diff --git a/Biobase/BLAST/Import.hs b/Biobase/BLAST/Import.hs
--- a/Biobase/BLAST/Import.hs
+++ b/Biobase/BLAST/Import.hs
@@ -36,7 +36,7 @@
        bs <- B.readFile filePath
        let json = parseJSONBlastCmd bs
        return json
-     else fail "# JSON2 blast file \"%s\" does not exist\n" filePath
+     else error "# JSON2 blast file \"%s\" does not exist\n" filePath
 
 parseJSONBlastCmd :: B.ByteString -> Either String BlastCmdJSON2
 parseJSONBlastCmd bs = A.eitherDecode bs :: Either String BlastCmdJSON2
@@ -51,7 +51,7 @@
   blastFileExists <- doesFileExist filePath
   if blastFileExists
      then parseTabularBlasts <$> B.readFile filePath
-     else fail "# tabular blast file \"%s\" does not exist\n" filePath
+     else error "# tabular blast file \"%s\" does not exist\n" filePath
 
 -- | reads and parses tabular HTTP Blast result from provided filePath
 blastHTTPFromFile :: String -> IO [BlastTabularResult]
@@ -60,7 +60,7 @@
   blastFileExists <- doesFileExist filePath
   if blastFileExists
       then parseTabularHTTPBlasts <$> B.readFile filePath
-      else fail "# tabular blast file \"%s\" does not exist\n" filePath
+      else error "# tabular blast file \"%s\" does not exist\n" filePath
 
 -- | Read a lazy bytestring and stream out a lsit of @BlastTabularResult@'s.
 -- In case, there is a parse error "late" in the file, we might have
diff --git a/Biobase/BLAST/Types.hs b/Biobase/BLAST/Types.hs
--- a/Biobase/BLAST/Types.hs
+++ b/Biobase/BLAST/Types.hs
@@ -26,7 +26,8 @@
 import Data.Aeson.Types
 import qualified Data.HashMap.Strict as HM
 import qualified Data.Sequence as DS
-import Control.Lens
+import Control.Lens(makeLenses)
+import Data.HashMap.Strict (elems)
 
 -- | Turn all keys in a JSON object to lowercase.
 jsonLower :: Value -> Value
@@ -204,15 +205,37 @@
 data BlastProgram = BlastX | BlastP | BlastN
   deriving (Show, Eq)
 
+makeLenses ''BlastTabularResult
+makeLenses ''BlastTabularHit
+makeLenses ''SearchTarget
+deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''SearchTarget
+makeLenses ''BlastProgram
+deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''BlastProgram
+makeLenses ''SearchStat
+deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''SearchStat
+makeLenses ''HitDescription
+deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''HitDescription
+makeLenses ''Hit
+deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''Hit
+makeLenses ''Hsp
+makeLenses ''Search
+deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''Search
+makeLenses ''BlastJSONResult
+deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''BlastJSONResult
+makeLenses ''Params
+deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''Params
+makeLenses ''BlastReport
+deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''BlastReport
+makeLenses ''BlastOutput2
+deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''BlastOutput2
 makeLenses ''BlastCmdJSON2
 --deriveJSON defaultOptions{fieldLabelModifier = (map toLower) . drop 1} ''BlastJSON2
 instance FromJSON BlastCmdJSON2 where
-  parseJSON (Object v) =
-    BlastCmdJSON2 <$> (v .: "BlastOutput2")
+  parseJSON (Object v) = BlastCmdJSON2 <$> (v .: "BlastOutput2")
   parseJSON _ = mzero
 instance ToJSON BlastCmdJSON2 where
   toJSON (BlastCmdJSON2 _blastoutput2) =
-        object [ "BlastOutput2"  Data.Aeson.Types..= _blastoutput2 ]
+        object [ "BlastOutput2" .= _blastoutput2 ]
 
