dspgv

NAME

dspgv - compute 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

SYNOPSIS

  SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, A, B, W, Z, LDZ, WORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  INTEGER ITYPE, N, LDZ, INFO
  DOUBLE PRECISION A(*), B(*), W(*), Z(LDZ,*), WORK(*)
 
  SUBROUTINE DSPGV_64( ITYPE, JOBZ, UPLO, N, A, B, W, Z, LDZ, WORK, 
 *      INFO)
  CHARACTER * 1 JOBZ, UPLO
  INTEGER*8 ITYPE, N, LDZ, INFO
  DOUBLE PRECISION A(*), B(*), W(*), Z(LDZ,*), WORK(*)

F95 INTERFACE

  SUBROUTINE SPGV( ITYPE, JOBZ, UPLO, [N], A, B, W, Z, [LDZ], [WORK], 
 *       [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER :: ITYPE, N, LDZ, INFO
  REAL(8), DIMENSION(:) :: A, B, W, WORK
  REAL(8), DIMENSION(:,:) :: Z
 
  SUBROUTINE SPGV_64( ITYPE, JOBZ, UPLO, [N], A, B, W, Z, [LDZ], [WORK], 
 *       [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  INTEGER(8) :: ITYPE, N, LDZ, INFO
  REAL(8), DIMENSION(:) :: A, B, W, WORK
  REAL(8), DIMENSION(:,:) :: Z

C INTERFACE

#include <sunperf.h>

void dspgv(int itype, char jobz, char uplo, int n, double *a, double *b, double *w, double *z, int ldz, int *info);

void dspgv_64(long itype, char jobz, char uplo, long n, double *a, double *b, double *w, double *z, long ldz, long *info);

PURPOSE

dspgv 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, stored in packed format, and B is also positive definite.

ARGUMENTS

* ITYPE (input)

Specifies the problem type to be solved:

* JOBZ (input)

* UPLO (input)

* N (input)

The order of the matrices A and B. N >= 0.

* A (input/output)

(N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array A as follows: if UPLO = 'U', A(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', A(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, the contents of A are destroyed.

* B (input/output)

On entry, the upper or lower triangle of the symmetric matrix B, packed columnwise in a linear array. The j-th column of B is stored in the array B as follows: if UPLO = 'U', B(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', B(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.

On exit, the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T, in the same storage format as B.

* W (output)

If INFO = 0, the eigenvalues in ascending order.

* Z (input)

If JOBZ = 'V', then if INFO = 0, Z 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 Z is not referenced.

* LDZ (input)

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

* WORK (workspace)

dimension(3*N)

* INFO (output)