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Diffstat (limited to 'SRC/sgeqr2.f')
| -rw-r--r-- | SRC/sgeqr2.f | 133 |
1 files changed, 88 insertions, 45 deletions
diff --git a/SRC/sgeqr2.f b/SRC/sgeqr2.f index 4eb385ae..0120e816 100644 --- a/SRC/sgeqr2.f +++ b/SRC/sgeqr2.f @@ -1,67 +1,110 @@ - SUBROUTINE SGEQR2( M, N, A, LDA, TAU, WORK, INFO ) +*> \brief \b SGEQR2 * -* -- LAPACK routine (version 3.3.1) -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -- April 2011 -- +* =========== DOCUMENTATION =========== * -* .. Scalar Arguments .. - INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. - REAL A( LDA, * ), TAU( * ), WORK( * ) -* .. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * +* Definition +* ========== +* +* SUBROUTINE SGEQR2( M, N, A, LDA, TAU, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. +* REAL A( LDA, * ), TAU( * ), WORK( * ) +* .. +* * Purpose * ======= * -* SGEQR2 computes a QR factorization of a real m by n matrix A: -* A = Q * R. +*>\details \b Purpose: +*>\verbatim +*> +*> SGEQR2 computes a QR factorization of a real m by n matrix A: +*> A = Q * R. +*> +*>\endverbatim * * Arguments * ========= * -* M (input) INTEGER -* The number of rows of the matrix A. M >= 0. -* -* N (input) INTEGER -* The number of columns of the matrix A. N >= 0. -* -* A (input/output) REAL array, dimension (LDA,N) -* On entry, the m by n matrix A. -* On exit, the elements on and above the diagonal of the array -* contain the min(m,n) by n upper trapezoidal matrix R (R is -* upper triangular if m >= n); the elements below the diagonal, -* with the array TAU, represent the orthogonal matrix Q as a -* product of elementary reflectors (see Further Details). +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= 0. +*> \endverbatim +*> +* +* Authors +* ======= * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,M). +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* TAU (output) REAL array, dimension (min(M,N)) -* The scalar factors of the elementary reflectors (see Further -* Details). +*> \date November 2011 * -* WORK (workspace) REAL array, dimension (N) +*> \ingroup realGEcomputational * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +* product of elementary reflectors (see Further Details). +*> +*> LDA (input) INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> +*> TAU (output) REAL array, dimension (min(M,N)) +*> The scalar factors of the elementary reflectors (see Further +*> Details). +*> +*> WORK (workspace) REAL array, dimension (N) +*> +*> INFO (output) INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> +*> +*> The matrix Q is represented as a product of elementary reflectors +*> +*> Q = H(1) H(2) . . . H(k), where k = min(m,n). +*> +*> Each H(i) has the form +*> +*> H(i) = I - tau * v * v**T +*> +*> where tau is a real scalar, and v is a real vector with +*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), +*> and tau in TAU(i). +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SGEQR2( M, N, A, LDA, TAU, WORK, INFO ) * -* The matrix Q is represented as a product of elementary reflectors -* -* Q = H(1) H(2) . . . H(k), where k = min(m,n). -* -* Each H(i) has the form -* -* H(i) = I - tau * v * v**T +* -- LAPACK computational routine (version 3.3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* where tau is a real scalar, and v is a real vector with -* v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), -* and tau in TAU(i). +* .. Scalar Arguments .. + INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. + REAL A( LDA, * ), TAU( * ), WORK( * ) +* .. * * ===================================================================== * |