LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ cget02()

subroutine cget02 ( 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 
)

CGET02

Purpose:
 CGET02 computes the residual for a solution of a system of linear
 equations op(A)*X = B:
    RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
 where op(A) = A, A**T, or A**H, depending on TRANS, and EPS is the
 machine epsilon.
Parameters
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A    * X = B  (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose)
[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 - op(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 - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 132 of file cget02.f.

134 *
135 * -- LAPACK test routine --
136 * -- LAPACK is a software package provided by Univ. of Tennessee, --
137 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138 *
139 * .. Scalar Arguments ..
140  CHARACTER TRANS
141  INTEGER LDA, LDB, LDX, M, N, NRHS
142  REAL RESID
143 * ..
144 * .. Array Arguments ..
145  REAL RWORK( * )
146  COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
147 * ..
148 *
149 * =====================================================================
150 *
151 * .. Parameters ..
152  REAL ZERO, ONE
153  parameter( zero = 0.0e+0, one = 1.0e+0 )
154  COMPLEX CONE
155  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
156 * ..
157 * .. Local Scalars ..
158  INTEGER J, N1, N2
159  REAL ANORM, BNORM, EPS, XNORM
160 * ..
161 * .. External Functions ..
162  LOGICAL LSAME
163  REAL CLANGE, SCASUM, SLAMCH
164  EXTERNAL lsame, clange, scasum, slamch
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL cgemm
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  n1 = n
183  n2 = m
184  ELSE
185  n1 = m
186  n2 = n
187  END IF
188 *
189 * Exit with RESID = 1/EPS if ANORM = 0.
190 *
191  eps = slamch( 'Epsilon' )
192  IF( lsame( trans, 'N' ) ) THEN
193  anorm = clange( '1', m, n, a, lda, rwork )
194  ELSE
195  anorm = clange( 'I', m, n, a, lda, rwork )
196  END IF
197  IF( anorm.LE.zero ) THEN
198  resid = one / eps
199  RETURN
200  END IF
201 *
202 * Compute B - op(A)*X and store in B.
203 *
204  CALL cgemm( trans, 'No transpose', n1, nrhs, n2, -cone, a, lda, x,
205  $ ldx, cone, b, ldb )
206 *
207 * Compute the maximum over the number of right hand sides of
208 * norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ) .
209 *
210  resid = zero
211  DO 10 j = 1, nrhs
212  bnorm = scasum( n1, b( 1, j ), 1 )
213  xnorm = scasum( n2, x( 1, j ), 1 )
214  IF( xnorm.LE.zero ) THEN
215  resid = one / eps
216  ELSE
217  resid = max( resid, ( ( bnorm/anorm )/xnorm )/eps )
218  END IF
219  10 CONTINUE
220 *
221  RETURN
222 *
223 * End of CGET02
224 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
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:115
real function scasum(N, CX, INCX)
SCASUM
Definition: scasum.f:72
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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