LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ 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 INTEGER 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 dzasum(n, zx, incx)
DZASUM
Definition dzasum.f:72
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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
subroutine zlaptm(uplo, n, nrhs, alpha, d, e, x, ldx, beta, b, ldb)
ZLAPTM
Definition zlaptm.f:129
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