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BLAS and LAPACK Subroutines of Real Skew-symmetric Matrix #1049

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BLAS and LAPACK Subroutines of Real Skew-symmetric Matrix #1049

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f46d51b
Add algorithms of skew-symmetric matrix
sh-zheng Aug 20, 2024
39d70a4
Add testcases for skew-symmetric algorithm
sh-zheng Aug 20, 2024
c17ac0a
Add cblas and lapacke interfaces for skew-symmetric subroutines
sh-zheng Aug 21, 2024
f9096df
Add cblas testcases for skew-symmetric subroutines
sh-zheng Aug 22, 2024
08a4705
Use blas subroutines to perform transformation in *kyeqr
sh-zheng Sep 3, 2024
63b8293
Update CMakelists
sh-zheng Sep 3, 2024
3275c32
Fix fortran text overflow in *kteqr
sh-zheng Sep 4, 2024
ace1953
Add missing subroutine parameter checks for linear solver
sh-zheng Sep 5, 2024
58ce56e
Fix a typo and resolve a conflict in BLAS/TESTING
sh-zheng Feb 8, 2025
ae2ea5d
Merge branch 'master' into skew-symmetric-new
sh-zheng Feb 9, 2025
b9b2875
Keep consistency with pr 1101
sh-zheng Feb 10, 2025
6731c0f
Delete unnecessary work buffer usage of *ktev and *kteqr in lapacke
sh-zheng Apr 10, 2025
b15a164
Remove redundant *lagky in TESTING/
sh-zheng May 7, 2025
2bb3d99
Merge branch 'master' into skew-symmetric-new
sh-zheng Jun 15, 2025
020cd26
Call *lasr to update eigenvector instead of *rot
sh-zheng Jul 3, 2025
fcbee19
Fix compiler error of column limit
sh-zheng Jul 4, 2025
eb160c9
Fix compiler error of column limit, supplementary submission
sh-zheng Jul 6, 2025
38f90b3
Update contributors information, and doxygen doc
sh-zheng Jul 6, 2025
30042e4
Merge branch 'Reference-LAPACK:master' into skew-symmetric-new
sh-zheng Aug 1, 2025
98d9c6a
implicit none of skew-symmetric subroutines, keep consistency with pr…
sh-zheng Sep 1, 2025
eec055e
Merge branch 'Reference-LAPACK:master' into skew-symmetric-new
sh-zheng Sep 1, 2025
ec0c276
End with newline in BLAS/TESTING
sh-zheng Sep 4, 2025
c9a448b
Add expert driver subroutines *kysvx, *kycon and *kyrfs
sh-zheng Oct 11, 2025
ff8bcde
Update doc and comment
sh-zheng Oct 12, 2025
9261f0f
Fix potential distrub of diagonal elements
sh-zheng Oct 26, 2025
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Fix compiler error of column limit
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@sh-zheng
sh-zheng committed Jul 4, 2025
commit fcbee19403e840483e6c762d71b35a7e78b0d32b
8 changes: 4 additions & 4 deletions SRC/dkteqr.f
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Expand Up @@ -777,11 +777,11 @@ SUBROUTINE DKTEQR( COMPZ, N, E, Z, LDZ, WORK, INFO )
*
140 CONTINUE
IF( ISCALE.EQ.1 ) THEN
CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV, 1, E(LSV),
$ N, INFO )
CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV, 1,
$ E(LSV), N, INFO )
ELSE IF( ISCALE.EQ.2 ) THEN
CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV, 1, E(LSV),
$ N, INFO )
CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV, 1,
$ E(LSV), N, INFO )
END IF
*
* Check for no convergence to an eigenvalue after a total
Expand Down
4 changes: 2 additions & 2 deletions SRC/dkyev.f
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Original file line number Diff line number Diff line change
Expand Up @@ -257,8 +257,8 @@ SUBROUTINE DKYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
* DORGTR to generate the orthogonal matrix, then call DKTEQR.
