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SUBROUTINE SGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
$ INFO )
*
* -- LAPACK routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
REAL A( LDA, * ), B( LDB, * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* Purpose
* =======
*
* Compute a minimum-norm solution
* min || A*X - B ||
* using the RQ factorization
* A = R*Q
* computed by SGERQF.
*
* 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 >= M >= 0.
*
* NRHS (input) INTEGER
* The number of columns of B. NRHS >= 0.
*
* A (input) REAL array, dimension (LDA,N)
* Details of the RQ factorization of the original matrix A as
* returned by SGERQF.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= M.
*
* TAU (input) REAL array, dimension (M)
* Details of the orthogonal matrix Q.
*
* B (input/output) REAL array, dimension (LDB,NRHS)
* On entry, the right hand side vectors for the linear system.
* On exit, the solution vectors X. Each solution vector
* is contained in rows 1:N of a column of B.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* WORK (workspace) REAL array, dimension (LWORK)
*
* LWORK (input) INTEGER
* The length of the array WORK. LWORK must be at least NRHS,
* and should be at least NRHS*NB, where NB is the block size
* for this environment.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. External Subroutines ..
EXTERNAL SLASET, SORMRQ, STRSM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 .OR. M.GT.N ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -8
ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
$ THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SGERQS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
$ RETURN
*
* Solve R*X = B(n-m+1:n,:)
*
CALL STRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', M, NRHS,
$ ONE, A( 1, N-M+1 ), LDA, B( N-M+1, 1 ), LDB )
*
* Set B(1:n-m,:) to zero
*
CALL SLASET( 'Full', N-M, NRHS, ZERO, ZERO, B, LDB )
*
* B := Q' * B
*
CALL SORMRQ( 'Left', 'Transpose', N, NRHS, M, A, LDA, TAU, B, LDB,
$ WORK, LWORK, INFO )
*
RETURN
*
* End of SGERQS
*
END
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