SSYGV (3) Linux Manual Page

ssygv.f –

Synopsis

Functions/Subroutines

subroutine ssygv (ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, INFO)
SSYGST

Function/Subroutine Documentation

subroutine ssygv (integerITYPE, characterJOBZ, characterUPLO, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( * )W, real, dimension( * )WORK, integerLWORK, integerINFO)

SSYGST

Purpose:

 SSYGV 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.

 

Parameters:

ITYPE

 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

JOBZ

 JOBZ is CHARACTER*1

 = ‘N’: Compute eigenvalues only;

 = ‘V’: Compute eigenvalues and eigenvectors.

UPLO

 UPLO is CHARACTER*1

 = ‘U’: Upper triangles of A and B are stored;

 = ‘L’: Lower triangles of A and B are stored.

N

 N is INTEGER

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

A

 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.

LDA

 LDA is INTEGER

 The leading dimension of the array A. LDA >= max(1,N).

B

 B is REAL array, dimension (LDB, N)

 On entry, the symmetric positive definite 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.

LDB

 LDB is INTEGER

 The leading dimension of the array B. LDB >= max(1,N).

W

 W is REAL array, dimension (N)

 If INFO = 0, the eigenvalues in ascending order.

WORK

 WORK is REAL array, dimension (MAX(1,LWORK))

 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

 LWORK is INTEGER

 The length of the array WORK. LWORK >= max(1,3*N-1).

 For optimal efficiency, LWORK >= (NB+2)*N,

 where NB is the blocksize for SSYTRD returned by ILAENV.

 If LWORK = -1, then a workspace query is assumed; the routine

 only calculates the optimal size of the WORK array, returns

 this value as the first entry of the WORK array, and no error

 message related to LWORK is issued by XERBLA.

INFO

 INFO is INTEGER

 = 0: successful exit

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

 > 0: SPOTRF or SSYEV returned an error code:

 <= N: if INFO = i, SSYEV failed to converge;

 i off-diagonal elements of an intermediate

 tridiagonal form did not converge to zero;

 > N: if INFO = N + i, for 1 <= i <= N, then the leading

 minor of order i of B is not positive definite.

 The factorization of B could not be completed and

 no eigenvalues or eigenvectors were computed.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 175 of file ssygv.f.

Author

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