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)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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