LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ dptt02()

 subroutine dptt02 ( integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( ldb, * ) b, integer ldb, double precision resid )

DPTT02

Purpose:
``` DPTT02 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] 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 DOUBLE PRECISION array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A.``` [in] X ``` X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 103 of file dptt02.f.

104*
105* -- LAPACK test routine --
106* -- LAPACK is a software package provided by Univ. of Tennessee, --
107* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
108*
109* .. Scalar Arguments ..
110 INTEGER LDB, LDX, N, NRHS
111 DOUBLE PRECISION RESID
112* ..
113* .. Array Arguments ..
114 DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), X( LDX, * )
115* ..
116*
117* =====================================================================
118*
119* .. Parameters ..
120 DOUBLE PRECISION ONE, ZERO
121 parameter( one = 1.0d+0, zero = 0.0d+0 )
122* ..
123* .. Local Scalars ..
124 INTEGER J
125 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
126* ..
127* .. External Functions ..
128 DOUBLE PRECISION DASUM, DLAMCH, DLANST
129 EXTERNAL dasum, dlamch, dlanst
130* ..
131* .. Intrinsic Functions ..
132 INTRINSIC max
133* ..
134* .. External Subroutines ..
135 EXTERNAL dlaptm
136* ..
137* .. Executable Statements ..
138*
139* Quick return if possible
140*
141 IF( n.LE.0 ) THEN
142 resid = zero
143 RETURN
144 END IF
145*
146* Compute the 1-norm of the tridiagonal matrix A.
147*
148 anorm = dlanst( '1', n, d, e )
149*
150* Exit with RESID = 1/EPS if ANORM = 0.
151*
152 eps = dlamch( 'Epsilon' )
153 IF( anorm.LE.zero ) THEN
154 resid = one / eps
155 RETURN
156 END IF
157*
158* Compute B - A*X.
159*
160 CALL dlaptm( n, nrhs, -one, d, e, x, ldx, one, b, ldb )
161*
162* Compute the maximum over the number of right hand sides of
163* norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
164*
165 resid = zero
166 DO 10 j = 1, nrhs
167 bnorm = dasum( n, b( 1, j ), 1 )
168 xnorm = dasum( n, x( 1, j ), 1 )
169 IF( xnorm.LE.zero ) THEN
170 resid = one / eps
171 ELSE
172 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
173 END IF
174 10 CONTINUE
175*
176 RETURN
177*
178* End of DPTT02
179*
subroutine dlaptm(n, nrhs, alpha, d, e, x, ldx, beta, b, ldb)
DLAPTM
Definition dlaptm.f:116
double precision function dasum(n, dx, incx)
DASUM
Definition dasum.f:71
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
double precision function dlanst(norm, n, d, e)
DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition dlanst.f:100
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