 makeLenses ''BlastJSON2
 --deriveJSON defaultOptions{fieldLabelModifier = (map toLower) . drop 1} ''BlastJSON2
@@ -221,29 +244,4 @@
   parseJSON _ = mzero
 
 instance ToJSON BlastJSON2 where
-  toJSON (BlastJSON2 _blastoutput2) = object [ "BlastOutput2"  Data.Aeson.Types..= _blastoutput2 ]
---deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''BlastJSON2
-makeLenses ''BlastOutput2
-deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''BlastOutput2
-makeLenses ''BlastReport
-deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''BlastReport
-makeLenses ''Params
-deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''Params
-makeLenses ''BlastJSONResult
-deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''BlastJSONResult
-makeLenses ''Search
-deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''Search
-makeLenses ''Hit
-deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''Hit
-makeLenses ''Hsp
---deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''Hsp
-makeLenses ''HitDescription
-deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''HitDescription
-makeLenses ''SearchStat
-deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''SearchStat
-makeLenses ''BlastTabularResult
-makeLenses ''BlastTabularHit
-makeLenses ''SearchTarget
-deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''SearchTarget
-makeLenses ''BlastProgram
-deriveJSON defaultOptions{fieldLabelModifier = drop 1} ''BlastProgram
+  toJSON (BlastJSON2 _blastoutput2) = object [ "BlastOutput2"  .= _blastoutput2 ]
diff --git a/Biobase/SubstMatrix.hs b/Biobase/SubstMatrix.hs
--- a/Biobase/SubstMatrix.hs
+++ b/Biobase/SubstMatrix.hs
@@ -10,7 +10,9 @@
 import           Data.List (maximumBy,find)
 import           Data.Serialize (Serialize)
 import           Data.Vector.Unboxed.Deriving
+import           Debug.Trace (traceShow)
 import           GHC.Generics (Generic)
+import           GHC.Real(Ratio(..))
 import           Numeric.Log
 import qualified Data.Map.Strict as M
 import qualified Data.Vector.Unboxed as VU
@@ -36,6 +38,7 @@
 
 import           Biobase.SubstMatrix.Embedded
 import           Biobase.SubstMatrix.Import
+import           Biobase.SubstMatrix.Statistics
 import           Biobase.SubstMatrix.Types
 
 
@@ -46,28 +49,32 @@
 -- The resulting @AA@ are tagged with the name type from the @DNA n@.
 --
 -- TODO Definitely use the correct upper bound constants here!
+--
+-- TODO the amino-acid range produces wrong reads from @m@. We should have this in ExceptT to make
+-- sure we do not read from undefined memory.
 
 mkANuc3SubstMat
   ∷ TranslationTable (Letter DNA n) (Letter AA n)
-  → AASubstMat t (DiscLogOdds k) n
+  → AASubstMat t (DiscLogOdds k) n n
   → ANuc3SubstMat t (Letter AA n, (DiscLogOdds k)) n n
-mkANuc3SubstMat tbl (AASubstMat m)
+mkANuc3SubstMat tbl (AASubstMat m l)
   = ANuc3SubstMat
   $ fromAssocs (ZZ:..LtLetter AA.Undef:..LtLetter DNA.N:..LtLetter DNA.N:..LtLetter DNA.N) (AA.Undef, DiscLogOdds . Discretized $ -999)
     [ ( (Z:.a:.u:.v:.w)
-      , (t, m!(Z:.a:.t))
+      , (t, x)
       )
     | a <- VU.toList aaRange
     , u <- [DNA.A .. DNA.N], v <- [DNA.A .. DNA.N], w <- [DNA.A .. DNA.N]
     , let b = Codon u v w
     , let t = translate tbl b
+    , x <- maybe [] (:[]) $ m!?(Z:.a:.t)
     ]
 
 -- | This function does the following:
 -- 1. check if @fname@ is a file, and if so try to load it.
 -- 2. if not, check if @fname@ happens to be the name of one of the known @PAM/BLOSUM@ tables.
 
