Mercurial > octave-antonio
changeset 8414:36c8a3696ae7
add yet more missing LAPACK sources
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Sun, 21 Dec 2008 17:10:38 +0100 |
| parents | b8de157b4948 |
| children | fa12c67683d3 |
| files | libcruft/ChangeLog libcruft/lapack/Makefile.in libcruft/lapack/chegs2.f libcruft/lapack/chegst.f libcruft/lapack/chegv.f libcruft/lapack/dsygs2.f libcruft/lapack/dsygst.f libcruft/lapack/dsygv.f libcruft/lapack/ssygs2.f libcruft/lapack/ssygst.f libcruft/lapack/ssygv.f libcruft/lapack/zhegs2.f libcruft/lapack/zhegst.f libcruft/lapack/zhegv.f |
| diffstat | 14 files changed, 2819 insertions(+), 1 deletions(-) [+] |
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--- a/libcruft/ChangeLog Thu Dec 18 21:06:20 2008 +0100 +++ b/libcruft/ChangeLog Sun Dec 21 17:10:38 2008 +0100 @@ -1,3 +1,11 @@ +2008-12-21 Jaroslav Hajek <highegg@gmail.com> + + * lapack/chegs2.f lapack/chegst.f lapack/chegv.f lapack/dsygs2.f + lapack/dsygst.f lapack/dsygv.f lapack/ssygs2.f lapack/ssygst.f + lapack/ssygv.f lapack/zhegs2.f lapack/zhegst.f lapack/zhegv.f: + New sources. + * lapack/Makefile.in: Include them. + 2008-12-15 Jaroslav Hajek <highegg@gmail.com> * blas/zsyrk.f: New source.
--- a/libcruft/lapack/Makefile.in Thu Dec 18 21:06:20 2008 +0100 +++ b/libcruft/lapack/Makefile.in Sun Dec 21 17:10:38 2008 +0100 @@ -146,7 +146,9 @@ ztrti2.f ztrtri.f ztrtrs.f ztzrzf.f zung2l.f zung2l.f \ zung2r.f zungbr.f zunghr.f zungl2.f zunglq.f zunglq.f \ zungql.f zungqr.f zungtr.f zunm2r.f zunmbr.f zunmbr.f \ - zunml2.f zunmlq.f zunmqr.f zunmr3.f zunmrz.f zunmrz.f + zunml2.f zunmlq.f zunmqr.f zunmr3.f zunmrz.f zunmrz.f \ + chegs2.f chegst.f chegv.f dsygs2.f dsygst.f dsygv.f \ + ssygs2.f ssygst.f ssygv.f zhegs2.f zhegst.f zhegv.f include $(TOPDIR)/Makeconf
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/chegs2.f Sun Dec 21 17:10:38 2008 +0100 @@ -0,0 +1,224 @@ + SUBROUTINE CHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, ITYPE, LDA, LDB, N +* .. +* .. Array Arguments .. + COMPLEX A( LDA, * ), B( LDB, * ) +* .. +* +* Purpose +* ======= +* +* CHEGS2 reduces a complex Hermitian-definite generalized +* eigenproblem to standard form. +* +* If ITYPE = 1, the problem is A*x = lambda*B*x, +* and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L') +* +* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or +* B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L. +* +* B must have been previously factorized as U'*U or L*L' by CPOTRF. +* +* Arguments +* ========= +* +* ITYPE (input) INTEGER +* = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L'); +* = 2 or 3: compute U*A*U' or L'*A*L. +* +* UPLO (input) CHARACTER*1 +* Specifies whether the upper or lower triangular part of the +* Hermitian matrix A is stored, and how B has been factorized. +* = 'U': Upper triangular +* = 'L': Lower triangular +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* A (input/output) COMPLEX array, dimension (LDA,N) +* On entry, the Hermitian matrix A. If UPLO = 'U', the leading +* n by n upper triangular part of A contains the upper +* triangular part of the matrix A, and the strictly lower +* triangular part of A is not referenced. If UPLO = 'L', the +* leading n by n lower triangular part of A contains the lower +* triangular part of the matrix A, and the strictly upper +* triangular part of A is not referenced. +* +* On exit, if INFO = 0, the transformed matrix, stored in the +* same format as A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input) COMPLEX array, dimension (LDB,N) +* The triangular factor from the Cholesky factorization of B, +* as returned by CPOTRF. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* INFO (output) INTEGER +* = 0: successful exit. +* < 0: if INFO = -i, the i-th argument had an illegal value. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE, HALF + PARAMETER ( ONE = 1.0E+0, HALF = 0.5E+0 ) + COMPLEX CONE + PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) +* .. +* .. Local Scalars .. + LOGICAL UPPER + INTEGER K + REAL AKK, BKK + COMPLEX CT +* .. +* .. External Subroutines .. + EXTERNAL CAXPY, CHER2, CLACGV, CSSCAL, CTRMV, CTRSV, + $ XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + UPPER = LSAME( UPLO, 'U' ) + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'CHEGS2', -INFO ) + RETURN + END IF +* + IF( ITYPE.EQ.1 ) THEN + IF( UPPER ) THEN +* +* Compute inv(U')*A*inv(U) +* + DO 10 K = 1, N +* +* Update the upper triangle of A(k:n,k:n) +* + AKK = A( K, K ) + BKK = B( K, K ) + AKK = AKK / BKK**2 + A( K, K ) = AKK + IF( K.LT.N ) THEN + CALL CSSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA ) + CT = -HALF*AKK + CALL CLACGV( N-K, A( K, K+1 ), LDA ) + CALL CLACGV( N-K, B( K, K+1 ), LDB ) + CALL CAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), + $ LDA ) + CALL CHER2( UPLO, N-K, -CONE, A( K, K+1 ), LDA, + $ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA ) + CALL CAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), + $ LDA ) + CALL CLACGV( N-K, B( K, K+1 ), LDB ) + CALL CTRSV( UPLO, 'Conjugate transpose', 'Non-unit', + $ N-K, B( K+1, K+1 ), LDB, A( K, K+1 ), + $ LDA ) + CALL CLACGV( N-K, A( K, K+1 ), LDA ) + END IF + 10 CONTINUE + ELSE +* +* Compute inv(L)*A*inv(L') +* + DO 20 K = 1, N +* +* Update the lower triangle of A(k:n,k:n) +* + AKK = A( K, K ) + BKK = B( K, K ) + AKK = AKK / BKK**2 + A( K, K ) = AKK + IF( K.LT.N ) THEN + CALL CSSCAL( N-K, ONE / BKK, A( K+1, K ), 1 ) + CT = -HALF*AKK + CALL CAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) + CALL CHER2( UPLO, N-K, -CONE, A( K+1, K ), 1, + $ B( K+1, K ), 1, A( K+1, K+1 ), LDA ) + CALL CAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) + CALL CTRSV( UPLO, 'No transpose', 'Non-unit', N-K, + $ B( K+1, K+1 ), LDB, A( K+1, K ), 1 ) + END IF + 20 CONTINUE + END IF + ELSE + IF( UPPER ) THEN +* +* Compute U*A*U' +* + DO 30 K = 1, N +* +* Update the upper triangle of A(1:k,1:k) +* + AKK = A( K, K ) + BKK = B( K, K ) + CALL CTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B, + $ LDB, A( 1, K ), 1 ) + CT = HALF*AKK + CALL CAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) + CALL CHER2( UPLO, K-1, CONE, A( 1, K ), 1, B( 1, K ), 1, + $ A, LDA ) + CALL CAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) + CALL CSSCAL( K-1, BKK, A( 1, K ), 1 ) + A( K, K ) = AKK*BKK**2 + 30 CONTINUE + ELSE +* +* Compute L'*A*L +* + DO 40 K = 1, N +* +* Update the lower triangle of A(1:k,1:k) +* + AKK = A( K, K ) + BKK = B( K, K ) + CALL CLACGV( K-1, A( K, 1 ), LDA ) + CALL CTRMV( UPLO, 'Conjugate transpose', 'Non-unit', K-1, + $ B, LDB, A( K, 1 ), LDA ) + CT = HALF*AKK + CALL CLACGV( K-1, B( K, 1 ), LDB ) + CALL CAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) + CALL CHER2( UPLO, K-1, CONE, A( K, 1 ), LDA, B( K, 1 ), + $ LDB, A, LDA ) + CALL CAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) + CALL CLACGV( K-1, B( K, 1 ), LDB ) + CALL CSSCAL( K-1, BKK, A( K, 1 ), LDA ) + CALL CLACGV( K-1, A( K, 1 ), LDA ) + A( K, K ) = AKK*BKK**2 + 40 CONTINUE + END IF + END IF + RETURN +* +* End of CHEGS2 +* + END
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/chegst.f Sun Dec 21 17:10:38 2008 +0100 @@ -0,0 +1,259 @@ + SUBROUTINE CHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, ITYPE, LDA, LDB, N +* .. +* .. Array Arguments .. + COMPLEX A( LDA, * ), B( LDB, * ) +* .. +* +* Purpose +* ======= +* +* CHEGST reduces a complex Hermitian-definite generalized +* eigenproblem to standard form. +* +* If ITYPE = 1, the problem is A*x = lambda*B*x, +* and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) +* +* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or +* B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. +* +* B must have been previously factorized as U**H*U or L*L**H by CPOTRF. +* +* Arguments +* ========= +* +* ITYPE (input) INTEGER +* = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); +* = 2 or 3: compute U*A*U**H or L**H*A*L. +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangle of A is stored and B is factored as +* U**H*U; +* = 'L': Lower triangle of A is stored and B is factored as +* L*L**H. +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* A (input/output) COMPLEX array, dimension (LDA,N) +* On entry, the Hermitian matrix A. If UPLO = 'U', the leading +* N-by-N upper triangular part of A contains the upper +* triangular part of the matrix A, and the strictly lower +* triangular part of A is not referenced. If UPLO = 'L', the +* leading N-by-N lower triangular part of A contains the lower +* triangular part of the matrix A, and the strictly upper +* triangular part of A is not referenced. +* +* On exit, if INFO = 0, the transformed matrix, stored in the +* same format as A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input) COMPLEX array, dimension (LDB,N) +* The triangular factor from the Cholesky factorization of B, +* as returned by CPOTRF. