LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
subroutine dgeqrs ( 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 
)

DGEQRS

Purpose: 
 Solve the least squares problem
     min || A*X - B ||
 using the QR factorization
     A = Q*R
 computed by DGEQRF.
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 DOUBLE PRECISION array, dimension (LDA,N)
          Details of the QR factorization of the original matrix A as
          returned by DGEQRF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= M.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (N)
          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 >= M.
[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.
Date
November 2011

Definition at line 123 of file dgeqrs.f.

123 *
124 * -- LAPACK test routine (version 3.4.0) --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 * November 2011
128 *
129 * .. Scalar Arguments ..
130  INTEGER info, lda, ldb, lwork, m, n, nrhs
131 * ..
132 * .. Array Arguments ..
133  DOUBLE PRECISION a( lda, * ), b( ldb, * ), tau( * ),
134  $ work( lwork )
135 * ..
136 *
137 * =====================================================================
138 *
139 * .. Parameters ..
140  DOUBLE PRECISION one
141  parameter ( one = 1.0d+0 )
142 * ..
143 * .. External Subroutines ..
144  EXTERNAL dormqr, dtrsm, xerbla
145 * ..
146 * .. Intrinsic Functions ..
147  INTRINSIC max
148 * ..
149 * .. Executable Statements ..
150 *
151 * Test the input arguments.
152 *
153  info = 0
154  IF( m.LT.0 ) THEN
155  info = -1
156  ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
157  info = -2
158  ELSE IF( nrhs.LT.0 ) THEN
159  info = -3
160  ELSE IF( lda.LT.max( 1, m ) ) THEN
161  info = -5
162  ELSE IF( ldb.LT.max( 1, m ) ) THEN
163  info = -8
164  ELSE IF( lwork.LT.1 .OR. lwork.LT.nrhs .AND. m.GT.0 .AND. n.GT.0 )
165  $ THEN
166  info = -10
167  END IF
168  IF( info.NE.0 ) THEN
169  CALL xerbla( 'DGEQRS', -info )
170  RETURN
171  END IF
172 *
173 * Quick return if possible
174 *
175  IF( n.EQ.0 .OR. nrhs.EQ.0 .OR. m.EQ.0 )
176  $ RETURN
177 *
178 * B := Q' * B
179 *
180  CALL dormqr( 'Left', 'Transpose', m, nrhs, n, a, lda, tau, b, ldb,
181  $ work, lwork, info )
182 *
183 * Solve R*X = B(1:n,:)
184 *
185  CALL dtrsm( 'Left', 'Upper', 'No transpose', 'Non-unit', n, nrhs,
186  $ one, a, lda, b, ldb )
187 *
188  RETURN
189 *
190 * End of DGEQRS
191 *
dtrsm
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:183
dormqr
subroutine dormqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMQR
Definition: dormqr.f:169
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62

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