.TH DSYGS2 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME DSYGS2 - a real symmetric-definite generalized eigenproblem to standard form .SH SYNOPSIS .TP 19 SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) .TP 19 .ti +4 CHARACTER UPLO .TP 19 .ti +4 INTEGER INFO, ITYPE, LDA, LDB, N .TP 19 .ti +4 DOUBLE PRECISION A( LDA, * ), B( LDB, * ) .SH PURPOSE DSYGS2 reduces a real symmetric-definite generalized eigenproblem to standard form. If ITYPE = 1, the problem is A*x = lambda*B*x, .br and A is overwritten by inv(U\(aq)*A*inv(U) or inv(L)*A*inv(L\(aq) If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or .br B*A*x = lambda*x, and A is overwritten by U*A*U` or L\(aq*A*L. B must have been previously factorized as U\(aq*U or L*L\(aq by DPOTRF. .SH ARGUMENTS .TP 8 ITYPE (input) INTEGER = 1: compute inv(U\(aq)*A*inv(U) or inv(L)*A*inv(L\(aq); .br = 2 or 3: compute U*A*U\(aq or L\(aq*A*L. .TP 8 UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored, and how B has been factorized. = \(aqU\(aq: Upper triangular .br = \(aqL\(aq: Lower triangular .TP 8 N (input) INTEGER The order of the matrices A and B. N >= 0. .TP 8 A (input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = \(aqU\(aq, 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 = \(aqL\(aq, 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. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). .TP 8 B (input) DOUBLE PRECISION array, dimension (LDB,N) The triangular factor from the Cholesky factorization of B, as returned by DPOTRF. .TP 8 LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). .TP 8 INFO (output) INTEGER = 0: successful exit. .br < 0: if INFO = -i, the i-th argument had an illegal value.