LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ ztpt02()

 subroutine ztpt02 ( character uplo, character trans, character diag, integer n, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, double precision resid )

ZTPT02

Purpose:
``` ZTPT02 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, A**T, or A**H, b is the column of B, x is the
solution vector, and EPS is the machine epsilon.```
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)``` [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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (N)` [out] RWORK ` RWORK 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 145 of file ztpt02.f.

147*
148* -- LAPACK test routine --
149* -- LAPACK is a software package provided by Univ. of Tennessee, --
150* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151*
152* .. Scalar Arguments ..
153 CHARACTER DIAG, TRANS, UPLO
154 INTEGER LDB, LDX, N, NRHS
155 DOUBLE PRECISION RESID
156* ..
157* .. Array Arguments ..
158 DOUBLE PRECISION RWORK( * )
159 COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
160* ..
161*
162* =====================================================================
163*
164* .. Parameters ..
165 DOUBLE PRECISION ZERO, ONE
166 parameter( zero = 0.0d+0, one = 1.0d+0 )
167* ..
168* .. Local Scalars ..
169 INTEGER J
170 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
171* ..
172* .. External Functions ..
173 LOGICAL LSAME
174 DOUBLE PRECISION DLAMCH, DZASUM, ZLANTP
175 EXTERNAL lsame, dlamch, dzasum, zlantp
176* ..
177* .. External Subroutines ..
178 EXTERNAL zaxpy, zcopy, ztpmv
179* ..
180* .. Intrinsic Functions ..
181 INTRINSIC dcmplx, max
182* ..
183* .. Executable Statements ..
184*
185* Quick exit if N = 0 or NRHS = 0
186*
187 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
188 resid = zero
189 RETURN
190 END IF
191*
192* Compute the 1-norm of op(A).
193*
194 IF( lsame( trans, 'N' ) ) THEN
195 anorm = zlantp( '1', uplo, diag, n, ap, rwork )
196 ELSE
197 anorm = zlantp( 'I', uplo, diag, n, ap, rwork )
198 END IF
199*
200* Exit with RESID = 1/EPS if ANORM = 0.
201*
202 eps = dlamch( 'Epsilon' )
203 IF( anorm.LE.zero ) THEN
204 resid = one / eps
205 RETURN
206 END IF
207*
208* Compute the maximum over the number of right hand sides of
209* norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).
210*
211 resid = zero
212 DO 10 j = 1, nrhs
213 CALL zcopy( n, x( 1, j ), 1, work, 1 )
214 CALL ztpmv( uplo, trans, diag, n, ap, work, 1 )
215 CALL zaxpy( n, dcmplx( -one ), b( 1, j ), 1, work, 1 )
216 bnorm = dzasum( n, work, 1 )
217 xnorm = dzasum( n, x( 1, j ), 1 )
218 IF( xnorm.LE.zero ) THEN
219 resid = one / eps
220 ELSE
221 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
222 END IF
223 10 CONTINUE
224*
225 RETURN
226*
227* End of ZTPT02
228*
double precision function dzasum(n, zx, incx)
DZASUM
Definition dzasum.f:72
subroutine zaxpy(n, za, zx, incx, zy, incy)
ZAXPY
Definition zaxpy.f:88
subroutine zcopy(n, zx, incx, zy, incy)
ZCOPY
Definition zcopy.f:81
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
double precision function zlantp(norm, uplo, diag, n, ap, work)
ZLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition zlantp.f:125
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine ztpmv(uplo, trans, diag, n, ap, x, incx)
ZTPMV
Definition ztpmv.f:142
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