 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dgerqs()

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

DGERQS

Purpose:
``` Compute a minimum-norm solution
min || A*X - B ||
using the RQ factorization
A = R*Q
computed by DGERQF.```
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 DOUBLE PRECISION array, dimension (LDA,N) Details of the RQ factorization of the original matrix A as returned by DGERQF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= M.``` [in] TAU ``` TAU is DOUBLE PRECISION array, dimension (M) Details of the orthogonal matrix Q.``` [in,out] B ``` B is DOUBLE PRECISION 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 DOUBLE PRECISION 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 dgerqs.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  DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TAU( * ),
132  \$ WORK( LWORK )
133 * ..
134 *
135 * =====================================================================
136 *
137 * .. Parameters ..
138  DOUBLE PRECISION ZERO, ONE
139  parameter( zero = 0.0d+0, one = 1.0d+0 )
140 * ..
141 * .. External Subroutines ..
142  EXTERNAL dlaset, dormrq, dtrsm, 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( 'DGERQS', -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 dtrsm( '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 dlaset( 'Full', n-m, nrhs, zero, zero, b, ldb )
184 *
185 * B := Q' * B
186 *
187  CALL dormrq( 'Left', 'Transpose', n, nrhs, m, a, lda, tau, b, ldb,
188  \$ work, lwork, info )
189 *
190  RETURN
191 *
192 * End of DGERQS
193 *
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: dlaset.f:110
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:181
subroutine dormrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMRQ
Definition: dormrq.f:167
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