chptrd.f man page

chptrd.f —

Synopsis

Functions/Subroutines

subroutine chptrd (UPLO, N, AP, D, E, TAU, INFO)
CHPTRD

Function/Subroutine Documentation

subroutine chptrd (characterUPLO, integerN, complex, dimension( * )AP, real, dimension( * )D, real, dimension( * )E, complex, dimension( * )TAU, integerINFO)

CHPTRD

Purpose:

CHPTRD reduces a complex Hermitian matrix A stored in packed form to
real symmetric tridiagonal form T by a unitary similarity
transformation: Q**H * A * Q = T.

Parameters:

UPLO

UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N

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

AP

AP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian 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, if UPLO = 'U', the diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the unitary
matrix Q as a product of elementary reflectors; if UPLO
= 'L', the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the unitary matrix Q as a product
of elementary reflectors. See Further Details.

D

D is REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).

E

E is REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.

TAU

TAU is COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details:

If UPLO = 'U', the matrix Q is represented as a product of elementary
reflectors

   Q = H(n-1) . . . H(2) H(1).

Each H(i) has the form

   H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,
overwriting A(1:i-1,i+1), and tau is stored in TAU(i).

If UPLO = 'L', the matrix Q is represented as a product of elementary
reflectors

   Q = H(1) H(2) . . . H(n-1).

Each H(i) has the form

   H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
overwriting A(i+2:n,i), and tau is stored in TAU(i).

Definition at line 152 of file chptrd.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

chptrd(3) is an alias of chptrd.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK