spteqr (3)

Functions/Subroutines

subroutine spteqr (COMPZ, N, D, E, Z, LDZ, WORK, INFO)

SPTEQR

subroutine spteqr (characterCOMPZ, integerN, real, dimension( * )D, real, dimension( * )E, real, dimension( ldz, * )Z, integerLDZ, real, dimension( * )WORK, integerINFO)

SPTEQR

Purpose:

 SPTEQR computes all eigenvalues and, optionally, eigenvectors of a
 symmetric positive definite tridiagonal matrix by first factoring the
 matrix using SPTTRF, and then calling SBDSQR to compute the singular
 values of the bidiagonal factor.

 This routine computes the eigenvalues of the positive definite
 tridiagonal matrix to high relative accuracy.  This means that if the
 eigenvalues range over many orders of magnitude in size, then the
 small eigenvalues and corresponding eigenvectors will be computed
 more accurately than, for example, with the standard QR method.

 The eigenvectors of a full or band symmetric positive definite matrix
 can also be found if SSYTRD, SSPTRD, or SSBTRD has been used to
 reduce this matrix to tridiagonal form. (The reduction to tridiagonal
 form, however, may preclude the possibility of obtaining high
 relative accuracy in the small eigenvalues of the original matrix, if
 these eigenvalues range over many orders of magnitude.)

Parameters:

COMPZ

          COMPZ is CHARACTER*1
          = 'N':  Compute eigenvalues only.
          = 'V':  Compute eigenvectors of original symmetric
                  matrix also.  Array Z contains the orthogonal
                  matrix used to reduce the original matrix to
                  tridiagonal form.
          = 'I':  Compute eigenvectors of tridiagonal matrix also.

N

          N is INTEGER
          The order of the matrix.  N >= 0.

D

          D is REAL array, dimension (N)
          On entry, the n diagonal elements of the tridiagonal
          matrix.
          On normal exit, D contains the eigenvalues, in descending
          order.

E

          E is REAL array, dimension (N-1)
          On entry, the (n-1) subdiagonal elements of the tridiagonal
          matrix.
          On exit, E has been destroyed.

Z

          Z is REAL array, dimension (LDZ, N)
          On entry, if COMPZ = 'V', the orthogonal matrix used in the
          reduction to tridiagonal form.
          On exit, if COMPZ = 'V', the orthonormal eigenvectors of the
          original symmetric matrix;
          if COMPZ = 'I', the orthonormal eigenvectors of the
          tridiagonal matrix.
          If INFO > 0 on exit, Z contains the eigenvectors associated
          with only the stored eigenvalues.
          If  COMPZ = 'N', then Z is not referenced.

LDZ

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

WORK

          WORK is REAL array, dimension (4*N)

INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  if INFO = i, and i is:
                <= N  the Cholesky factorization of the matrix could
                      not be performed because the i-th principal minor
                      was not positive definite.
                > N   the SVD algorithm failed to converge;
                      if INFO = N+i, i off-diagonal elements of the
                      bidiagonal factor did not converge to zero.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 146 of file spteqr.f.

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