LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zgtt02()

 subroutine zgtt02 ( character TRANS, integer N, integer NRHS, complex*16, dimension( * ) DL, complex*16, dimension( * ) D, complex*16, dimension( * ) DU, complex*16, dimension( ldx, * ) X, integer LDX, complex*16, dimension( ldb, * ) B, integer LDB, double precision RESID )

ZGTT02

Purpose:
``` ZGTT02 computes the residual for the solution to a tridiagonal
system of equations:
RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
where EPS is the machine epsilon.```
Parameters
 [in] TRANS ``` TRANS is CHARACTER Specifies the form of the residual. = 'N': B - A * X (No transpose) = 'T': B - A**T * X (Transpose) = 'C': B - A**H * X (Conjugate transpose)``` [in] N ``` N is INTEGTER The order of the matrix A. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.``` [in] DL ``` DL is COMPLEX*16 array, dimension (N-1) The (n-1) sub-diagonal elements of A.``` [in] D ``` D is COMPLEX*16 array, dimension (N) The diagonal elements of A.``` [in] DU ``` DU is COMPLEX*16 array, dimension (N-1) The (n-1) super-diagonal elements of A.``` [in] X ``` X is COMPLEX*16 array, dimension (LDX,NRHS) The computed solution vectors X.``` [in] LDX ``` LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).``` [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 - op(A)*X.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] RESID ``` RESID is DOUBLE PRECISION norm(B - op(A)*X) / (norm(A) * norm(X) * EPS)```
Date
December 2016

Definition at line 126 of file zgtt02.f.

126 *
127 * -- LAPACK test routine (version 3.7.0) --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 * December 2016
131 *
132 * .. Scalar Arguments ..
133  CHARACTER trans
134  INTEGER ldb, ldx, n, nrhs
135  DOUBLE PRECISION resid
136 * ..
137 * .. Array Arguments ..
138  COMPLEX*16 b( ldb, * ), d( * ), dl( * ), du( * ),
139  \$ x( ldx, * )
140 * ..
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145  DOUBLE PRECISION one, zero
146  parameter( one = 1.0d+0, zero = 0.0d+0 )
147 * ..
148 * .. Local Scalars ..
149  INTEGER j
150  DOUBLE PRECISION anorm, bnorm, eps, xnorm
151 * ..
152 * .. External Functions ..
153  LOGICAL lsame
154  DOUBLE PRECISION dlamch, dzasum, zlangt
155  EXTERNAL lsame, dlamch, dzasum, zlangt
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL zlagtm
159 * ..
160 * .. Intrinsic Functions ..
161  INTRINSIC max
162 * ..
163 * .. Executable Statements ..
164 *
165 * Quick exit if N = 0 or NRHS = 0
166 *
167  resid = zero
168  IF( n.LE.0 .OR. nrhs.EQ.0 )
169  \$ RETURN
170 *
171 * Compute the maximum over the number of right hand sides of
172 * norm(B - op(A)*X) / ( norm(A) * norm(X) * EPS ).
173 *
174  IF( lsame( trans, 'N' ) ) THEN
175  anorm = zlangt( '1', n, dl, d, du )
176  ELSE
177  anorm = zlangt( 'I', n, dl, d, du )
178  END IF
179 *
180 * Exit with RESID = 1/EPS if ANORM = 0.
181 *
182  eps = dlamch( 'Epsilon' )
183  IF( anorm.LE.zero ) THEN
184  resid = one / eps
185  RETURN
186  END IF
187 *
188 * Compute B - op(A)*X.
189 *
190  CALL zlagtm( trans, n, nrhs, -one, dl, d, du, x, ldx, one, b,
191  \$ ldb )
192 *
193  DO 10 j = 1, nrhs
194  bnorm = dzasum( n, b( 1, j ), 1 )
195  xnorm = dzasum( n, x( 1, j ), 1 )
196  IF( xnorm.LE.zero ) THEN
197  resid = one / eps
198  ELSE
199  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
200  END IF
201  10 CONTINUE
202 *
203  RETURN
204 *
205 * End of ZGTT02
206 *
subroutine zlagtm(TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB)
ZLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix...
Definition: zlagtm.f:147
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:74
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
double precision function zlangt(NORM, N, DL, D, DU)
ZLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlangt.f:108
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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