LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
spot01.f
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00001 *> \brief \b SPOT01
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE SPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       CHARACTER          UPLO
00015 *       INTEGER            LDA, LDAFAC, N
00016 *       REAL               RESID
00017 *       ..
00018 *       .. Array Arguments ..
00019 *       REAL               A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
00020 *       ..
00021 *  
00022 *
00023 *> \par Purpose:
00024 *  =============
00025 *>
00026 *> \verbatim
00027 *>
00028 *> SPOT01 reconstructs a symmetric positive definite matrix  A  from
00029 *> its L*L' or U'*U factorization and computes the residual
00030 *>    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
00031 *>    norm( U'*U - A ) / ( N * norm(A) * EPS ),
00032 *> where EPS is the machine epsilon.
00033 *> \endverbatim
00034 *
00035 *  Arguments:
00036 *  ==========
00037 *
00038 *> \param[in] UPLO
00039 *> \verbatim
00040 *>          UPLO is CHARACTER*1
00041 *>          Specifies whether the upper or lower triangular part of the
00042 *>          symmetric matrix A is stored:
00043 *>          = 'U':  Upper triangular
00044 *>          = 'L':  Lower triangular
00045 *> \endverbatim
00046 *>
00047 *> \param[in] N
00048 *> \verbatim
00049 *>          N is INTEGER
00050 *>          The number of rows and columns of the matrix A.  N >= 0.
00051 *> \endverbatim
00052 *>
00053 *> \param[in] A
00054 *> \verbatim
00055 *>          A is REAL array, dimension (LDA,N)
00056 *>          The original symmetric matrix A.
00057 *> \endverbatim
00058 *>
00059 *> \param[in] LDA
00060 *> \verbatim
00061 *>          LDA is INTEGER
00062 *>          The leading dimension of the array A.  LDA >= max(1,N)
00063 *> \endverbatim
00064 *>
00065 *> \param[in,out] AFAC
00066 *> \verbatim
00067 *>          AFAC is REAL array, dimension (LDAFAC,N)
00068 *>          On entry, the factor L or U from the L*L' or U'*U
00069 *>          factorization of A.
00070 *>          Overwritten with the reconstructed matrix, and then with the
00071 *>          difference L*L' - A (or U'*U - A).
00072 *> \endverbatim
00073 *>
00074 *> \param[in] LDAFAC
00075 *> \verbatim
00076 *>          LDAFAC is INTEGER
00077 *>          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
00078 *> \endverbatim
00079 *>
00080 *> \param[out] RWORK
00081 *> \verbatim
00082 *>          RWORK is REAL array, dimension (N)
00083 *> \endverbatim
00084 *>
00085 *> \param[out] RESID
00086 *> \verbatim
00087 *>          RESID is REAL
00088 *>          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
00089 *>          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
00090 *> \endverbatim
00091 *
00092 *  Authors:
00093 *  ========
00094 *
00095 *> \author Univ. of Tennessee 
00096 *> \author Univ. of California Berkeley 
00097 *> \author Univ. of Colorado Denver 
00098 *> \author NAG Ltd. 
00099 *
00100 *> \date November 2011
00101 *
00102 *> \ingroup single_lin
00103 *
00104 *  =====================================================================
00105       SUBROUTINE SPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
00106 *
00107 *  -- LAPACK test routine (version 3.4.0) --
00108 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00109 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00110 *     November 2011
00111 *
00112 *     .. Scalar Arguments ..
00113       CHARACTER          UPLO
00114       INTEGER            LDA, LDAFAC, N
00115       REAL               RESID
00116 *     ..
00117 *     .. Array Arguments ..
00118       REAL               A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
00119 *     ..
00120 *
00121 *  =====================================================================
00122 *
00123 *     .. Parameters ..
00124       REAL               ZERO, ONE
00125       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00126 *     ..
00127 *     .. Local Scalars ..
00128       INTEGER            I, J, K
00129       REAL               ANORM, EPS, T
00130 *     ..
00131 *     .. External Functions ..
00132       LOGICAL            LSAME
00133       REAL               SDOT, SLAMCH, SLANSY
00134       EXTERNAL           LSAME, SDOT, SLAMCH, SLANSY
00135 *     ..
00136 *     .. External Subroutines ..
00137       EXTERNAL           SSCAL, SSYR, STRMV
00138 *     ..
00139 *     .. Intrinsic Functions ..
00140       INTRINSIC          REAL
00141 *     ..
00142 *     .. Executable Statements ..
00143 *
00144 *     Quick exit if N = 0.
00145 *
00146       IF( N.LE.0 ) THEN
00147          RESID = ZERO
00148          RETURN
00149       END IF
00150 *
00151 *     Exit with RESID = 1/EPS if ANORM = 0.
00152 *
00153       EPS = SLAMCH( 'Epsilon' )
00154       ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
00155       IF( ANORM.LE.ZERO ) THEN
00156          RESID = ONE / EPS
00157          RETURN
00158       END IF
00159 *
00160 *     Compute the product U'*U, overwriting U.
00161 *
00162       IF( LSAME( UPLO, 'U' ) ) THEN
00163          DO 10 K = N, 1, -1
00164 *
00165 *           Compute the (K,K) element of the result.
00166 *
00167             T = SDOT( K, AFAC( 1, K ), 1, AFAC( 1, K ), 1 )
00168             AFAC( K, K ) = T
00169 *
00170 *           Compute the rest of column K.
00171 *
00172             CALL STRMV( 'Upper', 'Transpose', 'Non-unit', K-1, AFAC,
00173      $                  LDAFAC, AFAC( 1, K ), 1 )
00174 *
00175    10    CONTINUE
00176 *
00177 *     Compute the product L*L', overwriting L.
00178 *
00179       ELSE
00180          DO 20 K = N, 1, -1
00181 *
00182 *           Add a multiple of column K of the factor L to each of
00183 *           columns K+1 through N.
00184 *
00185             IF( K+1.LE.N )
00186      $         CALL SSYR( 'Lower', N-K, ONE, AFAC( K+1, K ), 1,
00187      $                    AFAC( K+1, K+1 ), LDAFAC )
00188 *
00189 *           Scale column K by the diagonal element.
00190 *
00191             T = AFAC( K, K )
00192             CALL SSCAL( N-K+1, T, AFAC( K, K ), 1 )
00193 *
00194    20    CONTINUE
00195       END IF
00196 *
00197 *     Compute the difference  L*L' - A (or U'*U - A).
00198 *
00199       IF( LSAME( UPLO, 'U' ) ) THEN
00200          DO 40 J = 1, N
00201             DO 30 I = 1, J
00202                AFAC( I, J ) = AFAC( I, J ) - A( I, J )
00203    30       CONTINUE
00204    40    CONTINUE
00205       ELSE
00206          DO 60 J = 1, N
00207             DO 50 I = J, N
00208                AFAC( I, J ) = AFAC( I, J ) - A( I, J )
00209    50       CONTINUE
00210    60    CONTINUE
00211       END IF
00212 *
00213 *     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
00214 *
00215       RESID = SLANSY( '1', UPLO, N, AFAC, LDAFAC, RWORK )
00216 *
00217       RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS
00218 *
00219       RETURN
00220 *
00221 *     End of SPOT01
00222 *
00223       END
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