 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ sgeqls()

 subroutine sgeqls ( 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 )

SGEQLS

Purpose:
``` Solve the least squares problem
min || A*X - B ||
using the QL factorization
A = Q*L
computed by SGEQLF.```
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 REAL array, dimension (LDA,N) Details of the QL factorization of the original matrix A as returned by SGEQLF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= M.``` [in] TAU ``` TAU is REAL array, dimension (N) 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, 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 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 120 of file sgeqls.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  REAL A( LDA, * ), B( LDB, * ), TAU( * ),
132  \$ WORK( LWORK )
133 * ..
134 *
135 * =====================================================================
136 *
137 * .. Parameters ..
138  REAL ONE
139  parameter( one = 1.0e+0 )
140 * ..
141 * .. External Subroutines ..
142  EXTERNAL sormql, strsm, 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( 'SGEQLS', -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 sormql( '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 strsm( '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 SGEQLS
189 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sormql(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMQL
Definition: sormql.f:168
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
Definition: strsm.f:181
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