LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ dgelqs()

subroutine dgelqs ( 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 
)

DGELQS

Purpose:
 Compute a minimum-norm solution
     min || A*X - B ||
 using the LQ factorization
     A = L*Q
 computed by DGELQF.
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 DOUBLE PRECISION array, dimension (LDA,N)
          Details of the LQ factorization of the original matrix A as
          returned by DGELQF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= M.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (M)
          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.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B. LDB >= N.
[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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 119 of file dgelqs.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 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TAU( * ),
131 $ WORK( LWORK )
132* ..
133*
134* =====================================================================
135*
136* .. Parameters ..
137 DOUBLE PRECISION ZERO, ONE
138 parameter( zero = 0.0d+0, one = 1.0d+0 )
139* ..
140* .. External Subroutines ..
141 EXTERNAL dlaset, dormlq, dtrsm, 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( 'DGELQS', -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 dtrsm( '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 dlaset( 'Full', n-m, nrhs, zero, zero, b( m+1, 1 ), ldb )
184*
185* B := Q' * B
186*
187 CALL dormlq( 'Left', 'Transpose', n, nrhs, m, a, lda, tau, b, ldb,
188 $ work, lwork, info )
189*
190 RETURN
191*
192* End of DGELQS
193*
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: dlaset.f:110
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:181
subroutine dormlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMLQ
Definition: dormlq.f:167
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