LAPACK  3.10.1
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 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 ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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