cpteqr (l)  Linux Man Pages
cpteqr: computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor
Command to display cpteqr
manual in Linux: $ man l cpteqr
NAME
CPTEQR  computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor
SYNOPSIS
 SUBROUTINE CPTEQR(

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

CHARACTER
COMPZ

INTEGER
INFO, LDZ, N

REAL
D( * ), E( * ), WORK( * )

COMPLEX
Z( LDZ, * )
PURPOSE
CPTEQR computes all eigenvalues and, optionally, eigenvectors of a
symmetric positive definite tridiagonal matrix by first factoring the
matrix using SPTTRF and then calling CBDSQR 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 positive definite Hermitian matrix
can also be found if CHETRD, CHPTRD, or CHBTRD 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 Hermitian
matrix also. Array Z contains the unitary 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) COMPLEX array, dimension (LDZ, N)

On entry, if COMPZ = aqVaq, the unitary matrix used in the
reduction to tridiagonal form.
On exit, if COMPZ = aqVaq, the orthonormal eigenvectors of the
original Hermitian 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 cpteqr
 cpteqr (3)
 cptcon (l)  computes the reciprocal of the condition number (in the 1norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF
 cptrfs (l)  improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
 cptsv (l)  computes the solution to a complex system of linear equations A*X = B, where A is an NbyN Hermitian positive definite tridiagonal matrix, and X and B are NbyNRHS matrices
 cptsvx (l)  uses the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an NbyN Hermitian positive definite tridiagonal matrix and X and B are NbyNRHS matrices
 cpttrf (l)  computes the L*D*Laq factorization of a complex Hermitian positive definite tridiagonal matrix A
 cpttrs (l)  solves a tridiagonal system of the form A * X = B using the factorization A = Uaq*D*U or A = L*D*Laq computed by CPTTRF
 cptts2 (l)  solves a tridiagonal system of the form A * X = B using the factorization A = Uaq*D*U or A = L*D*Laq computed by CPTTRF