LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ ctpt03()

subroutine ctpt03 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
complex, dimension( * )  AP,
real  SCALE,
real, dimension( * )  CNORM,
real  TSCAL,
complex, dimension( ldx, * )  X,
integer  LDX,
complex, dimension( ldb, * )  B,
integer  LDB,
complex, dimension( * )  WORK,
real  RESID 
)

CTPT03

Purpose:
 CTPT03 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 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 REAL
          The scaling factor s used in solving the triangular system.
[in]CNORM
          CNORM is REAL array, dimension (N)
          The 1-norms of the columns of A, not counting the diagonal.
[in]TSCAL
          TSCAL is REAL
          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 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 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 array, dimension (N)
[out]RESID
          RESID is REAL
          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 ctpt03.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  REAL resid, scale, tscal
174 * ..
175 * .. Array Arguments ..
176  REAL cnorm( * )
177  COMPLEX ap( * ), b( ldb, * ), work( * ), x( ldx, * )
178 * ..
179 *
180 * =====================================================================
181 *
182 * .. Parameters ..
183  REAL one, zero
184  parameter( one = 1.0e+0, zero = 0.0e+0 )
185 * ..
186 * .. Local Scalars ..
187  INTEGER ix, j, jj
188  REAL eps, err, smlnum, tnorm, xnorm, xscal
189 * ..
190 * .. External Functions ..
191  LOGICAL lsame
192  INTEGER icamax
193  REAL slamch
194  EXTERNAL lsame, icamax, slamch
195 * ..
196 * .. External Subroutines ..
197  EXTERNAL caxpy, ccopy, csscal, ctpmv
198 * ..
199 * .. Intrinsic Functions ..
200  INTRINSIC abs, cmplx, max, real
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 = slamch( 'Epsilon' )
211  smlnum = slamch( 'Safe minimum' )
212 *
213 * Compute the norm of the triangular matrix A using the column
214 * norms already computed by CLATPS.
215 *
216  tnorm = 0.
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 + 1
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 ccopy( n, x( 1, j ), 1, work, 1 )
243  ix = icamax( n, work, 1 )
244  xnorm = max( one, abs( x( ix, j ) ) )
245  xscal = ( one / xnorm ) / REAL( n )
246  CALL csscal( n, xscal, work, 1 )
247  CALL ctpmv( uplo, trans, diag, n, ap, work, 1 )
248  CALL caxpy( n, cmplx( -scale*xscal ), b( 1, j ), 1, work, 1 )
249  ix = icamax( n, work, 1 )
250  err = tscal*abs( work( ix ) )
251  ix = icamax( 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 CTPT03
273 *
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:144
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:73
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:83
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:90
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:80
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