diff options
Diffstat (limited to 'packages')
-rw-r--r-- | packages/base/CHANGELOG | 26 | ||||
-rw-r--r-- | packages/base/hmatrix.cabal | 4 | ||||
-rw-r--r-- | packages/base/src/Internal/Algorithms.hs | 89 | ||||
-rw-r--r-- | packages/base/src/Internal/Modular.hs | 2 | ||||
-rw-r--r-- | packages/base/src/Internal/Util.hs | 2 | ||||
-rw-r--r-- | packages/base/src/Numeric/LinearAlgebra.hs | 21 | ||||
-rw-r--r-- | packages/base/src/Numeric/LinearAlgebra/Static.hs | 2 | ||||
-rw-r--r-- | packages/tests/src/Numeric/LinearAlgebra/Tests.hs | 6 | ||||
-rw-r--r-- | packages/tests/src/Numeric/LinearAlgebra/Tests/Instances.hs | 13 | ||||
-rw-r--r-- | packages/tests/src/Numeric/LinearAlgebra/Tests/Properties.hs | 2 |
10 files changed, 95 insertions, 72 deletions
diff --git a/packages/base/CHANGELOG b/packages/base/CHANGELOG index 0336a28..581d2ac 100644 --- a/packages/base/CHANGELOG +++ b/packages/base/CHANGELOG | |||
@@ -1,24 +1,32 @@ | |||
1 | 0.17.0.0 | 1 | 0.17.0.0 |
2 | -------- | 2 | -------- |
3 | 3 | ||
4 | * improved matrix extraction (??) and rectangular matrix slices without data copy | 4 | * eigSH, chol, and other functions that work with Hermitian or symmetric matrices |
5 | now take a special "Herm" argument that can be created by means of "sym" | ||
6 | or "mTm". The unchecked versions of those functions have been removed and we | ||
7 | use "trustSym" to create the Herm type when the matrix is known to be Hermitian/symmetric. | ||
8 | |||
9 | * Improved matrix extraction (??) and rectangular matrix slices without data copy | ||
10 | |||
11 | * Basic support of Int32 and Int64 elements | ||
5 | 12 | ||
6 | * basic support of Int32 and Int64 elements | ||
7 | |||
8 | * remap, more general cond, sortIndex | 13 | * remap, more general cond, sortIndex |
9 | 14 | ||
10 | * experimental support of type safe modular arithmetic, including linear | 15 | * Experimental support of type safe modular arithmetic, including linear |
11 | systems and lu factorization | 16 | system solver and LU factorization |
12 | 17 | ||
13 | * elementary row operations and inplace matrix slice products in the ST monad | 18 | * Elementary row operations and inplace matrix slice products in the ST monad |
14 | 19 | ||
15 | * Improved development tools. | 20 | * Improved development tools. |
16 | 21 | ||
17 | * old compatibility modules removed, simpler organization of internal modules | 22 | * Old compatibility modules removed, simpler organization of internal modules |
18 | 23 | ||
19 | * unitary, pairwiseD2, tr' | 24 | * unitary, pairwiseD2, tr' |
20 | 25 | ||
21 | * ldlPacked, ldlSolve | 26 | * ldlPacked, ldlSolve for indefinite symmetric systems (apparently not faster |
27 | than the general solver based on the LU) | ||
28 | |||
29 | * LU, LDL, and QR types for these compact decompositions. | ||
22 | 30 | ||
23 | 0.16.1.0 | 31 | 0.16.1.0 |
24 | -------- | 32 | -------- |
diff --git a/packages/base/hmatrix.cabal b/packages/base/hmatrix.cabal index 93ca3d7..e248886 100644 --- a/packages/base/hmatrix.cabal +++ b/packages/base/hmatrix.cabal | |||
@@ -9,9 +9,9 @@ Homepage: https://github.com/albertoruiz/hmatrix | |||
9 | Synopsis: Numeric Linear Algebra | 9 | Synopsis: Numeric Linear Algebra |
