SRC/DEPRECATED/zlahrd.f(3)                            Library Functions Manual

NAME
       SRC/DEPRECATED/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 (integer n, integer k, integer nb, complex*16, dimension(
       lda, * ) a, integer lda, complex*16, dimension( nb ) tau, complex*16,
       dimension( ldt, nb ) t, integer ldt, complex*16, dimension( ldy, nb )
       y, integer 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.

       Purpose:


            This routine is deprecated and has been replaced by routine ZLAHR2.

            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.

       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.

       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 166 of file zlahrd.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0      SRC/DEPRECATED/zlahrd.f(3)