*
IF( WANTZ ) THEN
CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ),
$ LLWORK, IINFO )
CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ),
$ WORK( INDWRK ), LLWORK, IINFO )
END IF
IF(.NOT.LOWER)
$ CALL DSCAL(N-1, -ONE, W, 1)
Expand Down
12 changes: 6 additions & 6 deletions SRC/dkygs2.f
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Expand Up @@ -227,8 +227,8 @@ SUBROUTINE DKYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
BKK = B( K, K )
CALL DTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B,
$ LDB, A( 1, K ), 1 )
CALL DKYR2( UPLO, K-1, -ONE, A( 1, K ), 1, B( 1, K ), 1,
$ A, LDA )
CALL DKYR2( UPLO, K-1, -ONE, A( 1, K ), 1, B( 1, K ),
$ 1, A, LDA )
CALL DSCAL( K-1, BKK, A( 1, K ), 1 )
30 CONTINUE
ELSE
Expand All @@ -240,10 +240,10 @@ SUBROUTINE DKYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
* Update the lower triangle of A(1:k,1:k)
*
BKK = B( K, K )
CALL DTRMV( UPLO, 'Transpose', 'Non-unit', K-1, B, LDB,
$ A( K, 1 ), LDA )
CALL DKYR2( UPLO, K-1, ONE, A( K, 1 ), LDA, B( K, 1 ),
$ LDB, A, LDA )
CALL DTRMV( UPLO, 'Transpose', 'Non-unit', K-1, B,
$ LDB, A( K, 1 ), LDA )
CALL DKYR2( UPLO, K-1, ONE, A( K, 1 ), LDA,
$ B( K, 1 ), LDB, A, LDA )
CALL DSCAL( K-1, BKK, A( K, 1 ), LDA )
40 CONTINUE
END IF
Expand Down
91 changes: 50 additions & 41 deletions SRC/dkygst.f
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Original file line number Diff line number Diff line change
Expand Up @@ -210,18 +210,19 @@ SUBROUTINE DKYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
CALL DKYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
$ B( K, K ), LDB, INFO )
IF( K+KB.LE.N ) THEN
CALL DTRSM( 'Left', UPLO, 'Transpose', 'Non-unit',
$ KB, N-K-KB+1, ONE, B( K, K ), LDB,
$ A( K, K+KB ), LDA )
CALL DTRSM( 'Left', UPLO, 'Transpose',
$ 'Non-unit', KB, N-K-KB+1, ONE,
$ B( K, K ), LDB, A( K, K+KB ), LDA )
CALL DKYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
$ A( K, K ), LDA, B( K, K+KB ), LDB, ONE,
$ A( K, K+KB ), LDA )
CALL DKYR2K( UPLO, 'Transpose', N-K-KB+1, KB, -ONE,
$ A( K, K+KB ), LDA, B( K, K+KB ), LDB,
$ ONE, A( K+KB, K+KB ), LDA )
$ A( K, K ), LDA, B( K, K+KB ), LDB,
$ ONE, A( K, K+KB ), LDA )
CALL DKYR2K( UPLO, 'Transpose', N-K-KB+1, KB,
$ -ONE, A( K, K+KB ), LDA,
$ B( K, K+KB ), LDB, ONE,
$ A( K+KB, K+KB ), LDA )
CALL DKYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
$ A( K, K ), LDA, B( K, K+KB ), LDB, ONE,
$ A( K, K+KB ), LDA )
$ A( K, K ), LDA, B( K, K+KB ), LDB,
$ ONE, A( K, K+KB ), LDA )
CALL DTRSM( 'Right', UPLO, 'No transpose',
$ 'Non-unit', KB, N-K-KB+1, ONE,
$ B( K+KB, K+KB ), LDB, A( K, K+KB ),
Expand All @@ -240,18 +241,19 @@ SUBROUTINE DKYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
CALL DKYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
$ B( K, K ), LDB, INFO )
IF( K+KB.LE.N ) THEN
CALL DTRSM( 'Right', UPLO, 'Transpose', 'Non-unit',
$ N-K-KB+1, KB, ONE, B( K, K ), LDB,
