SRC/DEPRECATED/slahrd.f(3)

NAME
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 This routine is deprecated and has been replaced by routine SLAHR2.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

    !>          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 Tennessee

    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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