LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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◆ sgtt02()

 subroutine sgtt02 ( character trans, integer n, integer nrhs, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer ldb, real resid )

SGTT02

Purpose:
SGTT02 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 INTEGER 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 REAL array, dimension (N-1) The (n-1) sub-diagonal elements of A. [in] D D is REAL array, dimension (N) The diagonal elements of A. [in] DU DU is REAL array, dimension (N-1) The (n-1) super-diagonal elements of A. [in] X X is REAL 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 REAL 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 REAL norm(B - op(A)*X) / (norm(op(A)) * norm(X) * EPS)

Definition at line 123 of file sgtt02.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 REAL RESID
134* ..
135* .. Array Arguments ..
136 REAL B( LDB, * ), D( * ), DL( * ), DU( * ),
137 \$ X( LDX, * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 REAL ONE, ZERO
144 parameter( one = 1.0e+0, zero = 0.0e+0 )
145* ..
146* .. Local Scalars ..
147 INTEGER J
148 REAL ANORM, BNORM, EPS, XNORM
149* ..
150* .. External Functions ..
151 LOGICAL LSAME
152 REAL SASUM, SLAMCH, SLANGT
153 EXTERNAL lsame, sasum, slamch, slangt
154* ..
155* .. External Subroutines ..
156 EXTERNAL slagtm
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 = slangt( '1', n, dl, d, du )
174 ELSE
175 anorm = slangt( 'I', n, dl, d, du )
176 END IF
177*
178* Exit with RESID = 1/EPS if ANORM = 0.
179*
180 eps = slamch( '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 slagtm( trans, n, nrhs, -one, dl, d, du, x, ldx, one, b,
189 \$ ldb )
190*
191 DO 10 j = 1, nrhs
192 bnorm = sasum( n, b( 1, j ), 1 )
193 xnorm = sasum( 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 SGTT02
204*
real function sasum(n, sx, incx)
SASUM
Definition sasum.f:72
subroutine slagtm(trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb)
SLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix,...
Definition slagtm.f:145
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function slangt(norm, n, dl, d, du)
SLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition slangt.f:106
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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