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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine cgrqts | ( | integer | M, |
| integer | P, | ||
| integer | N, | ||
| complex, dimension( lda, * ) | A, | ||
| complex, dimension( lda, * ) | AF, | ||
| complex, dimension( lda, * ) | Q, | ||
| complex, dimension( lda, * ) | R, | ||
| integer | LDA, | ||
| complex, dimension( * ) | TAUA, | ||
| complex, dimension( ldb, * ) | B, | ||
| complex, dimension( ldb, * ) | BF, | ||
| complex, dimension( ldb, * ) | Z, | ||
| complex, dimension( ldb, * ) | T, | ||
| complex, dimension( ldb, * ) | BWK, | ||
| integer | LDB, | ||
| complex, dimension( * ) | TAUB, | ||
| complex, dimension( lwork ) | WORK, | ||
| integer | LWORK, | ||
| real, dimension( * ) | RWORK, | ||
| real, dimension( 4 ) | RESULT | ||
| ) |
CGRQTS
CGRQTS tests CGGRQF, 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.
| [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 COMPLEX array, dimension (LDA,N)
The M-by-N matrix A. |
| [out] | AF | AF is COMPLEX array, dimension (LDA,N)
Details of the GRQ factorization of A and B, as returned
by CGGRQF, see CGGRQF for further details. |
| [out] | Q | Q is COMPLEX array, dimension (LDA,N)
The N-by-N unitary matrix Q. |
| [out] | R | R is COMPLEX 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 COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by SGGQRC. |
| [in] | B | B is COMPLEX array, dimension (LDB,N)
On entry, the P-by-N matrix A. |
| [out] | BF | BF is COMPLEX array, dimension (LDB,N)
Details of the GQR factorization of A and B, as returned
by CGGRQF, see CGGRQF for further details. |
| [out] | Z | Z is REAL array, dimension (LDB,P)
The P-by-P unitary matrix Z. |
| [out] | T | T is COMPLEX array, dimension (LDB,max(P,N)) |
| [out] | BWK | BWK is COMPLEX 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 COMPLEX array, dimension (min(P,N))
The scalar factors of the elementary reflectors, as returned
by SGGRQF. |
| [out] | WORK | WORK is COMPLEX 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 ) |
1.9.4