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE + PARAMETER ( ONE = 1.0E+0 ) + COMPLEX CONE, HALF + PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ), + $ HALF = ( 0.5E+0, 0.0E+0 ) ) +* .. +* .. Local Scalars .. + LOGICAL UPPER + INTEGER K, KB, NB +* .. +* .. External Subroutines .. + EXTERNAL CHEGS2, CHEMM, CHER2K, CTRMM, CTRSM, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + UPPER = LSAME( UPLO, 'U' ) + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'CHEGST', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* Determine the block size for this environment. +* + NB = ILAENV( 1, 'CHEGST', UPLO, N, -1, -1, -1 ) +* + IF( NB.LE.1 .OR. NB.GE.N ) THEN +* +* Use unblocked code +* + CALL CHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) + ELSE +* +* Use blocked code +* + IF( ITYPE.EQ.1 ) THEN + IF( UPPER ) THEN +* +* Compute inv(U')*A*inv(U) +* + DO 10 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the upper triangle of A(k:n,k:n) +* + CALL CHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + IF( K+KB.LE.N ) THEN + CALL CTRSM( 'Left', UPLO, 'Conjugate transpose', + $ 'Non-unit', KB, N-K-KB+1, CONE, + $ B( K, K ), LDB, A( K, K+KB ), LDA ) + CALL CHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, + $ A( K, K ), LDA, B( K, K+KB ), LDB, + $ CONE, A( K, K+KB ), LDA ) + CALL CHER2K( UPLO, 'Conjugate transpose', N-K-KB+1, + $ KB, -CONE, A( K, K+KB ), LDA, + $ B( K, K+KB ), LDB, ONE, + $ A( K+KB, K+KB ), LDA ) + CALL CHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, + $ A( K, K ), LDA, B( K, K+KB ), LDB, + $ CONE, A( K, K+KB ), LDA ) + CALL CTRSM( 'Right', UPLO, 'No transpose', + $ 'Non-unit', KB, N-K-KB+1, CONE, + $ B( K+KB, K+KB ), LDB, A( K, K+KB ), + $ LDA ) + END IF + 10 CONTINUE + ELSE +* +* Compute inv(L)*A*inv(L') +* + DO 20 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the lower triangle of A(k:n,k:n) +* + CALL CHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + IF( K+KB.LE.N ) THEN + CALL CTRSM( 'Right', UPLO, 'Conjugate transpose', + $ 'Non-unit', N-K-KB+1, KB, CONE, + $ B( K, K ), LDB, A( K+KB, K ), LDA ) + CALL CHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, + $ A( K, K ), LDA, B( K+KB, K ), LDB, + $ CONE, A( K+KB, K ), LDA ) + CALL CHER2K( UPLO, 'No transpose', N-K-KB+1, KB, + $ -CONE, A( K+KB, K ), LDA, + $ B( K+KB, K ), LDB, ONE, + $ A( K+KB, K+KB ), LDA ) + CALL CHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, + $ A( K, K ), LDA, B( K+KB, K ), LDB, + $ CONE, A( K+KB, K ), LDA ) + CALL CTRSM( 'Left', UPLO, 'No transpose', + $ 'Non-unit', N-K-KB+1, KB, CONE, + $ B( K+KB, K+KB ), LDB, A( K+KB, K ), + $ LDA ) + END IF + 20 CONTINUE + END IF + ELSE + IF( UPPER ) THEN +* +* Compute U*A*U' +* + DO 30 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) +* + CALL CTRMM( 'Left', UPLO, 'No transpose', 'Non-unit', + $ K-1, KB, CONE, B, LDB, A( 1, K ), LDA ) + CALL CHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), + $ LDA, B( 1, K ), LDB, CONE, A( 1, K ), + $ LDA ) + CALL CHER2K( UPLO, 'No transpose', K-1, KB, CONE, + $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A, + $ LDA ) + CALL CHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), + $ LDA, B( 1, K ), LDB, CONE, A( 1, K ), + $ LDA ) + CALL CTRMM( 'Right', UPLO, 'Conjugate transpose', + $ 'Non-unit', K-1, KB, CONE, B( K, K ), LDB, + $ A( 1, K ), LDA ) + CALL CHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + 30 CONTINUE + ELSE +* +* Compute L'*A*L +* + DO 40 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) +* + CALL CTRMM( 'Right', UPLO, 'No transpose', 'Non-unit', + $ KB, K-1, CONE, B, LDB, A( K, 1 ), LDA ) + CALL CHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), + $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ), + $ LDA ) + CALL CHER2K( UPLO, 'Conjugate transpose', K-1, KB, + $ CONE, A( K, 1 ), LDA, B( K, 1 ), LDB, + $ ONE, A, LDA ) + CALL CHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), + $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ), + $ LDA ) + CALL CTRMM( 'Left', UPLO, 'Conjugate transpose', + $ 'Non-unit', KB, K-1, CONE, B( K, K ), LDB, + $ A( K, 1 ), LDA ) + CALL CHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + 40 CONTINUE + END IF + END IF + END IF + RETURN +* +* End of CHEGST +* + END
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/chegv.f Sun Dec 21 17:10:38 2008 +0100 @@ -0,0 +1,232 @@ + SUBROUTINE CHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, + $ LWORK, RWORK, INFO ) +* +* -- LAPACK driver routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER JOBZ, UPLO + INTEGER INFO, ITYPE, LDA, LDB, LWORK, N +* .. +* .. Array Arguments .. + REAL RWORK( * ), W( * ) + COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* CHEGV computes all the eigenvalues, and optionally, the eigenvectors +* of a complex generalized Hermitian-definite eigenproblem, of the form +* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. +* Here A and B are assumed to be Hermitian and B is also +* positive definite. +* +* Arguments +* ========= +* +* ITYPE (input) INTEGER +* Specifies the problem type to be solved: +* = 1: A*x = (lambda)*B*x +* = 2: A*B*x = (lambda)*x +* = 3: B*A*x = (lambda)*x +* +* JOBZ (input) CHARACTER*1 +* = 'N': Compute eigenvalues only; +* = 'V': Compute eigenvalues and eigenvectors. +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangles of A and B are stored; +* = 'L': Lower triangles of A and B are stored. +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* A (input/output) COMPLEX array, dimension (LDA, N) +* On entry, the Hermitian matrix A. If UPLO = 'U', the +* leading N-by-N upper triangular part of A contains the +* upper triangular part of the matrix A. If UPLO = 'L', +* the leading N-by-N lower triangular part of A contains +* the lower triangular part of the matrix A. +* +* On exit, if JOBZ = 'V', then if INFO = 0, A contains the +* matrix Z of eigenvectors. The eigenvectors are normalized +* as follows: +* if ITYPE = 1 or 2, Z**H*B*Z = I; +* if ITYPE = 3, Z**H*inv(B)*Z = I. +* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') +* or the lower triangle (if UPLO='L') of A, including the +* diagonal, is destroyed. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input/output) COMPLEX array, dimension (LDB, N) +* On entry, the Hermitian positive definite matrix B. +* If UPLO = 'U', the leading N-by-N upper triangular part of B +* contains the upper triangular part of the matrix B. +* If UPLO = 'L', the leading N-by-N lower triangular part of B +* contains the lower triangular part of the matrix B. +* +* On exit, if INFO <= N, the part of B containing the matrix is +* overwritten by the triangular factor U or L from the Cholesky +* factorization B = U**H*U or B = L*L**H. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* W (output) REAL array, dimension (N) +* If INFO = 0, the eigenvalues in ascending order. +* +* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) +* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +* +* LWORK (input) INTEGER +* The length of the array WORK. LWORK >= max(1,2*N-1). +* For optimal efficiency, LWORK >= (NB+1)*N, +* where NB is the blocksize for CHETRD returned by ILAENV. +* +* If LWORK = -1, then a workspace query is assumed; the routine +* only calculates the optimal size of the WORK array, returns +* this value as the first entry of the WORK array, and no error +* message related to LWORK is issued by XERBLA. +* +* RWORK (workspace) REAL array, dimension (max(1, 3*N-2)) +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* > 0: CPOTRF or CHEEV returned an error code: +* <= N: if INFO = i, CHEEV failed to converge; +* i off-diagonal elements of an intermediate +* tridiagonal form did not converge to zero; +* > N: if INFO = N + i, for 1 <= i <= N, then the leading +* minor of order i of B is not positive definite. +* The factorization of B could not be completed and +* no eigenvalues or eigenvectors were computed. