dlatrd (3)  Linux Man Pages
NAME
dlatrd.f 
SYNOPSIS
Functions/Subroutines
subroutine dlatrd (UPLO, N, NB, A, LDA, E, TAU, W, LDW)
DLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an orthogonal similarity transformation.
Function/Subroutine Documentation
subroutine dlatrd (characterUPLO, integerN, integerNB, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )E, double precision, dimension( * )TAU, double precision, dimension( ldw, * )W, integerLDW)
DLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an orthogonal similarity transformation.
Purpose:

DLATRD reduces NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q**T * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A. If UPLO = 'U', DLATRD reduces the last NB rows and columns of a matrix, of which the upper triangle is supplied; if UPLO = 'L', DLATRD reduces the first NB rows and columns of a matrix, of which the lower triangle is supplied. This is an auxiliary routine called by DSYTRD.
Parameters:

UPLO
UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
NN is INTEGER The order of the matrix A.
NBNB is INTEGER The number of rows and columns to be reduced.
AA is DOUBLE PRECISION array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = 'U', the leading nbyn upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading nbyn lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit: if UPLO = 'U', the last NB columns have been reduced to tridiagonal form, with the diagonal elements overwriting the diagonal elements of A; the elements above the diagonal with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors; if UPLO = 'L', the first NB columns have been reduced to tridiagonal form, with the diagonal elements overwriting the diagonal elements of A; the elements below the diagonal with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. See Further Details.
LDALDA is INTEGER The leading dimension of the array A. LDA >= (1,N).
EE is DOUBLE PRECISION array, dimension (N1) If UPLO = 'U', E(nnb:n1) contains the superdiagonal elements of the last NB columns of the reduced matrix; if UPLO = 'L', E(1:nb) contains the subdiagonal elements of the first NB columns of the reduced matrix.
TAUTAU is DOUBLE PRECISION array, dimension (N1) The scalar factors of the elementary reflectors, stored in TAU(nnb:n1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. See Further Details.
WW is DOUBLE PRECISION array, dimension (LDW,NB) The nbynb matrix W required to update the unreduced part of A.
LDWLDW is INTEGER The leading dimension of the array W. LDW >= max(1,N).
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
Further Details:

If UPLO = 'U', the matrix Q is represented as a product of elementary reflectors Q = H(n) H(n1) . . . H(nnb+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:n) = 0 and v(i1) = 1; v(1:i1) is stored on exit in A(1:i1,i), and tau in TAU(i1). If UPLO = 'L', the matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(nb). 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+1:n) is stored on exit in A(i+1:n,i), and tau in TAU(i). The elements of the vectors v together form the nbynb matrix V which is needed, with W, to apply the transformation to the unreduced part of the matrix, using a symmetric rank2k update of the form: A := A  V*W**T  W*V**T. The contents of A on exit are illustrated by the following examples with n = 5 and nb = 2: if UPLO = 'U': if UPLO = 'L': ( a a a v4 v5 ) ( d ) ( a a v4 v5 ) ( 1 d ) ( a 1 v5 ) ( v1 1 a ) ( d 1 ) ( v1 v2 a a ) ( d ) ( v1 v2 a a a ) where d denotes a diagonal element of the reduced matrix, a denotes an element of the original matrix that is unchanged, and vi denotes an element of the vector defining H(i).
Definition at line 199 of file dlatrd.f.
Author
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