LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine dqrt16 ( character TRANS, integer M, integer N, integer NRHS, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) RWORK, double precision RESID )

DQRT16

Purpose:
``` DQRT16 computes the residual for a solution of a system of linear
equations  A*x = b  or  A'*x = b:
RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ),
where EPS is the machine epsilon.```
Parameters
 [in] TRANS ``` TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A *x = b = 'T': A'*x = b, where A' is the transpose of A = 'C': A'*x = b, where A' is the transpose of A``` [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 >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of columns of B, the matrix of right hand sides. NRHS >= 0.``` [in] A ``` A is DOUBLE PRECISION array, dimension (LDA,N) The original M x N matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).``` [in] X ``` X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.``` [in] LDX ``` LDX is INTEGER The leading dimension of the array X. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).``` [in,out] B ``` B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (M)` [out] RESID ``` RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).```
Date
November 2011

Definition at line 135 of file dqrt16.f.

135 *
136 * -- LAPACK test routine (version 3.4.0) --
137 * -- LAPACK is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 * November 2011
140 *
141 * .. Scalar Arguments ..
142  CHARACTER trans
143  INTEGER lda, ldb, ldx, m, n, nrhs
144  DOUBLE PRECISION resid
145 * ..
146 * .. Array Arguments ..
147  DOUBLE PRECISION a( lda, * ), b( ldb, * ), rwork( * ),
148  \$ x( ldx, * )
149 * ..
150 *
151 * =====================================================================
152 *
153 * .. Parameters ..
154  DOUBLE PRECISION zero, one
155  parameter ( zero = 0.0d+0, one = 1.0d+0 )
156 * ..
157 * .. Local Scalars ..
158  INTEGER j, n1, n2
159  DOUBLE PRECISION anorm, bnorm, eps, xnorm
160 * ..
161 * .. External Functions ..
162  LOGICAL lsame
163  DOUBLE PRECISION dasum, dlamch, dlange
164  EXTERNAL lsame, dasum, dlamch, dlange
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL dgemm
168 * ..
169 * .. Intrinsic Functions ..
170  INTRINSIC max
171 * ..
172 * .. Executable Statements ..
173 *
174 * Quick exit if M = 0 or N = 0 or NRHS = 0
175 *
176  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.EQ.0 ) THEN
177  resid = zero
178  RETURN
179  END IF
180 *
181  IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
182  anorm = dlange( 'I', m, n, a, lda, rwork )
183  n1 = n
184  n2 = m
185  ELSE
186  anorm = dlange( '1', m, n, a, lda, rwork )
187  n1 = m
188  n2 = n
189  END IF
190 *
191  eps = dlamch( 'Epsilon' )
192 *
193 * Compute B - A*X (or B - A'*X ) and store in B.
194 *
195  CALL dgemm( trans, 'No transpose', n1, nrhs, n2, -one, a, lda, x,
196  \$ ldx, one, b, ldb )
197 *
198 * Compute the maximum over the number of right hand sides of
199 * norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ) .
200 *
201  resid = zero
202  DO 10 j = 1, nrhs
203  bnorm = dasum( n1, b( 1, j ), 1 )
204  xnorm = dasum( n2, x( 1, j ), 1 )
205  IF( anorm.EQ.zero .AND. bnorm.EQ.zero ) THEN
206  resid = zero
207  ELSE IF( anorm.LE.zero .OR. xnorm.LE.zero ) THEN
208  resid = one / eps
209  ELSE
210  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) /
211  \$ ( max( m, n )*eps ) )
212  END IF
213  10 CONTINUE
214 *
215  RETURN
216 *
217 * End of DQRT16
218 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:116
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:53
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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