-fromFileOrCached ∷ (MonadIO m, MonadError String m) ⇒ FilePath → m (AASubstMat t (DiscLogOdds Unknown) a)
+fromFileOrCached ∷ (MonadIO m, MonadError String m) ⇒ FilePath → m (AASubstMat t (DiscLogOdds (1 :% 1)) a b)
 fromFileOrCached fname = do
   dfe ← liftIO $ doesFileExist fname
   if | fname == "list" → do
@@ -79,13 +86,15 @@
 
 -- | Turn log-odds into log-probabilities. Normalizes over the whole set of
 -- values in the matrix.
+--
+-- TODO check if lambda should indeed be 1.0
 
 mkProbabilityMatrix
-  ∷ Double
-  → AASubstMat t (DiscLogOdds k) n
-  → AASubstMat t (Log (Probability NotNormalized Double)) n
-mkProbabilityMatrix invScale (AASubstMat dlo) = AASubstMat $ PA.map (/nrm) $ dbl
-  where dbl = PA.map (\(DiscLogOdds (Discretized k)) → stateLogProbability (negate invScale) $ fromIntegral @Int @Double k) dlo
+  :: Double
+  -> AASubstMat t (DiscLogOdds k) n m
+  -> AASubstMat t (Log (Probability NotNormalized Double)) n m
+mkProbabilityMatrix invScale (AASubstMat dlo l) = AASubstMat (mapArray (/nrm) $ dbl) 1.0
+  where dbl = mapArray (\(DiscLogOdds (Discretized k)) → stateLogProbability (negate invScale) $ fromIntegral @Int @Double k) dlo
         nrm = maximum . Prelude.map snd $ PA.assocs dbl
 
 
diff --git a/Biobase/SubstMatrix/Embedded.hs b/Biobase/SubstMatrix/Embedded.hs
--- a/Biobase/SubstMatrix/Embedded.hs
+++ b/Biobase/SubstMatrix/Embedded.hs
@@ -5,6 +5,7 @@
 import Data.ByteString (ByteString)
 import Data.FileEmbed
 import Control.Arrow (second)
+import GHC.Real(Ratio(..))
 
 import Numeric.Discretized
 import Statistics.Odds
@@ -15,9 +16,9 @@
 
 
 embeddedPamBlosumFiles ∷ [(FilePath,ByteString)]
-embeddedPamBlosumFiles = $(embedDir "sources/PamBlosum")
+embeddedPamBlosumFiles = $(makeRelativeToProject "sources/PamBlosum" >>= embedDir)
 
-embeddedPamBlosum ∷ [(FilePath,AASubstMat t (DiscLogOdds Unknown) a)]
+embeddedPamBlosum ∷ [(FilePath,AASubstMat t (DiscLogOdds (1:%1)) a b)]
 embeddedPamBlosum = either error id . runExcept
                   . mapM (\(k,v) → fromByteString v >>= \mv → return (k,mv))
                   $ embeddedPamBlosumFiles
diff --git a/Biobase/SubstMatrix/Import.hs b/Biobase/SubstMatrix/Import.hs
--- a/Biobase/SubstMatrix/Import.hs
+++ b/Biobase/SubstMatrix/Import.hs
@@ -20,6 +20,7 @@
 import           Statistics.Odds
 
 import           Biobase.SubstMatrix.Types
+import           Biobase.SubstMatrix.Statistics
 
 
 
@@ -27,19 +28,31 @@
 --
 -- TODO the parser is fragile, since it uses @read@. This should be fixed.
 
