LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dtbt02()

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 ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 156 of file dtbt02.f.

156 *
157 * -- LAPACK test routine (version 3.7.0) --
158 * -- LAPACK is a software package provided by Univ. of Tennessee, --
159 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
160 * December 2016
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 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:84
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:91
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:73
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
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