10 | Description: Linear systems, matrix decompositions, and other numerical computations based on BLAS and LAPACK. | 10 | Description: Linear systems, matrix decompositions, and other numerical computations based on BLAS and LAPACK. |
11 | . | 11 | . |
12 | The standard interface is provided by the module "Numeric.LinearAlgebra". | 12 | Standard interface: "Numeric.LinearAlgebra". |
13 | . | 13 | . |
14 | A safer interface with statically checked dimensions is provided by "Numeric.LinearAlgebra.Static". | 14 | Safer interface with statically checked dimensions: "Numeric.LinearAlgebra.Static". |
15 | . | 15 | . |
16 | Code examples: <http://dis.um.es/~alberto/hmatrix/hmatrix.html> | 16 | Code examples: <http://dis.um.es/~alberto/hmatrix/hmatrix.html> |
17 | 17 | ||
diff --git a/packages/base/src/Internal/Algorithms.hs b/packages/base/src/Internal/Algorithms.hs index d2f17f4..c4f1a60 100644 --- a/packages/base/src/Internal/Algorithms.hs +++ b/packages/base/src/Internal/Algorithms.hs | |||
@@ -4,12 +4,6 @@ | |||
4 | {-# LANGUAGE UndecidableInstances #-} | 4 | {-# LANGUAGE UndecidableInstances #-} |
5 | {-# LANGUAGE TypeFamilies #-} | 5 | {-# LANGUAGE TypeFamilies #-} |
6 | 6 | ||
7 | {-# LANGUAGE FlexibleContexts, FlexibleInstances #-} | ||
8 | {-# LANGUAGE CPP #-} | ||
9 | {-# LANGUAGE MultiParamTypeClasses #-} | ||
10 | {-# LANGUAGE UndecidableInstances #-} | ||
11 | {-# LANGUAGE TypeFamilies #-} | ||
12 | |||
13 | ----------------------------------------------------------------------------- | 7 | ----------------------------------------------------------------------------- |
14 | {- | | 8 | {- | |
15 | Module : Internal.Algorithms | 9 | Module : Internal.Algorithms |
@@ -376,8 +370,8 @@ ldlPackedSH x = {-# SCC "ldlPacked" #-} LDL m p | |||
376 | (m,p) = ldlPacked' x | 370 | (m,p) = ldlPacked' x |
377 | 371 | ||
378 | -- | Obtains the LDL decomposition of a matrix in a compact data structure suitable for 'ldlSolve'. | 372 | -- | Obtains the LDL decomposition of a matrix in a compact data structure suitable for 'ldlSolve'. |
379 | ldlPacked :: Field t => Her t -> LDL t | 373 | ldlPacked :: Field t => Herm t -> LDL t |
380 | ldlPacked (Her m) = ldlPackedSH m | 374 | ldlPacked (Herm m) = ldlPackedSH m |
381 | 375 | ||
382 | -- | Solution of a linear system (for several right hand sides) from a precomputed LDL factorization obtained by 'ldlPacked'. | 376 | -- | Solution of a linear system (for several right hand sides) from a precomputed LDL factorization obtained by 'ldlPacked'. |
383 | -- | 377 | -- |
@@ -461,26 +455,39 @@ fromList [11.344814282762075,0.17091518882717918,-0.5157294715892575] | |||
461 | 3.000 5.000 6.000 | 455 | 3.000 5.000 6.000 |
462 | 456 | ||
463 | -} | 457 | -} |
464 | eigSH :: Field t => Her t -> (Vector Double, Matrix t) | 458 | eigSH :: Field t => Herm t -> (Vector Double, Matrix t) |
465 | eigSH (Her m) = eigSH' m | 459 | eigSH (Herm m) = eigSH' m |
466 | 460 | ||
467 | -- | Eigenvalues (in descending order) of a complex hermitian or real symmetric matrix. | 461 | -- | Eigenvalues (in descending order) of a complex hermitian or real symmetric matrix. |
468 | eigenvaluesSH :: Field t => Her t -> Vector Double | 462 | eigenvaluesSH :: Field t => Herm t -> Vector Double |
469 | eigenvaluesSH (Her m) = eigenvaluesSH' m | 463 | eigenvaluesSH (Herm m) = eigenvaluesSH' m |