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ONE + PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) +* .. +* .. Local Scalars .. + LOGICAL LQUERY, UPPER, WANTZ + CHARACTER TRANS + INTEGER LWKOPT, NB, NEIG +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL ILAENV, LSAME +* .. +* .. External Subroutines .. + EXTERNAL CHEEV, CHEGST, CPOTRF, CTRMM, CTRSM, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + UPPER = LSAME( UPLO, 'U' ) + LQUERY = ( LWORK.EQ. -1 ) +* + INFO = 0 + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN + INFO = -2 + ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN + INFO = -3 + ELSE IF( N.LT.0 ) THEN + INFO = -4 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -6 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -8 + END IF +* + IF( INFO.EQ.0 ) THEN + NB = ILAENV( 1, 'CHETRD', UPLO, N, -1, -1, -1 ) + LWKOPT = MAX( 1, ( NB + 1 )*N ) + WORK( 1 ) = LWKOPT +* + IF( LWORK.LT.MAX( 1, 2*N-1 ) .AND. .NOT.LQUERY ) THEN + INFO = -11 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'CHEGV ', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* Form a Cholesky factorization of B. +* + CALL CPOTRF( UPLO, N, B, LDB, INFO ) + IF( INFO.NE.0 ) THEN + INFO = N + INFO + RETURN + END IF +* +* Transform problem to standard eigenvalue problem and solve. +* + CALL CHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) + CALL CHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO ) +* + IF( WANTZ ) THEN +* +* Backtransform eigenvectors to the original problem. +* + NEIG = N + IF( INFO.GT.0 ) + $ NEIG = INFO - 1 + IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN +* +* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; +* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y +* + IF( UPPER ) THEN + TRANS = 'N' + ELSE + TRANS = 'C' + END IF +* + CALL CTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, + $ B, LDB, A, LDA ) +* + ELSE IF( ITYPE.EQ.3 ) THEN +* +* For B*A*x=(lambda)*x; +* backtransform eigenvectors: x = L*y or U'*y +* + IF( UPPER ) THEN + TRANS = 'C' + ELSE + TRANS = 'N' + END IF +* + CALL CTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, + $ B, LDB, A, LDA ) + END IF + END IF +* + WORK( 1 ) = LWKOPT +* + RETURN +* +* End of CHEGV +* + END
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/dsygs2.f Sun Dec 21 17:10:38 2008 +0100 @@ -0,0 +1,211 @@ + SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, ITYPE, LDA, LDB, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), B( LDB, * ) +* .. +* +* Purpose +* ======= +* +* DSYGS2 reduces a real symmetric-definite generalized eigenproblem +* to standard form. +* +* If ITYPE = 1, the problem is A*x = lambda*B*x, +* and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L') +* +* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or +* B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L. +* +* B must have been previously factorized as U'*U or L*L' by DPOTRF. +* +* Arguments +* ========= +* +* ITYPE (input) INTEGER +* = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L'); +* = 2 or 3: compute U*A*U' or L'*A*L. +* +* UPLO (input) CHARACTER*1 +* Specifies whether the upper or lower triangular part of the +* symmetric matrix A is stored, and how B has been factorized. +* = 'U': Upper triangular +* = 'L': Lower triangular +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) +* On entry, the symmetric matrix A. If UPLO = 'U', the leading +* n by n upper triangular part of A contains the upper +* triangular part of the matrix A, and the strictly lower +* triangular part of A is not referenced. If UPLO = 'L', the +* leading n by n lower triangular part of A contains the lower +* triangular part of the matrix A, and the strictly upper +* triangular part of A is not referenced. +* +* On exit, if INFO = 0, the transformed matrix, stored in the +* same format as A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input) DOUBLE PRECISION array, dimension (LDB,N) +* The triangular factor from the Cholesky factorization of B, +* as returned by DPOTRF. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* INFO (output) INTEGER +* = 0: successful exit. +* < 0: if INFO = -i, the i-th argument had an illegal value. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, HALF + PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 ) +* .. +* .. Local Scalars .. + LOGICAL UPPER + INTEGER K + DOUBLE PRECISION AKK, BKK, CT +* .. +* .. External Subroutines .. + EXTERNAL DAXPY, DSCAL, DSYR2, DTRMV, DTRSV, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + UPPER = LSAME( UPLO, 'U' ) + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DSYGS2', -INFO ) + RETURN + END IF +* + IF( ITYPE.EQ.1 ) THEN + IF( UPPER ) THEN +* +* Compute inv(U')*A*inv(U) +* + DO 10 K = 1, N +* +* Update the upper triangle of A(k:n,k:n) +* + AKK = A( K, K ) + BKK = B( K, K ) + AKK = AKK / BKK**2 + A( K, K ) = AKK + IF( K.LT.N ) THEN + CALL DSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA ) + CT = -HALF*AKK + CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), + $ LDA ) + CALL DSYR2( UPLO, N-K, -ONE, A( K, K+1 ), LDA, + $ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA ) + CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), + $ LDA ) + CALL DTRSV( UPLO, 'Transpose', 'Non-unit', N-K, + $ B( K+1, K+1 ), LDB, A( K, K+1 ), LDA ) + END IF + 10 CONTINUE + ELSE +* +* Compute inv(L)*A*inv(L') +* + DO 20 K = 1, N +* +* Update the lower triangle of A(k:n,k:n) +* + AKK = A( K, K ) + BKK = B( K, K ) + AKK = AKK / BKK**2 + A( K, K ) = AKK + IF( K.LT.N ) THEN + CALL DSCAL( N-K, ONE / BKK, A( K+1, K ), 1 ) + CT = -HALF*AKK + CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) + CALL DSYR2( UPLO, N-K, -ONE, A( K+1, K ), 1, + $ B( K+1, K ), 1, A( K+1, K+1 ), LDA ) + CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) + CALL DTRSV( UPLO, 'No transpose', 'Non-unit', N-K, + $ B( K+1, K+1 ), LDB, A( K+1, K ), 1 ) + END IF + 20 CONTINUE + END IF + ELSE + IF( UPPER ) THEN +* +* Compute U*A*U' +* + DO 30 K = 1, N +* +* Update the upper triangle of A(1:k,1:k) +* + AKK = A( K, K ) + BKK = B( K, K ) + CALL DTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B, + $ LDB, A( 1, K ), 1 ) + CT = HALF*AKK + CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) + CALL DSYR2( UPLO, K-1, ONE, A( 1, K ), 1, B( 1, K ), 1, + $ A, LDA ) + CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) + CALL DSCAL( K-1, BKK, A( 1, K ), 1 ) + A( K, K ) = AKK*BKK**2 + 30 CONTINUE + ELSE +* +* Compute L'*A*L +* + DO 40 K = 1, N +* +* Update the lower triangle of A(1:k,1:k) +* + AKK = A( K, K ) + BKK = B( K, K ) + CALL DTRMV( UPLO, 'Transpose', 'Non-unit', K-1, B, LDB, + $ A( K, 1 ), LDA ) + CT = HALF*AKK + CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) + CALL DSYR2( UPLO, K-1, ONE, A( K, 1 ), LDA, B( K, 1 ), + $ LDB, A, LDA ) + CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) + CALL DSCAL( K-1, BKK, A( K, 1 ), LDA ) + A( K, K ) = AKK*BKK**2 + 40 CONTINUE + END IF + END IF + RETURN +* +* End of DSYGS2 +* + END
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/dsygst.f Sun Dec 21 17:10:38 2008 +0100 @@ -0,0 +1,249 @@ + SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, ITYPE, LDA, LDB, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), B( LDB, * ) +* .. +* +* Purpose +* ======= +* +* DSYGST reduces a real symmetric-definite generalized eigenproblem +* to standard form. +* +* If ITYPE = 1, the problem is A*x = lambda*B*x, +* and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) +* +* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or +* B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L. +* +* B must have been previously factorized as U**T*U or L*L**T by DPOTRF. +* +* Arguments +* ========= +* +* ITYPE (input) INTEGER +* = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); +* = 2 or 3: compute U*A*U**T or L**T*A*L. +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangle of A is stored and B is factored as +* U**T*U; +* = 'L': Lower triangle of A is stored and B is factored as +* L*L**T. +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) +* On entry, the symmetric matrix A. If UPLO = 'U', the leading +* N-by-N upper triangular part of A contains the upper +* triangular part of the matrix A, and the strictly lower +* triangular part of A is not referenced. If UPLO = 'L', the +* leading N-by-N lower triangular part of A contains the lower +* triangular part of the matrix A, and the strictly upper +* triangular part of A is not referenced. +* +* On exit, if INFO = 0, the transformed matrix, stored in the +* same format as A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input) DOUBLE PRECISION array, dimension (LDB,N) +* The triangular factor from the Cholesky factorization of B, +* as returned by DPOTRF. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, HALF + PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 ) +* .. +* .. Local Scalars .. + LOGICAL UPPER + INTEGER K, KB, NB +* .. +* .. External Subroutines .. + EXTERNAL DSYGS2, DSYMM, DSYR2K, DTRMM, DTRSM, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + UPPER = LSAME( UPLO, 'U' ) + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DSYGST', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* Determine the block size for this environment. +* + NB = ILAENV( 1, 'DSYGST', UPLO, N, -1, -1, -1 ) +* + IF( NB.LE.1 .OR. NB.GE.N ) THEN +* +* Use unblocked code +* + CALL DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) + ELSE +* +* Use blocked code +* + IF( ITYPE.EQ.1 ) THEN + IF( UPPER ) THEN +* +* Compute inv(U')*A*inv(U) +* + DO 10 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the upper triangle of A(k:n,k:n) +* + CALL DSYGS2( 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 DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, + $ A( K, K ), LDA, B( K, K+KB ), LDB, ONE, + $ A( K, K+KB ), LDA ) + CALL DSYR2K( 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 DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, + $ 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 ), + $ LDA ) + END IF + 10 CONTINUE + ELSE +* +* Compute inv(L)*A*inv(L') +* + DO 20 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the lower triangle of A(k:n,k:n) +* + CALL DSYGS2( 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 DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, + $ A( K, K ), LDA, B( K+KB, K ), LDB, ONE, + $ A( K+KB, K ), LDA ) + CALL DSYR2K( 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 DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, + $ 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 ), + $ LDA ) + END IF + 20 CONTINUE + END IF + ELSE + IF( UPPER ) THEN +* +* Compute U*A*U' +* + DO 30 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* 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 DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), + $ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA ) + CALL DSYR2K( UPLO, 'No transpose', K-1, KB, ONE, + $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A, + $ LDA ) + CALL DSYMM( '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 DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + 30 CONTINUE + ELSE +* +* Compute L'*A*L +* + DO 40 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* 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 DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), + $ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA ) + CALL DSYR2K( UPLO, 'Transpose', K-1, KB, ONE, + $ A( K, 1 ), LDA, B( K, 1 ), LDB, ONE, A, + $ LDA ) + CALL DSYMM( '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 DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + 40 CONTINUE + END IF + END IF + END IF + RETURN +* +* End of DSYGST +* + END
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/dsygv.f Sun Dec 21 17:10:38 2008 +0100 @@ -0,0 +1,229 @@ + SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, + $ LWORK, INFO ) +* +* -- LAPACK driver routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER JOBZ, UPLO + INTEGER INFO, ITYPE, LDA, LDB, LWORK, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* DSYGV computes all the eigenvalues, and optionally, the eigenvectors +* of a real generalized symmetric-definite eigenproblem, of the form +* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. +* Here A and B are assumed to be symmetric and B is also +* positive definite. +* +* Arguments +* ========= +* +* ITYPE (input) INTEGER +* Specifies the problem type to be solved: +* = 1: A*x = (lambda)*B*x +* = 2: A*B*x = (lambda)*x +* = 3: B*A*x = (lambda)*x +* +* JOBZ (input) CHARACTER*1 +* = 'N': Compute eigenvalues only; +* = 'V': Compute eigenvalues and eigenvectors. +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangles of A and B are stored; +* = 'L': Lower triangles of A and B are stored. +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* A (input/output) DOUBLE PRECISION array, dimension (LDA, N) +* On entry, the symmetric matrix A. If UPLO = 'U', the +* leading N-by-N upper triangular part of A contains the +* upper triangular part of the matrix A. If UPLO = 'L', +* the leading N-by-N lower triangular part of A contains +* the lower triangular part of the matrix A. +* +* On exit, if JOBZ = 'V', then if INFO = 0, A contains the +* matrix Z of eigenvectors. The eigenvectors are normalized +* as follows: +* if ITYPE = 1 or 2, Z**T*B*Z = I; +* if ITYPE = 3, Z**T*inv(B)*Z = I. +* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') +* or the lower triangle (if UPLO='L') of A, including the +* diagonal, is destroyed. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input/output) DOUBLE PRECISION array, dimension (LDB, N) +* On entry, the symmetric positive definite matrix B. +* If UPLO = 'U', the leading N-by-N upper triangular part of B +* contains the upper triangular part of the matrix B. +* If UPLO = 'L', the leading N-by-N lower triangular part of B +* contains the lower triangular part of the matrix B. +* +* On exit, if INFO <= N, the part of B containing the matrix is +* overwritten by the triangular factor U or L from the Cholesky +* factorization B = U**T*U or B = L*L**T. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* W (output) DOUBLE PRECISION array, dimension (N) +* If INFO = 0, the eigenvalues in ascending order. +* +* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) +* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +* +* LWORK (input) INTEGER +* The length of the array WORK. LWORK >= max(1,3*N-1). +* For optimal efficiency, LWORK >= (NB+2)*N, +* where NB is the blocksize for DSYTRD returned by ILAENV. +* +* If LWORK = -1, then a workspace query is assumed; the routine +* only calculates the optimal size of the WORK array, returns +* this value as the first entry of the WORK array, and no error +* message related to LWORK is issued by XERBLA. +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* > 0: DPOTRF or DSYEV returned an error code: +* <= N: if INFO = i, DSYEV failed to converge; +* i off-diagonal elements of an intermediate +* tridiagonal form did not converge to zero; +* > N: if INFO = N + i, for 1 <= i <= N, then the leading +* minor of order i of B is not positive definite. +* The factorization of B could not be completed and +* no eigenvalues or eigenvectors were computed. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL LQUERY, UPPER, WANTZ + CHARACTER TRANS + INTEGER LWKMIN, LWKOPT, NB, NEIG +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV +* .. +* .. External Subroutines .. + EXTERNAL DPOTRF, DSYEV, DSYGST, DTRMM, DTRSM, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + UPPER = LSAME( UPLO, 'U' ) + LQUERY = ( LWORK.EQ.-1 ) +* + INFO = 0 + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN + INFO = -2 + ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN + INFO = -3 + ELSE IF( N.LT.0 ) THEN + INFO = -4 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -6 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -8 + END IF +* + IF( INFO.EQ.0 ) THEN + LWKMIN = MAX( 1, 3*N - 1 ) + NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) + LWKOPT = MAX( LWKMIN, ( NB + 2 )*N ) + WORK( 1 ) = LWKOPT +* + IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN + INFO = -11 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DSYGV ', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* Form a Cholesky factorization of B. +* + CALL DPOTRF( UPLO, N, B, LDB, INFO ) + IF( INFO.NE.0 ) THEN + INFO = N + INFO + RETURN + END IF +* +* Transform problem to standard eigenvalue problem and solve. +* + CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) + CALL DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO ) +* + IF( WANTZ ) THEN +* +* Backtransform eigenvectors to the original problem. +* + NEIG = N + IF( INFO.GT.0 ) + $ NEIG = INFO - 1 + IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN +* +* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; +* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y +* + IF( UPPER ) THEN + TRANS = 'N' + ELSE + TRANS = 'T' + END IF +* + CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, + $ B, LDB, A, LDA ) +* + ELSE IF( ITYPE.EQ.3 ) THEN +* +* For B*A*x=(lambda)*x; +* backtransform eigenvectors: x = L*y or U'*y +* + IF( UPPER ) THEN + TRANS = 'T' + ELSE + TRANS = 'N' + END IF +* + CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, + $ B, LDB, A, LDA ) + END IF + END IF +* + WORK( 1 ) = LWKOPT + RETURN +* +* End of DSYGV +* + END
