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 ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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