LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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```
Date
December 2016

Definition at line 123 of file zgelqs.f.

123 *
124 * -- LAPACK test routine (version 3.7.0) --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 * December 2016
128 *
129 * .. Scalar Arguments ..
130  INTEGER info, lda, ldb, lwork, m, n, nrhs
131 * ..
132 * .. Array Arguments ..
133  COMPLEX*16 a( lda, * ), b( ldb, * ), tau( * ),
134  \$ work( lwork )
135 * ..
136 *
137 * =====================================================================
138 *
139 * .. Parameters ..
140  COMPLEX*16 czero, cone
141  parameter( czero = ( 0.0d+0, 0.0d+0 ),
142  \$ cone = ( 1.0d+0, 0.0d+0 ) )
143 * ..
144 * .. External Subroutines ..
145  EXTERNAL xerbla, zlaset, ztrsm, zunmlq
146 * ..
147 * .. Intrinsic Functions ..
148  INTRINSIC max
149 * ..
150 * .. Executable Statements ..
151 *
152 * Test the input parameters.
153 *
154  info = 0
155  IF( m.LT.0 ) THEN
156  info = -1
157  ELSE IF( n.LT.0 .OR. m.GT.n ) THEN
158  info = -2
159  ELSE IF( nrhs.LT.0 ) THEN
160  info = -3
161  ELSE IF( lda.LT.max( 1, m ) ) THEN
162  info = -5
163  ELSE IF( ldb.LT.max( 1, n ) ) THEN
164  info = -8
165  ELSE IF( lwork.LT.1 .OR. lwork.LT.nrhs .AND. m.GT.0 .AND. n.GT.0 )
166  \$ THEN
167  info = -10
168  END IF
169  IF( info.NE.0 ) THEN
170  CALL xerbla( 'ZGELQS', -info )
171  RETURN
172  END IF
173 *
174 * Quick return if possible
175 *
176  IF( n.EQ.0 .OR. nrhs.EQ.0 .OR. m.EQ.0 )
177  \$ RETURN
178 *
179 * Solve L*X = B(1:m,:)
180 *
181  CALL ztrsm( 'Left', 'Lower', 'No transpose', 'Non-unit', m, nrhs,
182  \$ cone, a, lda, b, ldb )
183 *
184 * Set B(m+1:n,:) to zero
185 *
186  IF( m.LT.n )
187  \$ CALL zlaset( 'Full', n-m, nrhs, czero, czero, b( m+1, 1 ),
188  \$ ldb )
189 *
190 * B := Q' * B
191 *
192  CALL zunmlq( 'Left', 'Conjugate transpose', n, nrhs, m, a, lda,
193  \$ tau, b, ldb, work, lwork, info )
194 *
195  RETURN
196 *
197 * End of ZGELQS
198 *
subroutine zunmlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMLQ
Definition: zunmlq.f:169
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:108
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:182
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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