LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ dtrt02()

subroutine dtrt02 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  WORK,
double precision  RESID 
)

DTRT02

Purpose:
 DTRT02 computes the residual for the computed solution to a
 triangular system of linear equations op(A)*X = B, where A is a
 triangular matrix. The test ratio is the maximum over
    norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
 where op(A) = A or A**T, b is the column of B, x is the solution
 vector, and EPS is the machine epsilon.
 The norm used is the 1-norm.
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 = 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          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 148 of file dtrt02.f.

150 *
151 * -- LAPACK test routine --
152 * -- LAPACK is a software package provided by Univ. of Tennessee, --
153 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154 *
155 * .. Scalar Arguments ..
156  CHARACTER DIAG, TRANS, UPLO
157  INTEGER LDA, LDB, LDX, N, NRHS
158  DOUBLE PRECISION RESID
159 * ..
160 * .. Array Arguments ..
161  DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ),
162  $ X( LDX, * )
163 * ..
164 *
165 * =====================================================================
166 *
167 * .. Parameters ..
168  DOUBLE PRECISION ZERO, ONE
169  parameter( zero = 0.0d+0, one = 1.0d+0 )
170 * ..
171 * .. Local Scalars ..
172  INTEGER J
173  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
174 * ..
175 * .. External Functions ..
176  LOGICAL LSAME
177  DOUBLE PRECISION DASUM, DLAMCH, DLANTR
178  EXTERNAL lsame, dasum, dlamch, dlantr
179 * ..
180 * .. External Subroutines ..
181  EXTERNAL daxpy, dcopy, dtrmv
182 * ..
183 * .. Intrinsic Functions ..
184  INTRINSIC max
185 * ..
186 * .. Executable Statements ..
187 *
188 * Quick exit if N = 0 or NRHS = 0
189 *
190  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
191  resid = zero
192  RETURN
193  END IF
194 *
195 * Compute the 1-norm of op(A).
196 *
197  IF( lsame( trans, 'N' ) ) THEN
198  anorm = dlantr( '1', uplo, diag, n, n, a, lda, work )
199  ELSE
200  anorm = dlantr( 'I', uplo, diag, n, n, a, lda, work )
201  END IF
202 *
203 * Exit with RESID = 1/EPS if ANORM = 0.
204 *
205  eps = dlamch( 'Epsilon' )
206  IF( anorm.LE.zero ) THEN
207  resid = one / eps
208  RETURN
209  END IF
210 *
211 * Compute the maximum over the number of right hand sides of
212 * norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS )
213 *
214  resid = zero
215  DO 10 j = 1, nrhs
216  CALL dcopy( n, x( 1, j ), 1, work, 1 )
217  CALL dtrmv( uplo, trans, diag, n, a, lda, work, 1 )
218  CALL daxpy( n, -one, b( 1, j ), 1, work, 1 )
219  bnorm = dasum( n, work, 1 )
220  xnorm = dasum( n, x( 1, j ), 1 )
221  IF( xnorm.LE.zero ) THEN
222  resid = one / eps
223  ELSE
224  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
225  END IF
226  10 CONTINUE
227 *
228  RETURN
229 *
230 * End of DTRT02
231 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:71
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:89
subroutine dtrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
DTRMV
Definition: dtrmv.f:147
double precision function dlantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlantr.f:141
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