# zlahrd(3) [centos man page]

zlahrd.f(3) LAPACK zlahrd.f(3)NAME

zlahrd.f-SYNOPSIS

Functions/Subroutines subroutine zlahrd (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY) ZLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below the k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A.Function/Subroutine Documentation subroutine zlahrd (integerN, integerK, integerNB, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( nb )TAU, complex*16, dimension( ldt, nb )T, integerLDT, complex*16, dimension( ldy, nb )Y, integerLDY) ZLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below the k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A. Purpose: ZLAHRD reduces the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero. The reduction is performed by a unitary similarity transformation Q**H * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T. This is an OBSOLETE auxiliary routine. This routine will be 'deprecated' in a future release. Please use the new routine ZLAHR2 instead. Parameters: N N is INTEGER The order of the matrix A. K K is INTEGER The offset for the reduction. Elements below the k-th subdiagonal in the first NB columns are reduced to zero. NB NB is INTEGER The number of columns to be reduced. A A is COMPLEX*16 array, dimension (LDA,N-K+1) On entry, the n-by-(n-k+1) general matrix A. On exit, the elements on and above the k-th subdiagonal in the first NB columns are overwritten with the corresponding elements of the reduced matrix; the elements below the k-th subdiagonal, with the array TAU, represent the matrix Q as a product of elementary reflectors. The other columns of A are unchanged. See Further Details. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). TAU TAU is COMPLEX*16 array, dimension (NB) The scalar factors of the elementary reflectors. See Further Details. T T is COMPLEX*16 array, dimension (LDT,NB) The upper triangular matrix T. LDT LDT is INTEGER The leading dimension of the array T. LDT >= NB. Y Y is COMPLEX*16 array, dimension (LDY,NB) The n-by-nb matrix Y. LDY LDY is INTEGER The leading dimension of the array Y. LDY >= max(1,N). Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Further Details: The matrix Q is represented as a product of nb elementary reflectors Q = H(1) H(2) . . . H(nb). 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+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in A(i+k+1:n,i), and tau in TAU(i). The elements of the vectors v together form the (n-k+1)-by-nb matrix V which is needed, with T and Y, to apply the transformation to the unreduced part of the matrix, using an update of the form: A := (I - V*T*V**H) * (A - Y*V**H). The contents of A on exit are illustrated by the following example with n = 7, k = 3 and nb = 2: ( a h a a a ) ( a h a a a ) ( a h a a a ) ( h h a a a ) ( v1 h a a a ) ( v1 v2 a a a ) ( v1 v2 a a a ) where a denotes an element of the original matrix A, h denotes a modified element of the upper Hessenberg matrix H, and vi denotes an element of the vector defining H(i). Definition at line 170 of file zlahrd.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 zlahrd.f(3)