 LAPACK  3.10.1 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(op(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(op(A)) * norm(X) * EPS)```

Definition at line 122 of file zgtt02.f.

124 *
125 * -- LAPACK test routine --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 *
129 * .. Scalar Arguments ..
130  CHARACTER TRANS
131  INTEGER LDB, LDX, N, NRHS
132  DOUBLE PRECISION RESID
133 * ..
134 * .. Array Arguments ..
135  COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
136  \$ X( LDX, * )
137 * ..
138 *
139 * =====================================================================
140 *
141 * .. Parameters ..
142  DOUBLE PRECISION ONE, ZERO
143  parameter( one = 1.0d+0, zero = 0.0d+0 )
144 * ..
145 * .. Local Scalars ..
146  INTEGER J
147  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
148 * ..
149 * .. External Functions ..
150  LOGICAL LSAME
151  DOUBLE PRECISION DLAMCH, DZASUM, ZLANGT
152  EXTERNAL lsame, dlamch, dzasum, zlangt
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL zlagtm
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC max
159 * ..
160 * .. Executable Statements ..
161 *
162 * Quick exit if N = 0 or NRHS = 0
163 *
164  resid = zero
165  IF( n.LE.0 .OR. nrhs.EQ.0 )
166  \$ RETURN
167 *
168 * Compute the maximum over the number of right hand sides of
169 * norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
170 *
171  IF( lsame( trans, 'N' ) ) THEN
172  anorm = zlangt( '1', n, dl, d, du )
173  ELSE
174  anorm = zlangt( 'I', n, dl, d, du )
175  END IF
176 *
177 * Exit with RESID = 1/EPS if ANORM = 0.
178 *
179  eps = dlamch( 'Epsilon' )
180  IF( anorm.LE.zero ) THEN
181  resid = one / eps
182  RETURN
183  END IF
184 *
185 * Compute B - op(A)*X and store in B.
186 *
187  CALL zlagtm( trans, n, nrhs, -one, dl, d, du, x, ldx, one, b,
188  \$ ldb )
189 *
190  DO 10 j = 1, nrhs
191  bnorm = dzasum( n, b( 1, j ), 1 )
192  xnorm = dzasum( n, x( 1, j ), 1 )
193  IF( xnorm.LE.zero ) THEN
194  resid = one / eps
195  ELSE
196  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
197  END IF
198  10 CONTINUE
199 *
200  RETURN
201 *
202 * End of ZGTT02
203 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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:106
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:145
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:72
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