LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ ctpt02()

subroutine ctpt02 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
complex, dimension( * )  AP,
complex, dimension( ldx, * )  X,
integer  LDX,
complex, dimension( ldb, * )  B,
integer  LDB,
complex, dimension( * )  WORK,
real, dimension( * )  RWORK,
real  RESID 
)

CTPT02

Purpose:
 CTPT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b,  A**T *x = b,  or
 A**H *x = 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, and x and b are N by NRHS matrices.  The test ratio
 is the maximum over the number of right hand sides of
 the maximum over the number of right hand sides of
    norm(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 = b     (No transpose)
          = 'T':  A**T *x = b  (Transpose)
          = 'C':  A**H *x = 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]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]RWORK
          RWORK is REAL array, dimension (N)
[out]RESID
          RESID is REAL
          The maximum over the number of right hand sides of
          norm(op(A)*x - 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 151 of file ctpt02.f.

151 *
152 * -- LAPACK test routine (version 3.7.0) --
153 * -- LAPACK is a software package provided by Univ. of Tennessee, --
154 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
155 * December 2016
156 *
157 * .. Scalar Arguments ..
158  CHARACTER diag, trans, uplo
159  INTEGER ldb, ldx, n, nrhs
160  REAL resid
161 * ..
162 * .. Array Arguments ..
163  REAL rwork( * )
164  COMPLEX ap( * ), b( ldb, * ), work( * ), x( ldx, * )
165 * ..
166 *
167 * =====================================================================
168 *
169 * .. Parameters ..
170  REAL zero, one
171  parameter( zero = 0.0e+0, one = 1.0e+0 )
172 * ..
173 * .. Local Scalars ..
174  INTEGER j
175  REAL anorm, bnorm, eps, xnorm
176 * ..
177 * .. External Functions ..
178  LOGICAL lsame
179  REAL clantp, scasum, slamch
180  EXTERNAL lsame, clantp, scasum, slamch
181 * ..
182 * .. External Subroutines ..
183  EXTERNAL caxpy, ccopy, ctpmv
184 * ..
185 * .. Intrinsic Functions ..
186  INTRINSIC cmplx, max
187 * ..
188 * .. Executable Statements ..
189 *
190 * Quick exit if N = 0 or NRHS = 0
191 *
192  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
193  resid = zero
194  RETURN
195  END IF
196 *
197 * Compute the 1-norm of A or A**H.
198 *
199  IF( lsame( trans, 'N' ) ) THEN
200  anorm = clantp( '1', uplo, diag, n, ap, rwork )
201  ELSE
202  anorm = clantp( 'I', uplo, diag, n, ap, rwork )
203  END IF
204 *
205 * Exit with RESID = 1/EPS if ANORM = 0.
206 *
207  eps = slamch( 'Epsilon' )
208  IF( anorm.LE.zero ) THEN
209  resid = one / eps
210  RETURN
211  END IF
212 *
213 * Compute the maximum over the number of right hand sides of
214 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
215 *
216  resid = zero
217  DO 10 j = 1, nrhs
218  CALL ccopy( n, x( 1, j ), 1, work, 1 )
219  CALL ctpmv( uplo, trans, diag, n, ap, work, 1 )
220  CALL caxpy( n, cmplx( -one ), b( 1, j ), 1, work, 1 )
221  bnorm = scasum( n, work, 1 )
222  xnorm = scasum( n, x( 1, j ), 1 )
223  IF( xnorm.LE.zero ) THEN
224  resid = one / eps
225  ELSE
226  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
227  END IF
228  10 CONTINUE
229 *
230  RETURN
231 *
232 * End of CTPT02
233 *
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:144
real function scasum(N, CX, INCX)
SCASUM
Definition: scasum.f:74
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
real function clantp(NORM, UPLO, DIAG, N, AP, WORK)
CLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.
Definition: clantp.f:127
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