# sspgv.f - Man Page

SRC/sspgv.f

## Synopsis

### Functions/Subroutines

subroutine **sspgv** (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, info)**SSPGV**

## Function/Subroutine Documentation

### subroutine sspgv (integer itype, character jobz, character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) bp, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer info)

**SSPGV**

**Purpose:**

SSPGV 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, stored in packed format, 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.

*AP*AP is 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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, the contents of AP are destroyed.

*BP*BP is REAL array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix B, packed columnwise in a linear array. The j-th column of B is stored in the array BP as follows: if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. On exit, the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T, in the same storage format as B.

*W*W is REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order.

*Z*Z is REAL array, dimension (LDZ, N) If JOBZ = 'V', then if INFO = 0, Z 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 Z is not referenced.

*LDZ*LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).

*WORK*WORK is REAL array, dimension (3*N)

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: SPPTRF or SSPEV returned an error code: <= N: if INFO = i, SSPEV 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 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.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **158** of file **sspgv.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sspgv(3) is an alias of sspgv.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK