LAPACK 3.3.1
Linear Algebra PACKage

spot03.f

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00001       SUBROUTINE SPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
00002      $                   RWORK, RCOND, 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, LDAINV, LDWORK, N
00011       REAL               RCOND, RESID
00012 *     ..
00013 *     .. Array Arguments ..
00014       REAL               A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
00015      $                   WORK( LDWORK, * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  SPOT03 computes the residual for a symmetric matrix times its
00022 *  inverse:
00023 *     norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
00024 *  where EPS is the machine epsilon.
00025 *
00026 *  Arguments
00027 *  ==========
00028 *
00029 *  UPLO    (input) CHARACTER*1
00030 *          Specifies whether the upper or lower triangular part of the
00031 *          symmetric matrix A is stored:
00032 *          = 'U':  Upper triangular
00033 *          = 'L':  Lower triangular
00034 *
00035 *  N       (input) INTEGER
00036 *          The number of rows and columns of the matrix A.  N >= 0.
00037 *
00038 *  A       (input) REAL array, dimension (LDA,N)
00039 *          The original symmetric matrix A.
00040 *
00041 *  LDA     (input) INTEGER
00042 *          The leading dimension of the array A.  LDA >= max(1,N)
00043 *
00044 *  AINV    (input/output) REAL array, dimension (LDAINV,N)
00045 *          On entry, the inverse of the matrix A, stored as a symmetric
00046 *          matrix in the same format as A.
00047 *          In this version, AINV is expanded into a full matrix and
00048 *          multiplied by A, so the opposing triangle of AINV will be
00049 *          changed; i.e., if the upper triangular part of AINV is
00050 *          stored, the lower triangular part will be used as work space.
00051 *
00052 *  LDAINV  (input) INTEGER
00053 *          The leading dimension of the array AINV.  LDAINV >= max(1,N).
00054 *
00055 *  WORK    (workspace) REAL array, dimension (LDWORK,N)
00056 *
00057 *  LDWORK  (input) INTEGER
00058 *          The leading dimension of the array WORK.  LDWORK >= max(1,N).
00059 *
00060 *  RWORK   (workspace) REAL array, dimension (N)
00061 *
00062 *  RCOND   (output) REAL
00063 *          The reciprocal of the condition number of A, computed as
00064 *          ( 1/norm(A) ) / norm(AINV).
00065 *
00066 *  RESID   (output) REAL
00067 *          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * 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            I, J
00077       REAL               AINVNM, ANORM, EPS
00078 *     ..
00079 *     .. External Functions ..
00080       LOGICAL            LSAME
00081       REAL               SLAMCH, SLANGE, SLANSY
00082       EXTERNAL           LSAME, SLAMCH, SLANGE, SLANSY
00083 *     ..
00084 *     .. External Subroutines ..
00085       EXTERNAL           SSYMM
00086 *     ..
00087 *     .. Intrinsic Functions ..
00088       INTRINSIC          REAL
00089 *     ..
00090 *     .. Executable Statements ..
00091 *
00092 *     Quick exit if N = 0.
00093 *
00094       IF( N.LE.0 ) THEN
00095          RCOND = ONE
00096          RESID = ZERO
00097          RETURN
00098       END IF
00099 *
00100 *     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
00101 *
00102       EPS = SLAMCH( 'Epsilon' )
00103       ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
00104       AINVNM = SLANSY( '1', UPLO, N, AINV, LDAINV, RWORK )
00105       IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
00106          RCOND = ZERO
00107          RESID = ONE / EPS
00108          RETURN
00109       END IF
00110       RCOND = ( ONE / ANORM ) / AINVNM
00111 *
00112 *     Expand AINV into a full matrix and call SSYMM to multiply
00113 *     AINV on the left by A.
00114 *
00115       IF( LSAME( UPLO, 'U' ) ) THEN
00116          DO 20 J = 1, N
00117             DO 10 I = 1, J - 1
00118                AINV( J, I ) = AINV( I, J )
00119    10       CONTINUE
00120    20    CONTINUE
00121       ELSE
00122          DO 40 J = 1, N
00123             DO 30 I = J + 1, N
00124                AINV( J, I ) = AINV( I, J )
00125    30       CONTINUE
00126    40    CONTINUE
00127       END IF
00128       CALL SSYMM( 'Left', UPLO, N, N, -ONE, A, LDA, AINV, LDAINV, ZERO,
00129      $            WORK, LDWORK )
00130 *
00131 *     Add the identity matrix to WORK .
00132 *
00133       DO 50 I = 1, N
00134          WORK( I, I ) = WORK( I, I ) + ONE
00135    50 CONTINUE
00136 *
00137 *     Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
00138 *
00139       RESID = SLANGE( '1', N, N, WORK, LDWORK, RWORK )
00140 *
00141       RESID = ( ( RESID*RCOND ) / EPS ) / REAL( N )
00142 *
00143       RETURN
00144 *
00145 *     End of SPOT03
00146 *
00147       END
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