LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ zqrt16()

subroutine zqrt16 ( character  TRANS,
integer  M,
integer  N,
integer  NRHS,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( ldx, * )  X,
integer  LDX,
complex*16, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

ZQRT16

Purpose:
 ZQRT16 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*16 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*16 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*16 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 ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 131 of file zqrt16.f.

133 *
134 * -- LAPACK test routine --
135 * -- LAPACK is a software package provided by Univ. of Tennessee, --
136 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137 *
138 * .. Scalar Arguments ..
139  CHARACTER TRANS
140  INTEGER LDA, LDB, LDX, M, N, NRHS
141  DOUBLE PRECISION RESID
142 * ..
143 * .. Array Arguments ..
144  DOUBLE PRECISION RWORK( * )
145  COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
146 * ..
147 *
148 * =====================================================================
149 *
150 * .. Parameters ..
151  DOUBLE PRECISION ZERO, ONE
152  parameter( zero = 0.0d+0, one = 1.0d+0 )
153  COMPLEX*16 CONE
154  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
155 * ..
156 * .. Local Scalars ..
157  INTEGER J, N1, N2
158  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
159 * ..
160 * .. External Functions ..
161  LOGICAL LSAME
162  DOUBLE PRECISION DLAMCH, DZASUM, ZLANGE
163  EXTERNAL lsame, dlamch, dzasum, zlange
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL zgemm
167 * ..
168 * .. Intrinsic Functions ..
169  INTRINSIC max
170 * ..
171 * .. Executable Statements ..
172 *
173 * Quick exit if M = 0 or N = 0 or NRHS = 0
174 *
175  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.EQ.0 ) THEN
176  resid = zero
177  RETURN
178  END IF
179 *
180  IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
181  anorm = zlange( 'I', m, n, a, lda, rwork )
182  n1 = n
183  n2 = m
184  ELSE
185  anorm = zlange( '1', m, n, a, lda, rwork )
186  n1 = m
187  n2 = n
188  END IF
189 *
190  eps = dlamch( 'Epsilon' )
191 *
192 * Compute B - A*X (or B - A'*X ) and store in B.
193 *
194  CALL zgemm( trans, 'No transpose', n1, nrhs, n2, -cone, a, lda, x,
195  $ ldx, cone, b, ldb )
196 *
197 * Compute the maximum over the number of right hand sides of
198 * norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ) .
199 *
200  resid = zero
201  DO 10 j = 1, nrhs
202  bnorm = dzasum( n1, b( 1, j ), 1 )
203  xnorm = dzasum( n2, x( 1, j ), 1 )
204  IF( anorm.EQ.zero .AND. bnorm.EQ.zero ) THEN
205  resid = zero
206  ELSE IF( anorm.LE.zero .OR. xnorm.LE.zero ) THEN
207  resid = one / eps
208  ELSE
209  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) /
210  $ ( max( m, n )*eps ) )
211  END IF
212  10 CONTINUE
213 *
214  RETURN
215 *
216 * End of ZQRT16
217 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:115
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:72
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