spteqr (l)  Linux Manuals
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
Command to display spteqr
manual in Linux: $ man l spteqr
NAME
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
SYNOPSIS
 SUBROUTINE SPTEQR(

COMPZ, N, D, E, Z, LDZ, WORK, INFO )

CHARACTER
COMPZ

INTEGER
INFO, LDZ, N

REAL
D( * ), E( * ), WORK( * ), Z( LDZ, * )
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.)
ARGUMENTS
 COMPZ (input) CHARACTER*1

= aqNaq: Compute eigenvalues only.
= aqVaq: Compute eigenvectors of original symmetric
matrix also. Array Z contains the orthogonal
matrix used to reduce the original matrix to
tridiagonal form.
= aqIaq: Compute eigenvectors of tridiagonal matrix also.
 N (input) INTEGER

The order of the matrix. N >= 0.
 D (input/output) 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 (input/output) REAL array, dimension (N1)

On entry, the (n1) subdiagonal elements of the tridiagonal
matrix.
On exit, E has been destroyed.
 Z (input/output) REAL array, dimension (LDZ, N)

On entry, if COMPZ = aqVaq, the orthogonal matrix used in the
reduction to tridiagonal form.
On exit, if COMPZ = aqVaq, the orthonormal eigenvectors of the
original symmetric matrix;
if COMPZ = aqIaq, the orthonormal eigenvectors of the
tridiagonal matrix.
If INFO > 0 on exit, Z contains the eigenvectors associated
with only the stored eigenvalues.
If COMPZ = aqNaq, then Z is not referenced.
 LDZ (input) INTEGER

The leading dimension of the array Z. LDZ >= 1, and if
COMPZ = aqVaq or aqIaq, LDZ >= max(1,N).
 WORK (workspace) REAL array, dimension (4*N)

 INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = i, the ith 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 ith principal minor
was not positive definite.
> N the SVD algorithm failed to converge;
if INFO = N+i, i offdiagonal elements of the
bidiagonal factor did not converge to zero.
Pages related to spteqr
 spteqr (3)
 sptcon (l)  computes the reciprocal of the condition number (in the 1norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF
 sptrfs (l)  improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
 sptsv (l)  computes the solution to a real system of linear equations A*X = B, where A is an NbyN symmetric positive definite tridiagonal matrix, and X and B are NbyNRHS matrices
 sptsvx (l)  uses the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an NbyN symmetric positive definite tridiagonal matrix and X and B are NbyNRHS matrices
 spttrf (l)  computes the L*D*Laq factorization of a real symmetric positive definite tridiagonal matrix A
 spttrs (l)  solves a tridiagonal system of the form A * X = B using the L*D*Laq factorization of A computed by SPTTRF
 sptts2 (l)  solves a tridiagonal system of the form A * X = B using the L*D*Laq factorization of A computed by SPTTRF