sspgv.f - Man Page

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

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.