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authorjulie <julielangou@users.noreply.github.com>2011-10-06 06:53:11 +0000
committerjulie <julielangou@users.noreply.github.com>2011-10-06 06:53:11 +0000
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- SUBROUTINE SGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
-*
-* -- 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 --
-*
-* .. Scalar Arguments ..
- INTEGER INFO, LDA, LWORK, M, N
-* ..
-* .. Array Arguments ..
- INTEGER JPVT( * )
- REAL A( LDA, * ), TAU( * ), WORK( * )
-* ..
-*
+*> \brief \b SGEQP3
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition
+* ==========
+*
+* SUBROUTINE SGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, LDA, LWORK, M, N
+* ..
+* .. Array Arguments ..
+* INTEGER JPVT( * )
+* REAL A( LDA, * ), TAU( * ), WORK( * )
+* ..
+*
* Purpose
* =======
*
-* SGEQP3 computes a QR factorization with column pivoting of a
-* matrix A: A*P = Q*R using Level 3 BLAS.
+*>\details \b Purpose:
+*>\verbatim
+*>
+*> SGEQP3 computes a QR factorization with column pivoting of a
+*> matrix A: A*P = Q*R using Level 3 BLAS.
+*>
+*>\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 upper triangle of the array contains the
-* min(M,N)-by-N upper trapezoidal matrix R; the elements below
-* the diagonal, together with the array TAU, represent the
-* orthogonal matrix Q as a product of min(M,N) elementary
-* reflectors.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,M).
-*
-* JPVT (input/output) INTEGER array, dimension (N)
-* On entry, if JPVT(J).ne.0, the J-th column of A is permuted
-* to the front of A*P (a leading column); if JPVT(J)=0,
-* the J-th column of A is a free column.
-* On exit, if JPVT(J)=K, then the J-th column of A*P was the
-* the K-th column of A.
-*
-* TAU (output) REAL array, dimension (min(M,N))
-* The scalar factors of the elementary reflectors.
+*> \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
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is REAL array, dimension (LDA,N)
+*> On entry, the M-by-N matrix A.
+*> On exit, the upper triangle of the array contains the
+*> min(M,N)-by-N upper trapezoidal matrix R; the elements below
+*> the diagonal, together with the array TAU, represent the
+*> orthogonal matrix Q as a product of min(M,N) elementary
+*> reflectors.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[in,out] JPVT
+*> \verbatim
+*> JPVT is INTEGER array, dimension (N)
+*> On entry, if JPVT(J).ne.0, the J-th column of A is permuted
+*> to the front of A*P (a leading column); if JPVT(J)=0,
+*> the J-th column of A is a free column.
+*> On exit, if JPVT(J)=K, then the J-th column of A*P was the
+*> the K-th column of A.
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*> TAU is REAL array, dimension (min(M,N))
+*> The scalar factors of the elementary reflectors.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is REAL array, dimension (MAX(1,LWORK))
+*> On exit, if INFO=0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The dimension of the array WORK. LWORK >= 3*N+1.
+*> For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB
+*> is the optimal blocksize.
+*> \endverbatim
+*> \verbatim
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal size of the WORK array, returns
+*> this value as the first entry of the WORK array, and no error
+*> message related to LWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit.
+*> < 0: if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*>
+*
+* Authors
+* =======
*
-* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
-* On exit, if INFO=0, WORK(1) returns the optimal LWORK.
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
-* LWORK (input) INTEGER
-* The dimension of the array WORK. LWORK >= 3*N+1.
-* For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB
-* is the optimal blocksize.
+*> \date November 2011
*
-* If LWORK = -1, then a workspace query is assumed; the routine
-* only calculates the optimal size of the WORK array, returns
-* this value as the first entry of the WORK array, and no error
-* message related to LWORK is issued by XERBLA.
+*> \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
+*>
+*> 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/complex scalar, and v is a real/complex 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).
+*>
+*> Based on contributions by
+*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
+*> X. Sun, Computer Science Dept., Duke University, USA
+*>
+*> \endverbatim
+*>
+* =====================================================================
+ SUBROUTINE SGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, 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
-*
-* where tau is a real/complex scalar, and v is a real/complex 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).
+* -- 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
*
-* Based on contributions by
-* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
-* X. Sun, Computer Science Dept., Duke University, USA
+* .. Scalar Arguments ..
+ INTEGER INFO, LDA, LWORK, M, N
+* ..
+* .. Array Arguments ..
+ INTEGER JPVT( * )
+ REAL A( LDA, * ), TAU( * ), WORK( * )
+* ..
*
* =====================================================================
*