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SUBROUTINE SPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
$ RESID )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER LDB, LDX, N, NRHS
REAL RESID
* ..
* .. Array Arguments ..
REAL A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
* ..
*
* 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.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* Specifies whether the upper or lower triangular part of the
* symmetric matrix A is stored:
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (input) INTEGER
* The number of rows and columns of the matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of columns of B, the matrix of right hand sides.
* NRHS >= 0.
*
* A (input) REAL array, dimension (N*(N+1)/2)
* The original symmetric matrix A, stored as a packed
* triangular matrix.
*
* X (input) REAL array, dimension (LDX,NRHS)
* The computed solution vectors for the system of linear
* equations.
*
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= max(1,N).
*
* B (input/output) 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.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* RWORK (workspace) REAL array, dimension (N)
*
* RESID (output) REAL
* The maximum over the number of right hand sides of
* norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
INTEGER J
REAL ANORM, BNORM, EPS, XNORM
* ..
* .. External Functions ..
REAL SASUM, SLAMCH, SLANSP
EXTERNAL SASUM, SLAMCH, SLANSP
* ..
* .. External Subroutines ..
EXTERNAL SSPMV
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0 or NRHS = 0.
*
IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0.
*
EPS = SLAMCH( 'Epsilon' )
ANORM = SLANSP( '1', UPLO, N, A, RWORK )
IF( ANORM.LE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
*
* Compute B - A*X for the matrix of right hand sides B.
*
DO 10 J = 1, NRHS
CALL SSPMV( UPLO, N, -ONE, A, X( 1, J ), 1, ONE, B( 1, J ), 1 )
10 CONTINUE
*
* Compute the maximum over the number of right hand sides of
* norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
*
RESID = ZERO
DO 20 J = 1, NRHS
BNORM = SASUM( N, B( 1, J ), 1 )
XNORM = SASUM( N, X( 1, J ), 1 )
IF( XNORM.LE.ZERO ) THEN
RESID = ONE / EPS
ELSE
RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
END IF
20 CONTINUE
*
RETURN
*
* End of SPPT02
*
END
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