LAPACK 3.3.0

# spot02.f

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```00001       SUBROUTINE SPOT02( UPLO, N, NRHS, A, LDA, 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            LDA, LDB, LDX, N, NRHS
00011       REAL               RESID
00012 *     ..
00013 *     .. Array Arguments ..
00014       REAL               A( LDA, * ), B( LDB, * ), RWORK( * ),
00015      \$                   X( LDX, * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  SPOT02 computes the residual for the solution of a symmetric system
00022 *  of linear equations  A*x = b:
00023 *
00024 *     RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
00025 *
00026 *  where EPS is the machine epsilon.
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 (LDA,N)
00045 *          The original symmetric matrix A.
00046 *
00047 *  LDA     (input) INTEGER
00048 *          The leading dimension of the array A.  LDA >= max(1,N)
00049 *
00050 *  X       (input) REAL array, dimension (LDX,NRHS)
00051 *          The computed solution vectors for the system of linear
00052 *          equations.
00053 *
00054 *  LDX     (input) INTEGER
00055 *          The leading dimension of the array X.   LDX >= max(1,N).
00056 *
00057 *  B       (input/output) REAL array, dimension (LDB,NRHS)
00058 *          On entry, the right hand side vectors for the system of
00059 *          linear equations.
00060 *          On exit, B is overwritten with the difference B - A*X.
00061 *
00062 *  LDB     (input) INTEGER
00063 *          The leading dimension of the array B.  LDB >= max(1,N).
00064 *
00065 *  RWORK   (workspace) REAL array, dimension (N)
00066 *
00067 *  RESID   (output) REAL
00068 *          The maximum over the number of right hand sides of
00069 *          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
00070 *
00071 *  =====================================================================
00072 *
00073 *     .. Parameters ..
00074       REAL               ZERO, ONE
00075       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00076 *     ..
00077 *     .. Local Scalars ..
00078       INTEGER            J
00079       REAL               ANORM, BNORM, EPS, XNORM
00080 *     ..
00081 *     .. External Functions ..
00082       REAL               SASUM, SLAMCH, SLANSY
00083       EXTERNAL           SASUM, SLAMCH, SLANSY
00084 *     ..
00085 *     .. External Subroutines ..
00086       EXTERNAL           SSYMM
00087 *     ..
00088 *     .. Intrinsic Functions ..
00089       INTRINSIC          MAX
00090 *     ..
00091 *     .. Executable Statements ..
00092 *
00093 *     Quick exit if N = 0 or NRHS = 0.
00094 *
00095       IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
00096          RESID = ZERO
00097          RETURN
00098       END IF
00099 *
00100 *     Exit with RESID = 1/EPS if ANORM = 0.
00101 *
00102       EPS = SLAMCH( 'Epsilon' )
00103       ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
00104       IF( ANORM.LE.ZERO ) THEN
00105          RESID = ONE / EPS
00106          RETURN
00107       END IF
00108 *
00109 *     Compute  B - A*X
00110 *
00111       CALL SSYMM( 'Left', UPLO, N, NRHS, -ONE, A, LDA, X, LDX, ONE, B,
00112      \$            LDB )
00113 *
00114 *     Compute the maximum over the number of right hand sides of
00115 *        norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
00116 *
00117       RESID = ZERO
00118       DO 10 J = 1, NRHS
00119          BNORM = SASUM( N, B( 1, J ), 1 )
00120          XNORM = SASUM( N, X( 1, J ), 1 )
00121          IF( XNORM.LE.ZERO ) THEN
00122             RESID = ONE / EPS
00123          ELSE
00124             RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
00125          END IF
00126    10 CONTINUE
00127 *
00128       RETURN
00129 *
00130 *     End of SPOT02
00131 *
00132       END
```