470 | 464 | ||
471 | -------------------------------------------------------------- | 465 | -------------------------------------------------------------- |
472 | 466 | ||
467 | -- | QR decomposition of a matrix in compact form. (The orthogonal matrix is not explicitly formed.) | ||
468 | data QR t = QR (Matrix t) (Vector t) | ||
469 | |||
470 | instance (NFData t, Numeric t) => NFData (QR t) | ||
471 | where | ||
472 | rnf (QR m _) = rnf m | ||
473 | |||
474 | |||
473 | -- | QR factorization. | 475 | -- | QR factorization. |
474 | -- | 476 | -- |
475 | -- If @(q,r) = qr m@ then @m == q \<> r@, where q is unitary and r is upper triangular. | 477 | -- If @(q,r) = qr m@ then @m == q \<> r@, where q is unitary and r is upper triangular. |
476 | qr :: Field t => Matrix t -> (Matrix t, Matrix t) | 478 | qr :: Field t => Matrix t -> (Matrix t, Matrix t) |
477 | qr = {-# SCC "qr" #-} unpackQR . qr' | 479 | qr = {-# SCC "qr" #-} unpackQR . qr' |
478 | 480 | ||
479 | qrRaw m = qr' m | 481 | -- | Compute the QR decomposition of a matrix in compact form. |
482 | qrRaw :: Field t => Matrix t -> QR t | ||
483 | qrRaw m = QR x v | ||
484 | where | ||
485 | (x,v) = qr' m | ||
480 | 486 | ||
481 | {- | generate a matrix with k orthogonal columns from the output of qrRaw | 487 | -- | generate a matrix with k orthogonal columns from the compact QR decomposition obtained by 'qrRaw'. |
482 | -} | 488 | -- |
483 | qrgr n (a,t) | 489 | qrgr :: Field t => Int -> QR t -> Matrix t |
490 | qrgr n (QR a t) | ||
484 | | dim t > min (cols a) (rows a) || n < 0 || n > dim t = error "qrgr expects k <= min(rows,cols)" | 491 | | dim t > min (cols a) (rows a) || n < 0 || n > dim t = error "qrgr expects k <= min(rows,cols)" |
485 | | otherwise = qrgr' n (a,t) | 492 | | otherwise = qrgr' n (a,t) |
486 | 493 | ||
@@ -525,12 +532,12 @@ cholSH = cholSH' | |||
525 | -- | Cholesky factorization of a positive definite hermitian or symmetric matrix. | 532 | -- | Cholesky factorization of a positive definite hermitian or symmetric matrix. |
526 | -- | 533 | -- |
527 | -- If @c = chol m@ then @c@ is upper triangular and @m == tr c \<> c@. | 534 | -- If @c = chol m@ then @c@ is upper triangular and @m == tr c \<> c@. |
528 | chol :: Field t => Her t -> Matrix t | 535 | chol :: Field t => Herm t -> Matrix t |
529 | chol (Her m) = {-# SCC "chol" #-} cholSH' m | 536 | chol (Herm m) = {-# SCC "chol" #-} cholSH' m |
530 | 537 | ||
531 | -- | Similar to 'chol', but instead of an error (e.g., caused by a matrix not positive definite) it returns 'Nothing'. | 538 | -- | Similar to 'chol', but instead of an error (e.g., caused by a matrix not positive definite) it returns 'Nothing'. |
532 | mbChol :: Field t => Her t -> Maybe (Matrix t) | 539 | mbChol :: Field t => Herm t -> Maybe (Matrix t) |
533 | mbChol (Her m) = {-# SCC "mbChol" #-} mbCholSH' m | 540 | mbChol (Herm m) = {-# SCC "mbChol" #-} mbCholSH' m |
534 | 541 | ||
535 | 542 | ||
536 | 543 | ||
@@ -870,6 +877,8 @@ fixPerm' s = res $ mutable f s0 | |||
870 | triang r c h v = (r><c) [el s t | s<-[0..r-1], t<-[0..c-1]] | 877 | triang r c h v = (r><c) [el s t | s<-[0..r-1], t<-[0..c-1]] |
871 | where el p q = if q-p>=h then v else 1 - v | 878 | where el p q = if q-p>=h then v else 1 - v |
872 | 879 | ||
