LAPACK  3.8.0
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.
Date
December 2016

Definition at line 135 of file zqrt16.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  DOUBLE PRECISION resid
145 * ..
146 * .. Array Arguments ..
147  DOUBLE PRECISION rwork( * )
148  COMPLEX*16 a( lda, * ), b( ldb, * ), x( ldx, * )
149 * ..
150 *
151 * =====================================================================
152 *
153 * .. Parameters ..
154  DOUBLE PRECISION zero, one
155  parameter( zero = 0.0d+0, one = 1.0d+0 )
156  COMPLEX*16 cone
157  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
158 * ..
159 * .. Local Scalars ..
160  INTEGER j, n1, n2
161  DOUBLE PRECISION anorm, bnorm, eps, xnorm
162 * ..
163 * .. External Functions ..
164  LOGICAL lsame
165  DOUBLE PRECISION dlamch, dzasum, zlange
166  EXTERNAL lsame, dlamch, dzasum, zlange
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL zgemm
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 = zlange( 'I', m, n, a, lda, rwork )
185  n1 = n
186  n2 = m
187  ELSE
188  anorm = zlange( '1', m, n, a, lda, rwork )
189  n1 = m
190  n2 = n
191  END IF
192 *
193  eps = dlamch( 'Epsilon' )
194 *
195 * Compute B - A*X (or B - A'*X ) and store in B.
196 *
197  CALL zgemm( 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 = dzasum( n1, b( 1, j ), 1 )
206  xnorm = dzasum( 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 ZQRT16
220 *
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:117
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:74
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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