-fromByteString ∷ (MonadError String m) ⇒ ByteString → m (AASubstMat t (DiscLogOdds k) a)
-fromByteString bs = do
-  let (x:xs) = dropWhile (("#"==).take 1) . lines $ unpack bs
-  let cs = map head . words $ x -- should give us the characters encoding an amino acid
-  let ss = map (map (DiscLogOdds . Discretized) . map read . drop 1 . words) $ xs
-  let xs = [ ((Z:.charAA k1:.charAA k2),z)
+fromByteString
+  :: ( MonadError String m
+     , Real (Discretized k)
+     )
+  => ByteString
+  -> m (AASubstMat t (DiscLogOdds k) a b)
+fromByteString bstring = do
+  let (b:bs) = dropWhile (("#"==).take 1) . lines $ unpack bstring
+      cs = map head . words $ b -- should give us the characters encoding an amino acid
+      ss = map (map (DiscLogOdds . Discretized) . map read . drop 1 . words) $ bs
+      xs = [ ((Z:.charAA k1:.charAA k2),z)
            | (k1,s) <- zip cs ss
            , (k2,z) <- zip cs s
            ]
-  return . AASubstMat $ fromAssocs (ZZ:..LtLetter AA.Z:..LtLetter AA.Z) (DiscLogOdds . Discretized $ -999) xs
+      as = fromAssocs (ZZ:..LtLetter AA.Z:..LtLetter AA.Z) (DiscLogOdds . Discretized $ -999) xs
+      mat = AASubstMat as (estimateLambda mat)
+  return mat
 
 -- | Import substitution matrix from file.
 
-fromFile ∷ (MonadIO m, MonadError String m) ⇒ FilePath → m (AASubstMat t (DiscLogOdds k) a)
+fromFile
+  :: ( MonadIO m, MonadError String m
+     , Real (Discretized k)
+     )
+  => FilePath
+  -> m (AASubstMat t (DiscLogOdds k) a b)
 fromFile fname = liftIO (BS.readFile fname) >>= fromByteString
 
diff --git a/Biobase/SubstMatrix/Statistics.hs b/Biobase/SubstMatrix/Statistics.hs
new file mode 100644
--- /dev/null
+++ b/Biobase/SubstMatrix/Statistics.hs
@@ -0,0 +1,41 @@
+
+-- | This module provides statistics needed for substitution matrices. It is a
+-- very modest attempt to replicate some of the Blast statistics.
+
+module Biobase.SubstMatrix.Statistics where
+
+import Data.Vector.Unboxed (Unbox)
+import Data.Vector.Fusion.Util
+import Data.Vector.Fusion.Stream.Monadic as SM
+import Debug.Trace
+
+import Data.PrimitiveArray as PA
+import           Biobase.Primary.Letter
+
+import Biobase.SubstMatrix.Types
+
+
+
+-- | estimate Blast lambda.
+--
+-- TODO use ExceptT
+
+estimateLambda
+  :: (Unbox s, Num s, Real s)
+  => AASubstMat t s a b -> Double
+{-# Inlinable estimateLambda #-}
+estimateLambda (AASubstMat mat _) = go 1000 1 2 0 where
+  go count lambda high low
+    | count <= 0 = error "no convergence?!"
+    | (high-low) <= 0.001 = lambda
+    | s >  1              = go (count-1) ((lambda+low)/2)  lambda low
+    | s <= 1              = go (count-1) ((lambda+high)/2) high   lambda
+    where
+      -- get the rows and columns, needed to get the probs for each row/column right.
+      (ZZ:..r':..c') = PA.upperBound mat
+      r = fromRational $ toRational $ size r'
+      c = fromRational $ toRational $ size c'
+      -- sum of all scores
+      s = unId . SM.foldl' (+) 0 $ SM.map eachElem $ PA.assocsS mat
+      eachElem (Z:.i:.j, z) = (1/r) * (1/c) * exp (lambda * (fromRational $ toRational z))
+
diff --git a/Biobase/SubstMatrix/Types.hs b/Biobase/SubstMatrix/Types.hs
--- a/Biobase/SubstMatrix/Types.hs
+++ b/Biobase/SubstMatrix/Types.hs
@@ -27,7 +27,10 @@
 
 -- An amino-acid substitution matrix. Tagged with the type of scoring used.
 