880 | -- | Compute the explicit LU decomposition from the compact one obtained by 'luPacked'. | ||
881 | luFact :: Numeric t => LU t -> (Matrix t, Matrix t, Matrix t, t) | ||
873 | luFact (LU l_u perm) | 882 | luFact (LU l_u perm) |
874 | | r <= c = (l ,u ,p, s) | 883 | | r <= c = (l ,u ,p, s) |
875 | | otherwise = (l',u',p, s) | 884 | | otherwise = (l',u',p, s) |
@@ -967,10 +976,10 @@ relativeError norm a b = r | |||
967 | -- | Generalized symmetric positive definite eigensystem Av = lBv, | 976 | -- | Generalized symmetric positive definite eigensystem Av = lBv, |
968 | -- for A and B symmetric, B positive definite. | 977 | -- for A and B symmetric, B positive definite. |
969 | geigSH :: Field t | 978 | geigSH :: Field t |
970 | => Her t -- ^ A | 979 | => Herm t -- ^ A |
971 | -> Her t -- ^ B | 980 | -> Herm t -- ^ B |
972 | -> (Vector Double, Matrix t) | 981 | -> (Vector Double, Matrix t) |
973 | geigSH (Her a) (Her b) = geigSH' a b | 982 | geigSH (Herm a) (Herm b) = geigSH' a b |
974 | 983 | ||
975 | geigSH' :: Field t | 984 | geigSH' :: Field t |
976 | => Matrix t -- ^ A | 985 | => Matrix t -- ^ A |
@@ -989,29 +998,33 @@ geigSH' a b = (l,v') | |||
989 | 998 | ||
990 | -- | A matrix that, by construction, it is known to be complex Hermitian or real symmetric. | 999 | -- | A matrix that, by construction, it is known to be complex Hermitian or real symmetric. |
991 | -- | 1000 | -- |
992 | -- It can be created using 'sym', 'xTx', or 'trustSym', and the matrix can be extracted using 'her'. | 1001 | -- It can be created using 'sym', 'mTm', or 'trustSym', and the matrix can be extracted using 'unSym'. |
993 | data Her t = Her (Matrix t) deriving Show | 1002 | newtype Herm t = Herm (Matrix t) deriving Show |
1003 | |||
1004 | instance (NFData t, Numeric t) => NFData (Herm t) | ||
1005 | where | ||
1006 | rnf (Herm m) = rnf m | ||
994 | 1007 | ||
995 | -- | Extract the general matrix from a 'Her' structure, forgetting its symmetric or Hermitian property. | 1008 | -- | Extract the general matrix from a 'Herm' structure, forgetting its symmetric or Hermitian property. |
996 | her :: Her t -> Matrix t | 1009 | unSym :: Herm t -> Matrix t |
997 | her (Her x) = x | 1010 | unSym (Herm x) = x |
998 | 1011 | ||
999 | -- | Compute the complex Hermitian or real symmetric part of a square matrix (@(x + tr x)/2@). | 1012 | -- | Compute the complex Hermitian or real symmetric part of a square matrix (@(x + tr x)/2@). |
1000 | sym :: Field t => Matrix t -> Her t | 1013 | sym :: Field t => Matrix t -> Herm t |
1001 | sym x = Her (scale 0.5 (tr x `add` x)) | 1014 | sym x = Herm (scale 0.5 (tr x `add` x)) |
1002 | 1015 | ||
1003 | -- | Compute the contraction @tr x <> x@ of a general matrix. | 1016 | -- | Compute the contraction @tr x <> x@ of a general matrix. |
1004 | xTx :: Numeric t => Matrix t -> Her t | 1017 | mTm :: Numeric t => Matrix t -> Herm t |
1005 | xTx x = Her (tr x `mXm` x) | 1018 | mTm x = Herm (tr x `mXm` x) |
1006 | 1019 | ||
1007 | instance Field t => Linear t Her where | 1020 | instance Field t => Linear t Herm where |
1008 | scale x (Her m) = Her (scale x m) | 1021 | scale x (Herm m) = Herm (scale x m) |
1009 | 1022 | ||
1010 | instance Field t => Additive (Her t) where | 1023 | instance Field t => Additive (Herm t) where |
