LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ ctbt03()

 subroutine ctbt03 ( character UPLO, character TRANS, character DIAG, integer N, integer KD, integer NRHS, complex, dimension( ldab, * ) AB, integer LDAB, real SCALE, real, dimension( * ) CNORM, real TSCAL, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( * ) WORK, real RESID )

CTBT03

Purpose:
``` CTBT03 computes the residual for the solution to a scaled triangular
system of equations  A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b
when A is a triangular band matrix.  Here A**T  denotes the transpose
of A, A**H denotes the conjugate 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, A**T, or A**H, 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**T *x = s*b (Transpose) = 'C': A**H *x = s*b (Conjugate 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 ).```
Date
December 2016

Definition at line 179 of file ctbt03.f.

179 *
180 * -- LAPACK test routine (version 3.7.0) --
181 * -- LAPACK is a software package provided by Univ. of Tennessee, --
182 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
183 * December 2016
184 *
185 * .. Scalar Arguments ..
186  CHARACTER diag, trans, uplo
187  INTEGER kd, ldab, ldb, ldx, n, nrhs
188  REAL resid, scale, tscal
189 * ..
190 * .. Array Arguments ..
191  REAL cnorm( * )
192  COMPLEX ab( ldab, * ), b( ldb, * ), work( * ),
193  \$ x( ldx, * )
194 * ..
195 *
196 * =====================================================================
197 *
198 *
199 * .. Parameters ..
200  REAL one, zero
201  parameter( one = 1.0e+0, zero = 0.0e+0 )
202 * ..
203 * .. Local Scalars ..
204  INTEGER ix, j
205  REAL eps, err, smlnum, tnorm, xnorm, xscal
206 * ..
207 * .. External Functions ..
208  LOGICAL lsame
209  INTEGER icamax
210  REAL slamch
211  EXTERNAL lsame, icamax, slamch
212 * ..
213 * .. External Subroutines ..
214  EXTERNAL caxpy, ccopy, csscal, ctbmv
215 * ..
216 * .. Intrinsic Functions ..
217  INTRINSIC abs, cmplx, max, real
218 * ..
219 * .. Executable Statements ..
220 *
221 * Quick exit if N = 0
222 *
223  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
224  resid = zero
225  RETURN
226  END IF
227  eps = slamch( 'Epsilon' )
228  smlnum = slamch( 'Safe minimum' )
229 *
230 * Compute the norm of the triangular matrix A using the column
231 * norms already computed by CLATBS.
232 *
233  tnorm = zero
234  IF( lsame( diag, 'N' ) ) THEN
235  IF( lsame( uplo, 'U' ) ) THEN
236  DO 10 j = 1, n
237  tnorm = max( tnorm, tscal*abs( ab( kd+1, j ) )+
238  \$ cnorm( j ) )
239  10 CONTINUE
240  ELSE
241  DO 20 j = 1, n
242  tnorm = max( tnorm, tscal*abs( ab( 1, j ) )+cnorm( j ) )
243  20 CONTINUE
244  END IF
245  ELSE
246  DO 30 j = 1, n
247  tnorm = max( tnorm, tscal+cnorm( j ) )
248  30 CONTINUE
249  END IF
250 *
251 * Compute the maximum over the number of right hand sides of
252 * norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
253 *
254  resid = zero
255  DO 40 j = 1, nrhs
256  CALL ccopy( n, x( 1, j ), 1, work, 1 )
257  ix = icamax( n, work, 1 )
258  xnorm = max( one, abs( x( ix, j ) ) )
259  xscal = ( one / xnorm ) / REAL( kd+1 )
260  CALL csscal( n, xscal, work, 1 )
261  CALL ctbmv( uplo, trans, diag, n, kd, ab, ldab, work, 1 )
262  CALL caxpy( n, cmplx( -scale*xscal ), b( 1, j ), 1, work, 1 )
263  ix = icamax( n, work, 1 )
264  err = tscal*abs( work( ix ) )
265  ix = icamax( n, x( 1, j ), 1 )
266  xnorm = abs( x( ix, j ) )
267  IF( err*smlnum.LE.xnorm ) THEN
268  IF( xnorm.GT.zero )
269  \$ err = err / xnorm
270  ELSE
271  IF( err.GT.zero )
272  \$ err = one / eps
273  END IF
274  IF( err*smlnum.LE.tnorm ) THEN
275  IF( tnorm.GT.zero )
276  \$ err = err / tnorm
277  ELSE
278  IF( err.GT.zero )
279  \$ err = one / eps
280  END IF
281  resid = max( resid, err )
282  40 CONTINUE
283 *
284  RETURN
285 *
286 * End of CTBT03
287 *
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:73
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:90
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:83
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:80
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine ctbmv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
CTBMV
Definition: ctbmv.f:188
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