LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

◆ cqrt16()

 subroutine cqrt16 ( character TRANS, integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID )

CQRT16

Purpose:
CQRT16 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^T*x = b, where A^T is the transpose of A = 'C': A^H*x = b, where A^H is the conjugate 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 REAL array, dimension (M) [out] RESID RESID is REAL The maximum over the number of right hand sides of norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).
Date
December 2016

Definition at line 135 of file cqrt16.f.

135 *
136 * -- LAPACK test routine (version 3.7.0) --
137 * -- LAPACK is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 * December 2016
140 *
141 * .. Scalar Arguments ..
142  CHARACTER trans
143  INTEGER lda, ldb, ldx, m, n, nrhs
144  REAL resid
145 * ..
146 * .. Array Arguments ..
147  REAL rwork( * )
148  COMPLEX a( lda, * ), b( ldb, * ), x( ldx, * )
149 * ..
150 *
151 * =====================================================================
152 *
153 * .. Parameters ..
154  REAL zero, one
155  parameter( zero = 0.0e+0, one = 1.0e+0 )
156  COMPLEX cone
157  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
158 * ..
159 * .. Local Scalars ..
160  INTEGER j, n1, n2
161  REAL anorm, bnorm, eps, xnorm
162 * ..
163 * .. External Functions ..
164  LOGICAL lsame
165  REAL clange, scasum, slamch
166  EXTERNAL lsame, clange, scasum, slamch
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL cgemm
170 * ..
171 * .. Intrinsic Functions ..
172  INTRINSIC max
173 * ..
174 * .. Executable Statements ..
175 *
176 * Quick exit if M = 0 or N = 0 or NRHS = 0
177 *
178  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.EQ.0 ) THEN
179  resid = zero
180  RETURN
181  END IF
182 *
183  IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
184  anorm = clange( 'I', m, n, a, lda, rwork )
185  n1 = n
186  n2 = m
187  ELSE
188  anorm = clange( '1', m, n, a, lda, rwork )
189  n1 = m
190  n2 = n
191  END IF
192 *
193  eps = slamch( 'Epsilon' )
194 *
195 * Compute B - A*X (or B - A'*X ) and store in B.
196 *
197  CALL cgemm( trans, 'No transpose', n1, nrhs, n2, -cone, a, lda, x,
198  \$ ldx, cone, b, ldb )
199 *
200 * Compute the maximum over the number of right hand sides of
201 * norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ) .
202 *
203  resid = zero
204  DO 10 j = 1, nrhs
205  bnorm = scasum( n1, b( 1, j ), 1 )
206  xnorm = scasum( n2, x( 1, j ), 1 )
207  IF( anorm.EQ.zero .AND. bnorm.EQ.zero ) THEN
208  resid = zero
209  ELSE IF( anorm.LE.zero .OR. xnorm.LE.zero ) THEN
210  resid = one / eps
211  ELSE
212  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) /
213  \$ ( max( m, n )*eps ) )
214  END IF
215  10 CONTINUE
216 *
217  RETURN
218 *
219 * End of CQRT16
220 *
real function scasum(N, CX, INCX)
SCASUM
Definition: scasum.f:74
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:117
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:189
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