LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ dpbt02()

subroutine dpbt02 ( character  UPLO,
integer  N,
integer  KD,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DPBT02

Purpose:
 DPBT02 computes the residual for a solution of a symmetric 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
          symmetric 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 DOUBLE PRECISION array, dimension (LDA,N)
          The original symmetric 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 DPBTRF for further details.
[in]LDA
          LDA is INTEGER.
          The leading dimension of the array A.  LDA >= max(1,KD+1).
[in]X
          X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 dpbt02.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 A( LDA, * ), B( LDB, * ), RWORK( * ),
148 $ X( LDX, * )
149* ..
150*
151* =====================================================================
152*
153* .. Parameters ..
154 DOUBLE PRECISION ZERO, ONE
155 parameter( zero = 0.0d+0, one = 1.0d+0 )
156* ..
157* .. Local Scalars ..
158 INTEGER J
159 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
160* ..
161* .. External Functions ..
162 DOUBLE PRECISION DASUM, DLAMCH, DLANSB
163 EXTERNAL dasum, dlamch, dlansb
164* ..
165* .. External Subroutines ..
166 EXTERNAL dsbmv
167* ..
168* .. Intrinsic Functions ..
169 INTRINSIC max
170* ..
171* .. Executable Statements ..
172*
173* Quick exit if N = 0 or NRHS = 0.
174*
175 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
176 resid = zero
177 RETURN
178 END IF
179*
180* Exit with RESID = 1/EPS if ANORM = 0.
181*
182 eps = dlamch( 'Epsilon' )
183 anorm = dlansb( '1', uplo, n, kd, a, lda, rwork )
184 IF( anorm.LE.zero ) THEN
185 resid = one / eps
186 RETURN
187 END IF
188*
189* Compute B - A*X
190*
191 DO 10 j = 1, nrhs
192 CALL dsbmv( uplo, n, kd, -one, a, lda, x( 1, j ), 1, one,
193 $ b( 1, j ), 1 )
194 10 CONTINUE
195*
196* Compute the maximum over the number of right hand sides of
197* norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
198*
199 resid = zero
200 DO 20 j = 1, nrhs
201 bnorm = dasum( n, b( 1, j ), 1 )
202 xnorm = dasum( n, x( 1, j ), 1 )
203 IF( xnorm.LE.zero ) THEN
204 resid = one / eps
205 ELSE
206 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
207 END IF
208 20 CONTINUE
209*
210 RETURN
211*
212* End of DPBT02
213*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:71
subroutine dsbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DSBMV
Definition: dsbmv.f:184
double precision function dlansb(NORM, UPLO, N, K, AB, LDAB, WORK)
DLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlansb.f:129
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