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author | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
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committer | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
commit | baba851215b44ac3b60b9248eb02bcce7eb76247 (patch) | |
tree | 8c0f5c006875532a30d4409f5e94b0f310ff00a7 /SRC/ssygvd.f | |
download | lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.gz lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.bz2 lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.zip |
Move LAPACK trunk into position.
Diffstat (limited to 'SRC/ssygvd.f')
-rw-r--r-- | SRC/ssygvd.f | 282 |
1 files changed, 282 insertions, 0 deletions
diff --git a/SRC/ssygvd.f b/SRC/ssygvd.f new file mode 100644 index 00000000..4984fffb --- /dev/null +++ b/SRC/ssygvd.f @@ -0,0 +1,282 @@ + SUBROUTINE SSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, + $ LWORK, IWORK, LIWORK, 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, LIWORK, LWORK, N +* .. +* .. Array Arguments .. + INTEGER IWORK( * ) + REAL A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* SSYGVD 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. +* If eigenvectors are desired, it uses a divide and conquer algorithm. +* +* The divide and conquer algorithm makes very mild assumptions about +* floating point arithmetic. It will work on machines with a guard +* digit in add/subtract, or on those binary machines without guard +* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or +* Cray-2. It could conceivably fail on hexadecimal or decimal machines +* without guard digits, but we know of none. +* +* 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 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 dimension of the array WORK. +* If N <= 1, LWORK >= 1. +* If JOBZ = 'N' and N > 1, LWORK >= 2*N+1. +* If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. +* +* If LWORK = -1, then a workspace query is assumed; the routine +* only calculates the optimal sizes of the WORK and IWORK +* arrays, returns these values as the first entries of the WORK +* and IWORK arrays, and no error message related to LWORK or +* LIWORK is issued by XERBLA. +* +* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) +* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. +* +* LIWORK (input) INTEGER +* The dimension of the array IWORK. +* If N <= 1, LIWORK >= 1. +* If JOBZ = 'N' and N > 1, LIWORK >= 1. +* If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. +* +* If LIWORK = -1, then a workspace query is assumed; the +* routine only calculates the optimal sizes of the WORK and +* IWORK arrays, returns these values as the first entries of +* the WORK and IWORK arrays, and no error message related to +* LWORK or LIWORK 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 SSYEVD returned an error code: +* <= N: if INFO = i and JOBZ = 'N', then the algorithm +* failed to converge; i off-diagonal elements of an +* intermediate tridiagonal form did not converge to +* zero; +* if INFO = i and JOBZ = 'V', then the algorithm +* failed to compute an eigenvalue while working on +* the submatrix lying in rows and columns INFO/(N+1) +* through mod(INFO,N+1); +* > 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. +* +* Further Details +* =============== +* +* Based on contributions by +* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA +* +* Modified so that no backsubstitution is performed if SSYEVD fails to +* converge (NEIG in old code could be greater than N causing out of +* bounds reference to A - reported by Ralf Meyer). Also corrected the +* description of INFO and the test on ITYPE. Sven, 16 Feb 05. +* ===================================================================== +* +* .. Parameters .. + REAL ONE + PARAMETER ( ONE = 1.0E+0 ) +* .. +* .. Local Scalars .. + LOGICAL LQUERY, UPPER, WANTZ + CHARACTER TRANS + INTEGER LIOPT, LIWMIN, LOPT, LWMIN +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL SPOTRF, SSYEVD, SSYGST, STRMM, STRSM, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, REAL +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + UPPER = LSAME( UPLO, 'U' ) + LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) +* + INFO = 0 + IF( N.LE.1 ) THEN + LIWMIN = 1 + LWMIN = 1 + ELSE IF( WANTZ ) THEN + LIWMIN = 3 + 5*N + LWMIN = 1 + 6*N + 2*N**2 + ELSE + LIWMIN = 1 + LWMIN = 2*N + 1 + END IF + LOPT = LWMIN + LIOPT = LIWMIN + 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 + WORK( 1 ) = LOPT + IWORK( 1 ) = LIOPT +* + IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN + INFO = -11 + ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN + INFO = -13 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'SSYGVD', -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 SSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK, + $ INFO ) + LOPT = MAX( REAL( LOPT ), REAL( WORK( 1 ) ) ) + LIOPT = MAX( REAL( LIOPT ), REAL( IWORK( 1 ) ) ) +* + IF( WANTZ .AND. INFO.EQ.0 ) THEN +* +* Backtransform eigenvectors to the original problem. +* + 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, N, 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, N, ONE, + $ B, LDB, A, LDA ) + END IF + END IF +* + WORK( 1 ) = LOPT + IWORK( 1 ) = LIOPT +* + RETURN +* +* End of SSYGVD +* + END |