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 ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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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