Loading...
Searching...
No Matches

## sspgvd()

subroutine sspgvd | ( | 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 | lwork,
|  | integer, dimension( * ) | iwork,
|  | integer | liwork,
|  | integer | info )

SSPGVD

Download SSPGVD + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> SSPGVD 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.
      !> If eigenvectors are desired, it uses a divide and conquer algorithm.
      !>
      !>

Parameters

  [in]

  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
      !>

  [in]

  JOBZ

      !>          JOBZ is CHARACTER*1
      !>          = 'N':  Compute eigenvalues only;
      !>          = 'V':  Compute eigenvalues and eigenvectors.
      !>

  [in]

  UPLO

      !>          UPLO is CHARACTER*1
      !>          = 'U':  Upper triangles of A and B are stored;
      !>          = 'L':  Lower triangles of A and B are stored.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The order of the matrices A and B.  N >= 0.
      !>

  [in,out]

  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.
      !>

  [in,out]

  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.
      !>

  [out]

  W

      !>          W is REAL array, dimension (N)
      !>          If INFO = 0, the eigenvalues in ascending order.
      !>

  [out]

  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.
      !>

  [in]

  LDZ

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

  [out]

  WORK

      !>          WORK is REAL array, dimension (MAX(1,LWORK))
      !>          On exit, if INFO = 0, WORK(1) returns the required LWORK.
      !>

  [in]

  LWORK

      !>          LWORK is INTEGER
      !>          The dimension of the array WORK.
      !>          If N <= 1,               LWORK >= 1.
      !>          If JOBZ = 'N' and N > 1, LWORK >= 2*N.
      !>          If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
      !>
      !>          If LWORK = -1, then a workspace query is assumed; the routine
      !>          only calculates the required sizes of the WORK and IWORK
      !>          arrays, returns these values as the first entries of the WORK
      !>          and IWORK arrays, and no error message related to LWORK or
      !>          LIWORK is issued by XERBLA.
      !>

  [out]

  IWORK

      !>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
      !>          On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
      !>

  [in]

  LIWORK

      !>          LIWORK is INTEGER
      !>          The dimension of the array IWORK.
      !>          If JOBZ  = 'N' or N <= 1, LIWORK >= 1.
      !>          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.
      !>
      !>          If LIWORK = -1, then a workspace query is assumed; the
      !>          routine only calculates the required sizes of the WORK and
      !>          IWORK arrays, returns these values as the first entries of
      !>          the WORK and IWORK arrays, and no error message related to
      !>          LWORK or LIWORK is issued by XERBLA.
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0:  successful exit
      !>          < 0:  if INFO = -i, the i-th argument had an illegal value
      !>          > 0:  SPPTRF or SSPEVD returned an error code:
      !>             <= N:  if INFO = i, SSPEVD 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.

Contributors:
  Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA