LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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```
Date
December 2016

Definition at line 123 of file sgelqs.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  REAL a( lda, * ), b( ldb, * ), tau( * ),
134  \$ work( lwork )
135 * ..
136 *
137 * =====================================================================
138 *
139 * .. Parameters ..
140  REAL zero, one
141  parameter( zero = 0.0e+0, one = 1.0e+0 )
142 * ..
143 * .. External Subroutines ..
144  EXTERNAL slaset, sormlq, strsm, xerbla
145 * ..
146 * .. Intrinsic Functions ..
147  INTRINSIC max
148 * ..
149 * .. Executable Statements ..
150 *
151 * Test the input parameters.
152 *
153  info = 0
154  IF( m.LT.0 ) THEN
155  info = -1
156  ELSE IF( n.LT.0 .OR. m.GT.n ) THEN
157  info = -2
158  ELSE IF( nrhs.LT.0 ) THEN
159  info = -3
160  ELSE IF( lda.LT.max( 1, m ) ) THEN
161  info = -5
162  ELSE IF( ldb.LT.max( 1, n ) ) THEN
163  info = -8
164  ELSE IF( lwork.LT.1 .OR. lwork.LT.nrhs .AND. m.GT.0 .AND. n.GT.0 )
165  \$ THEN
166  info = -10
167  END IF
168  IF( info.NE.0 ) THEN
169  CALL xerbla( 'SGELQS', -info )
170  RETURN
171  END IF
172 *
173 * Quick return if possible
174 *
175  IF( n.EQ.0 .OR. nrhs.EQ.0 .OR. m.EQ.0 )
176  \$ RETURN
177 *
178 * Solve L*X = B(1:m,:)
179 *
180  CALL strsm( 'Left', 'Lower', 'No transpose', 'Non-unit', m, nrhs,
181  \$ one, a, lda, b, ldb )
182 *
183 * Set B(m+1:n,:) to zero
184 *
185  IF( m.LT.n )
186  \$ CALL slaset( 'Full', n-m, nrhs, zero, zero, b( m+1, 1 ), ldb )
187 *
188 * B := Q' * B
189 *
190  CALL sormlq( 'Left', 'Transpose', n, nrhs, m, a, lda, tau, b, ldb,
191  \$ work, lwork, info )
192 *
193  RETURN
194 *
195 * End of SGELQS
196 *
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
Definition: strsm.f:183
subroutine sormlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMLQ
Definition: sormlq.f:170
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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:112
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