LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ stpt03()

subroutine stpt03 ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
integer  NRHS,
real, dimension( * )  AP,
real  SCALE,
real, dimension( * )  CNORM,
real  TSCAL,
real, dimension( ldx, * )  X,
integer  LDX,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( * )  WORK,
real  RESID 
)

STPT03

Purpose:
 STPT03 computes the residual for the solution to a scaled triangular
 system of equations A*x = s*b  or  A'*x = s*b  when the triangular
 matrix A is stored in packed format.  Here 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]AP
          AP is REAL array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in
          a linear array.  The j-th column of A is stored in the array
          AP as follows:
          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
          if UPLO = 'L',
             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=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 163 of file stpt03.f.

163 *
164 * -- LAPACK test routine (version 3.7.0) --
165 * -- LAPACK is a software package provided by Univ. of Tennessee, --
166 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
167 * December 2016
168 *
169 * .. Scalar Arguments ..
170  CHARACTER diag, trans, uplo
171  INTEGER ldb, ldx, n, nrhs
172  REAL resid, scale, tscal
173 * ..
174 * .. Array Arguments ..
175  REAL ap( * ), b( ldb, * ), cnorm( * ), work( * ),
176  $ x( ldx, * )
177 * ..
178 *
179 * =====================================================================
180 *
181 * .. Parameters ..
182  REAL one, zero
183  parameter( one = 1.0e+0, zero = 0.0e+0 )
184 * ..
185 * .. Local Scalars ..
186  INTEGER ix, j, jj
187  REAL bignum, eps, err, smlnum, tnorm, xnorm, xscal
188 * ..
189 * .. External Functions ..
190  LOGICAL lsame
191  INTEGER isamax
192  REAL slamch
193  EXTERNAL lsame, isamax, slamch
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL saxpy, scopy, slabad, sscal, stpmv
197 * ..
198 * .. Intrinsic Functions ..
199  INTRINSIC abs, max, real
200 * ..
201 * .. Executable Statements ..
202 *
203 * Quick exit if N = 0.
204 *
205  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
206  resid = zero
207  RETURN
208  END IF
209  eps = slamch( 'Epsilon' )
210  smlnum = slamch( 'Safe minimum' )
211  bignum = one / smlnum
212  CALL slabad( smlnum, bignum )
213 *
214 * Compute the norm of the triangular matrix A using the column
215 * norms already computed by SLATPS.
216 *
217  tnorm = zero
218  IF( lsame( diag, 'N' ) ) THEN
219  IF( lsame( uplo, 'U' ) ) THEN
220  jj = 1
221  DO 10 j = 1, n
222  tnorm = max( tnorm, tscal*abs( ap( jj ) )+cnorm( j ) )
223  jj = jj + j + 1
224  10 CONTINUE
225  ELSE
226  jj = 1
227  DO 20 j = 1, n
228  tnorm = max( tnorm, tscal*abs( ap( jj ) )+cnorm( j ) )
229  jj = jj + n - j + 1
230  20 CONTINUE
231  END IF
232  ELSE
233  DO 30 j = 1, n
234  tnorm = max( tnorm, tscal+cnorm( j ) )
235  30 CONTINUE
236  END IF
237 *
238 * Compute the maximum over the number of right hand sides of
239 * norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
240 *
241  resid = zero
242  DO 40 j = 1, nrhs
243  CALL scopy( n, x( 1, j ), 1, work, 1 )
244  ix = isamax( n, work, 1 )
245  xnorm = max( one, abs( x( ix, j ) ) )
246  xscal = ( one / xnorm ) / REAL( n )
247  CALL sscal( n, xscal, work, 1 )
248  CALL stpmv( uplo, trans, diag, n, ap, work, 1 )
249  CALL saxpy( n, -scale*xscal, b( 1, j ), 1, work, 1 )
250  ix = isamax( n, work, 1 )
251  err = tscal*abs( work( ix ) )
252  ix = isamax( n, x( 1, j ), 1 )
253  xnorm = abs( x( ix, j ) )
254  IF( err*smlnum.LE.xnorm ) THEN
255  IF( xnorm.GT.zero )
256  $ err = err / xnorm
257  ELSE
258  IF( err.GT.zero )
259  $ err = one / eps
260  END IF
261  IF( err*smlnum.LE.tnorm ) THEN
262  IF( tnorm.GT.zero )
263  $ err = err / tnorm
264  ELSE
265  IF( err.GT.zero )
266  $ err = one / eps
267  END IF
268  resid = max( resid, err )
269  40 CONTINUE
270 *
271  RETURN
272 *
273 * End of STPT03
274 *
subroutine stpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
STPMV
Definition: stpmv.f:144
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:73
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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