LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ strt02()

 subroutine strt02 ( character UPLO, character TRANS, character DIAG, integer N, integer NRHS, real, dimension( lda, * ) A, integer LDA, real, dimension( ldx, * ) X, integer LDX, real, dimension( ldb, * ) B, integer LDB, real, dimension( * ) WORK, real RESID )

STRT02

Purpose:
``` STRT02 computes the residual for the computed solution to a
triangular system of linear equations  A*x = b  or  A'*x = b.
Here A is a triangular matrix, A' is the 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 or A' 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'*x = b (Transpose) = 'C': A'*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 REAL 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 REAL 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 REAL 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 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 ).```

Definition at line 149 of file strt02.f.

151 *
152 * -- LAPACK test routine --
153 * -- LAPACK is a software package provided by Univ. of Tennessee, --
154 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
155 *
156 * .. Scalar Arguments ..
157  CHARACTER DIAG, TRANS, UPLO
158  INTEGER LDA, LDB, LDX, N, NRHS
159  REAL RESID
160 * ..
161 * .. Array Arguments ..
162  REAL A( LDA, * ), B( LDB, * ), WORK( * ),
163  \$ X( LDX, * )
164 * ..
165 *
166 * =====================================================================
167 *
168 * .. Parameters ..
169  REAL ZERO, ONE
170  parameter( zero = 0.0e+0, one = 1.0e+0 )
171 * ..
172 * .. Local Scalars ..
173  INTEGER J
174  REAL ANORM, BNORM, EPS, XNORM
175 * ..
176 * .. External Functions ..
177  LOGICAL LSAME
178  REAL SASUM, SLAMCH, SLANTR
179  EXTERNAL lsame, sasum, slamch, slantr
180 * ..
181 * .. External Subroutines ..
182  EXTERNAL saxpy, scopy, strmv
183 * ..
184 * .. Intrinsic Functions ..
185  INTRINSIC max
186 * ..
187 * .. Executable Statements ..
188 *
189 * Quick exit if N = 0 or NRHS = 0
190 *
191  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
192  resid = zero
193  RETURN
194  END IF
195 *
196 * Compute the 1-norm of A or A'.
197 *
198  IF( lsame( trans, 'N' ) ) THEN
199  anorm = slantr( '1', uplo, diag, n, n, a, lda, work )
200  ELSE
201  anorm = slantr( 'I', uplo, diag, n, n, a, lda, work )
202  END IF
203 *
204 * Exit with RESID = 1/EPS if ANORM = 0.
205 *
206  eps = slamch( 'Epsilon' )
207  IF( anorm.LE.zero ) THEN
208  resid = one / eps
209  RETURN
210  END IF
211 *
212 * Compute the maximum over the number of right hand sides of
213 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS )
214 *
215  resid = zero
216  DO 10 j = 1, nrhs
217  CALL scopy( n, x( 1, j ), 1, work, 1 )
218  CALL strmv( uplo, trans, diag, n, a, lda, work, 1 )
219  CALL saxpy( n, -one, b( 1, j ), 1, work, 1 )
220  bnorm = sasum( n, work, 1 )
221  xnorm = sasum( n, x( 1, j ), 1 )
222  IF( xnorm.LE.zero ) THEN
223  resid = one / eps
224  ELSE
225  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
226  END IF
227  10 CONTINUE
228 *
229  RETURN
230 *
231 * End of STRT02
232 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
SLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slantr.f:141
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:147
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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