sspgv.f man page

sspgv.f —

Synopsis

Functions/Subroutines

subroutine sspgv (ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO)
SSPGST

Function/Subroutine Documentation

subroutine sspgv (integerITYPE, characterJOBZ, characterUPLO, integerN, real, dimension( * )AP, real, dimension( * )BP, real, dimension( * )W, real, dimension( ldz, * )Z, integerLDZ, real, dimension( * )WORK, integerINFO)

SSPGST

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
          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 161 of file sspgv.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

sspgv(3) is an alias of sspgv.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK