NAME¶

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

SYNOPSIS¶

SUBROUTINE DSPGST(

ITYPE, UPLO, N, AP, BP, INFO )

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

PURPOSE¶

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 DPPTRF.

ARGUMENTS¶

ITYPE (input) INTEGER

= 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) CHARACTER*1

= '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) INTEGER

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

AP (input/output) DOUBLE PRECISION array, dimension (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 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) DOUBLE PRECISION array, dimension (N*(N+1)/2)

The triangular factor from the Cholesky factorization of B, stored in the same format as A, as returned by DPPTRF.

INFO (output) INTEGER

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