 LAPACK  3.10.1 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 op(A)*X = B, when A is a
triangular band matrix. The test ratio is the maximum over
norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
where op(A) = A or A**T, b is the column of B, x is the solution
vector, and EPS is the machine epsilon.
The norm used is the 1-norm.```
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**T * X = B (Transpose) = 'C': A**H * 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 ).```

Definition at line 152 of file dtbt02.f.

154 *
155 * -- LAPACK test routine --
156 * -- LAPACK is a software package provided by Univ. of Tennessee, --
157 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158 *
159 * .. Scalar Arguments ..
160  CHARACTER DIAG, TRANS, UPLO
161  INTEGER KD, LDAB, LDB, LDX, N, NRHS
162  DOUBLE PRECISION RESID
163 * ..
164 * .. Array Arguments ..
165  DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ), WORK( * ),
166  \$ X( LDX, * )
167 * ..
168 *
169 * =====================================================================
170 *
171 * .. Parameters ..
172  DOUBLE PRECISION ZERO, ONE
173  parameter( zero = 0.0d+0, one = 1.0d+0 )
174 * ..
175 * .. Local Scalars ..
176  INTEGER J
177  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
178 * ..
179 * .. External Functions ..
180  LOGICAL LSAME
181  DOUBLE PRECISION DASUM, DLAMCH, DLANTB
182  EXTERNAL lsame, dasum, dlamch, dlantb
183 * ..
184 * .. External Subroutines ..
185  EXTERNAL daxpy, dcopy, dtbmv
186 * ..
187 * .. Intrinsic Functions ..
188  INTRINSIC max
189 * ..
190 * .. Executable Statements ..
191 *
192 * Quick exit if N = 0 or NRHS = 0
193 *
194  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
195  resid = zero
196  RETURN
197  END IF
198 *
199 * Compute the 1-norm of op(A).
200 *
201  IF( lsame( trans, 'N' ) ) THEN
202  anorm = dlantb( '1', uplo, diag, n, kd, ab, ldab, work )
203  ELSE
204  anorm = dlantb( 'I', uplo, diag, n, kd, ab, ldab, work )
205  END IF
206 *
207 * Exit with RESID = 1/EPS if ANORM = 0.
208 *
209  eps = dlamch( 'Epsilon' )
210  IF( anorm.LE.zero ) THEN
211  resid = one / eps
212  RETURN
213  END IF
214 *
215 * Compute the maximum over the number of right hand sides of
216 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
217 *
218  resid = zero
219  DO 10 j = 1, nrhs
220  CALL dcopy( n, x( 1, j ), 1, work, 1 )
221  CALL dtbmv( uplo, trans, diag, n, kd, ab, ldab, work, 1 )
222  CALL daxpy( n, -one, b( 1, j ), 1, work, 1 )
223  bnorm = dasum( n, work, 1 )
224  xnorm = dasum( n, x( 1, j ), 1 )
225  IF( xnorm.LE.zero ) THEN
226  resid = one / eps
227  ELSE
228  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
229  END IF
230  10 CONTINUE
231 *
232  RETURN
233 *
234 * End of DTBT02
235 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:71
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:89
subroutine dtbmv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
DTBMV
Definition: dtbmv.f:186
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,...
Definition: dlantb.f:140
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