LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ strt03()

subroutine strt03 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
real, dimension( lda, * )  A,
integer  LDA,
real  SCALE,
real, dimension( * )  CNORM,
real  TSCAL,
real, dimension( ldx, * )  X,
integer  LDX,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( * )  WORK,
real  RESID 
)

STRT03

Purpose:
 STRT03 computes the residual for the solution to a scaled triangular
 system of equations A*x = s*b  or  A'*x = s*b.
 Here A is a triangular matrix, A' is the transpose of A, s is a
 scalar, and x and b are N by NRHS matrices.  The test ratio is the
 maximum over the number of right hand sides of
    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' 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 = s*b  (No transpose)
          = 'T':  A'*x = s*b  (Transpose)
          = 'C':  A'*x = s*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]SCALE
          SCALE is REAL
          The scaling factor s used in solving the triangular system.
[in]CNORM
          CNORM is REAL array, dimension (N)
          The 1-norms of the columns of A, not counting the diagonal.
[in]TSCAL
          TSCAL is REAL
          The scaling factor used in computing the 1-norms in CNORM.
          CNORM actually contains the column norms of TSCAL*A.
[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 - s*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 171 of file strt03.f.

171 *
172 * -- LAPACK test routine (version 3.7.0) --
173 * -- LAPACK is a software package provided by Univ. of Tennessee, --
174 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175 * December 2016
176 *
177 * .. Scalar Arguments ..
178  CHARACTER diag, trans, uplo
179  INTEGER lda, ldb, ldx, n, nrhs
180  REAL resid, scale, tscal
181 * ..
182 * .. Array Arguments ..
183  REAL a( lda, * ), b( ldb, * ), cnorm( * ),
184  $ work( * ), x( ldx, * )
185 * ..
186 *
187 * =====================================================================
188 *
189 * .. Parameters ..
190  REAL one, zero
191  parameter( one = 1.0e+0, zero = 0.0e+0 )
192 * ..
193 * .. Local Scalars ..
194  INTEGER ix, j
195  REAL bignum, eps, err, smlnum, tnorm, xnorm, xscal
196 * ..
197 * .. External Functions ..
198  LOGICAL lsame
199  INTEGER isamax
200  REAL slamch
201  EXTERNAL lsame, isamax, slamch
202 * ..
203 * .. External Subroutines ..
204  EXTERNAL saxpy, scopy, slabad, sscal, strmv
205 * ..
206 * .. Intrinsic Functions ..
207  INTRINSIC abs, max, real
208 * ..
209 * .. Executable Statements ..
210 *
211 * Quick exit if N = 0
212 *
213  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
214  resid = zero
215  RETURN
216  END IF
217  eps = slamch( 'Epsilon' )
218  smlnum = slamch( 'Safe minimum' )
219  bignum = one / smlnum
220  CALL slabad( smlnum, bignum )
221 *
222 * Compute the norm of the triangular matrix A using the column
223 * norms already computed by SLATRS.
224 *
225  tnorm = zero
226  IF( lsame( diag, 'N' ) ) THEN
227  DO 10 j = 1, n
228  tnorm = max( tnorm, tscal*abs( a( j, j ) )+cnorm( j ) )
229  10 CONTINUE
230  ELSE
231  DO 20 j = 1, n
232  tnorm = max( tnorm, tscal+cnorm( j ) )
233  20 CONTINUE
234  END IF
235 *
236 * Compute the maximum over the number of right hand sides of
237 * norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
238 *
239  resid = zero
240  DO 30 j = 1, nrhs
241  CALL scopy( n, x( 1, j ), 1, work, 1 )
242  ix = isamax( n, work, 1 )
243  xnorm = max( one, abs( x( ix, j ) ) )
244  xscal = ( one / xnorm ) / REAL( n )
245  CALL sscal( n, xscal, work, 1 )
246  CALL strmv( uplo, trans, diag, n, a, lda, work, 1 )
247  CALL saxpy( n, -scale*xscal, b( 1, j ), 1, work, 1 )
248  ix = isamax( n, work, 1 )
249  err = tscal*abs( work( ix ) )
250  ix = isamax( n, x( 1, j ), 1 )
251  xnorm = abs( x( ix, j ) )
252  IF( err*smlnum.LE.xnorm ) THEN
253  IF( xnorm.GT.zero )
254  $ err = err / xnorm
255  ELSE
256  IF( err.GT.zero )
257  $ err = one / eps
258  END IF
259  IF( err*smlnum.LE.tnorm ) THEN
260  IF( tnorm.GT.zero )
261  $ err = err / tnorm
262  ELSE
263  IF( err.GT.zero )
264  $ err = one / eps
265  END IF
266  resid = max( resid, err )
267  30 CONTINUE
268 *
269  RETURN
270 *
271 * End of STRT03
272 *
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:73
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:149
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:91
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:76
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:81
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:84
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