
dsptrd.f(3) LAPACK dsptrd.f(3)
NAME
dsptrd.f 
SYNOPSIS
Functions/Subroutines
subroutine dsptrd (UPLO, N, AP, D, E, TAU, INFO)
DSPTRD
Function/Subroutine Documentation
subroutine dsptrd (characterUPLO, integerN, double precision, dimension( * )AP, double
precision, dimension( * )D, double precision, dimension( * )E, double precision,
dimension( * )TAU, integerINFO)
DSPTRD
Purpose:
DSPTRD reduces a real symmetric matrix A stored in packed form to
symmetric tridiagonal form T by an orthogonal similarity
transformation: Q**T * 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 DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The jth column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j1)*(2*nj)/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 orthogonal
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 orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
D
D is DOUBLE PRECISION array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
E
E is DOUBLE PRECISION array, dimension (N1)
The offdiagonal 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 DOUBLE PRECISION array, dimension (N1)
The scalar factors of the elementary reflectors (see Further
Details).
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = i, the ith 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(n1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I  tau * v * v**T
where tau is a real scalar, and v is a real vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i1) is stored on exit in AP,
overwriting A(1:i1,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(n1).
Each H(i) has the form
H(i) = I  tau * v * v**T
where tau is a real scalar, and v is a real 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 151 of file dsptrd.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 dsptrd.f(3) 
