ssygvx
ssygvx - compute selected eigenvalues, and optionally, 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
SUBROUTINE SSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL,
* VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL,
* INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
INTEGER IWORK(*), IFAIL(*)
REAL VL, VU, ABSTOL
REAL A(LDA,*), B(LDB,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SSYGVX_64( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
* VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL,
* INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER*8 ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
INTEGER*8 IWORK(*), IFAIL(*)
REAL VL, VU, ABSTOL
REAL A(LDA,*), B(LDB,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SYGVX( ITYPE, JOBZ, RANGE, UPLO, [N], A, [LDA], B, [LDB],
* VL, VU, IL, IU, ABSTOL, M, W, Z, [LDZ], [WORK], [LWORK], [IWORK],
* IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER :: ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
INTEGER, DIMENSION(:) :: IWORK, IFAIL
REAL :: VL, VU, ABSTOL
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: A, B, Z
SUBROUTINE SYGVX_64( ITYPE, JOBZ, RANGE, UPLO, [N], A, [LDA], B,
* [LDB], VL, VU, IL, IU, ABSTOL, M, W, Z, [LDZ], [WORK], [LWORK],
* [IWORK], IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER(8) :: ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK, IFAIL
REAL :: VL, VU, ABSTOL
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: A, B, Z
#include <sunperf.h>
void ssygvx(int itype, char jobz, char range, char uplo, int n, float *a, int lda, float *b, int ldb, float vl, float vu, int il, int iu, float abstol, int *m, float *w, float *z, int ldz, int *ifail, int *info);
void ssygvx_64(long itype, char jobz, char range, char uplo, long n, float *a, long lda, float *b, long ldb, float vl, float vu, long il, long iu, float abstol, long *m, float *w, float *z, long ldz, long *ifail, long *info);
ssygvx computes selected eigenvalues, and optionally, 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.
Eigenvalues and eigenvectors can be selected by specifying either a
range of values or a range of indices for the desired eigenvalues.
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* ITYPE (input)
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Specifies the problem type to be solved:
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* JOBZ (input)
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* RANGE (input)
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* UPLO (input)
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* N (input)
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The order of the matrix pencil (A,B). N >= 0.
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* A (input/output)
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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, the lower triangle (if UPLO='L') or the upper
triangle (if UPLO='U') of A, including the diagonal, is
destroyed.
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* LDA (input)
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The leading dimension of the array A. LDA >= max(1,N).
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* B (input/output)
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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.
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* LDB (input)
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The leading dimension of the array B. LDB >= max(1,N).
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* VL (input)
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If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'.
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* VU (input)
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See the description of VL.
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* IL (input)
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If RANGE='I', the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = 'A' or 'V'.
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* IU (input)
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See the description of IL.
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* ABSTOL (input)
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The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to
ABSTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained
by reducing A to tridiagonal form.
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*DLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*SLAMCH('S').
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* M (output)
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The total number of eigenvalues found. 0 <= M <= N.
If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
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* W (output)
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On normal exit, the first M elements contain the selected
eigenvalues in ascending order.
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* Z (input)
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If JOBZ = 'N', then Z is not referenced.
If JOBZ = 'V', then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
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 an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
Note: the user must ensure that at least max(1,M) columns are
supplied in the array Z; if RANGE = 'V', the exact value of M
is not known in advance and an upper bound must be used.
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* LDZ (input)
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The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N).
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* WORK (workspace)
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On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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* LWORK (input)
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The length of the array WORK. LWORK >= max(1,8*N).
For optimal efficiency, LWORK >= (NB+3)*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.
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* IWORK (workspace)
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dimension(5*N)
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* IFAIL (output)
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If JOBZ = 'V', then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = 'N', then IFAIL is not referenced.
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* INFO (output)
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