 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ztbt02()

 subroutine ztbt02 ( character UPLO, character TRANS, character DIAG, integer N, integer KD, integer NRHS, complex*16, dimension( ldab, * ) AB, integer LDAB, complex*16, dimension( ldx, * ) X, integer LDX, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, double precision RESID )

ZTBT02

Purpose:
``` ZTBT02 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, A**T, or A**H, b is the column of B, x is the
solution vector, 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**T * X = B (Transpose) = 'C': A**H * X = 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*16 array, dimension (LDA,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 >= max(1,KD+1).``` [in] X ``` X is COMPLEX*16 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*16 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*16 array, dimension (N)` [out] RWORK ` RWORK 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 157 of file ztbt02.f.

159*
160* -- LAPACK test routine --
161* -- LAPACK is a software package provided by Univ. of Tennessee, --
162* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163*
164* .. Scalar Arguments ..
165 CHARACTER DIAG, TRANS, UPLO
166 INTEGER KD, LDAB, LDB, LDX, N, NRHS
167 DOUBLE PRECISION RESID
168* ..
169* .. Array Arguments ..
170 DOUBLE PRECISION RWORK( * )
171 COMPLEX*16 AB( LDAB, * ), B( LDB, * ), WORK( * ),
172 \$ X( LDX, * )
173* ..
174*
175* =====================================================================
176*
177* .. Parameters ..
178 DOUBLE PRECISION ZERO, ONE
179 parameter( zero = 0.0d+0, one = 1.0d+0 )
180* ..
181* .. Local Scalars ..
182 INTEGER J
183 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
184* ..
185* .. External Functions ..
186 LOGICAL LSAME
187 DOUBLE PRECISION DLAMCH, DZASUM, ZLANTB
188 EXTERNAL lsame, dlamch, dzasum, zlantb
189* ..
190* .. External Subroutines ..
191 EXTERNAL zaxpy, zcopy, ztbmv
192* ..
193* .. Intrinsic Functions ..
194 INTRINSIC dcmplx, max
195* ..
196* .. Executable Statements ..
197*
198* Quick exit if N = 0 or NRHS = 0
199*
200 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
201 resid = zero
202 RETURN
203 END IF
204*
205* Compute the 1-norm of op(A).
206*
207 IF( lsame( trans, 'N' ) ) THEN
208 anorm = zlantb( '1', uplo, diag, n, kd, ab, ldab, rwork )
209 ELSE
210 anorm = zlantb( 'I', uplo, diag, n, kd, ab, ldab, rwork )
211 END IF
212*
213* Exit with RESID = 1/EPS if ANORM = 0.
214*
215 eps = dlamch( 'Epsilon' )
216 IF( anorm.LE.zero ) THEN
217 resid = one / eps
218 RETURN
219 END IF
220*
221* Compute the maximum over the number of right hand sides of
222* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
223*
224 resid = zero
225 DO 10 j = 1, nrhs
226 CALL zcopy( n, x( 1, j ), 1, work, 1 )
227 CALL ztbmv( uplo, trans, diag, n, kd, ab, ldab, work, 1 )
228 CALL zaxpy( n, dcmplx( -one ), b( 1, j ), 1, work, 1 )
229 bnorm = dzasum( n, work, 1 )
230 xnorm = dzasum( n, x( 1, j ), 1 )
231 IF( xnorm.LE.zero ) THEN
232 resid = one / eps
233 ELSE
234 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
235 END IF
236 10 CONTINUE
237*
238 RETURN
239*
240* End of ZTBT02
241*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:88
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
subroutine ztbmv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
ZTBMV
Definition: ztbmv.f:186
double precision function zlantb(NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
ZLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlantb.f:141
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:72
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