SSPGV (3lapack)

compute 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.