LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ dgeqls()

 subroutine dgeqls ( 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 )

DGEQLS

Purpose:
``` Solve the least squares problem
min || A*X - B ||
using the QL factorization
A = Q*L
computed by DGEQLF.```
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. M >= N >= 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 QL factorization of the original matrix A as returned by DGEQLF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= M.``` [in] TAU ``` TAU is DOUBLE PRECISION array, dimension (N) Details of the orthogonal matrix Q.``` [in,out] B ``` B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the m-by-nrhs right hand side matrix B. On exit, the n-by-nrhs solution matrix X, stored in rows m-n+1:m.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= M.``` [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 dgeqls.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 ONE
139 parameter( one = 1.0d+0 )
140* ..
141* .. External Subroutines ..
142 EXTERNAL dormql, dtrsm, xerbla
143* ..
144* .. Intrinsic Functions ..
145 INTRINSIC max
146* ..
147* .. Executable Statements ..
148*
149* Test the input arguments.
150*
151 info = 0
152 IF( m.LT.0 ) THEN
153 info = -1
154 ELSE IF( n.LT.0 .OR. n.GT.m ) 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, m ) ) 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( 'DGEQLS', -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* B := Q' * B
177*
178 CALL dormql( 'Left', 'Transpose', m, nrhs, n, a, lda, tau, b, ldb,
179 \$ work, lwork, info )
180*
181* Solve L*X = B(m-n+1:m,:)
182*
183 CALL dtrsm( 'Left', 'Lower', 'No transpose', 'Non-unit', n, nrhs,
184 \$ one, a( m-n+1, 1 ), lda, b( m-n+1, 1 ), ldb )
185*
186 RETURN
187*
188* End of DGEQLS
189*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine dtrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
DTRSM
Definition dtrsm.f:181
subroutine dormql(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
DORMQL
Definition dormql.f:167
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