---
name: "sspgv.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/sspgv.f"
---

# sspgv.f(3)

## NAME

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.