chegvx

NAME

chegvx - compute selected eigenvalues, and optionally, 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

SYNOPSIS 

  SUBROUTINE CHEGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL, 
 *      VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, 
 *      IFAIL, INFO)
  CHARACTER * 1 JOBZ, RANGE, UPLO
  COMPLEX A(LDA,*), B(LDB,*), Z(LDZ,*), WORK(*)
  INTEGER ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
  INTEGER IWORK(*), IFAIL(*)
  REAL VL, VU, ABSTOL
  REAL W(*), RWORK(*)
 
  SUBROUTINE CHEGVX_64( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, 
 *      VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, 
 *      IFAIL, INFO)
  CHARACTER * 1 JOBZ, RANGE, UPLO
  COMPLEX A(LDA,*), B(LDB,*), Z(LDZ,*), WORK(*)
  INTEGER*8 ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
  INTEGER*8 IWORK(*), IFAIL(*)
  REAL VL, VU, ABSTOL
  REAL W(*), RWORK(*)

F95 INTERFACE 

  SUBROUTINE HEGVX( ITYPE, JOBZ, RANGE, UPLO, [N], A, [LDA], B, [LDB], 
 *       VL, VU, IL, IU, ABSTOL, M, W, Z, [LDZ], [WORK], [LWORK], [RWORK], 
 *       [IWORK], IFAIL, [INFO])
  CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A, B, Z
  INTEGER :: ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
  INTEGER, DIMENSION(:) :: IWORK, IFAIL
  REAL :: VL, VU, ABSTOL
  REAL, DIMENSION(:) :: W, RWORK
 
  SUBROUTINE HEGVX_64( ITYPE, JOBZ, RANGE, UPLO, [N], A, [LDA], B, 
 *       [LDB], VL, VU, IL, IU, ABSTOL, M, W, Z, [LDZ], [WORK], [LWORK], 
 *       [RWORK], [IWORK], IFAIL, [INFO])
  CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A, B, Z
  INTEGER(8) :: ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
  INTEGER(8), DIMENSION(:) :: IWORK, IFAIL
  REAL :: VL, VU, ABSTOL
  REAL, DIMENSION(:) :: W, RWORK

C INTERFACE

#include <sunperf.h>

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

void chegvx_64(long itype, char jobz, char range, char uplo, long n, complex *a, long lda, complex *b, long ldb, float vl, float vu, long il, long iu, float abstol, long *m, float *w, complex *z, long ldz, long *ifail, long *info);

PURPOSE

chegvx computes selected eigenvalues, and optionally, 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. 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 matrices A and B. N >= 0.

* A (input/output)
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, 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 Hermitian 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)
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)
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'.

* 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)
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'.

* 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*SLAMCH('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)
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(1,2*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)
dimension(7*N)

* 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)