.TH "SRC/ssygvd.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/ssygvd.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBssygvd\fP (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, iwork, liwork, info)" .br .RI "\fBSSYGVD\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine ssygvd (integer itype, character jobz, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) w, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)" .PP \fBSSYGVD\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> SSYGVD 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\&. Here A and !> B are assumed to be symmetric and B is also positive definite\&. !> If eigenvectors are desired, it uses a divide and conquer algorithm\&. !> !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIITYPE\fP .PP .nf !> ITYPE is INTEGER !> Specifies the problem type to be solved: !> = 1: A*x = (lambda)*B*x !> = 2: A*B*x = (lambda)*x !> = 3: B*A*x = (lambda)*x !> .fi .PP .br \fIJOBZ\fP .PP .nf !> JOBZ is CHARACTER*1 !> = 'N': Compute eigenvalues only; !> = 'V': Compute eigenvalues and eigenvectors\&. !> .fi .PP .br \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangles of A and B are stored; !> = 'L': Lower triangles of A and B are stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrices A and B\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is REAL array, dimension (LDA, N) !> On entry, the symmetric matrix A\&. If UPLO = 'U', the !> leading N-by-N upper triangular part of A contains the !> upper triangular part of the matrix A\&. If UPLO = 'L', !> the leading N-by-N lower triangular part of A contains !> the lower triangular part of the matrix A\&. !> !> On exit, if JOBZ = 'V', then if INFO = 0, A contains the !> matrix Z of eigenvectors\&. The eigenvectors are normalized !> as follows: !> if ITYPE = 1 or 2, Z**T*B*Z = I; !> if ITYPE = 3, Z**T*inv(B)*Z = I\&. !> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') !> or the lower triangle (if UPLO='L') of A, including the !> diagonal, is destroyed\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is REAL array, dimension (LDB, N) !> On entry, the symmetric matrix B\&. If UPLO = 'U', the !> leading N-by-N upper triangular part of B contains the !> upper triangular part of the matrix B\&. If UPLO = 'L', !> the leading N-by-N lower triangular part of B contains !> the lower triangular part of the matrix B\&. !> !> On exit, if INFO <= N, the part of B containing the matrix is !> overwritten by the triangular factor U or L from the Cholesky !> factorization B = U**T*U or B = L*L**T\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIW\fP .PP .nf !> W is REAL array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The dimension of the array WORK\&. !> If N <= 1, LWORK >= 1\&. !> If JOBZ = 'N' and N > 1, LWORK >= 2*N+1\&. !> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2\&. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal sizes of the WORK and IWORK !> arrays, returns these values as the first entries of the WORK !> and IWORK arrays, and no error message related to LWORK or !> LIWORK is issued by XERBLA\&. !> .fi .PP .br \fIIWORK\fP .PP .nf !> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) !> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK\&. !> .fi .PP .br \fILIWORK\fP .PP .nf !> LIWORK is INTEGER !> The dimension of the array IWORK\&. !> If N <= 1, LIWORK >= 1\&. !> If JOBZ = 'N' and N > 1, LIWORK >= 1\&. !> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N\&. !> !> If LIWORK = -1, then a workspace query is assumed; the !> routine only calculates the optimal sizes of the WORK and !> IWORK arrays, returns these values as the first entries of !> the WORK and IWORK arrays, and no error message related to !> LWORK or LIWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: SPOTRF or SSYEVD returned an error code: !> <= N: if INFO = i and JOBZ = 'N', then the algorithm !> failed to converge; i off-diagonal elements of an !> intermediate tridiagonal form did not converge to !> zero; !> if INFO = i and JOBZ = 'V', then the algorithm !> failed to compute an eigenvalue while working on !> the submatrix lying in rows and columns INFO/(N+1) !> through mod(INFO,N+1); !> > N: if INFO = N + i, for 1 <= i <= N, then the leading !> principal minor of order i of B is not positive\&. !> The factorization of B could not be completed and !> no eigenvalues or eigenvectors were computed\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf !> !> Modified so that no backsubstitution is performed if SSYEVD fails to !> converge (NEIG in old code could be greater than N causing out of !> bounds reference to A - reported by Ralf Meyer)\&. Also corrected the !> description of INFO and the test on ITYPE\&. Sven, 16 Feb 05\&. !> .fi .PP .RE .PP \fBContributors:\fP .RS 4 Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA .RE .PP .PP Definition at line \fB219\fP of file \fBssygvd\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.