LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ ctrt02()

subroutine ctrt02 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldx, * )  X,
integer  LDX,
complex, dimension( ldb, * )  B,
integer  LDB,
complex, dimension( * )  WORK,
real, dimension( * )  RWORK,
real  RESID 
)

CTRT02

Purpose:
 CTRT02 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.  Here A is a triangular matrix, A**T is the transpose
 of A, A**H is 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
    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]A
          A is COMPLEX array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,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.

Definition at line 155 of file ctrt02.f.

157 *
158 * -- LAPACK test routine --
159 * -- LAPACK is a software package provided by Univ. of Tennessee, --
160 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
161 *
162 * .. Scalar Arguments ..
163  CHARACTER DIAG, TRANS, UPLO
164  INTEGER LDA, LDB, LDX, N, NRHS
165  REAL RESID
166 * ..
167 * .. Array Arguments ..
168  REAL RWORK( * )
169  COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ),
170  $ X( LDX, * )
171 * ..
172 *
173 * =====================================================================
174 *
175 * .. Parameters ..
176  REAL ZERO, ONE
177  parameter( zero = 0.0e+0, one = 1.0e+0 )
178 * ..
179 * .. Local Scalars ..
180  INTEGER J
181  REAL ANORM, BNORM, EPS, XNORM
182 * ..
183 * .. External Functions ..
184  LOGICAL LSAME
185  REAL CLANTR, SCASUM, SLAMCH
186  EXTERNAL lsame, clantr, scasum, slamch
187 * ..
188 * .. External Subroutines ..
189  EXTERNAL caxpy, ccopy, ctrmv
190 * ..
191 * .. Intrinsic Functions ..
192  INTRINSIC cmplx, max
193 * ..
194 * .. Executable Statements ..
195 *
196 * Quick exit if N = 0 or NRHS = 0
197 *
198  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
199  resid = zero
200  RETURN
201  END IF
202 *
203 * Compute the 1-norm of A or A**H.
204 *
205  IF( lsame( trans, 'N' ) ) THEN
206  anorm = clantr( '1', uplo, diag, n, n, a, lda, rwork )
207  ELSE
208  anorm = clantr( 'I', uplo, diag, n, n, a, lda, rwork )
209  END IF
210 *
211 * Exit with RESID = 1/EPS if ANORM = 0.
212 *
213  eps = slamch( 'Epsilon' )
214  IF( anorm.LE.zero ) THEN
215  resid = one / eps
216  RETURN
217  END IF
218 *
219 * Compute the maximum over the number of right hand sides of
220 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS )
221 *
222  resid = zero
223  DO 10 j = 1, nrhs
224  CALL ccopy( n, x( 1, j ), 1, work, 1 )
225  CALL ctrmv( uplo, trans, diag, n, a, lda, work, 1 )
226  CALL caxpy( n, cmplx( -one ), b( 1, j ), 1, work, 1 )
227  bnorm = scasum( n, work, 1 )
228  xnorm = scasum( n, x( 1, j ), 1 )
229  IF( xnorm.LE.zero ) THEN
230  resid = one / eps
231  ELSE
232  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
233  END IF
234  10 CONTINUE
235 *
236  RETURN
237 *
238 * End of CTRT02
239 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:81
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:88
subroutine ctrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
CTRMV
Definition: ctrmv.f:147
real function clantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
CLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clantr.f:142
real function scasum(N, CX, INCX)
SCASUM
Definition: scasum.f:72
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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