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

 subroutine zgelqs ( integer M, integer N, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) TAU, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( lwork ) WORK, integer LWORK, integer INFO )

ZGELQS

Purpose:
``` Compute a minimum-norm solution
min || A*X - B ||
using the LQ factorization
A = L*Q
computed by ZGELQF.```
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*16 array, dimension (LDA,N) Details of the LQ factorization of the original matrix A as returned by ZGELQF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= M.``` [in] TAU ``` TAU is COMPLEX*16 array, dimension (M) Details of the orthogonal matrix Q.``` [in,out] B ``` B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the m-by-nrhs right hand side matrix B. On exit, the n-by-nrhs solution matrix X.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= N.``` [out] WORK ` WORK is COMPLEX*16 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 119 of file zgelqs.f.

121*
122* -- LAPACK test routine --
123* -- LAPACK is a software package provided by Univ. of Tennessee, --
124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126* .. Scalar Arguments ..
127 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
128* ..
129* .. Array Arguments ..
130 COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ),
131 \$ WORK( LWORK )
132* ..
133*
134* =====================================================================
135*
136* .. Parameters ..
137 COMPLEX*16 CZERO, CONE
138 parameter( czero = ( 0.0d+0, 0.0d+0 ),
139 \$ cone = ( 1.0d+0, 0.0d+0 ) )
140* ..
141* .. External Subroutines ..
142 EXTERNAL xerbla, zlaset, ztrsm, zunmlq
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( 'ZGELQS', -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 L*X = B(1:m,:)
177*
178 CALL ztrsm( 'Left', 'Lower', 'No transpose', 'Non-unit', m, nrhs,
179 \$ cone, a, lda, b, ldb )
180*
181* Set B(m+1:n,:) to zero
182*
183 IF( m.LT.n )
184 \$ CALL zlaset( 'Full', n-m, nrhs, czero, czero, b( m+1, 1 ),
185 \$ ldb )
186*
187* B := Q' * B
188*
189 CALL zunmlq( 'Left', 'Conjugate transpose', n, nrhs, m, a, lda,
190 \$ tau, b, ldb, work, lwork, info )
191*
192 RETURN
193*
194* End of ZGELQS
195*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:180
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
subroutine zunmlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMLQ
Definition: zunmlq.f:167
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