 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zptt02()

 subroutine zptt02 ( character UPLO, integer N, integer NRHS, double precision, dimension( * ) D, complex*16, dimension( * ) E, complex*16, dimension( ldx, * ) X, integer LDX, complex*16, dimension( ldb, * ) B, integer LDB, double precision RESID )

ZPTT02

Purpose:
``` ZPTT02 computes the residual for the solution to a symmetric
tridiagonal system of equations:
RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
where EPS is the machine epsilon.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored. = 'U': E is the superdiagonal of A = 'L': E is the subdiagonal of A``` [in] N ``` N is INTEGTER The order of the matrix A.``` [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] D ``` D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the tridiagonal matrix A.``` [in] E ``` E is COMPLEX*16 array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A.``` [in] X ``` X is COMPLEX*16 array, dimension (LDX,NRHS) The n by nrhs matrix of 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 n by nrhs matrix of right hand side vectors B. On exit, B is overwritten with the difference B - 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 - A*X) / (norm(A) * norm(X) * EPS)```

Definition at line 114 of file zptt02.f.

115 *
116 * -- LAPACK test routine --
117 * -- LAPACK is a software package provided by Univ. of Tennessee, --
118 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119 *
120 * .. Scalar Arguments ..
121  CHARACTER UPLO
122  INTEGER LDB, LDX, N, NRHS
123  DOUBLE PRECISION RESID
124 * ..
125 * .. Array Arguments ..
126  DOUBLE PRECISION D( * )
127  COMPLEX*16 B( LDB, * ), E( * ), X( LDX, * )
128 * ..
129 *
130 * =====================================================================
131 *
132 * .. Parameters ..
133  DOUBLE PRECISION ONE, ZERO
134  parameter( one = 1.0d+0, zero = 0.0d+0 )
135 * ..
136 * .. Local Scalars ..
137  INTEGER J
138  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
139 * ..
140 * .. External Functions ..
141  DOUBLE PRECISION DLAMCH, DZASUM, ZLANHT
142  EXTERNAL dlamch, dzasum, zlanht
143 * ..
144 * .. Intrinsic Functions ..
145  INTRINSIC max
146 * ..
147 * .. External Subroutines ..
148  EXTERNAL zlaptm
149 * ..
150 * .. Executable Statements ..
151 *
152 * Quick return if possible
153 *
154  IF( n.LE.0 ) THEN
155  resid = zero
156  RETURN
157  END IF
158 *
159 * Compute the 1-norm of the tridiagonal matrix A.
160 *
161  anorm = zlanht( '1', n, d, e )
162 *
163 * Exit with RESID = 1/EPS if ANORM = 0.
164 *
165  eps = dlamch( 'Epsilon' )
166  IF( anorm.LE.zero ) THEN
167  resid = one / eps
168  RETURN
169  END IF
170 *
171 * Compute B - A*X.
172 *
173  CALL zlaptm( uplo, n, nrhs, -one, d, e, x, ldx, one, b, ldb )
174 *
175 * Compute the maximum over the number of right hand sides of
176 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
177 *
178  resid = zero
179  DO 10 j = 1, nrhs
180  bnorm = dzasum( n, b( 1, j ), 1 )
181  xnorm = dzasum( n, x( 1, j ), 1 )
182  IF( xnorm.LE.zero ) THEN
183  resid = one / eps
184  ELSE
185  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
186  END IF
187  10 CONTINUE
188 *
189  RETURN
190 *
191 * End of ZPTT02
192 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zlaptm(UPLO, N, NRHS, ALPHA, D, E, X, LDX, BETA, B, LDB)
ZLAPTM
Definition: zlaptm.f:129
double precision function zlanht(NORM, N, D, E)
ZLANHT returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlanht.f:101
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:72
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