1011 | add (Her a) (Her b) = Her (a `add` b) | 1024 | add (Herm a) (Herm b) = Herm (a `add` b) |
1012 | 1025 | ||
1013 | -- | At your own risk, declare that a matrix is complex Hermitian or real symmetric | 1026 | -- | At your own risk, declare that a matrix is complex Hermitian or real symmetric |
1014 | -- for usage in 'chol', 'eigSH', etc. Only a triangular part of the matrix will be used. | 1027 | -- for usage in 'chol', 'eigSH', etc. Only a triangular part of the matrix will be used. |
1015 | trustSym :: Matrix t -> Her t | 1028 | trustSym :: Matrix t -> Herm t |
1016 | trustSym x = (Her x) | 1029 | trustSym x = (Herm x) |
1017 | 1030 | ||
diff --git a/packages/base/src/Internal/Modular.hs b/packages/base/src/Internal/Modular.hs index a3421a8..239c742 100644 --- a/packages/base/src/Internal/Modular.hs +++ b/packages/base/src/Internal/Modular.hs | |||
@@ -371,7 +371,7 @@ test = (ok, info) | |||
371 | 371 | ||
372 | checkLU okf t = norm_Inf $ flatten (l <> u <> p - t) | 372 | checkLU okf t = norm_Inf $ flatten (l <> u <> p - t) |
373 | where | 373 | where |
374 | (l,u,p,_ :: Int) = luFact (LU x' p') | 374 | (l,u,p,_) = luFact (LU x' p') |
375 | where | 375 | where |
376 | (x',p') = mutable (luST okf) t | 376 | (x',p') = mutable (luST okf) t |
377 | 377 | ||
diff --git a/packages/base/src/Internal/Util.hs b/packages/base/src/Internal/Util.hs index 36b7855..cf42961 100644 --- a/packages/base/src/Internal/Util.hs +++ b/packages/base/src/Internal/Util.hs | |||
@@ -462,7 +462,7 @@ null1 :: Matrix R -> Vector R | |||
462 | null1 = last . toColumns . snd . rightSV | 462 | null1 = last . toColumns . snd . rightSV |
463 | 463 | ||
464 | -- | solution of overconstrained homogeneous symmetric linear system | 464 | -- | solution of overconstrained homogeneous symmetric linear system |
465 | null1sym :: Her R -> Vector R | 465 | null1sym :: Herm R -> Vector R |
466 | null1sym = last . toColumns . snd . eigSH | 466 | null1sym = last . toColumns . snd . eigSH |
467 | 467 | ||
468 | -------------------------------------------------------------------------------- | 468 | -------------------------------------------------------------------------------- |
diff --git a/packages/base/src/Numeric/LinearAlgebra.hs b/packages/base/src/Numeric/LinearAlgebra.hs index 7be2600..6a9c33a 100644 --- a/packages/base/src/Numeric/LinearAlgebra.hs +++ b/packages/base/src/Numeric/LinearAlgebra.hs | |||
@@ -35,8 +35,9 @@ module Numeric.LinearAlgebra ( | |||
35 | 35 | ||
36 | -- * Autoconformable dimensions | 36 | -- * Autoconformable dimensions |
37 | -- | | 37 | -- | |
38 | -- In arithmetic operations single-element vectors and matrices | 38 | -- In most operations, single-element vectors and matrices |
39 | -- (created from numeric literals or using 'scalar') automatically | 39 | -- (created from numeric literals or using 'scalar'), and matrices |
40 | -- with just one row or column, automatically | ||
40 | -- expand to match the dimensions of the other operand: | 41 | -- expand to match the dimensions of the other operand: |
41 | -- | 42 | -- |
42 | -- >>> 5 + 2*ident 3 :: Matrix Double | 43 | -- >>> 5 + 2*ident 3 :: Matrix Double |
@@ -45,11 +46,12 @@ module Numeric.LinearAlgebra ( | |||
45 | -- , 5.0, 7.0, 5.0 | 46 | -- , 5.0, 7.0, 5.0 |
46 | -- , 5.0, 5.0, 7.0 ] | 47 | -- , 5.0, 5.0, 7.0 ] |
