• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

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:

   = 1:  A*x  = (lambda)*B*x

   = 2:  A*B*x  = (lambda)*x

   = 3:  B*A*x  = (lambda)*x

• JOBZ (input)
  

   = 'N':  Compute eigenvalues only;

   = 'V':  Compute eigenvalues and eigenvectors.

• UPLO (input)
  

   = 'U':  Upper triangles of A and B are stored;

   = 'L':  Lower triangles of A and B are stored.

• 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 (output)
  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)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value

   > 0:  SPPTRF or SSPEV returned an error code:

   < = N:  if INFO  = i, SSPEV failed to converge;
  i off-diagonal elements of an intermediate
  tridiagonal form did not converge to zero.
   > 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.