$ A( K+KB, K ), LDA )
CALL DTRSM( 'Right', UPLO, 'Transpose',
$ 'Non-unit', N-K-KB+1, KB, ONE,
$ B( K, K ), LDB, A( K+KB, K ), LDA )
CALL DKYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
$ A( K, K ), LDA, B( K+KB, K ), LDB, ONE,
$ A( K+KB, K ), LDA )
CALL DKYR2K( UPLO, 'No transpose', N-K-KB+1, KB,
$ ONE, A( K+KB, K ), LDA, B( K+KB, K ),
$ LDB, ONE, A( K+KB, K+KB ), LDA )
$ A( K, K ), LDA, B( K+KB, K ), LDB,
$ ONE, A( K+KB, K ), LDA )
CALL DKYR2K( UPLO, 'No transpose', N-K-KB+1,
$ KB, ONE, A( K+KB, K ), LDA,
$ B( K+KB, K ), LDB, ONE,
$ A( K+KB, K+KB ), LDA )
CALL DKYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
$ A( K, K ), LDA, B( K+KB, K ), LDB, ONE,
$ A( K+KB, K ), LDA )
$ A( K, K ), LDA, B( K+KB, K ), LDB,
$ ONE, A( K+KB, K ), LDA )
CALL DTRSM( 'Left', UPLO, 'No transpose',
$ 'Non-unit', N-K-KB+1, KB, ONE,
$ B( K+KB, K+KB ), LDB, A( K+KB, K ),
Expand All @@ -269,18 +271,21 @@ SUBROUTINE DKYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
*
* Update the upper triangle of A(1:k+kb-1,1:k+kb-1)
*
CALL DTRMM( 'Left', UPLO, 'No transpose', 'Non-unit',
$ K-1, KB, ONE, B, LDB, A( 1, K ), LDA )
CALL DKYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
$ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA )
CALL DTRMM( 'Left', UPLO, 'No transpose',
$ 'Non-unit', K-1, KB, ONE, B, LDB,
$ A( 1, K ), LDA )
CALL DKYMM( 'Right', UPLO, K-1, KB, HALF,
$ A( K, K ), LDA, B( 1, K ), LDB, ONE,
$ A( 1, K ), LDA )
CALL DKYR2K( UPLO, 'No transpose', K-1, KB, -ONE,
$ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A,
$ LDA )
CALL DKYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
$ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA )
CALL DTRMM( 'Right', UPLO, 'Transpose', 'Non-unit',
$ K-1, KB, ONE, B( K, K ), LDB, A( 1, K ),
$ LDA )
$ A( 1, K ), LDA, B( 1, K ), LDB, ONE,
$ A, LDA )
CALL DKYMM( 'Right', UPLO, K-1, KB, HALF,
$ A( K, K ), LDA, B( 1, K ), LDB, ONE,
$ A( 1, K ), LDA )
CALL DTRMM( 'Right', UPLO, 'Transpose',
$ 'Non-unit', K-1, KB, ONE, B( K, K ),
$ LDB, A( 1, K ), LDA )
CALL DKYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
$ B( K, K ), LDB, INFO )
30 CONTINUE
Expand All @@ -293,17 +298,21 @@ SUBROUTINE DKYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
*
* Update the lower triangle of A(1:k+kb-1,1:k+kb-1)
*
CALL DTRMM( 'Right', UPLO, 'No transpose', 'Non-unit',
$ KB, K-1, ONE, B, LDB, A( K, 1 ), LDA )
CALL DKYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
$ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA )
CALL DTRMM( 'Right', UPLO, 'No transpose',
$ 'Non-unit', KB, K-1, ONE, B, LDB,
$ A( K, 1 ), LDA )
CALL DKYMM( 'Left', UPLO, KB, K-1, HALF,
$ A( K, K ), LDA, B( K, 1 ), LDB, ONE,
$ A( K, 1 ), LDA )
CALL DKYR2K( UPLO, 'Transpose', K-1, KB, ONE,
$ A( K, 1 ), LDA, B( K, 1 ), LDB, ONE, A,
$ LDA )
CALL DKYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
$ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA )
CALL DTRMM( 'Left', UPLO, 'Transpose', 'Non-unit', KB,
$ K-1, ONE, B( K, K ), LDB, A( K, 1 ), LDA )
$ A( K, 1 ), LDA, B( K, 1 ), LDB, ONE,
$ A, LDA )
CALL DKYMM( 'Left', UPLO, KB, K-1, HALF,
$ A( K, K ), LDA, B( K, 1 ), LDB, ONE,
$ A( K, 1 ), LDA )
CALL DTRMM( 'Left', UPLO, 'Transpose',
$ 'Non-unit', KB, K-1, ONE, B( K, K ),
$ LDB, A( K, 1 ), LDA )
CALL DKYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
$ B( K, K ), LDB, INFO )
40 CONTINUE
Expand Down
2 changes: 1 addition & 1 deletion SRC/dkytf2.f
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Expand Up @@ -226,7 +226,7 @@ SUBROUTINE DKYTF2( UPLO, N, A, LDA, IPIV, INFO )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, IMAX1, IMAX2, J,KSTEP
INTEGER I, IMAX1, IMAX2, J, K, KP, KSTEP
DOUBLE PRECISION ABSAKP1K, COLMAX1, COLMAX2,
$ D21, T, WK, WKM1, WKP1
* ..
Expand Down
8 changes: 4 additions & 4 deletions SRC/dkytri2x.f
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Expand Up @@ -511,16 +511,16 @@ SUBROUTINE DKYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
DO WHILE ( I .GT. 1 )
IF( IPIV(I-1) .GT. 0 ) THEN
IP=IPIV(I-1)
IF ( I .LT. IP) CALL DKYSWAPR( UPLO, N, A, LDA, I ,
IF ( I .LT. IP) CALL DKYSWAPR( UPLO, N, A, LDA, I,
$ IP )
IF ( I .GT. IP) CALL DKYSWAPR( UPLO, N, A, LDA, IP ,
IF ( I .GT. IP) CALL DKYSWAPR( UPLO, N, A, LDA, IP,
$ I )
I=I-1
ELSEIF( IPIV(I-1) .LT. 0 ) THEN
IP=-IPIV(I-1)
IF ( I .LT. IP) CALL DKYSWAPR( UPLO, N, A, LDA, I ,
IF ( I .LT. IP) CALL DKYSWAPR( UPLO, N, A, LDA, I,
$ IP )
IF ( I .GT. IP) CALL DKYSWAPR( UPLO, N, A, LDA, IP ,
IF ( I .GT. IP) CALL DKYSWAPR( UPLO, N, A, LDA, IP,
$ I )
CALL DKYSWAPR( UPLO, N, A, LDA, I-1 ,I )
I=I-1
Expand Down
45 changes: 24 additions & 21 deletions SRC/dkytrs.f
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Expand Up @@ -206,8 +206,8 @@ SUBROUTINE DKYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
* Multiply by inv(U(K)), where U(K) is the transformation
* stored in columns K-1 and K of A.
*
CALL DGER( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
$ B( 1, 1 ), LDB )
CALL DGER( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ),
$ LDB, B( 1, 1 ), LDB )
CALL DGER( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
$ LDB, B( 1, 1 ), LDB )
*
Expand All @@ -233,8 +233,8 @@ SUBROUTINE DKYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
* Multiply by inv(U(K)), where U(K) is the transformation
* stored in columns K-1 and K of A.
*
CALL DGER( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
$ B( 1, 1 ), LDB )
CALL DGER( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ),
$ LDB, B( 1, 1 ), LDB )
CALL DGER( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
$ LDB, B( 1, 1 ), LDB )
*
Expand All @@ -252,8 +252,8 @@ SUBROUTINE DKYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
* Multiply by inv(U(K)), where U(K) is the transformation
* stored in columns K-1 and K of A.
