ssygv.f −

**Functions/Subroutines**

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

SSYGST

**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.

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