LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ ctbt02()

subroutine ctbt02 ( character  uplo,
character  trans,
character  diag,
integer  n,
integer  kd,
integer  nrhs,
complex, dimension( ldab, * )  ab,
integer  ldab,
complex, dimension( ldx, * )  x,
integer  ldx,
complex, dimension( ldb, * )  b,
integer  ldb,
complex, dimension( * )  work,
real, dimension( * )  rwork,
real  resid 
)

CTBT02

Purpose:
 CTBT02 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 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 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 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 array, dimension (N)
[out]RWORK
          RWORK is REAL array, dimension (N)
[out]RESID
          RESID is REAL
          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 ctbt02.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 REAL RESID
168* ..
169* .. Array Arguments ..
170 REAL RWORK( * )
171 COMPLEX AB( LDAB, * ), B( LDB, * ), WORK( * ),
172 $ X( LDX, * )
173* ..
174*
175* =====================================================================
176*
177* .. Parameters ..
178 REAL ZERO, ONE
179 parameter( zero = 0.0e+0, one = 1.0e+0 )
180* ..
181* .. Local Scalars ..
182 INTEGER J
183 REAL ANORM, BNORM, EPS, XNORM
184* ..
185* .. External Functions ..
186 LOGICAL LSAME
187 REAL CLANTB, SCASUM, SLAMCH
188 EXTERNAL lsame, clantb, scasum, slamch
189* ..
190* .. External Subroutines ..
191 EXTERNAL caxpy, ccopy, ctbmv
192* ..
193* .. Intrinsic Functions ..
194 INTRINSIC cmplx, 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 = clantb( '1', uplo, diag, n, kd, ab, ldab, rwork )
209 ELSE
210 anorm = clantb( 'I', uplo, diag, n, kd, ab, ldab, rwork )
211 END IF
212*
213* Exit with RESID = 1/EPS if ANORM = 0.
214*
215 eps = slamch( '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 ccopy( n, x( 1, j ), 1, work, 1 )
227 CALL ctbmv( uplo, trans, diag, n, kd, ab, ldab, work, 1 )
228 CALL caxpy( n, cmplx( -one ), b( 1, j ), 1, work, 1 )
229 bnorm = scasum( n, work, 1 )
230 xnorm = scasum( 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 CTBT02
241*
real function scasum(n, cx, incx)
SCASUM
Definition scasum.f:72
subroutine caxpy(n, ca, cx, incx, cy, incy)
CAXPY
Definition caxpy.f:88
subroutine ccopy(n, cx, incx, cy, incy)
CCOPY
Definition ccopy.f:81
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function clantb(norm, uplo, diag, n, k, ab, ldab, work)
CLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition clantb.f:141
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine ctbmv(uplo, trans, diag, n, k, a, lda, x, incx)
CTBMV
Definition ctbmv.f:186
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