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LAPACK: Linear Algebra PACKage
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zqrt02.f File Reference

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Functions/Subroutines

subroutine zqrt02 (M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
 ZQRT02 More...
 

Function/Subroutine Documentation

subroutine zqrt02 ( integer  M,
integer  N,
integer  K,
complex*16, dimension( lda, * )  A,
complex*16, dimension( lda, * )  AF,
complex*16, dimension( lda, * )  Q,
complex*16, dimension( lda, * )  R,
integer  LDA,
complex*16, dimension( * )  TAU,
complex*16, dimension( lwork )  WORK,
integer  LWORK,
double precision, dimension( * )  RWORK,
double precision, dimension( * )  RESULT 
)

ZQRT02

Purpose:
 ZQRT02 tests ZUNGQR, which generates an m-by-n matrix Q with
 orthonornmal columns that is defined as the product of k elementary
 reflectors.

 Given the QR factorization of an m-by-n matrix A, ZQRT02 generates
 the orthogonal matrix Q defined by the factorization of the first k
 columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
 and checks that the columns of Q are orthonormal.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix Q to be generated.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix Q to be generated.
          M >= N >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. N >= K >= 0.
[in]A
          A is COMPLEX*16 array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by ZQRT01.
[in]AF
          AF is COMPLEX*16 array, dimension (LDA,N)
          Details of the QR factorization of A, as returned by ZGEQRF.
          See ZGEQRF for further details.
[out]Q
          Q is COMPLEX*16 array, dimension (LDA,N)
[out]R
          R is COMPLEX*16 array, dimension (LDA,N)
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and R. LDA >= M.
[in]TAU
          TAU is COMPLEX*16 array, dimension (N)
          The scalar factors of the elementary reflectors corresponding
          to the QR factorization in AF.
[out]WORK
          WORK is COMPLEX*16 array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESULT
          RESULT is DOUBLE PRECISION array, dimension (2)
          The test ratios:
          RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011

Definition at line 135 of file zqrt02.f.

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