LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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dtzrzf.f File Reference

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Functions/Subroutines

subroutine dtzrzf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
 DTZRZF

Function/Subroutine Documentation

subroutine dtzrzf ( integer  M,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

DTZRZF

Download DTZRZF + dependencies [TGZ] [ZIP] [TXT]
Purpose: 
 DTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
 to upper triangular form by means of orthogonal transformations.

 The upper trapezoidal matrix A is factored as

    A = ( R  0 ) * Z,

 where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
 triangular matrix.
Parameters:
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= M.
[in,out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the leading M-by-N upper trapezoidal part of the
          array A must contain the matrix to be factorized.
          On exit, the leading M-by-M upper triangular part of A
          contains the upper triangular matrix R, and elements M+1 to
          N of the first M rows of A, with the array TAU, represent the
          orthogonal matrix Z as a product of M elementary reflectors.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (M)
          The scalar factors of the elementary reflectors.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= max(1,M).
          For optimum performance LWORK >= M*NB, where NB is
          the optimal blocksize.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[out]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:
April 2012
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
Further Details: 
  The N-by-N matrix Z can be computed by

     Z =  Z(1)*Z(2)* ... *Z(M)

  where each N-by-N Z(k) is given by

     Z(k) = I - tau(k)*v(k)*v(k)**T

  with v(k) is the kth row vector of the M-by-N matrix

     V = ( I   A(:,M+1:N) )

  I is the M-by-M identity matrix, A(:,M+1:N) 
  is the output stored in A on exit from DTZRZF,
  and tau(k) is the kth element of the array TAU.

Definition at line 152 of file dtzrzf.f.

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