LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ dgrqts()

subroutine dgrqts ( integer  m,
integer  p,
integer  n,
double precision, dimension( lda, * )  a,
double precision, dimension( lda, * )  af,
double precision, dimension( lda, * )  q,
double precision, dimension( lda, * )  r,
integer  lda,
double precision, dimension( * )  taua,
double precision, dimension( ldb, * )  b,
double precision, dimension( ldb, * )  bf,
double precision, dimension( ldb, * )  z,
double precision, dimension( ldb, * )  t,
double precision, dimension( ldb, * )  bwk,
integer  ldb,
double precision, dimension( * )  taub,
double precision, dimension( lwork )  work,
integer  lwork,
double precision, dimension( * )  rwork,
double precision, dimension( 4 )  result 
)

DGRQTS

Purpose:
 DGRQTS tests DGGRQF, 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 DOUBLE PRECISION array, dimension (LDA,N)
          The M-by-N matrix A.
[out]AF
          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the GRQ factorization of A and B, as returned
          by DGGRQF, see SGGRQF for further details.
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDA,N)
          The N-by-N orthogonal matrix Q.
[out]R
          R is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by DGGQRC.
[in]B
          B is DOUBLE PRECISION array, dimension (LDB,N)
          On entry, the P-by-N matrix A.
[out]BF
          BF is DOUBLE PRECISION array, dimension (LDB,N)
          Details of the GQR factorization of A and B, as returned
          by DGGRQF, see SGGRQF for further details.
[out]Z
          Z is DOUBLE PRECISION array, dimension (LDB,P)
          The P-by-P orthogonal matrix Z.
[out]T
          T is DOUBLE PRECISION array, dimension (LDB,max(P,N))
[out]BWK
          BWK is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(P,N))
          The scalar factors of the elementary reflectors, as returned
          by DGGRQF.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK, LWORK >= max(M,P,N)**2.
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (M)
[out]RESULT
          RESULT is DOUBLE PRECISION 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.