table of contents
/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/DEPRECATED/slahrd.f(3) | Library Functions Manual | /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/DEPRECATED/slahrd.f(3) |
NAME¶
/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/DEPRECATED/slahrd.f
SYNOPSIS¶
Functions/Subroutines¶
subroutine SLAHRD (n, k, nb, a, lda, tau, t, ldt, y, ldy)
SLAHRD 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 SLAHRD (integer n, integer k, integer nb, real, dimension( lda, * ) a, integer lda, real, dimension( nb ) tau, real, dimension( ldt, nb ) t, integer ldt, real, dimension( ldy, nb ) y, integer ldy)¶
SLAHRD 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:
!> !> This routine is deprecated and has been replaced by routine SLAHR2. !> !> SLAHRD reduces the first NB columns of a real general n-by-(n-k+1) !> matrix A so that elements below the k-th subdiagonal are zero. The !> reduction is performed by an orthogonal similarity transformation !> Q**T * A * Q. The routine returns the matrices V and T which determine !> Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T. !>
Parameters
!> 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 REAL 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 REAL array, dimension (NB) !> The scalar factors of the elementary reflectors. See Further !> Details. !>
T
!> T is REAL 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 REAL array, dimension (LDY,NB) !> The n-by-nb matrix Y. !>
LDY
!> LDY is INTEGER !> The leading dimension of the array Y. LDY >= N. !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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**T !> !> where tau is a real scalar, and v is a real 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**T) * (A - Y*V**T). !> !> 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 166 of file slahrd.f.
Author¶
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