LAPACK 3.3.1 Linear Algebra PACKage

sppt02.f

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00001       SUBROUTINE SPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
00002      \$                   RESID )
00003 *
00004 *  -- LAPACK test routine (version 3.1) --
00005 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          UPLO
00010       INTEGER            LDB, LDX, N, NRHS
00011       REAL               RESID
00012 *     ..
00013 *     .. Array Arguments ..
00014       REAL               A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
00015 *     ..
00016 *
00017 *  Purpose
00018 *  =======
00019 *
00020 *  SPPT02 computes the residual in the solution of a symmetric system
00021 *  of linear equations  A*x = b  when packed storage is used for the
00022 *  coefficient matrix.  The ratio computed is
00023 *
00024 *     RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),
00025 *
00026 *  where EPS is the machine precision.
00027 *
00028 *  Arguments
00029 *  =========
00030 *
00031 *  UPLO    (input) CHARACTER*1
00032 *          Specifies whether the upper or lower triangular part of the
00033 *          symmetric matrix A is stored:
00034 *          = 'U':  Upper triangular
00035 *          = 'L':  Lower triangular
00036 *
00037 *  N       (input) INTEGER
00038 *          The number of rows and columns of the matrix A.  N >= 0.
00039 *
00040 *  NRHS    (input) INTEGER
00041 *          The number of columns of B, the matrix of right hand sides.
00042 *          NRHS >= 0.
00043 *
00044 *  A       (input) REAL array, dimension (N*(N+1)/2)
00045 *          The original symmetric matrix A, stored as a packed
00046 *          triangular matrix.
00047 *
00048 *  X       (input) REAL array, dimension (LDX,NRHS)
00049 *          The computed solution vectors for the system of linear
00050 *          equations.
00051 *
00052 *  LDX     (input) INTEGER
00053 *          The leading dimension of the array X.   LDX >= max(1,N).
00054 *
00055 *  B       (input/output) REAL array, dimension (LDB,NRHS)
00056 *          On entry, the right hand side vectors for the system of
00057 *          linear equations.
00058 *          On exit, B is overwritten with the difference B - A*X.
00059 *
00060 *  LDB     (input) INTEGER
00061 *          The leading dimension of the array B.  LDB >= max(1,N).
00062 *
00063 *  RWORK   (workspace) REAL array, dimension (N)
00064 *
00065 *  RESID   (output) REAL
00066 *          The maximum over the number of right hand sides of
00067 *          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
00068 *
00069 *  =====================================================================
00070 *
00071 *     .. Parameters ..
00072       REAL               ZERO, ONE
00073       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00074 *     ..
00075 *     .. Local Scalars ..
00076       INTEGER            J
00077       REAL               ANORM, BNORM, EPS, XNORM
00078 *     ..
00079 *     .. External Functions ..
00080       REAL               SASUM, SLAMCH, SLANSP
00081       EXTERNAL           SASUM, SLAMCH, SLANSP
00082 *     ..
00083 *     .. External Subroutines ..
00084       EXTERNAL           SSPMV
00085 *     ..
00086 *     .. Intrinsic Functions ..
00087       INTRINSIC          MAX
00088 *     ..
00089 *     .. Executable Statements ..
00090 *
00091 *     Quick exit if N = 0 or NRHS = 0.
00092 *
00093       IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
00094          RESID = ZERO
00095          RETURN
00096       END IF
00097 *
00098 *     Exit with RESID = 1/EPS if ANORM = 0.
00099 *
00100       EPS = SLAMCH( 'Epsilon' )
00101       ANORM = SLANSP( '1', UPLO, N, A, RWORK )
00102       IF( ANORM.LE.ZERO ) THEN
00103          RESID = ONE / EPS
00104          RETURN
00105       END IF
00106 *
00107 *     Compute  B - A*X  for the matrix of right hand sides B.
00108 *
00109       DO 10 J = 1, NRHS
00110          CALL SSPMV( UPLO, N, -ONE, A, X( 1, J ), 1, ONE, B( 1, J ), 1 )
00111    10 CONTINUE
00112 *
00113 *     Compute the maximum over the number of right hand sides of
00114 *        norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
00115 *
00116       RESID = ZERO
00117       DO 20 J = 1, NRHS
00118          BNORM = SASUM( N, B( 1, J ), 1 )
00119          XNORM = SASUM( N, X( 1, J ), 1 )
00120          IF( XNORM.LE.ZERO ) THEN
00121             RESID = ONE / EPS
00122          ELSE
00123             RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
00124          END IF
00125    20 CONTINUE
00126 *
00127       RETURN
00128 *
00129 *     End of SPPT02
00130 *
00131       END