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/ssygs2.f Sun Dec 21 17:10:38 2008 +0100 @@ -0,0 +1,211 @@ + SUBROUTINE SSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, ITYPE, LDA, LDB, N +* .. +* .. Array Arguments .. + REAL A( LDA, * ), B( LDB, * ) +* .. +* +* Purpose +* ======= +* +* SSYGS2 reduces a real symmetric-definite generalized eigenproblem +* to standard form. +* +* If ITYPE = 1, the problem is A*x = lambda*B*x, +* and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L') +* +* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or +* B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L. +* +* B must have been previously factorized as U'*U or L*L' by SPOTRF. +* +* Arguments +* ========= +* +* ITYPE (input) INTEGER +* = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L'); +* = 2 or 3: compute U*A*U' or L'*A*L. +* +* UPLO (input) CHARACTER*1 +* Specifies whether the upper or lower triangular part of the +* symmetric matrix A is stored, and how B has been factorized. +* = 'U': Upper triangular +* = 'L': Lower triangular +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* A (input/output) REAL array, dimension (LDA,N) +* On entry, the symmetric matrix A. If UPLO = 'U', the leading +* n by n upper triangular part of A contains the upper +* triangular part of the matrix A, and the strictly lower +* triangular part of A is not referenced. If UPLO = 'L', the +* leading n by n lower triangular part of A contains the lower +* triangular part of the matrix A, and the strictly upper +* triangular part of A is not referenced. +* +* On exit, if INFO = 0, the transformed matrix, stored in the +* same format as A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input) REAL array, dimension (LDB,N) +* The triangular factor from the Cholesky factorization of B, +* as returned by SPOTRF. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* INFO (output) INTEGER +* = 0: successful exit. +* < 0: if INFO = -i, the i-th argument had an illegal value. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE, HALF + PARAMETER ( ONE = 1.0, HALF = 0.5 ) +* .. +* .. Local Scalars .. + LOGICAL UPPER + INTEGER K + REAL AKK, BKK, CT +* .. +* .. External Subroutines .. + EXTERNAL SAXPY, SSCAL, SSYR2, STRMV, STRSV, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + UPPER = LSAME( UPLO, 'U' ) + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'SSYGS2', -INFO ) + RETURN + END IF +* + IF( ITYPE.EQ.1 ) THEN + IF( UPPER ) THEN +* +* Compute inv(U')*A*inv(U) +* + DO 10 K = 1, N +* +* Update the upper triangle of A(k:n,k:n) +* + AKK = A( K, K ) + BKK = B( K, K ) + AKK = AKK / BKK**2 + A( K, K ) = AKK + IF( K.LT.N ) THEN + CALL SSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA ) + CT = -HALF*AKK + CALL SAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), + $ LDA ) + CALL SSYR2( UPLO, N-K, -ONE, A( K, K+1 ), LDA, + $ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA ) + CALL SAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), + $ LDA ) + CALL STRSV( UPLO, 'Transpose', 'Non-unit', N-K, + $ B( K+1, K+1 ), LDB, A( K, K+1 ), LDA ) + END IF + 10 CONTINUE + ELSE +* +* Compute inv(L)*A*inv(L') +* + DO 20 K = 1, N +* +* Update the lower triangle of A(k:n,k:n) +* + AKK = A( K, K ) + BKK = B( K, K ) + AKK = AKK / BKK**2 + A( K, K ) = AKK + IF( K.LT.N ) THEN + CALL SSCAL( N-K, ONE / BKK, A( K+1, K ), 1 ) + CT = -HALF*AKK + CALL SAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) + CALL SSYR2( UPLO, N-K, -ONE, A( K+1, K ), 1, + $ B( K+1, K ), 1, A( K+1, K+1 ), LDA ) + CALL SAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) + CALL STRSV( UPLO, 'No transpose', 'Non-unit', N-K, + $ B( K+1, K+1 ), LDB, A( K+1, K ), 1 ) + END IF + 20 CONTINUE + END IF + ELSE + IF( UPPER ) THEN +* +* Compute U*A*U' +* + DO 30 K = 1, N +* +* Update the upper triangle of A(1:k,1:k) +* + AKK = A( K, K ) + BKK = B( K, K ) + CALL STRMV( UPLO, 'No transpose', 'Non-unit', K-1, B, + $ LDB, A( 1, K ), 1 ) + CT = HALF*AKK + CALL SAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) + CALL SSYR2( UPLO, K-1, ONE, A( 1, K ), 1, B( 1, K ), 1, + $ A, LDA ) + CALL SAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) + CALL SSCAL( K-1, BKK, A( 1, K ), 1 ) + A( K, K ) = AKK*BKK**2 + 30 CONTINUE + ELSE +* +* Compute L'*A*L +* + DO 40 K = 1, N +* +* Update the lower triangle of A(1:k,1:k) +* + AKK = A( K, K ) + BKK = B( K, K ) + CALL STRMV( UPLO, 'Transpose', 'Non-unit', K-1, B, LDB, + $ A( K, 1 ), LDA ) + CT = HALF*AKK + CALL SAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) + CALL SSYR2( UPLO, K-1, ONE, A( K, 1 ), LDA, B( K, 1 ), + $ LDB, A, LDA ) + CALL SAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) + CALL SSCAL( K-1, BKK, A( K, 1 ), LDA ) + A( K, K ) = AKK*BKK**2 + 40 CONTINUE + END IF + END IF + RETURN +* +* End of SSYGS2 +* + END
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/ssygst.f Sun Dec 21 17:10:38 2008 +0100 @@ -0,0 +1,249 @@ + SUBROUTINE SSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, ITYPE, LDA, LDB, N +* .. +* .. Array Arguments .. + REAL A( LDA, * ), B( LDB, * ) +* .. +* +* Purpose +* ======= +* +* SSYGST reduces a real symmetric-definite generalized eigenproblem +* to standard form. +* +* If ITYPE = 1, the problem is A*x = lambda*B*x, +* and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) +* +* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or +* B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L. +* +* B must have been previously factorized as U**T*U or L*L**T by SPOTRF. +* +* Arguments +* ========= +* +* ITYPE (input) INTEGER +* = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); +* = 2 or 3: compute U*A*U**T or L**T*A*L. +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangle of A is stored and B is factored as +* U**T*U; +* = 'L': Lower triangle of A is stored and B is factored as +* L*L**T. +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* A (input/output) REAL array, dimension (LDA,N) +* On entry, the symmetric matrix A. If UPLO = 'U', the leading +* N-by-N upper triangular part of A contains the upper +* triangular part of the matrix A, and the strictly lower +* triangular part of A is not referenced. If UPLO = 'L', the +* leading N-by-N lower triangular part of A contains the lower +* triangular part of the matrix A, and the strictly upper +* triangular part of A is not referenced. +* +* On exit, if INFO = 0, the transformed matrix, stored in the +* same format as A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input) REAL array, dimension (LDB,N) +* The triangular factor from the Cholesky factorization of B, +* as returned by SPOTRF. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE, HALF + PARAMETER ( ONE = 1.0, HALF = 0.5 ) +* .. +* .. Local Scalars .. + LOGICAL UPPER + INTEGER K, KB, NB +* .. +* .. External Subroutines .. + EXTERNAL SSYGS2, SSYMM, SSYR2K, STRMM, STRSM, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + UPPER = LSAME( UPLO, 'U' ) + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'SSYGST', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* Determine the block size for this environment. +* + NB = ILAENV( 1, 'SSYGST', UPLO, N, -1, -1, -1 ) +* + IF( NB.LE.1 .OR. NB.GE.N ) THEN +* +* Use unblocked code +* + CALL SSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) + ELSE +* +* Use blocked code +* + IF( ITYPE.EQ.1 ) THEN + IF( UPPER ) THEN +* +* Compute inv(U')*A*inv(U) +* + DO 10 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the upper triangle of A(k:n,k:n) +* + CALL SSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + IF( K+KB.LE.N ) THEN + CALL STRSM( 'Left', UPLO, 'Transpose', 'Non-unit', + $ KB, N-K-KB+1, ONE, B( K, K ), LDB, + $ A( K, K+KB ), LDA ) + CALL SSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, + $ A( K, K ), LDA, B( K, K+KB ), LDB, ONE, + $ A( K, K+KB ), LDA ) + CALL SSYR2K( 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 SSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, + $ A( K, K ), LDA, B( K, K+KB ), LDB, ONE, + $ A( K, K+KB ), LDA ) + CALL STRSM( 'Right', UPLO, 'No transpose', + $ 'Non-unit', KB, N-K-KB+1, ONE, + $ B( K+KB, K+KB ), LDB, A( K, K+KB ), + $ LDA ) + END IF + 