LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
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sgrqts.f File Reference

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Functions/Subroutines

subroutine sgrqts (M, P, N, A, AF, Q, R, LDA, TAUA, B, BF, Z, T, BWK, LDB, TAUB, WORK, LWORK, RWORK, RESULT)
 SGRQTS More...
 

Function/Subroutine Documentation

subroutine sgrqts ( integer  M,
integer  P,
integer  N,
real, dimension( lda, * )  A,
real, dimension( lda, * )  AF,
real, dimension( lda, * )  Q,
real, dimension( lda, * )  R,
integer  LDA,
real, dimension( * )  TAUA,
real, dimension( ldb, * )  B,
real, dimension( ldb, * )  BF,
real, dimension( ldb, * )  Z,
real, dimension( ldb, * )  T,
real, dimension( ldb, * )  BWK,
integer  LDB,
real, dimension( * )  TAUB,
real, dimension( lwork )  WORK,
integer  LWORK,
real, dimension( * )  RWORK,
real, dimension( 4 )  RESULT 
)

SGRQTS

Purpose:
 SGRQTS tests SGGRQF, which computes the GRQ factorization of an
 M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]P
          P is INTEGER
          The number of rows of the matrix B.  P >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrices A and B.  N >= 0.
[in]A
          A is REAL array, dimension (LDA,N)
          The M-by-N matrix A.
[out]AF
          AF is REAL array, dimension (LDA,N)
          Details of the GRQ factorization of A and B, as returned
          by SGGRQF, see SGGRQF for further details.
[out]Q
          Q is REAL array, dimension (LDA,N)
          The N-by-N orthogonal matrix Q.
[out]R
          R is REAL array, dimension (LDA,MAX(M,N))
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A, AF, R and Q.
          LDA >= max(M,N).
[out]TAUA
          TAUA is REAL array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by SGGQRC.
[in]B
          B is REAL array, dimension (LDB,N)
          On entry, the P-by-N matrix A.
[out]BF
          BF is REAL array, dimension (LDB,N)
          Details of the GQR factorization of A and B, as returned
          by SGGRQF, see SGGRQF for further details.
[out]Z
          Z is REAL array, dimension (LDB,P)
          The P-by-P orthogonal matrix Z.
[out]T
          T is REAL array, dimension (LDB,max(P,N))
[out]BWK
          BWK is REAL array, dimension (LDB,N)
[in]LDB
          LDB is INTEGER
          The leading dimension of the arrays B, BF, Z and T.
          LDB >= max(P,N).
[out]TAUB
          TAUB is REAL array, dimension (min(P,N))
          The scalar factors of the elementary reflectors, as returned
          by SGGRQF.
[out]WORK
          WORK is REAL array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK, LWORK >= max(M,P,N)**2.
[out]RWORK
          RWORK is REAL array, dimension (M)
[out]RESULT
          RESULT is REAL array, dimension (4)
          The test ratios:
            RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP)
            RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP)
            RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
            RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011

Definition at line 177 of file sgrqts.f.

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