 LAPACK  3.10.1 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 ).```

Definition at line 159 of file stpt03.f.

161 *
162 * -- LAPACK test routine --
163 * -- LAPACK is a software package provided by Univ. of Tennessee, --
164 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
165 *
166 * .. Scalar Arguments ..
167  CHARACTER DIAG, TRANS, UPLO
168  INTEGER LDB, LDX, N, NRHS
169  REAL RESID, SCALE, TSCAL
170 * ..
171 * .. Array Arguments ..
172  REAL AP( * ), B( LDB, * ), CNORM( * ), WORK( * ),
173  \$ X( LDX, * )
174 * ..
175 *
176 * =====================================================================
177 *
178 * .. Parameters ..
179  REAL ONE, ZERO
180  parameter( one = 1.0e+0, zero = 0.0e+0 )
181 * ..
182 * .. Local Scalars ..
183  INTEGER IX, J, JJ
184  REAL BIGNUM, EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
185 * ..
186 * .. External Functions ..
187  LOGICAL LSAME
188  INTEGER ISAMAX
189  REAL SLAMCH
190  EXTERNAL lsame, isamax, slamch
191 * ..
192 * .. External Subroutines ..
193  EXTERNAL saxpy, scopy, slabad, sscal, stpmv
194 * ..
195 * .. Intrinsic Functions ..
196  INTRINSIC abs, max, real
197 * ..
198 * .. Executable Statements ..
199 *
200 * Quick exit if N = 0.
201 *
202  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
203  resid = zero
204  RETURN
205  END IF
206  eps = slamch( 'Epsilon' )
207  smlnum = slamch( 'Safe minimum' )
208  bignum = one / smlnum
209  CALL slabad( smlnum, bignum )
210 *
211 * Compute the norm of the triangular matrix A using the column
212 * norms already computed by SLATPS.
213 *
214  tnorm = zero
215  IF( lsame( diag, 'N' ) ) THEN
216  IF( lsame( uplo, 'U' ) ) THEN
217  jj = 1
218  DO 10 j = 1, n
219  tnorm = max( tnorm, tscal*abs( ap( jj ) )+cnorm( j ) )
220  jj = jj + j + 1
221  10 CONTINUE
222  ELSE
223  jj = 1
224  DO 20 j = 1, n
225  tnorm = max( tnorm, tscal*abs( ap( jj ) )+cnorm( j ) )
226  jj = jj + n - j + 1
227  20 CONTINUE
228  END IF
229  ELSE
230  DO 30 j = 1, n
231  tnorm = max( tnorm, tscal+cnorm( j ) )
232  30 CONTINUE
233  END IF
234 *
235 * Compute the maximum over the number of right hand sides of
236 * norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
237 *
238  resid = zero
239  DO 40 j = 1, nrhs
240  CALL scopy( n, x( 1, j ), 1, work, 1 )
241  ix = isamax( n, work, 1 )
242  xnorm = max( one, abs( x( ix, j ) ) )
243  xscal = ( one / xnorm ) / real( n )
244  CALL sscal( n, xscal, work, 1 )
245  CALL stpmv( uplo, trans, diag, n, ap, work, 1 )
246  CALL saxpy( n, -scale*xscal, b( 1, j ), 1, work, 1 )
247  ix = isamax( n, work, 1 )
248  err = tscal*abs( work( ix ) )
249  ix = isamax( n, x( 1, j ), 1 )
250  xnorm = abs( x( ix, j ) )
251  IF( err*smlnum.LE.xnorm ) THEN
252  IF( xnorm.GT.zero )
253  \$ err = err / xnorm
254  ELSE
255  IF( err.GT.zero )
256  \$ err = one / eps
257  END IF
258  IF( err*smlnum.LE.tnorm ) THEN
259  IF( tnorm.GT.zero )
260  \$ err = err / tnorm
261  ELSE
262  IF( err.GT.zero )
263  \$ err = one / eps
264  END IF
265  resid = max( resid, err )
266  40 CONTINUE
267 *
268  RETURN
269 *
270 * End of STPT03
271 *
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
subroutine stpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
STPMV
Definition: stpmv.f:142
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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