LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sgerqs()

subroutine sgerqs ( 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 
)

SGERQS

Purpose:
 Compute a minimum-norm solution
     min || A*X - B ||
 using the RQ factorization
     A = R*Q
 computed by SGERQF.
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 RQ factorization of the original matrix A as
          returned by SGERQF.
[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 right hand side vectors for the linear system.
          On exit, the solution vectors X.  Each solution vector
          is contained in rows 1:N of a column of B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 120 of file sgerqs.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 ZERO, ONE
139  parameter( zero = 0.0e+0, one = 1.0e+0 )
140 * ..
141 * .. External Subroutines ..
142  EXTERNAL slaset, sormrq, strsm, xerbla
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( 'SGERQS', -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 R*X = B(n-m+1:n,:)
177 *
178  CALL strsm( 'Left', 'Upper', 'No transpose', 'Non-unit', m, nrhs,
179  $ one, a( 1, n-m+1 ), lda, b( n-m+1, 1 ), ldb )
180 *
181 * Set B(1:n-m,:) to zero
182 *
183  CALL slaset( 'Full', n-m, nrhs, zero, zero, b, ldb )
184 *
185 * B := Q' * B
186 *
187  CALL sormrq( 'Left', 'Transpose', n, nrhs, m, a, lda, tau, b, ldb,
188  $ work, lwork, info )
189 *
190  RETURN
191 *
192 * End of SGERQS
193 *
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:110
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sormrq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMRQ
Definition: sormrq.f:168
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
Definition: strsm.f:181
Here is the call graph for this function:
Here is the caller graph for this function: