LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ zpbt02()

subroutine zpbt02 ( character  UPLO,
integer  N,
integer  KD,
integer  NRHS,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( ldx, * )  X,
integer  LDX,
complex*16, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

ZPBT02

Purpose:
 ZPBT02 computes the residual for a solution of a Hermitian banded
 system of equations  A*x = b:
    RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
 where EPS is the machine precision.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]KD
          KD is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides. NRHS >= 0.
[in]A
          A is COMPLEX*16 array, dimension (LDA,N)
          The original Hermitian band matrix A.  If UPLO = 'U', the
          upper triangular part of A is stored as a band matrix; if
          UPLO = 'L', the lower triangular part of A is stored.  The
          columns of the appropriate triangle are stored in the columns
          of A and the diagonals of the triangle are stored in the rows
          of A.  See ZPBTRF for further details.
[in]LDA
          LDA is INTEGER.
          The leading dimension of the array A.  LDA >= 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,out]B
          B is COMPLEX*16 array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,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(B - A*X) / ( norm(A) * norm(X) * EPS ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 134 of file zpbt02.f.

136 *
137 * -- LAPACK test routine --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 *
141 * .. Scalar Arguments ..
142  CHARACTER UPLO
143  INTEGER KD, LDA, LDB, LDX, N, NRHS
144  DOUBLE PRECISION RESID
145 * ..
146 * .. Array Arguments ..
147  DOUBLE PRECISION RWORK( * )
148  COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
149 * ..
150 *
151 * =====================================================================
152 *
153 * .. Parameters ..
154  DOUBLE PRECISION ZERO, ONE
155  parameter( zero = 0.0d+0, one = 1.0d+0 )
156  COMPLEX*16 CONE
157  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
158 * ..
159 * .. Local Scalars ..
160  INTEGER J
161  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
162 * ..
163 * .. External Functions ..
164  DOUBLE PRECISION DLAMCH, DZASUM, ZLANHB
165  EXTERNAL dlamch, dzasum, zlanhb
166 * ..
167 * .. External Subroutines ..
168  EXTERNAL zhbmv
169 * ..
170 * .. Intrinsic Functions ..
171  INTRINSIC max
172 * ..
173 * .. Executable Statements ..
174 *
175 * Quick exit if N = 0 or NRHS = 0.
176 *
177  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
178  resid = zero
179  RETURN
180  END IF
181 *
182 * Exit with RESID = 1/EPS if ANORM = 0.
183 *
184  eps = dlamch( 'Epsilon' )
185  anorm = zlanhb( '1', uplo, n, kd, a, lda, rwork )
186  IF( anorm.LE.zero ) THEN
187  resid = one / eps
188  RETURN
189  END IF
190 *
191 * Compute B - A*X
192 *
193  DO 10 j = 1, nrhs
194  CALL zhbmv( uplo, n, kd, -cone, a, lda, x( 1, j ), 1, cone,
195  $ b( 1, j ), 1 )
196  10 CONTINUE
197 *
198 * Compute the maximum over the number of right hand sides of
199 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
200 *
201  resid = zero
202  DO 20 j = 1, nrhs
203  bnorm = dzasum( n, b( 1, j ), 1 )
204  xnorm = dzasum( n, x( 1, j ), 1 )
205  IF( xnorm.LE.zero ) THEN
206  resid = one / eps
207  ELSE
208  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
209  END IF
210  20 CONTINUE
211 *
212  RETURN
213 *
214 * End of ZPBT02
215 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zhbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZHBMV
Definition: zhbmv.f:187
double precision function zlanhb(NORM, UPLO, N, K, AB, LDAB, WORK)
ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlanhb.f:132
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:72
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