47 | -- | 48 | -- |
48 | -- >>> matrix 3 [1..9] + matrix 1 [10,20,30] | 49 | -- >>> (4><3) [1..] + row [10,20,30] |
49 | -- (3><3) | 50 | -- (4><3) |
50 | -- [ 11.0, 12.0, 13.0 | 51 | -- [ 11.0, 22.0, 33.0 |
51 | -- , 24.0, 25.0, 26.0 | 52 | -- , 14.0, 25.0, 36.0 |
52 | -- , 37.0, 38.0, 39.0 ] | 53 | -- , 17.0, 28.0, 39.0 |
54 | -- , 20.0, 31.0, 42.0 ] | ||
53 | -- | 55 | -- |
54 | 56 | ||
55 | -- * Products | 57 | -- * Products |
@@ -152,9 +154,9 @@ module Numeric.LinearAlgebra ( | |||
152 | -- * Misc | 154 | -- * Misc |
153 | meanCov, rowOuters, pairwiseD2, unitary, peps, relativeError, magnit, | 155 | meanCov, rowOuters, pairwiseD2, unitary, peps, relativeError, magnit, |
154 | haussholder, optimiseMult, udot, nullspaceSVD, orthSVD, ranksv, | 156 | haussholder, optimiseMult, udot, nullspaceSVD, orthSVD, ranksv, |
155 | iC, sym, xTx, trustSym, her, | 157 | iC, sym, mTm, trustSym, unSym, |
156 | -- * Auxiliary classes | 158 | -- * Auxiliary classes |
157 | Element, Container, Product, Numeric, LSDiv, Her, | 159 | Element, Container, Product, Numeric, LSDiv, Herm, |
158 | Complexable, RealElement, | 160 | Complexable, RealElement, |
159 | RealOf, ComplexOf, SingleOf, DoubleOf, | 161 | RealOf, ComplexOf, SingleOf, DoubleOf, |
160 | IndexOf, | 162 | IndexOf, |
@@ -162,6 +164,7 @@ module Numeric.LinearAlgebra ( | |||
162 | Transposable, | 164 | Transposable, |
163 | LU(..), | 165 | LU(..), |
164 | LDL(..), | 166 | LDL(..), |
167 | QR(..), | ||
165 | CGState(..), | 168 | CGState(..), |
166 | Testable(..) | 169 | Testable(..) |
167 | ) where | 170 | ) where |
diff --git a/packages/base/src/Numeric/LinearAlgebra/Static.hs b/packages/base/src/Numeric/LinearAlgebra/Static.hs index ded69fa..843c727 100644 --- a/packages/base/src/Numeric/LinearAlgebra/Static.hs +++ b/packages/base/src/Numeric/LinearAlgebra/Static.hs | |||
@@ -65,7 +65,7 @@ import Numeric.LinearAlgebra hiding ( | |||
65 | row,col,vector,matrix,linspace,toRows,toColumns, | 65 | row,col,vector,matrix,linspace,toRows,toColumns, |
66 | (<\>),fromList,takeDiag,svd,eig,eigSH, | 66 | (<\>),fromList,takeDiag,svd,eig,eigSH, |
67 | eigenvalues,eigenvaluesSH,build, | 67 | eigenvalues,eigenvaluesSH,build, |
68 | qr,size,dot,chol,range,R,C,Her,her,sym) | 68 | qr,size,dot,chol,range,R,C,sym,mTm,unSym) |
69 | import qualified Numeric.LinearAlgebra as LA | 69 | import qualified Numeric.LinearAlgebra as LA |
70 | import Data.Proxy(Proxy) | 70 | import Data.Proxy(Proxy) |
71 | import Internal.Static | 71 | import Internal.Static |
diff --git a/packages/tests/src/Numeric/LinearAlgebra/Tests.hs b/packages/tests/src/Numeric/LinearAlgebra/Tests.hs index 30480d7..ecda6c1 100644 --- a/packages/tests/src/Numeric/LinearAlgebra/Tests.hs +++ b/packages/tests/src/Numeric/LinearAlgebra/Tests.hs | |||
@@ -500,10 +500,10 @@ sliceTest = utest "slice test" $ and | |||
500 | , testSlice (test_qrgr 4 tau2) qrr2 | 500 | , testSlice (test_qrgr 4 tau2) qrr2 |
501 | ] | 501 | ] |
502 | where | 502 | where |
503 | (qrr1,tau1) = qrRaw (rec :: Matrix R) | 503 | QR qrr1 tau1 = qrRaw (rec :: Matrix R) |
504 | (qrr2,tau2) = qrRaw (rec :: Matrix C) | 504 | QR qrr2 tau2 = qrRaw (rec :: Matrix C) |
505 | 505 | ||
506 | test_qrgr n t x = qrgr n (x,t) | 506 | test_qrgr n t x = qrgr n (QR x t) |
507 | 507 | ||
