LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zgerqs()

 subroutine zgerqs ( 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 )

ZGERQS

Purpose:
``` Compute a minimum-norm solution
min || A*X - B ||
using the RQ factorization
A = R*Q
computed by ZGERQF.```
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 RQ factorization of the original matrix A as returned by ZGERQF.``` [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 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*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 120 of file zgerqs.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*16 A( LDA, * ), B( LDB, * ), TAU( * ),
132  \$ WORK( LWORK )
133 * ..
134 *
135 * =====================================================================
136 *
137 * .. Parameters ..
138  COMPLEX*16 CZERO, CONE
139  parameter( czero = ( 0.0d+0, 0.0d+0 ),
140  \$ cone = ( 1.0d+0, 0.0d+0 ) )
141 * ..
142 * .. External Subroutines ..
143  EXTERNAL xerbla, zlaset, ztrsm, zunmrq
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( 'ZGERQS', -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 ztrsm( '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 zlaset( 'Full', n-m, nrhs, czero, czero, b, ldb )
185 *
186 * B := Q' * B
187 *
188  CALL zunmrq( 'Left', 'Conjugate transpose', n, nrhs, m, a, lda,
189  \$ tau, b, ldb, work, lwork, info )
190 *
191  RETURN
192 *
193 * End of ZGERQS
194 *
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 zunmrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMRQ
Definition: zunmrq.f:167
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