 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ 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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