---
name: "sspgv"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/sspgv/3lapack"
---

# sspgv(3lapack)

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

## NAME

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

## SYNOPSIS

- SUBROUTINE SSPGV(

  ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO )

- CHARACTER

  JOBZ, UPLO

- INTEGER

  INFO, ITYPE, LDZ, N

- REAL

  AP( \* ), BP( \* ), W( \* ), WORK( \* ), Z( LDZ, \* )

## 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.\

## ARGUMENTS

- ITYPE (input) 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 (input) CHARACTER\*1

  \= 'N':  Compute eigenvalues only;\
   \= 'V':  Compute eigenvalues and eigenvectors.

- UPLO (input) CHARACTER\*1

  \= 'U':  Upper triangles of A and B are stored;\
   \= 'L':  Lower triangles of A and B are stored.

- N (input) INTEGER

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

- AP (input/output) 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 (input/output) 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 (output) REAL array, dimension (N)

  If INFO = 0, the eigenvalues in ascending order.

- Z (output) 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 (input) INTEGER

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

- WORK (workspace) REAL array, dimension (3\*N)

  - INFO (output) 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 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.