# dspgvd.f - Man Page

SRC/dspgvd.f

## Synopsis

### Functions/Subroutines

subroutine **dspgvd** (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, lwork, iwork, liwork, info)**DSPGVD**

## Function/Subroutine Documentation

### subroutine dspgvd (integer itype, character jobz, character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) bp, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

**DSPGVD** Ā

**Purpose:**

DSPGVD 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. If eigenvectors are desired, it uses a divide and conquer algorithm.

**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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order.

*Z*Z is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the required LWORK.

*LWORK*LWORK is INTEGER The dimension of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= 2*N. 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 required 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.

*IWORK*IWORK is INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the required LIWORK.

*LIWORK*LIWORK is INTEGER The dimension of the array IWORK. If JOBZ = 'N' or 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 required 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.

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

**Contributors:**Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line **202** of file **dspgvd.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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