LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sppt02()

subroutine sppt02 ( character  UPLO,
integer  N,
integer  NRHS,
real, dimension( * )  A,
real, dimension( ldx, * )  X,
integer  LDX,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( * )  RWORK,
real  RESID 
)

SPPT02

Purpose:
 SPPT02 computes the residual in the solution of a symmetric system
 of linear equations  A*x = b  when packed storage is used for the
 coefficient matrix.  The ratio computed is

    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]NRHS
          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.
[in]A
          A is REAL array, dimension (N*(N+1)/2)
          The original symmetric matrix A, stored as a packed
          triangular matrix.
[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 120 of file sppt02.f.

122 *
123 * -- LAPACK test routine --
124 * -- LAPACK is a software package provided by Univ. of Tennessee, --
125 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126 *
127 * .. Scalar Arguments ..
128  CHARACTER UPLO
129  INTEGER LDB, LDX, N, NRHS
130  REAL RESID
131 * ..
132 * .. Array Arguments ..
133  REAL A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
134 * ..
135 *
136 * =====================================================================
137 *
138 * .. Parameters ..
139  REAL ZERO, ONE
140  parameter( zero = 0.0e+0, one = 1.0e+0 )
141 * ..
142 * .. Local Scalars ..
143  INTEGER J
144  REAL ANORM, BNORM, EPS, XNORM
145 * ..
146 * .. External Functions ..
147  REAL SASUM, SLAMCH, SLANSP
148  EXTERNAL sasum, slamch, slansp
149 * ..
150 * .. External Subroutines ..
151  EXTERNAL sspmv
152 * ..
153 * .. Intrinsic Functions ..
154  INTRINSIC max
155 * ..
156 * .. Executable Statements ..
157 *
158 * Quick exit if N = 0 or NRHS = 0.
159 *
160  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
161  resid = zero
162  RETURN
163  END IF
164 *
165 * Exit with RESID = 1/EPS if ANORM = 0.
166 *
167  eps = slamch( 'Epsilon' )
168  anorm = slansp( '1', uplo, n, a, rwork )
169  IF( anorm.LE.zero ) THEN
170  resid = one / eps
171  RETURN
172  END IF
173 *
174 * Compute B - A*X for the matrix of right hand sides B.
175 *
176  DO 10 j = 1, nrhs
177  CALL sspmv( uplo, n, -one, a, x( 1, j ), 1, one, b( 1, j ), 1 )
178  10 CONTINUE
179 *
180 * Compute the maximum over the number of right hand sides of
181 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
182 *
183  resid = zero
184  DO 20 j = 1, nrhs
185  bnorm = sasum( n, b( 1, j ), 1 )
186  xnorm = sasum( n, x( 1, j ), 1 )
187  IF( xnorm.LE.zero ) THEN
188  resid = one / eps
189  ELSE
190  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
191  END IF
192  20 CONTINUE
193 *
194  RETURN
195 *
196 * End of SPPT02
197 *
real function slansp(NORM, UPLO, N, AP, WORK)
SLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansp.f:114
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
subroutine sspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
SSPMV
Definition: sspmv.f:147
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
Here is the call graph for this function:
Here is the caller graph for this function: