LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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 ).```
Date
December 2016

Definition at line 164 of file ztpt03.f.

164 *
165 * -- LAPACK test routine (version 3.7.0) --
166 * -- LAPACK is a software package provided by Univ. of Tennessee, --
167 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168 * December 2016
169 *
170 * .. Scalar Arguments ..
171  CHARACTER diag, trans, uplo
172  INTEGER ldb, ldx, n, nrhs
173  DOUBLE PRECISION resid, scale, tscal
174 * ..
175 * .. Array Arguments ..
176  DOUBLE PRECISION cnorm( * )
177  COMPLEX*16 ap( * ), b( ldb, * ), work( * ), x( ldx, * )
178 * ..
179 *
180 * =====================================================================
181 *
182 * .. Parameters ..
183  DOUBLE PRECISION one, zero
184  parameter( one = 1.0d+0, zero = 0.0d+0 )
185 * ..
186 * .. Local Scalars ..
187  INTEGER ix, j, jj
188  DOUBLE PRECISION eps, err, smlnum, tnorm, xnorm, xscal
189 * ..
190 * .. External Functions ..
191  LOGICAL lsame
192  INTEGER izamax
193  DOUBLE PRECISION dlamch
194  EXTERNAL lsame, izamax, dlamch
195 * ..
196 * .. External Subroutines ..
197  EXTERNAL zaxpy, zcopy, zdscal, ztpmv
198 * ..
199 * .. Intrinsic Functions ..
200  INTRINSIC abs, dble, dcmplx, max
201 * ..
202 * .. Executable Statements ..
203 *
204 * Quick exit if N = 0.
205 *
206  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
207  resid = zero
208  RETURN
209  END IF
210  eps = dlamch( 'Epsilon' )
211  smlnum = dlamch( 'Safe minimum' )
212 *
213 * Compute the norm of the triangular matrix A using the column
214 * norms already computed by ZLATPS.
215 *
216  tnorm = 0.d0
217  IF( lsame( diag, 'N' ) ) THEN
218  IF( lsame( uplo, 'U' ) ) THEN
219  jj = 1
220  DO 10 j = 1, n
221  tnorm = max( tnorm, tscal*abs( ap( jj ) )+cnorm( j ) )
222  jj = jj + j
223  10 CONTINUE
224  ELSE
225  jj = 1
226  DO 20 j = 1, n
227  tnorm = max( tnorm, tscal*abs( ap( jj ) )+cnorm( j ) )
228  jj = jj + n - j + 1
229  20 CONTINUE
230  END IF
231  ELSE
232  DO 30 j = 1, n
233  tnorm = max( tnorm, tscal+cnorm( j ) )
234  30 CONTINUE
235  END IF
236 *
237 * Compute the maximum over the number of right hand sides of
238 * norm(op(A)*x - s*b) / ( norm(A) * norm(x) * EPS ).
239 *
240  resid = zero
241  DO 40 j = 1, nrhs
242  CALL zcopy( n, x( 1, j ), 1, work, 1 )
243  ix = izamax( n, work, 1 )
244  xnorm = max( one, abs( x( ix, j ) ) )
245  xscal = ( one / xnorm ) / dble( n )
246  CALL zdscal( n, xscal, work, 1 )
247  CALL ztpmv( uplo, trans, diag, n, ap, work, 1 )
248  CALL zaxpy( n, dcmplx( -scale*xscal ), b( 1, j ), 1, work, 1 )
249  ix = izamax( n, work, 1 )
250  err = tscal*abs( work( ix ) )
251  ix = izamax( n, x( 1, j ), 1 )
252  xnorm = abs( x( ix, j ) )
253  IF( err*smlnum.LE.xnorm ) THEN
254  IF( xnorm.GT.zero )
255  \$ err = err / xnorm
256  ELSE
257  IF( err.GT.zero )
258  \$ err = one / eps
259  END IF
260  IF( err*smlnum.LE.tnorm ) THEN
261  IF( tnorm.GT.zero )
262  \$ err = err / tnorm
263  ELSE
264  IF( err.GT.zero )
265  \$ err = one / eps
266  END IF
267  resid = max( resid, err )
268  40 CONTINUE
269 *
270  RETURN
271 *
272 * End of ZTPT03
273 *
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:90
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:83
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:80
subroutine ztpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
ZTPMV
Definition: ztpmv.f:144
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
integer function izamax(N, ZX, INCX)
IZAMAX
Definition: izamax.f:73
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