dsygst (l) - Linux Manuals

dsygst: reduces a real symmetric-definite generalized eigenproblem to standard form

NAME

DSYGST - reduces a real symmetric-definite generalized eigenproblem to standard form

SYNOPSIS

SUBROUTINE DSYGST(
ITYPE, UPLO, N, A, LDA, B, LDB, INFO )

    
CHARACTER UPLO

    
INTEGER INFO, ITYPE, LDA, LDB, N

    
DOUBLE PRECISION A( LDA, * ), B( LDB, * )

PURPOSE

DSYGST reduces a real symmetric-definite generalized eigenproblem to standard form. 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 DPOTRF.

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

= aqUaq: Upper triangle of A is stored and B is factored as U**T*U; = aqLaq: 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.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = aqUaq, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = aqLaq, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the transformed matrix, stored in the same format as A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input) DOUBLE PRECISION array, dimension (LDB,N)
The triangular factor from the Cholesky factorization of B, as returned by DPOTRF.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Pages related to dsygst

  • dsygst (3)
  • dsygs2 (l) - reduces a real symmetric-definite generalized eigenproblem to standard form
  • dsygv (l) - 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
  • dsygvd (l) - 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
  • dsygvx (l) - computes selected eigenvalues, and optionally, 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
  • dsycon (l) - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF
  • dsyequb (l) - computes row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number (with respect to the two-norm)
  • dsyev (l) - computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A