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

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

SGELQS

Purpose:
``` Compute a minimum-norm solution
min || A*X - B ||
using the LQ factorization
A = L*Q
computed by SGELQF.```
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 REAL array, dimension (LDA,N) Details of the LQ factorization of the original matrix A as returned by SGELQF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= M.``` [in] TAU ``` TAU is REAL array, dimension (M) Details of the orthogonal matrix Q.``` [in,out] B ``` B is REAL 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 REAL 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 sgelqs.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 REAL A( LDA, * ), B( LDB, * ), TAU( * ),
131 \$ WORK( LWORK )
132* ..
133*
134* =====================================================================
135*
136* .. Parameters ..
137 REAL ZERO, ONE
138 parameter( zero = 0.0e+0, one = 1.0e+0 )
139* ..
140* .. External Subroutines ..
141 EXTERNAL slaset, sormlq, strsm, xerbla
142* ..
143* .. Intrinsic Functions ..
144 INTRINSIC max
145* ..
146* .. Executable Statements ..
147*
148* Test the input parameters.
149*
150 info = 0
151 IF( m.LT.0 ) THEN
152 info = -1
153 ELSE IF( n.LT.0 .OR. m.GT.n ) THEN
154 info = -2
155 ELSE IF( nrhs.LT.0 ) THEN
156 info = -3
157 ELSE IF( lda.LT.max( 1, m ) ) THEN
158 info = -5
159 ELSE IF( ldb.LT.max( 1, n ) ) THEN
160 info = -8
161 ELSE IF( lwork.LT.1 .OR. lwork.LT.nrhs .AND. m.GT.0 .AND. n.GT.0 )
162 \$ THEN
163 info = -10
164 END IF
165 IF( info.NE.0 ) THEN
166 CALL xerbla( 'SGELQS', -info )
167 RETURN
168 END IF
169*
170* Quick return if possible
171*
172 IF( n.EQ.0 .OR. nrhs.EQ.0 .OR. m.EQ.0 )
173 \$ RETURN
174*
175* Solve L*X = B(1:m,:)
176*
177 CALL strsm( 'Left', 'Lower', 'No transpose', 'Non-unit', m, nrhs,
178 \$ one, a, lda, b, ldb )
179*
180* Set B(m+1:n,:) to zero
181*
182 IF( m.LT.n )
183 \$ CALL slaset( 'Full', n-m, nrhs, zero, zero, b( m+1, 1 ), ldb )
184*
185* B := Q' * B
186*
187 CALL sormlq( 'Left', 'Transpose', n, nrhs, m, a, lda, tau, b, ldb,
188 \$ work, lwork, info )
189*
190 RETURN
191*
192* End of SGELQS
193*
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sormlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMLQ
Definition: sormlq.f:168
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
Definition: strsm.f:181
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