dsygvx

NAME

dsygvx - 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

SYNOPSIS 

  SUBROUTINE DSYGVX( 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(*)
  DOUBLE PRECISION VL, VU, ABSTOL
  DOUBLE PRECISION A(LDA,*), B(LDB,*), W(*), Z(LDZ,*), WORK(*)
 
  SUBROUTINE DSYGVX_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(*)
  DOUBLE PRECISION VL, VU, ABSTOL
  DOUBLE PRECISION A(LDA,*), B(LDB,*), W(*), Z(LDZ,*), WORK(*)

F95 INTERFACE 

  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(8) :: VL, VU, ABSTOL
  REAL(8), DIMENSION(:) :: W, WORK
  REAL(8), 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(8) :: VL, VU, ABSTOL
  REAL(8), DIMENSION(:) :: W, WORK
  REAL(8), DIMENSION(:,:) :: A, B, Z

C INTERFACE

#include <sunperf.h>

void dsygvx(int itype, char jobz, char range, char uplo, int n, double *a, int lda, double *b, int ldb, double vl, double vu, int il, int iu, double abstol, int *m, double *w, double *z, int ldz, int *ifail, int *info);

void dsygvx_64(long itype, char jobz, char range, char uplo, long n, double *a, long lda, double *b, long ldb, double vl, double vu, long il, long iu, double abstol, long *m, double *w, double *z, long ldz, long *ifail, long *info);

PURPOSE

dsygvx 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.

ARGUMENTS

* ITYPE (input)
Specifies the problem type to be solved:

* JOBZ (input)

* RANGE (input)

* UPLO (input)

* N (input)
The order of the matrix pencil (A,B). N >= 0.

* A (input/output)
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.

* LDA (input)
The leading dimension of the array A. LDA >= max(1,N).

* B (input/output)
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)
The leading dimension of the array B. LDB >= max(1,N).

* VL (input)
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'.

* VU (input)
See the description of VL.

* IL (input)
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'.

* IU (input)
See the description of IL.

* ABSTOL (input)
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').

* M (output)
The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

* W (output)
On normal exit, the first M elements contain the selected eigenvalues in ascending order.

* Z (input)
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.

* LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).

* WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

* LWORK (input)
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.

* IWORK (workspace)
dimension(5*N)

* IFAIL (output)
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.

* INFO (output)