sgeqrt3.f (3) - Linux Manuals

NAME

sgeqrt3.f -

SYNOPSIS

Functions/Subroutines

recursive subroutine sgeqrt3 (M, N, A, LDA, T, LDT, INFO)
SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Function/Subroutine Documentation

recursive subroutine sgeqrt3 (integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( ldt, * )T, integerLDT, integerINFO)

SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

 SGEQRT3 recursively computes a QR factorization of a real 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 REAL array, dimension (LDA,N)
          On entry, the real 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 REAL 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.

Date:

September 2012

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**T

  where V**T is the transpose of V.

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

 

Definition at line 133 of file sgeqrt3.f.

Author

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