LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine dtbt02 ( character UPLO, character TRANS, character DIAG, integer N, integer KD, integer NRHS, double precision, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) WORK, double precision RESID )

DTBT02

Purpose:
``` DTBT02 computes the residual for the computed solution to a
triangular system of linear equations  A*x = b  or  A' *x = b when
A is a triangular band matrix.  Here A' is the transpose of A and
x and b are N by NRHS matrices.  The test ratio is the maximum over
the number of right hand sides of
norm(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 DOUBLE PRECISION 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] X ``` X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).```
Date
November 2011

Definition at line 156 of file dtbt02.f.

156 *
157 * -- LAPACK test routine (version 3.4.0) --
158 * -- LAPACK is a software package provided by Univ. of Tennessee, --
159 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
160 * November 2011
161 *
162 * .. Scalar Arguments ..
163  CHARACTER diag, trans, uplo
164  INTEGER kd, ldab, ldb, ldx, n, nrhs
165  DOUBLE PRECISION resid
166 * ..
167 * .. Array Arguments ..
168  DOUBLE PRECISION ab( ldab, * ), b( ldb, * ), work( * ),
169  \$ x( ldx, * )
170 * ..
171 *
172 * =====================================================================
173 *
174 * .. Parameters ..
175  DOUBLE PRECISION zero, one
176  parameter ( zero = 0.0d+0, one = 1.0d+0 )
177 * ..
178 * .. Local Scalars ..
179  INTEGER j
180  DOUBLE PRECISION anorm, bnorm, eps, xnorm
181 * ..
182 * .. External Functions ..
183  LOGICAL lsame
184  DOUBLE PRECISION dasum, dlamch, dlantb
185  EXTERNAL lsame, dasum, dlamch, dlantb
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL daxpy, dcopy, dtbmv
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC max
192 * ..
193 * .. Executable Statements ..
194 *
195 * Quick exit if N = 0 or NRHS = 0
196 *
197  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
198  resid = zero
199  RETURN
200  END IF
201 *
202 * Compute the 1-norm of A or A'.
203 *
204  IF( lsame( trans, 'N' ) ) THEN
205  anorm = dlantb( '1', uplo, diag, n, kd, ab, ldab, work )
206  ELSE
207  anorm = dlantb( 'I', uplo, diag, n, kd, ab, ldab, work )
208  END IF
209 *
210 * Exit with RESID = 1/EPS if ANORM = 0.
211 *
212  eps = dlamch( 'Epsilon' )
213  IF( anorm.LE.zero ) THEN
214  resid = one / eps
215  RETURN
216  END IF
217 *
218 * Compute the maximum over the number of right hand sides of
219 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
220 *
221  resid = zero
222  DO 10 j = 1, nrhs
223  CALL dcopy( n, x( 1, j ), 1, work, 1 )
224  CALL dtbmv( uplo, trans, diag, n, kd, ab, ldab, work, 1 )
225  CALL daxpy( n, -one, b( 1, j ), 1, work, 1 )
226  bnorm = dasum( n, work, 1 )
227  xnorm = dasum( n, x( 1, j ), 1 )
228  IF( xnorm.LE.zero ) THEN
229  resid = one / eps
230  ELSE
231  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
232  END IF
233  10 CONTINUE
234 *
235  RETURN
236 *
237 * End of DTBT02
238 *
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:53
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:54
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:53
subroutine dtbmv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
DTBMV
Definition: dtbmv.f:188
double precision function dlantb(NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
DLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
Definition: dlantb.f:142
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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