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 ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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 dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:74
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:90
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:83
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine ztbmv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
ZTBMV
Definition: ztbmv.f:188
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
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