 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cgerqs()

 subroutine cgerqs ( integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( lwork ) WORK, integer LWORK, integer INFO )

CGERQS

Purpose:
``` Compute a minimum-norm solution
min || A*X - B ||
using the RQ factorization
A = R*Q
computed by CGERQF.```
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 COMPLEX array, dimension (LDA,N) Details of the RQ factorization of the original matrix A as returned by CGERQF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= M.``` [in] TAU ``` TAU is COMPLEX array, dimension (M) Details of the orthogonal matrix Q.``` [in,out] B ``` B is COMPLEX 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 COMPLEX 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 cgerqs.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 COMPLEX A( LDA, * ), B( LDB, * ), TAU( * ),
132 \$ WORK( LWORK )
133* ..
134*
135* =====================================================================
136*
137* .. Parameters ..
138 COMPLEX CZERO, CONE
139 parameter( czero = ( 0.0e+0, 0.0e+0 ),
140 \$ cone = ( 1.0e+0, 0.0e+0 ) )
141* ..
142* .. External Subroutines ..
143 EXTERNAL claset, ctrsm, cunmrq, xerbla
144* ..
145* .. Intrinsic Functions ..
146 INTRINSIC max
147* ..
148* .. Executable Statements ..
149*
150* Test the input parameters.
151*
152 info = 0
153 IF( m.LT.0 ) THEN
154 info = -1
155 ELSE IF( n.LT.0 .OR. m.GT.n ) THEN
156 info = -2
157 ELSE IF( nrhs.LT.0 ) THEN
158 info = -3
159 ELSE IF( lda.LT.max( 1, m ) ) THEN
160 info = -5
161 ELSE IF( ldb.LT.max( 1, n ) ) THEN
162 info = -8
163 ELSE IF( lwork.LT.1 .OR. lwork.LT.nrhs .AND. m.GT.0 .AND. n.GT.0 )
164 \$ THEN
165 info = -10
166 END IF
167 IF( info.NE.0 ) THEN
168 CALL xerbla( 'CGERQS', -info )
169 RETURN
170 END IF
171*
172* Quick return if possible
173*
174 IF( n.EQ.0 .OR. nrhs.EQ.0 .OR. m.EQ.0 )
175 \$ RETURN
176*
177* Solve R*X = B(n-m+1:n,:)
178*
179 CALL ctrsm( 'Left', 'Upper', 'No transpose', 'Non-unit', m, nrhs,
180 \$ cone, a( 1, n-m+1 ), lda, b( n-m+1, 1 ), ldb )
181*
182* Set B(1:n-m,:) to zero
183*
184 CALL claset( 'Full', n-m, nrhs, czero, czero, b, ldb )
185*
186* B := Q' * B
187*
188 CALL cunmrq( 'Left', 'Conjugate transpose', n, nrhs, m, a, lda,
189 \$ tau, b, ldb, work, lwork, info )
190*
191 RETURN
192*
193* End of CGERQS
194*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:180
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
subroutine cunmrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
CUNMRQ
Definition: cunmrq.f:168
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