LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ 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 INTEGER 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 dzasum(n, zx, incx)
DZASUM
Definition dzasum.f:72
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 dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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