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spteqr.f(3) LAPACK spteqr.f(3)

NAME

spteqr.f

SYNOPSIS

Functions/Subroutines


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

Function/Subroutine Documentation

subroutine spteqr (character COMPZ, integer N, real, dimension( * ) D, real, dimension( * ) E, real, dimension( ldz, * ) Z, integer LDZ, real, dimension( * ) WORK, integer INFO)

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:

December 2016

Definition at line 147 of file spteqr.f.

Author

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Tue Nov 14 2017 Version 3.8.0