LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ sgerqs()

 subroutine sgerqs ( integer m, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldb, * ) b, integer ldb, real, dimension( lwork ) work, integer lwork, integer info )

SGERQS

Purpose:
``` Compute a minimum-norm solution
min || A*X - B ||
using the RQ factorization
A = R*Q
computed by SGERQF.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix A. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix A. N >= M >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of columns of B. NRHS >= 0.``` [in] A ``` A is REAL array, dimension (LDA,N) Details of the RQ factorization of the original matrix A as returned by SGERQF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= M.``` [in] TAU ``` TAU is REAL array, dimension (M) Details of the orthogonal matrix Q.``` [in,out] B ``` B is 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.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] WORK ` WORK is REAL array, dimension (LWORK)` [in] LWORK ``` LWORK is 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.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 120 of file sgerqs.f.

122*
123* -- LAPACK test routine --
124* -- LAPACK is a software package provided by Univ. of Tennessee, --
125* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126*
127* .. Scalar Arguments ..
128 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
129* ..
130* .. Array Arguments ..
131 REAL A( LDA, * ), B( LDB, * ), TAU( * ),
132 \$ WORK( LWORK )
133* ..
134*
135* =====================================================================
136*
137* .. Parameters ..
138 REAL ZERO, ONE
139 parameter( zero = 0.0e+0, one = 1.0e+0 )
140* ..
141* .. External Subroutines ..
142 EXTERNAL slaset, sormrq, strsm, xerbla
143* ..
144* .. Intrinsic Functions ..
145 INTRINSIC max
146* ..
147* .. Executable Statements ..
148*
149* Test the input parameters.
150*
151 info = 0
152 IF( m.LT.0 ) THEN
153 info = -1
154 ELSE IF( n.LT.0 .OR. m.GT.n ) THEN
155 info = -2
156 ELSE IF( nrhs.LT.0 ) THEN
157 info = -3
158 ELSE IF( lda.LT.max( 1, m ) ) THEN
159 info = -5
160 ELSE IF( ldb.LT.max( 1, n ) ) THEN
161 info = -8
162 ELSE IF( lwork.LT.1 .OR. lwork.LT.nrhs .AND. m.GT.0 .AND. n.GT.0 )
163 \$ THEN
164 info = -10
165 END IF
166 IF( info.NE.0 ) THEN
167 CALL xerbla( 'SGERQS', -info )
168 RETURN
169 END IF
170*
171* Quick return if possible
172*
173 IF( n.EQ.0 .OR. nrhs.EQ.0 .OR. m.EQ.0 )
174 \$ RETURN
175*
176* Solve R*X = B(n-m+1:n,:)
177*
178 CALL strsm( 'Left', 'Upper', 'No transpose', 'Non-unit', m, nrhs,
179 \$ one, a( 1, n-m+1 ), lda, b( n-m+1, 1 ), ldb )
180*
181* Set B(1:n-m,:) to zero
182*
183 CALL slaset( 'Full', n-m, nrhs, zero, zero, b, ldb )
184*
185* B := Q' * B
186*
187 CALL sormrq( 'Left', 'Transpose', n, nrhs, m, a, lda, tau, b, ldb,
188 \$ work, lwork, info )
189*
190 RETURN
191*
192* End of SGERQS
193*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine slaset(uplo, m, n, alpha, beta, a, lda)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition slaset.f:110
subroutine strsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
STRSM
Definition strsm.f:181
subroutine sormrq(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
SORMRQ
Definition sormrq.f:168
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