LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ zgelqs()

subroutine zgelqs ( integer  M,
integer  N,
integer  NRHS,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( * )  TAU,
complex*16, dimension( ldb, * )  B,
integer  LDB,
complex*16, dimension( lwork )  WORK,
integer  LWORK,
integer  INFO 
)

ZGELQS

Purpose:
 Compute a minimum-norm solution
     min || A*X - B ||
 using the LQ factorization
     A = L*Q
 computed by ZGELQF.
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 COMPLEX*16 array, dimension (LDA,N)
          Details of the LQ factorization of the original matrix A as
          returned by ZGELQF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= M.
[in]TAU
          TAU is COMPLEX*16 array, dimension (M)
          Details of the orthogonal matrix Q.
[in,out]B
          B is COMPLEX*16 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 COMPLEX*16 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 zgelqs.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  COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ),
131  $ WORK( LWORK )
132 * ..
133 *
134 * =====================================================================
135 *
136 * .. Parameters ..
137  COMPLEX*16 CZERO, CONE
138  parameter( czero = ( 0.0d+0, 0.0d+0 ),
139  $ cone = ( 1.0d+0, 0.0d+0 ) )
140 * ..
141 * .. External Subroutines ..
142  EXTERNAL xerbla, zlaset, ztrsm, zunmlq
143 * ..
144 * .. Intrinsic Functions ..
145  INTRINSIC max
146 * ..
147 * .. Executable Statements ..
148 *
149 * Test the input parameters.
150 *
151  info = 0
152  IF( m.LT.0 ) THEN
153  info = -1
154  ELSE IF( n.LT.0 .OR. m.GT.n ) 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, n ) ) 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( 'ZGELQS', -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 * Solve L*X = B(1:m,:)
177 *
178  CALL ztrsm( 'Left', 'Lower', 'No transpose', 'Non-unit', m, nrhs,
179  $ cone, a, lda, b, ldb )
180 *
181 * Set B(m+1:n,:) to zero
182 *
183  IF( m.LT.n )
184  $ CALL zlaset( 'Full', n-m, nrhs, czero, czero, b( m+1, 1 ),
185  $ ldb )
186 *
187 * B := Q' * B
188 *
189  CALL zunmlq( 'Left', 'Conjugate transpose', n, nrhs, m, a, lda,
190  $ tau, b, ldb, work, lwork, info )
191 *
192  RETURN
193 *
194 * End of ZGELQS
195 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:180
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
subroutine zunmlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMLQ
Definition: zunmlq.f:167
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