NAME

dspgst - reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage

SYNOPSIS

  SUBROUTINE DSPGST( ITYPE, UPLO, N, AP, BP, INFO)
  CHARACTER * 1 UPLO
  INTEGER ITYPE, N, INFO
  DOUBLE PRECISION AP(*), BP(*)

  SUBROUTINE DSPGST_64( ITYPE, UPLO, N, AP, BP, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 ITYPE, N, INFO
  DOUBLE PRECISION AP(*), BP(*)

  SUBROUTINE SPGST( ITYPE, UPLO, N, AP, BP, [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: ITYPE, N, INFO
  REAL(8), DIMENSION(:) :: AP, BP

  SUBROUTINE SPGST_64( ITYPE, UPLO, N, AP, BP, [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: ITYPE, N, INFO
  REAL(8), DIMENSION(:) :: AP, BP

#include <sunperf.h>

void dspgst(int itype, char uplo, int n, double *ap, double *bp, int *info);

void dspgst_64(long itype, char uplo, long n, double *ap, double *bp, long *info);

dspgst reduces a real symmetric-definite generalized eigenproblem to standard form, using packed storage.

If ITYPE = 1, the problem is A*x = lambda*B*x,

and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)

If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or

B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.

B must have been previously factorized as U**T*U or L*L**T by SPPTRF.

ITYPE (input)

 = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);

 = 2 or 3: compute U*A*U**T or L**T*A*L.

UPLO (input)

 = 'U':  Upper triangle of A is stored and B is factored as
U**T*U;
 = 'L':  Lower triangle of A is stored and B is factored as
L*L**T.

N (input)
The order of the matrices A and B. N > = 0.
AP (input/output)
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 AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1 < =i < =j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j < =i < =n.
On exit, if INFO = 0, the transformed matrix, stored in the same format as A.
BP (input)
The triangular factor from the Cholesky factorization of B, stored in the same format as A, as returned by SPPTRF.

INFO (output)

 = 0:  successful exit

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