LAPACK  3.10.0
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.

Definition at line 160 of file ctpt03.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  REAL RESID, SCALE, TSCAL
171 * ..
172 * .. Array Arguments ..
173  REAL CNORM( * )
174  COMPLEX AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
175 * ..
176 *
177 * =====================================================================
178 *
179 * .. Parameters ..
180  REAL ONE, ZERO
181  parameter( one = 1.0e+0, zero = 0.0e+0 )
182 * ..
183 * .. Local Scalars ..
184  INTEGER IX, J, JJ
185  REAL EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
186 * ..
187 * .. External Functions ..
188  LOGICAL LSAME
189  INTEGER ICAMAX
190  REAL SLAMCH
191  EXTERNAL lsame, icamax, slamch
192 * ..
193 * .. External Subroutines ..
194  EXTERNAL caxpy, ccopy, csscal, ctpmv
195 * ..
196 * .. Intrinsic Functions ..
197  INTRINSIC abs, cmplx, max, real
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 = slamch( 'Epsilon' )
208  smlnum = slamch( 'Safe minimum' )
209 *
210 * Compute the norm of the triangular matrix A using the column
211 * norms already computed by CLATPS.
212 *
213  tnorm = 0.
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 + 1
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 ccopy( n, x( 1, j ), 1, work, 1 )
240  ix = icamax( n, work, 1 )
241  xnorm = max( one, abs( x( ix, j ) ) )
242  xscal = ( one / xnorm ) / real( n )
243  CALL csscal( n, xscal, work, 1 )
244  CALL ctpmv( uplo, trans, diag, n, ap, work, 1 )
245  CALL caxpy( n, cmplx( -scale*xscal ), b( 1, j ), 1, work, 1 )
246  ix = icamax( n, work, 1 )
247  err = tscal*abs( work( ix ) )
248  ix = icamax( 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 CTPT03
270 *
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:81
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:78
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:88
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:142
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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