508 | ok_qrgr x = simeq 1E-15 q q' | 508 | ok_qrgr x = simeq 1E-15 q q' |
509 | where | 509 | where |
diff --git a/packages/tests/src/Numeric/LinearAlgebra/Tests/Instances.hs b/packages/tests/src/Numeric/LinearAlgebra/Tests/Instances.hs index 4704989..3d5441d 100644 --- a/packages/tests/src/Numeric/LinearAlgebra/Tests/Instances.hs +++ b/packages/tests/src/Numeric/LinearAlgebra/Tests/Instances.hs | |||
@@ -81,8 +81,7 @@ instance (Field a, Arbitrary a) => Arbitrary (Rot a) where | |||
81 | 81 | ||
82 | 82 | ||
83 | -- a complex hermitian or real symmetric matrix | 83 | -- a complex hermitian or real symmetric matrix |
84 | --newtype (Her a) = Her (Matrix a) deriving Show | 84 | instance (Field a, Arbitrary a, Num (Vector a)) => Arbitrary (Herm a) where |
85 | instance (Field a, Arbitrary a, Num (Vector a)) => Arbitrary (Her a) where | ||
86 | arbitrary = do | 85 | arbitrary = do |
87 | Sq m <- arbitrary | 86 | Sq m <- arbitrary |
88 | let m' = m/2 | 87 | let m' = m/2 |
@@ -127,7 +126,7 @@ instance (Numeric a, ArbitraryField a, Num (Vector a)) | |||
127 | arbitrary = do | 126 | arbitrary = do |
128 | m <- arbitrary | 127 | m <- arbitrary |
129 | let (_,v) = eigSH m | 128 | let (_,v) = eigSH m |
130 | n = rows (her m) | 129 | n = rows (unSym m) |
131 | l <- replicateM n (choose (0,100)) | 130 | l <- replicateM n (choose (0,100)) |
132 | let s = diag (fromList l) | 131 | let s = diag (fromList l) |
133 | p = v <> real s <> tr v | 132 | p = v <> real s <> tr v |
@@ -161,8 +160,8 @@ fM m = m :: FM | |||
161 | zM m = m :: ZM | 160 | zM m = m :: ZM |
162 | 161 | ||
163 | 162 | ||
164 | rHer m = her m :: RM | 163 | rHer m = unSym m :: RM |
165 | cHer m = her m :: CM | 164 | cHer m = unSym m :: CM |
166 | 165 | ||
167 | rRot (Rot m) = m :: RM | 166 | rRot (Rot m) = m :: RM |
168 | cRot (Rot m) = m :: CM | 167 | cRot (Rot m) = m :: CM |
@@ -176,8 +175,8 @@ cWC (WC m) = m :: CM | |||
176 | rSqWC (SqWC m) = m :: RM | 175 | rSqWC (SqWC m) = m :: RM |
177 | cSqWC (SqWC m) = m :: CM | 176 | cSqWC (SqWC m) = m :: CM |
178 | 177 | ||
179 | rSymWC (SqWC m) = sym m :: Her R | 178 | rSymWC (SqWC m) = sym m :: Herm R |
180 | cSymWC (SqWC m) = sym m :: Her C | 179 | cSymWC (SqWC m) = sym m :: Herm C |
181 | 180 | ||
182 | rPosDef (PosDef m) = m :: RM | 181 | rPosDef (PosDef m) = m :: RM |
183 | cPosDef (PosDef m) = m :: CM | 182 | cPosDef (PosDef m) = m :: CM |
diff --git a/packages/tests/src/Numeric/LinearAlgebra/Tests/Properties.hs b/packages/tests/src/Numeric/LinearAlgebra/Tests/Properties.hs index 2ac3588..720b7bd 100644 --- a/packages/tests/src/Numeric/LinearAlgebra/Tests/Properties.hs +++ b/packages/tests/src/Numeric/LinearAlgebra/Tests/Properties.hs | |||
@@ -263,7 +263,7 @@ multProp2 p (a,b) = (tr (a <> b)) :~p~: (tr b <> tr a) | |||
263 | 263 | ||
264 | linearSolveProp f m = f m m |~| ident (rows m) | 264 | linearSolveProp f m = f m m |~| ident (rows m) |
265 | 265 | ||
266 | linearSolvePropH f m = f m (her m) |~| ident (rows (her m)) | 266 | linearSolvePropH f m = f m (unSym m) |~| ident (rows (unSym m)) |
267 | 267 | ||
268 | linearSolveProp2 f (a,x) = not wc `trivial` (not wc || a <> f a b |~| b) | 268 | linearSolveProp2 f (a,x) = not wc `trivial` (not wc || a <> f a b |~| b) |
269 | where q = min (rows a) (cols a) | 269 | where q = min (rows a) (cols a) |