-newtype AASubstMat t s a = AASubstMat { _aaSubstMat :: Unboxed (Z:.Letter AA a:.Letter AA a) s }
+data AASubstMat t s a b = AASubstMat
+  { _aaSubstMat     :: !(Unboxed (Z:.Letter AA a:.Letter AA b) s)
+  , _aaSubstLambda  :: Double
+  }
   deriving (Generic,Eq,Read,Show)
 makeLenses ''AASubstMat
 
@@ -40,11 +43,11 @@
 
 -- | @PAM@ matrices are similarity matrices.
 
-type SubstPAM = AASubstMat Similarity (DiscLogOdds Unknown)
+type SubstPAM = AASubstMat Similarity (DiscLogOdds (RTyId 1))
 
 -- | @BLOSUM@ matrices are distance matrices.
 
-type SubstBLOSUM = AASubstMat Distance (DiscLogOdds Unknown)
+type SubstBLOSUM = AASubstMat Distance (DiscLogOdds (RTyId 1))
 
 -- | Substitution matrix from amino acids to nucleotide triplets.
 
diff --git a/BiobaseBlast.cabal b/BiobaseBlast.cabal
--- a/BiobaseBlast.cabal
+++ b/BiobaseBlast.cabal
@@ -1,5 +1,5 @@
 name:           BiobaseBlast
-version:        0.3.1.0
+version:        0.3.3.0
 author:         Christian Hoener zu Siederdissen, Florian Eggenhofer
 maintainer:     choener@bioinf.uni-leipzig.de
 homepage:       https://github.com/choener/BiobaseBlast
@@ -11,7 +11,7 @@
 build-type:     Simple
 stability:      experimental
 cabal-version:  >= 1.10.0
-tested-with:    GHC == 8.4.4
+tested-with:    GHC == 8.8, GHC == 8.10, GHC == 9.0
 synopsis:       BLAST-related tools
 description:
                 This library contains BLAST-related functionality:
@@ -151,10 +151,10 @@
                , vector-th-unbox  >= 0.2
                --
                , BiobaseENA       == 0.0.0.*
-               , BiobaseTypes     == 0.2.0.*
-               , BiobaseXNA       == 0.11.0.*
-               , PrimitiveArray   == 0.9.1.*
-               , SciBaseTypes     == 0.1.0.*
+               , BiobaseTypes     == 0.2.1.*
+               , BiobaseXNA       == 0.11.1.*
+               , PrimitiveArray   == 0.10.1.*
+               , SciBaseTypes     == 0.1.1.*
 
   default-language:
     Haskell2010
@@ -178,6 +178,7 @@
     Biobase.SubstMatrix.Embedded
     Biobase.SubstMatrix.Hints
     Biobase.SubstMatrix.Import
+    Biobase.SubstMatrix.Statistics
     Biobase.SubstMatrix.Types
 
   ghc-options:
diff --git a/README.md b/README.md
--- a/README.md
+++ b/README.md
@@ -1,6 +1,5 @@
-[![Build Status](https://travis-ci.org/choener/BiobaseBlast.svg?branch=master)](https://travis-ci.org/choener/BiobaseBlast)
+# BiobaseBlast [![Hackage](https://img.shields.io/hackage/v/BiobaseBlast.svg)](https://hackage.haskell.org/package/BiobaseBlast) ![github action: CI](https://github.com/choener/BiobaseBlast/actions/workflows/ci.yml/badge.svg)
 
-# BiobaseBlast
 
 This library contains BLAST-related functionality.
 
diff --git a/changelog.md b/changelog.md
--- a/changelog.md
+++ b/changelog.md
@@ -1,3 +1,10 @@
+0.3.3.0
+-------
+
+- Compatibility with GHC 9
+- Switched testing to github actions
+
+
 0.3.1.0
 -------