LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ spbt02()

subroutine spbt02 ( character  UPLO,
integer  N,
integer  KD,
integer  NRHS,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldx, * )  X,
integer  LDX,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( * )  RWORK,
real  RESID 
)

SPBT02

Purpose:
 SPBT02 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 REAL 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 SPBTRF for further details.
[in]LDA
          LDA is INTEGER.
          The leading dimension of the array A.  LDA >= max(1,KD+1).
[in]X
          X is REAL 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 REAL 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 REAL array, dimension (N)
[out]RESID
          RESID is REAL
          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 spbt02.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  REAL RESID
145 * ..
146 * .. Array Arguments ..
147  REAL A( LDA, * ), B( LDB, * ), RWORK( * ),
148  $ X( LDX, * )
149 * ..
150 *
151 * =====================================================================
152 *
153 * .. Parameters ..
154  REAL ZERO, ONE
155  parameter( zero = 0.0e+0, one = 1.0e+0 )
156 * ..
157 * .. Local Scalars ..
158  INTEGER J
159  REAL ANORM, BNORM, EPS, XNORM
160 * ..
161 * .. External Functions ..
162  REAL SASUM, SLAMCH, SLANSB
163  EXTERNAL sasum, slamch, slansb
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL ssbmv
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 = slamch( 'Epsilon' )
183  anorm = slansb( '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 ssbmv( 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 = sasum( n, b( 1, j ), 1 )
202  xnorm = sasum( 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 SPBT02
213 *
real function slansb(NORM, UPLO, N, K, AB, LDAB, WORK)
SLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansb.f:129
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
subroutine ssbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SSBMV
Definition: ssbmv.f:184
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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