cgeqrt3.f - Man Page

SRC/cgeqrt3.f

Synopsis

Functions/Subroutines

recursive subroutine cgeqrt3 (m, n, a, lda, t, ldt, info)
CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Function/Subroutine Documentation

recursive subroutine cgeqrt3 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)

CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.  

Purpose:

 CGEQRT3 recursively computes a QR factorization of a complex M-by-N matrix A,
 using the compact WY representation of Q.

 Based on the algorithm of Elmroth and Gustavson,
 IBM J. Res. Develop. Vol 44 No. 4 July 2000.
Parameters

M

          M is INTEGER
          The number of rows of the matrix A.  M >= N.

N

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the complex M-by-N matrix A.  On exit, the elements on and
          above the diagonal contain the N-by-N upper triangular matrix R; the
          elements below the diagonal are the columns of V.  See below for
          further details.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

T

          T is COMPLEX array, dimension (LDT,N)
          The N-by-N upper triangular factor of the block reflector.
          The elements on and above the diagonal contain the block
          reflector T; the elements below the diagonal are not used.
          See below for further details.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max(1,N).

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  The matrix V stores the elementary reflectors H(i) in the i-th column
  below the diagonal. For example, if M=5 and N=3, the matrix V is

               V = (  1       )
                   ( v1  1    )
                   ( v1 v2  1 )
                   ( v1 v2 v3 )
                   ( v1 v2 v3 )

  where the vi's represent the vectors which define H(i), which are returned
  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
  block reflector H is then given by

               H = I - V * T * V**H

  where V**H is the conjugate transpose of V.

  For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line 131 of file cgeqrt3.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page cgeqrt3(3) is an alias of cgeqrt3.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK