LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ 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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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)
Definition cblat2.f:3285
subroutine strsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
STRSM
Definition strsm.f:181
subroutine sormql(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
SORMQL
Definition sormql.f:168
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