10 CONTINUE + ELSE +* +* Compute inv(L)*A*inv(L') +* + DO 20 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the lower triangle of A(k:n,k:n) +* + CALL SSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + IF( K+KB.LE.N ) THEN + CALL STRSM( 'Right', UPLO, 'Transpose', 'Non-unit', + $ N-K-KB+1, KB, ONE, B( K, K ), LDB, + $ A( K+KB, K ), LDA ) + CALL SSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, + $ A( K, K ), LDA, B( K+KB, K ), LDB, ONE, + $ A( K+KB, K ), LDA ) + CALL SSYR2K( 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 SSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, + $ A( K, K ), LDA, B( K+KB, K ), LDB, ONE, + $ A( K+KB, K ), LDA ) + CALL STRSM( 'Left', UPLO, 'No transpose', + $ 'Non-unit', N-K-KB+1, KB, ONE, + $ B( K+KB, K+KB ), LDB, A( K+KB, K ), + $ LDA ) + END IF + 20 CONTINUE + END IF + ELSE + IF( UPPER ) THEN +* +* Compute U*A*U' +* + DO 30 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) +* + CALL STRMM( 'Left', UPLO, 'No transpose', 'Non-unit', + $ K-1, KB, ONE, B, LDB, A( 1, K ), LDA ) + CALL SSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), + $ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA ) + CALL SSYR2K( UPLO, 'No transpose', K-1, KB, ONE, + $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A, + $ LDA ) + CALL SSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), + $ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA ) + CALL STRMM( 'Right', UPLO, 'Transpose', 'Non-unit', + $ K-1, KB, ONE, B( K, K ), LDB, A( 1, K ), + $ LDA ) + CALL SSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + 30 CONTINUE + ELSE +* +* Compute L'*A*L +* + DO 40 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) +* + CALL STRMM( 'Right', UPLO, 'No transpose', 'Non-unit', + $ KB, K-1, ONE, B, LDB, A( K, 1 ), LDA ) + CALL SSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), + $ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA ) + CALL SSYR2K( UPLO, 'Transpose', K-1, KB, ONE, + $ A( K, 1 ), LDA, B( K, 1 ), LDB, ONE, A, + $ LDA ) + CALL SSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), + $ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA ) + CALL STRMM( 'Left', UPLO, 'Transpose', 'Non-unit', KB, + $ K-1, ONE, B( K, K ), LDB, A( K, 1 ), LDA ) + CALL SSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + 40 CONTINUE + END IF + END IF + END IF + RETURN +* +* End of SSYGST +* + END
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/ssygv.f Sun Dec 21 17:10:38 2008 +0100 @@ -0,0 +1,229 @@ + SUBROUTINE SSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, + $ LWORK, INFO ) +* +* -- LAPACK driver routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER JOBZ, UPLO + INTEGER INFO, ITYPE, LDA, LDB, LWORK, N +* .. +* .. Array Arguments .. + REAL A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* SSYGV computes all the eigenvalues, and optionally, the eigenvectors +* of a real generalized symmetric-definite eigenproblem, of the form +* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. +* Here A and B are assumed to be symmetric and B is also +* positive definite. +* +* Arguments +* ========= +* +* ITYPE (input) INTEGER +* Specifies the problem type to be solved: +* = 1: A*x = (lambda)*B*x +* = 2: A*B*x = (lambda)*x +* = 3: B*A*x = (lambda)*x +* +* JOBZ (input) CHARACTER*1 +* = 'N': Compute eigenvalues only; +* = 'V': Compute eigenvalues and eigenvectors. +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangles of A and B are stored; +* = 'L': Lower triangles of A and B are stored. +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* A (input/output) REAL array, dimension (LDA, N) +* On entry, the symmetric matrix A. If UPLO = 'U', the +* leading N-by-N upper triangular part of A contains the +* upper triangular part of the matrix A. If UPLO = 'L', +* the leading N-by-N lower triangular part of A contains +* the lower triangular part of the matrix A. +* +* On exit, if JOBZ = 'V', then if INFO = 0, A contains the +* matrix Z of eigenvectors. The eigenvectors are normalized +* as follows: +* if ITYPE = 1 or 2, Z**T*B*Z = I; +* if ITYPE = 3, Z**T*inv(B)*Z = I. +* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') +* or the lower triangle (if UPLO='L') of A, including the +* diagonal, is destroyed. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input/output) REAL array, dimension (LDB, N) +* On entry, the symmetric positive definite matrix B. +* If UPLO = 'U', the leading N-by-N upper triangular part of B +* contains the upper triangular part of the matrix B. +* If UPLO = 'L', the leading N-by-N lower triangular part of B +* contains the lower triangular part of the matrix B. +* +* On exit, if INFO <= N, the part of B containing the matrix is +* overwritten by the triangular factor U or L from the Cholesky +* factorization B = U**T*U or B = L*L**T. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* W (output) REAL array, dimension (N) +* If INFO = 0, the eigenvalues in ascending order. +* +* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) +* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +* +* LWORK (input) INTEGER +* The length of the array WORK. LWORK >= max(1,3*N-1). +* For optimal efficiency, LWORK >= (NB+2)*N, +* where NB is the blocksize for SSYTRD returned by ILAENV. +* +* If LWORK = -1, then a workspace query is assumed; the routine +* only calculates the optimal size of the WORK array, returns +* this value as the first entry of the WORK array, and no error +* message related to LWORK is issued by XERBLA. +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* > 0: SPOTRF or SSYEV returned an error code: +* <= N: if INFO = i, SSYEV failed to converge; +* i off-diagonal elements of an intermediate +* tridiagonal form did not converge to zero; +* > N: if INFO = N + i, for 1 <= i <= N, then the leading +* minor of order i of B is not positive definite. +* The factorization of B could not be completed and +* no eigenvalues or eigenvectors were computed. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE + PARAMETER ( ONE = 1.0E+0 ) +* .. +* .. Local Scalars .. + LOGICAL LQUERY, UPPER, WANTZ + CHARACTER TRANS + INTEGER LWKMIN, LWKOPT, NB, NEIG +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL ILAENV, LSAME +* .. +* .. External Subroutines .. + EXTERNAL SPOTRF, SSYEV, SSYGST, STRMM, STRSM, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + UPPER = LSAME( UPLO, 'U' ) + LQUERY = ( LWORK.EQ.-1 ) +* + INFO = 0 + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN + INFO = -2 + ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN + INFO = -3 + ELSE IF( N.LT.0 ) THEN + INFO = -4 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -6 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -8 + END IF +* + IF( INFO.EQ.0 ) THEN + LWKMIN = MAX( 1, 3*N - 1 ) + NB = ILAENV( 1, 'SSYTRD', UPLO, N, -1, -1, -1 ) + LWKOPT = MAX( LWKMIN, ( NB + 2 )*N ) + WORK( 1 ) = LWKOPT +* + IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN + INFO = -11 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'SSYGV ', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* Form a Cholesky factorization of B. +* + CALL SPOTRF( UPLO, N, B, LDB, INFO ) + IF( INFO.NE.0 ) THEN + INFO = N + INFO + RETURN + END IF +* +* Transform problem to standard eigenvalue problem and solve. +* + CALL SSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) + CALL SSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO ) +* + IF( WANTZ ) THEN +* +* Backtransform eigenvectors to the original problem. +* + NEIG = N + IF( INFO.GT.0 ) + $ NEIG = INFO - 1 + IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN +* +* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; +* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y +* + IF( UPPER ) THEN + TRANS = 'N' + ELSE + TRANS = 'T' + END IF +* + CALL STRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, + $ B, LDB, A, LDA ) +* + ELSE IF( ITYPE.EQ.3 ) THEN +* +* For B*A*x=(lambda)*x; +* backtransform eigenvectors: x = L*y or U'*y +* + IF( UPPER ) THEN + TRANS = 'T' + ELSE + TRANS = 'N' + END IF +* + CALL STRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, + $ B, LDB, A, LDA ) + END IF + END IF +* + WORK( 1 ) = LWKOPT + RETURN +* +* End of SSYGV +* + END
