 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ stbt03()

 subroutine stbt03 ( character UPLO, character TRANS, character DIAG, integer N, integer KD, integer NRHS, real, dimension( ldab, * ) AB, integer LDAB, real SCALE, real, dimension( * ) CNORM, real TSCAL, real, dimension( ldx, * ) X, integer LDX, real, dimension( ldb, * ) B, integer LDB, real, dimension( * ) WORK, real RESID )

STBT03

Purpose:
``` STBT03 computes the residual for the solution to a scaled triangular
system of equations  A*x = s*b  or  A'*x = s*b  when A is a
triangular band matrix. 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 = 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] KD ``` KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 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] AB ``` AB is REAL array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).``` [in] LDAB ``` LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.``` [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 172 of file stbt03.f.

175 *
176 * -- LAPACK test routine --
177 * -- LAPACK is a software package provided by Univ. of Tennessee, --
178 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
179 *
180 * .. Scalar Arguments ..
181  CHARACTER DIAG, TRANS, UPLO
182  INTEGER KD, LDAB, LDB, LDX, N, NRHS
183  REAL RESID, SCALE, TSCAL
184 * ..
185 * .. Array Arguments ..
186  REAL AB( LDAB, * ), B( LDB, * ), CNORM( * ),
187  \$ WORK( * ), X( LDX, * )
188 * ..
189 *
190 * =====================================================================
191 *
192 * .. Parameters ..
193  REAL ONE, ZERO
194  parameter( one = 1.0e+0, zero = 0.0e+0 )
195 * ..
196 * .. Local Scalars ..
197  INTEGER IX, J
198  REAL BIGNUM, EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
199 * ..
200 * .. External Functions ..
201  LOGICAL LSAME
202  INTEGER ISAMAX
203  REAL SLAMCH
204  EXTERNAL lsame, isamax, slamch
205 * ..
206 * .. External Subroutines ..
207  EXTERNAL saxpy, scopy, slabad, sscal, stbmv
208 * ..
209 * .. Intrinsic Functions ..
210  INTRINSIC abs, max, real
211 * ..
212 * .. Executable Statements ..
213 *
214 * Quick exit if N = 0
215 *
216  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
217  resid = zero
218  RETURN
219  END IF
220  eps = slamch( 'Epsilon' )
221  smlnum = slamch( 'Safe minimum' )
222  bignum = one / smlnum
223  CALL slabad( smlnum, bignum )
224 *
225 * Compute the norm of the triangular matrix A using the column
226 * norms already computed by SLATBS.
227 *
228  tnorm = zero
229  IF( lsame( diag, 'N' ) ) THEN
230  IF( lsame( uplo, 'U' ) ) THEN
231  DO 10 j = 1, n
232  tnorm = max( tnorm, tscal*abs( ab( kd+1, j ) )+
233  \$ cnorm( j ) )
234  10 CONTINUE
235  ELSE
236  DO 20 j = 1, n
237  tnorm = max( tnorm, tscal*abs( ab( 1, j ) )+cnorm( j ) )
238  20 CONTINUE
239  END IF
240  ELSE
241  DO 30 j = 1, n
242  tnorm = max( tnorm, tscal+cnorm( j ) )
243  30 CONTINUE
244  END IF
245 *
246 * Compute the maximum over the number of right hand sides of
247 * norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
248 *
249  resid = zero
250  DO 40 j = 1, nrhs
251  CALL scopy( n, x( 1, j ), 1, work, 1 )
252  ix = isamax( n, work, 1 )
253  xnorm = max( one, abs( x( ix, j ) ) )
254  xscal = ( one / xnorm ) / real( kd+1 )
255  CALL sscal( n, xscal, work, 1 )
256  CALL stbmv( uplo, trans, diag, n, kd, ab, ldab, work, 1 )
257  CALL saxpy( n, -scale*xscal, b( 1, j ), 1, work, 1 )
258  ix = isamax( n, work, 1 )
259  err = tscal*abs( work( ix ) )
260  ix = isamax( n, x( 1, j ), 1 )
261  xnorm = abs( x( ix, j ) )
262  IF( err*smlnum.LE.xnorm ) THEN
263  IF( xnorm.GT.zero )
264  \$ err = err / xnorm
265  ELSE
266  IF( err.GT.zero )
267  \$ err = one / eps
268  END IF
269  IF( err*smlnum.LE.tnorm ) THEN
270  IF( tnorm.GT.zero )
271  \$ err = err / tnorm
272  ELSE
273  IF( err.GT.zero )
274  \$ err = one / eps
275  END IF
276  resid = max( resid, err )
277  40 CONTINUE
278 *
279  RETURN
280 *
281 * End of STBT03
282 *
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 stbmv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
STBMV
Definition: stbmv.f:186
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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