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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine sqrt02 | ( | integer | M, |
integer | N, | ||
integer | K, | ||
real, dimension( lda, * ) | A, | ||
real, dimension( lda, * ) | AF, | ||
real, dimension( lda, * ) | Q, | ||
real, dimension( lda, * ) | R, | ||
integer | LDA, | ||
real, dimension( * ) | TAU, | ||
real, dimension( lwork ) | WORK, | ||
integer | LWORK, | ||
real, dimension( * ) | RWORK, | ||
real, dimension( * ) | RESULT | ||
) |
SQRT02
SQRT02 tests SORGQR, 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, SQRT02 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.
[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 REAL array, dimension (LDA,N) The m-by-n matrix A which was factorized by SQRT01. |
[in] | AF | AF is REAL array, dimension (LDA,N) Details of the QR factorization of A, as returned by SGEQRF. See SGEQRF for further details. |
[out] | Q | Q is REAL array, dimension (LDA,N) |
[out] | R | R is REAL 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 REAL array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF. |
[out] | WORK | WORK is REAL array, dimension (LWORK) |
[in] | LWORK | LWORK is INTEGER The dimension of the array WORK. |
[out] | RWORK | RWORK is REAL array, dimension (M) |
[out] | RESULT | RESULT is REAL array, dimension (2) The test ratios: RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS ) RESULT(2) = norm( I - Q'*Q ) / ( M * EPS ) |
Definition at line 137 of file sqrt02.f.