LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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  A*x = b,  A**T *x = b,  or
A**H *x = b  when A is a triangular band matrix.  Here A**T denotes
the transpose of A, A**H denotes the conjugate 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, A**T, or A**H, 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 ).```
Date
December 2016

Definition at line 163 of file ztbt02.f.

163 *
164 * -- LAPACK test routine (version 3.7.0) --
165 * -- LAPACK is a software package provided by Univ. of Tennessee, --
166 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
167 * December 2016
168 *
169 * .. Scalar Arguments ..
170  CHARACTER diag, trans, uplo
171  INTEGER kd, ldab, ldb, ldx, n, nrhs
172  DOUBLE PRECISION resid
173 * ..
174 * .. Array Arguments ..
175  DOUBLE PRECISION rwork( * )
176  COMPLEX*16 ab( ldab, * ), b( ldb, * ), work( * ),
177  \$ x( ldx, * )
178 * ..
179 *
180 * =====================================================================
181 *
182 * .. Parameters ..
183  DOUBLE PRECISION zero, one
184  parameter( zero = 0.0d+0, one = 1.0d+0 )
185 * ..
186 * .. Local Scalars ..
187  INTEGER j
188  DOUBLE PRECISION anorm, bnorm, eps, xnorm
189 * ..
190 * .. External Functions ..
191  LOGICAL lsame
192  DOUBLE PRECISION dlamch, dzasum, zlantb
193  EXTERNAL lsame, dlamch, dzasum, zlantb
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL zaxpy, zcopy, ztbmv
197 * ..
198 * .. Intrinsic Functions ..
199  INTRINSIC dcmplx, max
200 * ..
201 * .. Executable Statements ..
202 *
203 * Quick exit if N = 0 or NRHS = 0
204 *
205  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
206  resid = zero
207  RETURN
208  END IF
209 *
210 * Compute the 1-norm of A or A'.
211 *
212  IF( lsame( trans, 'N' ) ) THEN
213  anorm = zlantb( '1', uplo, diag, n, kd, ab, ldab, rwork )
214  ELSE
215  anorm = zlantb( 'I', uplo, diag, n, kd, ab, ldab, rwork )
216  END IF
217 *
218 * Exit with RESID = 1/EPS if ANORM = 0.
219 *
220  eps = dlamch( 'Epsilon' )
221  IF( anorm.LE.zero ) THEN
222  resid = one / eps
223  RETURN
224  END IF
225 *
226 * Compute the maximum over the number of right hand sides of
227 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
228 *
229  resid = zero
230  DO 10 j = 1, nrhs
231  CALL zcopy( n, x( 1, j ), 1, work, 1 )
232  CALL ztbmv( uplo, trans, diag, n, kd, ab, ldab, work, 1 )
233  CALL zaxpy( n, dcmplx( -one ), b( 1, j ), 1, work, 1 )
234  bnorm = dzasum( n, work, 1 )
235  xnorm = dzasum( n, x( 1, j ), 1 )
236  IF( xnorm.LE.zero ) THEN
237  resid = one / eps
238  ELSE
239  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
240  END IF
241  10 CONTINUE
242 *
243  RETURN
244 *
245 * End of ZTBT02
246 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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, or the element of largest absolute value of a triangular band matrix.
Definition: zlantb.f:143
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:83
subroutine ztbmv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
ZTBMV
Definition: ztbmv.f:188
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:74
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:90
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