.TH SSPGST 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME SSPGST - a real symmetric-definite generalized eigenproblem to standard form, using packed storage .SH SYNOPSIS .TP 19 SUBROUTINE SSPGST( ITYPE, UPLO, N, AP, BP, INFO ) .TP 19 .ti +4 CHARACTER UPLO .TP 19 .ti +4 INTEGER INFO, ITYPE, N .TP 19 .ti +4 REAL AP( * ), BP( * ) .SH PURPOSE SSPGST reduces a real symmetric-definite generalized eigenproblem to standard form, using packed storage. If ITYPE = 1, the problem is A*x = lambda*B*x, .br 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 .br 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. .SH ARGUMENTS .TP 8 ITYPE (input) INTEGER = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); .br = 2 or 3: compute U*A*U**T or L**T*A*L. .TP 8 UPLO (input) CHARACTER*1 .br = \(aqU\(aq: Upper triangle of A is stored and B is factored as U**T*U; = \(aqL\(aq: Lower triangle of A is stored and B is factored as L*L**T. .TP 8 N (input) INTEGER The order of the matrices A and B. N >= 0. .TP 8 AP (input/output) REAL 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 = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = \(aqL\(aq, 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. .TP 8 BP (input) REAL 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 SPPTRF. .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value