LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ztpt03()

 subroutine ztpt03 ( character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex*16, dimension( * ) AP, double precision SCALE, double precision, dimension( * ) CNORM, double precision TSCAL, complex*16, dimension( ldx, * ) X, integer LDX, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( * ) WORK, double precision RESID )

ZTPT03

Purpose:
``` ZTPT03 computes the residual for the solution to a scaled triangular
system of equations A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b,
when the triangular matrix A is stored in packed format.  Here A**T
denotes the transpose of A, A**H denotes the conjugate transpose of
A, s is a scalar, and x and b are N by NRHS matrices.  The test ratio
is the maximum over the number of right hand sides of
norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A, A**T, or A**H, 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 = s*b (No transpose) = 'T': A**T *x = s*b (Transpose) = 'C': A**H *x = s*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] SCALE ``` SCALE is DOUBLE PRECISION The scaling factor s used in solving the triangular system.``` [in] CNORM ``` CNORM is DOUBLE PRECISION array, dimension (N) The 1-norms of the columns of A, not counting the diagonal.``` [in] TSCAL ``` TSCAL is DOUBLE PRECISION The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.``` [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] RESID ``` RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).```

Definition at line 160 of file ztpt03.f.

162*
163* -- LAPACK test routine --
164* -- LAPACK is a software package provided by Univ. of Tennessee, --
165* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166*
167* .. Scalar Arguments ..
168 CHARACTER DIAG, TRANS, UPLO
169 INTEGER LDB, LDX, N, NRHS
170 DOUBLE PRECISION RESID, SCALE, TSCAL
171* ..
172* .. Array Arguments ..
173 DOUBLE PRECISION CNORM( * )
174 COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
175* ..
176*
177* =====================================================================
178*
179* .. Parameters ..
180 DOUBLE PRECISION ONE, ZERO
181 parameter( one = 1.0d+0, zero = 0.0d+0 )
182* ..
183* .. Local Scalars ..
184 INTEGER IX, J, JJ
185 DOUBLE PRECISION EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
186* ..
187* .. External Functions ..
188 LOGICAL LSAME
189 INTEGER IZAMAX
190 DOUBLE PRECISION DLAMCH
191 EXTERNAL lsame, izamax, dlamch
192* ..
193* .. External Subroutines ..
194 EXTERNAL zaxpy, zcopy, zdscal, ztpmv
195* ..
196* .. Intrinsic Functions ..
197 INTRINSIC abs, dble, dcmplx, max
198* ..
199* .. Executable Statements ..
200*
201* Quick exit if N = 0.
202*
203 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
204 resid = zero
205 RETURN
206 END IF
207 eps = dlamch( 'Epsilon' )
208 smlnum = dlamch( 'Safe minimum' )
209*
210* Compute the norm of the triangular matrix A using the column
211* norms already computed by ZLATPS.
212*
213 tnorm = 0.d0
214 IF( lsame( diag, 'N' ) ) THEN
215 IF( lsame( uplo, 'U' ) ) THEN
216 jj = 1
217 DO 10 j = 1, n
218 tnorm = max( tnorm, tscal*abs( ap( jj ) )+cnorm( j ) )
219 jj = jj + j
220 10 CONTINUE
221 ELSE
222 jj = 1
223 DO 20 j = 1, n
224 tnorm = max( tnorm, tscal*abs( ap( jj ) )+cnorm( j ) )
225 jj = jj + n - j + 1
226 20 CONTINUE
227 END IF
228 ELSE
229 DO 30 j = 1, n
230 tnorm = max( tnorm, tscal+cnorm( j ) )
231 30 CONTINUE
232 END IF
233*
234* Compute the maximum over the number of right hand sides of
235* norm(op(A)*x - s*b) / ( norm(A) * norm(x) * EPS ).
236*
237 resid = zero
238 DO 40 j = 1, nrhs
239 CALL zcopy( n, x( 1, j ), 1, work, 1 )
240 ix = izamax( n, work, 1 )
241 xnorm = max( one, abs( x( ix, j ) ) )
242 xscal = ( one / xnorm ) / dble( n )
243 CALL zdscal( n, xscal, work, 1 )
244 CALL ztpmv( uplo, trans, diag, n, ap, work, 1 )
245 CALL zaxpy( n, dcmplx( -scale*xscal ), b( 1, j ), 1, work, 1 )
246 ix = izamax( n, work, 1 )
247 err = tscal*abs( work( ix ) )
248 ix = izamax( n, x( 1, j ), 1 )
249 xnorm = abs( x( ix, j ) )
250 IF( err*smlnum.LE.xnorm ) THEN
251 IF( xnorm.GT.zero )
252 \$ err = err / xnorm
253 ELSE
254 IF( err.GT.zero )
255 \$ err = one / eps
256 END IF
257 IF( err*smlnum.LE.tnorm ) THEN
258 IF( tnorm.GT.zero )
259 \$ err = err / tnorm
260 ELSE
261 IF( err.GT.zero )
262 \$ err = one / eps
263 END IF
264 resid = max( resid, err )
265 40 CONTINUE
266*
267 RETURN
268*
269* End of ZTPT03
270*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function izamax(N, ZX, INCX)
IZAMAX
Definition: izamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:78
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
subroutine ztpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
ZTPMV
Definition: ztpmv.f:142
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