL' (LA.cmap f) + +detL :: KnownNat n => Sq n -> ℝ +detL = LA.det . unwrap + +invlndetL :: KnownNat n => Sq n -> (L n n, (ℝ, ℝ)) +invlndetL = BF.first mkL . LA.invlndet . unwrap + +expmL :: KnownNat n => Sq n -> Sq n +expmL = overMatL' LA.expm + +sqrtmL :: KnownNat n => Sq n -> Sq n +sqrtmL = overMatL' LA.sqrtm + +invL :: KnownNat n => Sq n -> Sq n +invL = overMatL' LA.inv + -------------------------------------------------------------------------------- mulC :: forall m k n. (KnownNat m, KnownNat k, KnownNat n) => M m k -> M k n -> M m n @@ -485,9 +690,9 @@ a' = subVector 0 n a b' = subVector 0 n b -mulC (isDiagC -> Just (0,a,_)) (extract -> b) = mkM (asColumn a * takeRows (LA.size a) b) +-- mulC (isDiagC -> Just (0,a,_)) (extract -> b) = mkM (asColumn a * takeRows (LA.size a) b) -mulC (extract -> a) (isDiagC -> Just (0,b,_)) = mkM (takeColumns (LA.size b) a * asRow b) +-- mulC (extract -> a) (isDiagC -> Just (0,b,_)) = mkM (takeColumns (LA.size b) a * asRow b) mulC a b = mkM (extract a LA.<> extract b) @@ -498,9 +703,7 @@ dotC :: KnownNat n => C n -> C n -> ℂ -dotC (unwrap -> u) (unwrap -> v) - | singleV u || singleV v = sumElements (conj u * v) - | otherwise = u LA.<.> v +dotC (extract -> u) (extract -> v) = LA.dot u v crossC :: C 3 -> C 3 -> C 3 @@ -510,6 +713,33 @@ z2 = x!2*y!0-x!0*y!2 z3 = x!0*y!1-x!1*y!0 +outerC :: (KnownNat m, KnownNat n) => C n -> C m -> M n m +outerC (extract -> x) (extract -> y) = mkM (LA.outer x y) + +mapC :: KnownNat n => (ℂ -> ℂ) -> C n -> C n +mapC f (unwrap -> v) = mkC (LA.cmap f v) + +zipWithC :: KnownNat n => (ℂ -> ℂ -> ℂ) -> C n -> C n -> C n +zipWithC f (extract -> x) (extract -> y) = mkC (LA.zipVectorWith f x y) + +mapM' :: (KnownNat n, KnownNat m) => (ℂ -> ℂ) -> M n m -> M n m +mapM' f = overMatM' (LA.cmap f) + +detM :: KnownNat n => M n n -> ℂ +detM = LA.det . unwrap + +invlndetM :: KnownNat n => M n n -> (M n n, (ℂ, ℂ)) +invlndetM = BF.first mkM . LA.invlndet . unwrap + +expmM :: KnownNat n => M n n -> M n n +expmM = overMatM' LA.expm + +sqrtmM :: KnownNat n => M n n -> M n n +sqrtmM = overMatM' LA.sqrtm + +invM :: KnownNat n => M n n -> M n n +invM = overMatM' LA.inv + -------------------------------------------------------------------------------- diagRectR :: forall m n k . (KnownNat m, KnownNat n, KnownNat k) => ℝ -> R k -> L m n @@ -616,3 +846,67 @@ where checkT _ = test +-------------------------------------------------------------------------------- + +instance KnownNat n => Normed (R n) + where + norm_0 v = norm_0 (extract v) + norm_1 v = norm_1 (extract v) + norm_2 v = norm_2 (extract v) + norm_Inf v = norm_Inf (extract v) + +instance (KnownNat m, KnownNat n) => Normed (L m n) + where + norm_0 m = norm_0 (extract m) + norm_1 m = norm_1 (extract m) + norm_2 m = norm_2 (extract m) + norm_Inf m = norm_Inf (extract m) + +mkSym f = Sym . f . unSym +mkSym2 f x y = Sym (f (unSym x) (unSym y)) + +instance KnownNat n => Num (Sym n) + where + (+) = mkSym2 (+) + (*) = mkSym2 (*) + (-) = mkSym2 (-) + abs = mkSym abs + signum = mkSym signum + negate = mkSym negate + fromInteger = Sym . fromInteger + +instance KnownNat n => Fractional (Sym n) + where + fromRational = Sym . fromRational + (/) = mkSym2 (/) + +instance KnownNat n => Floating (Sym n) + where + sin = mkSym sin + cos = mkSym cos + tan = mkSym tan + asin = mkSym asin + acos = mkSym acos + atan = mkSym atan + sinh = mkSym sinh + cosh = mkSym cosh + tanh = mkSym tanh + asinh = mkSym asinh + acosh = mkSym acosh + atanh = mkSym atanh + exp = mkSym exp + log = mkSym log + sqrt = mkSym sqrt + (**) = mkSym2 (**) + pi = Sym pi + +instance KnownNat n => Additive (Sym n) where + add = (+) + +instance KnownNat n => Transposable (Sym n) (Sym n) where + tr = id + tr' = id + +instance KnownNat n => Transposable (Her n) (Her n) where + tr = id + tr' (Her m) = Her (tr' m) diff --git a/src/Numeric/Matrix.hs b/src/Numeric/Matrix.hs --- a/src/Numeric/Matrix.hs +++ b/src/Numeric/Matrix.hs @@ -4,6 +4,8 @@ {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} +{-# OPTIONS_GHC -fno-warn-orphans #-} + ----------------------------------------------------------------------------- -- | -- Module : Numeric.Matrix @@ -32,8 +34,12 @@ import Internal.Numeric import qualified Data.Monoid as M import Data.List(partition) +import qualified Data.Foldable as F +import qualified Data.Semigroup as S import Internal.Chain +import Foreign.Storable(Storable) + ------------------------------------------------------------------- instance Container Matrix a => Eq (Matrix a) where @@ -77,18 +83,31 @@ -------------------------------------------------------------------------------- +isScalar :: Matrix t -> Bool isScalar m = rows m == 1 && cols m == 1 +adaptScalarM :: (Foreign.Storable.Storable t1, Foreign.Storable.Storable t2) + => (t1 -> Matrix t2 -> t) + -> (Matrix t1 -> Matrix t2 -> t) + -> (Matrix t1 -> t2 -> t) + -> Matrix t1 + -> Matrix t2 + -> t adaptScalarM f1 f2 f3 x y | isScalar x = f1 (x @@>(0,0) ) y | isScalar y = f3 x (y @@>(0,0) ) | otherwise = f2 x y +instance (Container Vector t, Eq t, Num (Vector t), Product t) => S.Semigroup (Matrix t) + where + (<>) = mappend + sconcat = mconcat . F.toList + instance (Container Vector t, Eq t, Num (Vector t), Product t) => M.Monoid (Matrix t) where mempty = 1 mappend = adaptScalarM scale mXm (flip scale) - + mconcat xs = work (partition isScalar xs) where work (ss,[]) = product ss @@ -98,4 +117,3 @@ | otherwise = scale x00 m where x00 = x @@> (0,0) - diff --git a/src/Numeric/Vector.hs b/src/Numeric/Vector.hs --- a/src/Numeric/Vector.hs +++ b/src/Numeric/Vector.hs @@ -3,6 +3,9 @@ {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} + +{-# OPTIONS_GHC -fno-warn-orphans #-} + ----------------------------------------------------------------------------- -- | -- Module : Numeric.Vector @@ -14,7 +17,7 @@ -- -- Provides instances of standard classes 'Show', 'Read', 'Eq', -- 'Num', 'Fractional', and 'Floating' for 'Vector'. --- +-- ----------------------------------------------------------------------------- module Numeric.Vector () where @@ -23,9 +26,17 @@ import Internal.Vector import Internal.Numeric import Internal.Conversion +import Foreign.Storable(Storable) ------------------------------------------------------------------- +adaptScalar :: (Foreign.Storable.Storable t1, Foreign.Storable.Storable t2) + => (t1 -> Vector t2 -> t) + -> (Vector t1 -> Vector t2 -> t) + -> (Vector t1 -> t2 -> t) + -> Vector t1 + -> Vector t2 + -> t adaptScalar f1 f2 f3 x y | dim x == 1 = f1 (x@>0) y | dim y == 1 = f3 x (y@>0) @@ -172,4 +183,3 @@ sqrt = vectorMapQ Sqrt (**) = adaptScalar (vectorMapValQ PowSV) (vectorZipQ Pow) (flip (vectorMapValQ PowVS)) pi = fromList [pi] -