 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dgtt02()

 subroutine dgtt02 ( character TRANS, integer N, integer NRHS, double precision, dimension( * ) DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB, double precision RESID )

DGTT02

Purpose:
``` DGTT02 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.
The norm used is the 1-norm.```
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 = 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 DOUBLE PRECISION array, dimension (N-1) The (n-1) sub-diagonal elements of A.``` [in] D ``` D is DOUBLE PRECISION array, dimension (N) The diagonal elements of A.``` [in] DU ``` DU is DOUBLE PRECISION array, dimension (N-1) The (n-1) super-diagonal elements of A.``` [in] X ``` X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 123 of file dgtt02.f.

125*
126* -- LAPACK test routine --
127* -- LAPACK is a software package provided by Univ. of Tennessee, --
128* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130* .. Scalar Arguments ..
131 CHARACTER TRANS
132 INTEGER LDB, LDX, N, NRHS
133 DOUBLE PRECISION RESID
134* ..
135* .. Array Arguments ..
136 DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ),
137 \$ X( LDX, * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 DOUBLE PRECISION ONE, ZERO
144 parameter( one = 1.0d+0, zero = 0.0d+0 )
145* ..
146* .. Local Scalars ..
147 INTEGER J
148 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
149* ..
150* .. External Functions ..
151 LOGICAL LSAME
152 DOUBLE PRECISION DASUM, DLAMCH, DLANGT
153 EXTERNAL lsame, dasum, dlamch, dlangt
154* ..
155* .. External Subroutines ..
156 EXTERNAL dlagtm
157* ..
158* .. Intrinsic Functions ..
159 INTRINSIC max
160* ..
161* .. Executable Statements ..
162*
163* Quick exit if N = 0 or NRHS = 0
164*
165 resid = zero
166 IF( n.LE.0 .OR. nrhs.EQ.0 )
167 \$ RETURN
168*
169* Compute the maximum over the number of right hand sides of
170* norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
171*
172 IF( lsame( trans, 'N' ) ) THEN
173 anorm = dlangt( '1', n, dl, d, du )
174 ELSE
175 anorm = dlangt( 'I', n, dl, d, du )
176 END IF
177*
178* Exit with RESID = 1/EPS if ANORM = 0.
179*
180 eps = dlamch( 'Epsilon' )
181 IF( anorm.LE.zero ) THEN
182 resid = one / eps
183 RETURN
184 END IF
185*
186* Compute B - op(A)*X and store in B.
187*
188 CALL dlagtm( trans, n, nrhs, -one, dl, d, du, x, ldx, one, b,
189 \$ ldb )
190*
191 DO 10 j = 1, nrhs
192 bnorm = dasum( n, b( 1, j ), 1 )
193 xnorm = dasum( n, x( 1, j ), 1 )
194 IF( xnorm.LE.zero ) THEN
195 resid = one / eps
196 ELSE
197 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
198 END IF
199 10 CONTINUE
200*
201 RETURN
202*
203* End of DGTT02
204*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:71
double precision function dlangt(NORM, N, DL, D, DU)
DLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlangt.f:106
subroutine dlagtm(TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB)
DLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix,...
Definition: dlagtm.f:145
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