*
CALL DGER( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
$ B( 1, 1 ), LDB )
CALL DGER( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ),
$ LDB, B( 1, 1 ), LDB )
CALL DGER( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
$ LDB, B( 1, 1 ), LDB )
*
Expand Down Expand Up @@ -460,11 +460,12 @@ SUBROUTINE DKYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
* stored in columns K-1 and K of A.
*
IF( K.LT.N ) THEN
CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
$ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
$ LDB, A( K+1, K-1 ), 1, ONE, B( K-1, 1 ),
$ LDB )
CALL DGEMV( 'Transpose', N-K, NRHS, -ONE,
$ B( K+1, 1 ), LDB, A( K+1, K ),
$ 1, ONE, B( K, 1 ), LDB )
CALL DGEMV( 'Transpose', N-K, NRHS, -ONE,
$ B( K+1, 1 ), LDB, A( K+1, K-1 ), 1,
$ ONE, B( K-1, 1 ), LDB )
END IF
*
* Interchange rows K and IPIV(K).
Expand All @@ -482,11 +483,12 @@ SUBROUTINE DKYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
* stored in columns K-1 and K of A.
*
IF( K.LT.N ) THEN
CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
$ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
$ LDB, A( K+1, K-1 ), 1, ONE, B( K-1, 1 ),
$ LDB )
CALL DGEMV( 'Transpose', N-K, NRHS, -ONE,
$ B( K+1, 1 ), LDB, A( K+1, K ),
$ 1, ONE, B( K, 1 ), LDB )
CALL DGEMV( 'Transpose', N-K, NRHS, -ONE,
$ B( K+1, 1 ), LDB, A( K+1, K-1 ), 1,
$ ONE, B( K-1, 1 ), LDB )
END IF
*
* Interchange rows K and -IPIV(K), then K and K-1.
Expand All @@ -505,11 +507,12 @@ SUBROUTINE DKYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
* stored in columns K-1 and K of A.
*
IF( K.LT.N ) THEN
CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
$ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
$ LDB, A( K+1, K-1 ), 1, ONE, B( K-1, 1 ),
$ LDB )
CALL DGEMV( 'Transpose', N-K, NRHS, -ONE,
$ B( K+1, 1 ), LDB, A( K+1, K ),
$ 1, ONE, B( K, 1 ), LDB )
CALL DGEMV( 'Transpose', N-K, NRHS, -ONE,
$ B( K+1, 1 ), LDB, A( K+1, K-1 ), 1,
$ ONE, B( K-1, 1 ), LDB )
END IF
K = K - 2
END IF
Expand Down
11 changes: 6 additions & 5 deletions SRC/dlakyf.f
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Expand Up @@ -435,8 +435,8 @@ SUBROUTINE DLAKYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
* Interchange rows K and K-1, then K-1 and IMAX2 in last K+1 columns of A
*
IF( K.LT.N ) THEN
CALL DSWAP( N-K, A( K, K+1 ), LDA, A( K-1, K+1 ),
$ LDA )
CALL DSWAP( N-K, A( K, K+1 ), LDA,
$ A( K-1, K+1 ), LDA )

CALL DSWAP( N-K, A( K-1, K+1 ), LDA,
$ A( IMAX2, K+1 ), LDA )
Expand Down Expand Up @@ -795,9 +795,10 @@ SUBROUTINE DLAKYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
* Update the rectangular subdiagonal block
*
IF( J+JB.LE.N )
$ CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,
$ K-1, ONE, A( J+JB, 1 ), LDA, W( J, 1 ),
$ LDW, ONE, A( J+JB, J ), LDA )
$ CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1,
$ JB, K-1, ONE, A( J+JB, 1 ), LDA,
$ W( J, 1 ), LDW, ONE, A( J+JB, J ),
$ LDA )
110 CONTINUE
*
* Put L21 in standard form by partially undoing the interchanges
Expand Down
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