LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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◆ dtpt02()

 subroutine dtpt02 ( character UPLO, character TRANS, character DIAG, integer N, integer NRHS, double precision, dimension( * ) AP, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) WORK, double precision RESID )

DTPT02

Purpose:
DTPT02 computes the residual for the computed solution to a
triangular system of linear equations op(A)*X = B, when the
triangular matrix A is stored in packed format. The test ratio is
the maximum over
norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
where op(A) = A or A**T, b is the column of B, x is the solution
vector, and EPS is the machine epsilon.
The norm used is the 1-norm.
Parameters
 [in] UPLO UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular [in] TRANS TRANS is CHARACTER*1 Specifies the operation applied to A. = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose = Transpose) [in] DIAG DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular [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 X and B. NRHS >= 0. [in] AP AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. [in] X X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations. [in] LDX LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N). [in] B B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations. [in] LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). [out] WORK WORK is DOUBLE PRECISION array, dimension (N) [out] RESID RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).

Definition at line 140 of file dtpt02.f.

142*
143* -- LAPACK test routine --
144* -- LAPACK is a software package provided by Univ. of Tennessee, --
145* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146*
147* .. Scalar Arguments ..
148 CHARACTER DIAG, TRANS, UPLO
149 INTEGER LDB, LDX, N, NRHS
150 DOUBLE PRECISION RESID
151* ..
152* .. Array Arguments ..
153 DOUBLE PRECISION AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
154* ..
155*
156* =====================================================================
157*
158* .. Parameters ..
159 DOUBLE PRECISION ZERO, ONE
160 parameter( zero = 0.0d+0, one = 1.0d+0 )
161* ..
162* .. Local Scalars ..
163 INTEGER J
164 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
165* ..
166* .. External Functions ..
167 LOGICAL LSAME
168 DOUBLE PRECISION DASUM, DLAMCH, DLANTP
169 EXTERNAL lsame, dasum, dlamch, dlantp
170* ..
171* .. External Subroutines ..
172 EXTERNAL daxpy, dcopy, dtpmv
173* ..
174* .. Intrinsic Functions ..
175 INTRINSIC max
176* ..
177* .. Executable Statements ..
178*
179* Quick exit if N = 0 or NRHS = 0
180*
181 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
182 resid = zero
183 RETURN
184 END IF
185*
186* Compute the 1-norm of op(A).
187*
188 IF( lsame( trans, 'N' ) ) THEN
189 anorm = dlantp( '1', uplo, diag, n, ap, work )
190 ELSE
191 anorm = dlantp( 'I', uplo, diag, n, ap, work )
192 END IF
193*
194* Exit with RESID = 1/EPS if ANORM = 0.
195*
196 eps = dlamch( 'Epsilon' )
197 IF( anorm.LE.zero ) THEN
198 resid = one / eps
199 RETURN
200 END IF
201*
202* Compute the maximum over the number of right hand sides of
203* norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).
204*
205 resid = zero
206 DO 10 j = 1, nrhs
207 CALL dcopy( n, x( 1, j ), 1, work, 1 )
208 CALL dtpmv( uplo, trans, diag, n, ap, work, 1 )
209 CALL daxpy( n, -one, b( 1, j ), 1, work, 1 )
210 bnorm = dasum( n, work, 1 )
211 xnorm = dasum( n, x( 1, j ), 1 )
212 IF( xnorm.LE.zero ) THEN
213 resid = one / eps
214 ELSE
215 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
216 END IF
217 10 CONTINUE
218*
219 RETURN
220*
221* End of DTPT02
222*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:71
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:89
subroutine dtpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV
Definition: dtpmv.f:142
double precision function dlantp(NORM, UPLO, DIAG, N, AP, WORK)
DLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlantp.f:124
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