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/zhegs2.f Sun Dec 21 17:10:38 2008 +0100 @@ -0,0 +1,224 @@ + SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, ITYPE, LDA, LDB, N +* .. +* .. Array Arguments .. + COMPLEX*16 A( LDA, * ), B( LDB, * ) +* .. +* +* Purpose +* ======= +* +* ZHEGS2 reduces a complex Hermitian-definite generalized +* eigenproblem to standard form. +* +* If ITYPE = 1, the problem is A*x = lambda*B*x, +* and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L') +* +* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or +* B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L. +* +* B must have been previously factorized as U'*U or L*L' by ZPOTRF. +* +* Arguments +* ========= +* +* ITYPE (input) INTEGER +* = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L'); +* = 2 or 3: compute U*A*U' or L'*A*L. +* +* UPLO (input) CHARACTER*1 +* Specifies whether the upper or lower triangular part of the +* Hermitian matrix A is stored, and how B has been factorized. +* = 'U': Upper triangular +* = 'L': Lower triangular +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* A (input/output) COMPLEX*16 array, dimension (LDA,N) +* On entry, the Hermitian matrix A. If UPLO = 'U', the leading +* n by n upper triangular part of A contains the upper +* triangular part of the matrix A, and the strictly lower +* triangular part of A is not referenced. If UPLO = 'L', the +* leading n by n lower triangular part of A contains the lower +* triangular part of the matrix A, and the strictly upper +* triangular part of A is not referenced. +* +* On exit, if INFO = 0, the transformed matrix, stored in the +* same format as A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input) COMPLEX*16 array, dimension (LDB,N) +* The triangular factor from the Cholesky factorization of B, +* as returned by ZPOTRF. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* INFO (output) INTEGER +* = 0: successful exit. +* < 0: if INFO = -i, the i-th argument had an illegal value. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, HALF + PARAMETER ( ONE = 1.0D+0, HALF = 0.5D+0 ) + COMPLEX*16 CONE + PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + LOGICAL UPPER + INTEGER K + DOUBLE PRECISION AKK, BKK + COMPLEX*16 CT +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZAXPY, ZDSCAL, ZHER2, ZLACGV, ZTRMV, + $ ZTRSV +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + UPPER = LSAME( UPLO, 'U' ) + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZHEGS2', -INFO ) + RETURN + END IF +* + IF( ITYPE.EQ.1 ) THEN + IF( UPPER ) THEN +* +* Compute inv(U')*A*inv(U) +* + DO 10 K = 1, N +* +* Update the upper triangle of A(k:n,k:n) +* + AKK = A( K, K ) + BKK = B( K, K ) + AKK = AKK / BKK**2 + A( K, K ) = AKK + IF( K.LT.N ) THEN + CALL ZDSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA ) + CT = -HALF*AKK + CALL ZLACGV( N-K, A( K, K+1 ), LDA ) + CALL ZLACGV( N-K, B( K, K+1 ), LDB ) + CALL ZAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), + $ LDA ) + CALL ZHER2( UPLO, N-K, -CONE, A( K, K+1 ), LDA, + $ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA ) + CALL ZAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), + $ LDA ) + CALL ZLACGV( N-K, B( K, K+1 ), LDB ) + CALL ZTRSV( UPLO, 'Conjugate transpose', 'Non-unit', + $ N-K, B( K+1, K+1 ), LDB, A( K, K+1 ), + $ LDA ) + CALL ZLACGV( N-K, A( K, K+1 ), LDA ) + END IF + 10 CONTINUE + ELSE +* +* Compute inv(L)*A*inv(L') +* + DO 20 K = 1, N +* +* Update the lower triangle of A(k:n,k:n) +* + AKK = A( K, K ) + BKK = B( K, K ) + AKK = AKK / BKK**2 + A( K, K ) = AKK + IF( K.LT.N ) THEN + CALL ZDSCAL( N-K, ONE / BKK, A( K+1, K ), 1 ) + CT = -HALF*AKK + CALL ZAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) + CALL ZHER2( UPLO, N-K, -CONE, A( K+1, K ), 1, + $ B( K+1, K ), 1, A( K+1, K+1 ), LDA ) + CALL ZAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) + CALL ZTRSV( UPLO, 'No transpose', 'Non-unit', N-K, + $ B( K+1, K+1 ), LDB, A( K+1, K ), 1 ) + END IF + 20 CONTINUE + END IF + ELSE + IF( UPPER ) THEN +* +* Compute U*A*U' +* + DO 30 K = 1, N +* +* Update the upper triangle of A(1:k,1:k) +* + AKK = A( K, K ) + BKK = B( K, K ) + CALL ZTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B, + $ LDB, A( 1, K ), 1 ) + CT = HALF*AKK + CALL ZAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) + CALL ZHER2( UPLO, K-1, CONE, A( 1, K ), 1, B( 1, K ), 1, + $ A, LDA ) + CALL ZAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) + CALL ZDSCAL( K-1, BKK, A( 1, K ), 1 ) + A( K, K ) = AKK*BKK**2 + 30 CONTINUE + ELSE +* +* Compute L'*A*L +* + DO 40 K = 1, N +* +* Update the lower triangle of A(1:k,1:k) +* + AKK = A( K, K ) + BKK = B( K, K ) + CALL ZLACGV( K-1, A( K, 1 ), LDA ) + CALL ZTRMV( UPLO, 'Conjugate transpose', 'Non-unit', K-1, + $ B, LDB, A( K, 1 ), LDA ) + CT = HALF*AKK + CALL ZLACGV( K-1, B( K, 1 ), LDB ) + CALL ZAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) + CALL ZHER2( UPLO, K-1, CONE, A( K, 1 ), LDA, B( K, 1 ), + $ LDB, A, LDA ) + CALL ZAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) + CALL ZLACGV( K-1, B( K, 1 ), LDB ) + CALL ZDSCAL( K-1, BKK, A( K, 1 ), LDA ) + CALL ZLACGV( K-1, A( K, 1 ), LDA ) + A( K, K ) = AKK*BKK**2 + 40 CONTINUE + END IF + END IF + RETURN +* +* End of ZHEGS2 +* + END
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/zhegst.f Sun Dec 21 17:10:38 2008 +0100 @@ -0,0 +1,259 @@ + SUBROUTINE ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, ITYPE, LDA, LDB, N +* .. +* .. Array Arguments .. + COMPLEX*16 A( LDA, * ), B( LDB, * ) +* .. +* +* Purpose +* ======= +* +* ZHEGST reduces a complex Hermitian-definite generalized +* eigenproblem to standard form. +* +* If ITYPE = 1, the problem is A*x = lambda*B*x, +* and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) +* +* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or +* B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. +* +* B must have been previously factorized as U**H*U or L*L**H by ZPOTRF. +* +* Arguments +* ========= +* +* ITYPE (input) INTEGER +* = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); +* = 2 or 3: compute U*A*U**H or L**H*A*L. +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangle of A is stored and B is factored as +* U**H*U; +* = 'L': Lower triangle of A is stored and B is factored as +* L*L**H. +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* A (input/output) COMPLEX*16 array, dimension (LDA,N) +* On entry, the Hermitian matrix A. If UPLO = 'U', the leading +* N-by-N upper triangular part of A contains the upper +* triangular part of the matrix A, and the strictly lower +* triangular part of A is not referenced. If UPLO = 'L', the +* leading N-by-N lower triangular part of A contains the lower +* triangular part of the matrix A, and the strictly upper +* triangular part of A is not referenced. +* +* On exit, if INFO = 0, the transformed matrix, stored in the +* same format as A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input) COMPLEX*16 array, dimension (LDB,N) +* The triangular factor from the Cholesky factorization of B, +* as returned by ZPOTRF. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D+0 ) + COMPLEX*16 CONE, HALF + PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ), + $ HALF = ( 0.5D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + LOGICAL UPPER + INTEGER K, KB, NB +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZHEGS2, ZHEMM, ZHER2K, ZTRMM, ZTRSM +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + UPPER = LSAME( UPLO, 'U' ) + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZHEGST', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* Determine the block size for this environment. +* + NB = ILAENV( 1, 'ZHEGST', UPLO, N, -1, -1, -1 ) +* + IF( NB.LE.1 .OR. NB.GE.N ) THEN +* +* Use unblocked code +* + CALL ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) + ELSE +* +* Use blocked code +* + IF( ITYPE.EQ.1 ) THEN + IF( UPPER ) THEN +* +* Compute inv(U')*A*inv(U) +* + DO 10 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the upper triangle of A(k:n,k:n) +* + CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + IF( K+KB.LE.N ) THEN + CALL ZTRSM( 'Left', UPLO, 'Conjugate transpose', + $ 'Non-unit', KB, N-K-KB+1, CONE, + $ B( K, K ), LDB, A( K, K+KB ), LDA ) + CALL ZHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, + $ A( K, K ), LDA, B( K, K+KB ), LDB, + $ CONE, A( K, K+KB ), LDA ) + CALL ZHER2K( UPLO, 'Conjugate transpose', N-K-KB+1, + $ KB, -CONE, A( K, K+KB ), LDA, + $ B( K, K+KB ), LDB, ONE, + $ A( K+KB, K+KB ), LDA ) + CALL ZHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, + $ A( K, K ), LDA, B( K, K+KB ), LDB, + $ CONE, A( K, K+KB ), LDA ) + CALL ZTRSM( 'Right', UPLO, 'No transpose', + $ 'Non-unit', KB, N-K-KB+1, CONE, + $ B( K+KB, K+KB ), LDB, A( K, K+KB ), + $ LDA ) + END IF + 10 CONTINUE + ELSE +* +* Compute inv(L)*A*inv(L') +* + DO 20 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the lower triangle of A(k:n,k:n) +* + CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + IF( K+KB.LE.N ) THEN + CALL ZTRSM( 'Right', UPLO, 'Conjugate transpose', + $ 'Non-unit', N-K-KB+1, KB, CONE, + $ B( K, K ), LDB, A( K+KB, K ), LDA ) + CALL ZHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, + $ A( K, K ), LDA, B( K+KB, K ), LDB, + $ CONE, A( K+KB, K ), LDA ) + CALL ZHER2K( UPLO, 'No transpose', N-K-KB+1, KB, + $ -CONE, A( K+KB, K ), LDA, + $ B( K+KB, K ), LDB, ONE, + $ A( K+KB, K+KB ), LDA ) + CALL ZHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, + $ A( K, K ), LDA, B( K+KB, K ), LDB, + $ CONE, A( K+KB, K ), LDA ) + CALL ZTRSM( 'Left', UPLO, 'No transpose', + $ 'Non-unit', N-K-KB+1, KB, CONE, + $ B( K+KB, K+KB ), LDB, A( K+KB, K ), + $ LDA ) + END IF + 20 CONTINUE + END IF + ELSE + IF( UPPER ) THEN +* +* Compute U*A*U' +* + DO 30 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) +* + CALL ZTRMM( 'Left', UPLO, 'No transpose', 'Non-unit', + $ K-1, KB, CONE, B, LDB, A( 1, K ), LDA ) + CALL ZHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), + $ LDA, B( 1, K ), LDB, CONE, A( 1, K ), + $ LDA ) + CALL ZHER2K( UPLO, 'No transpose', K-1, KB, CONE, + $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A, + $ LDA ) + CALL ZHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), + $ LDA, B( 1, K ), LDB, CONE, A( 1, K ), + $ LDA ) + CALL ZTRMM( 'Right', UPLO, 'Conjugate transpose', + $ 'Non-unit', K-1, KB, CONE, B( K, K ), LDB, + $ A( 1, K ), LDA ) + CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + 30 CONTINUE + ELSE +* +* Compute L'*A*L +* + DO 40 K = 1, N, NB + KB = MIN( N-K+1, NB ) +* +* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) +* + CALL ZTRMM( 'Right', UPLO, 'No transpose', 'Non-unit', + $ KB, K-1, CONE, B, LDB, A( K, 1 ), LDA ) + CALL ZHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), + $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ), + $ LDA ) + CALL ZHER2K( UPLO, 'Conjugate transpose', K-1, KB, + $ CONE, A( K, 1 ), LDA, B( K, 1 ), LDB, + $ ONE, A, LDA ) + CALL ZHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), + $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ), + $ LDA ) + CALL ZTRMM( 'Left', UPLO, 'Conjugate transpose', + $ 'Non-unit', KB, K-1, CONE, B( K, K ), LDB, + $ A( K, 1 ), LDA ) + CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA, + $ B( K, K ), LDB, INFO ) + 40 CONTINUE + END IF + END IF + END IF + RETURN +* +* End of ZHEGST +* + END
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libcruft/lapack/zhegv.f Sun Dec 21 17:10:38 2008 +0100 @@ -0,0 +1,232 @@ + SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, + $ LWORK, RWORK, INFO ) +* +* -- LAPACK driver routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER JOBZ, UPLO + INTEGER INFO, ITYPE, LDA, LDB, LWORK, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION RWORK( * ), W( * ) + COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* ZHEGV computes all the eigenvalues, and optionally, the eigenvectors +* of a complex generalized Hermitian-definite eigenproblem, of the form +* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. +* Here A and B are assumed to be Hermitian and B is also +* positive definite. +* +* Arguments +* ========= +* +* ITYPE (input) INTEGER +* Specifies the problem type to be solved: +* = 1: A*x = (lambda)*B*x +* = 2: A*B*x = (lambda)*x +* = 3: B*A*x = (lambda)*x +* +* JOBZ (input) CHARACTER*1 +* = 'N': Compute eigenvalues only; +* = 'V': Compute eigenvalues and eigenvectors. +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangles of A and B are stored; +* = 'L': Lower triangles of A and B are stored. +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* A (input/output) COMPLEX*16 array, dimension (LDA, N) +* On entry, the Hermitian matrix A. If UPLO = 'U', the +* leading N-by-N upper triangular part of A contains the +* upper triangular part of the matrix A. If UPLO = 'L', +* the leading N-by-N lower triangular part of A contains +* the lower triangular part of the matrix A. +* +* On exit, if JOBZ = 'V', then if INFO = 0, A contains the +* matrix Z of eigenvectors. The eigenvectors are normalized +* as follows: +* if ITYPE = 1 or 2, Z**H*B*Z = I; +* if ITYPE = 3, Z**H*inv(B)*Z = I. +* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') +* or the lower triangle (if UPLO='L') of A, including the +* diagonal, is destroyed. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input/output) COMPLEX*16 array, dimension (LDB, N) +* On entry, the Hermitian positive definite matrix B. +* If UPLO = 'U', the leading N-by-N upper triangular part of B +* contains the upper triangular part of the matrix B. +* If UPLO = 'L', the leading N-by-N lower triangular part of B +* contains the lower triangular part of the matrix B. +* +* On exit, if INFO <= N, the part of B containing the matrix is +* overwritten by the triangular factor U or L from the Cholesky +* factorization B = U**H*U or B = L*L**H. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* W (output) DOUBLE PRECISION array, dimension (N) +* If INFO = 0, the eigenvalues in ascending order. +* +* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) +* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +* +* LWORK (input) INTEGER +* The length of the array WORK. LWORK >= max(1,2*N-1). +* For optimal efficiency, LWORK >= (NB+1)*N, +* where NB is the blocksize for ZHETRD returned by ILAENV. +* +* If LWORK = -1, then a workspace query is assumed; the routine +* only calculates the optimal size of the WORK array, returns +* this value as the first entry of the WORK array, and no error +* message related to LWORK is issued by XERBLA. +* +* RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2)) +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* > 0: ZPOTRF or ZHEEV returned an error code: +* <= N: if INFO = i, ZHEEV failed to converge; +* i off-diagonal elements of an intermediate +* tridiagonal form did not converge to zero; +* > N: if INFO = N + i, for 1 <= i <= N, then the leading +* minor of order i of B is not positive definite. +* The factorization of B could not be completed and +* no eigenvalues or eigenvectors were computed. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ONE + PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + LOGICAL LQUERY, UPPER, WANTZ + CHARACTER TRANS + INTEGER LWKOPT, NB, NEIG +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZHEEV, ZHEGST, ZPOTRF, ZTRMM, ZTRSM +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + UPPER = LSAME( UPLO, 'U' ) + LQUERY = ( LWORK.EQ.-1 ) +* + INFO = 0 + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN + INFO = -2 + ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN + INFO = -3 + ELSE IF( N.LT.0 ) THEN + INFO = -4 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -6 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -8 + END IF +* + IF( INFO.EQ.0 ) THEN + NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) + LWKOPT = MAX( 1, ( NB + 1 )*N ) + WORK( 1 ) = LWKOPT +* + IF( LWORK.LT.MAX( 1, 2*N - 1 ) .AND. .NOT.LQUERY ) THEN + INFO = -11 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZHEGV ', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* Form a Cholesky factorization of B. +* + CALL ZPOTRF( UPLO, N, B, LDB, INFO ) + IF( INFO.NE.0 ) THEN + INFO = N + INFO + RETURN + END IF +* +* Transform problem to standard eigenvalue problem and solve. +* + CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) + CALL ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO ) +* + IF( WANTZ ) THEN +* +* Backtransform eigenvectors to the original problem. +* + NEIG = N + IF( INFO.GT.0 ) + $ NEIG = INFO - 1 + IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN +* +* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; +* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y +* + IF( UPPER ) THEN + TRANS = 'N' + ELSE + TRANS = 'C' + END IF +* + CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, + $ B, LDB, A, LDA ) +* + ELSE IF( ITYPE.EQ.3 ) THEN +* +* For B*A*x=(lambda)*x; +* backtransform eigenvectors: x = L*y or U'*y +* + IF( UPPER ) THEN + TRANS = 'C' + ELSE + TRANS = 'N' + END IF +* + CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, + $ B, LDB, A, LDA ) + END IF + END IF +* + WORK( 1 ) = LWKOPT +* + RETURN +* +* End of ZHEGV +* + END