LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sppt01.f
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00001 *> \brief \b SPPT01
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 SPPT01( UPLO, N, A, AFAC, RWORK, RESID )
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       CHARACTER          UPLO
00015 *       INTEGER            N
00016 *       REAL               RESID
00017 *       ..
00018 *       .. Array Arguments ..
00019 *       REAL               A( * ), AFAC( * ), RWORK( * )
00020 *       ..
00021 *  
00022 *
00023 *> \par Purpose:
00024 *  =============
00025 *>
00026 *> \verbatim
00027 *>
00028 *> SPPT01 reconstructs a symmetric positive definite packed matrix A
00029 *> from 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 (N*(N+1)/2)
00056 *>          The original symmetric matrix A, stored as a packed
00057 *>          triangular matrix.
00058 *> \endverbatim
00059 *>
00060 *> \param[in,out] AFAC
00061 *> \verbatim
00062 *>          AFAC is REAL array, dimension (N*(N+1)/2)
00063 *>          On entry, the factor L or U from the L*L' or U'*U
00064 *>          factorization of A, stored as a packed triangular matrix.
00065 *>          Overwritten with the reconstructed matrix, and then with the
00066 *>          difference L*L' - A (or U'*U - A).
00067 *> \endverbatim
00068 *>
00069 *> \param[out] RWORK
00070 *> \verbatim
00071 *>          RWORK is REAL array, dimension (N)
00072 *> \endverbatim
00073 *>
00074 *> \param[out] RESID
00075 *> \verbatim
00076 *>          RESID is REAL
00077 *>          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
00078 *>          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
00079 *> \endverbatim
00080 *
00081 *  Authors:
00082 *  ========
00083 *
00084 *> \author Univ. of Tennessee 
00085 *> \author Univ. of California Berkeley 
00086 *> \author Univ. of Colorado Denver 
00087 *> \author NAG Ltd. 
00088 *
00089 *> \date November 2011
00090 *
00091 *> \ingroup single_lin
00092 *
00093 *  =====================================================================
00094       SUBROUTINE SPPT01( UPLO, N, A, AFAC, RWORK, RESID )
00095 *
00096 *  -- LAPACK test routine (version 3.4.0) --
00097 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00098 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00099 *     November 2011
00100 *
00101 *     .. Scalar Arguments ..
00102       CHARACTER          UPLO
00103       INTEGER            N
00104       REAL               RESID
00105 *     ..
00106 *     .. Array Arguments ..
00107       REAL               A( * ), AFAC( * ), RWORK( * )
00108 *     ..
00109 *
00110 *  =====================================================================
00111 *
00112 *     .. Parameters ..
00113       REAL               ZERO, ONE
00114       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00115 *     ..
00116 *     .. Local Scalars ..
00117       INTEGER            I, K, KC, NPP
00118       REAL               ANORM, EPS, T
00119 *     ..
00120 *     .. External Functions ..
00121       LOGICAL            LSAME
00122       REAL               SDOT, SLAMCH, SLANSP
00123       EXTERNAL           LSAME, SDOT, SLAMCH, SLANSP
00124 *     ..
00125 *     .. External Subroutines ..
00126       EXTERNAL           SSCAL, SSPR, STPMV
00127 *     ..
00128 *     .. Intrinsic Functions ..
00129       INTRINSIC          REAL
00130 *     ..
00131 *     .. Executable Statements ..
00132 *
00133 *     Quick exit if N = 0
00134 *
00135       IF( N.LE.0 ) THEN
00136          RESID = ZERO
00137          RETURN
00138       END IF
00139 *
00140 *     Exit with RESID = 1/EPS if ANORM = 0.
00141 *
00142       EPS = SLAMCH( 'Epsilon' )
00143       ANORM = SLANSP( '1', UPLO, N, A, RWORK )
00144       IF( ANORM.LE.ZERO ) THEN
00145          RESID = ONE / EPS
00146          RETURN
00147       END IF
00148 *
00149 *     Compute the product U'*U, overwriting U.
00150 *
00151       IF( LSAME( UPLO, 'U' ) ) THEN
00152          KC = ( N*( N-1 ) ) / 2 + 1
00153          DO 10 K = N, 1, -1
00154 *
00155 *           Compute the (K,K) element of the result.
00156 *
00157             T = SDOT( K, AFAC( KC ), 1, AFAC( KC ), 1 )
00158             AFAC( KC+K-1 ) = T
00159 *
00160 *           Compute the rest of column K.
00161 *
00162             IF( K.GT.1 ) THEN
00163                CALL STPMV( 'Upper', 'Transpose', 'Non-unit', K-1, AFAC,
00164      $                     AFAC( KC ), 1 )
00165                KC = KC - ( K-1 )
00166             END IF
00167    10    CONTINUE
00168 *
00169 *     Compute the product L*L', overwriting L.
00170 *
00171       ELSE
00172          KC = ( N*( N+1 ) ) / 2
00173          DO 20 K = N, 1, -1
00174 *
00175 *           Add a multiple of column K of the factor L to each of
00176 *           columns K+1 through N.
00177 *
00178             IF( K.LT.N )
00179      $         CALL SSPR( 'Lower', N-K, ONE, AFAC( KC+1 ), 1,
00180      $                    AFAC( KC+N-K+1 ) )
00181 *
00182 *           Scale column K by the diagonal element.
00183 *
00184             T = AFAC( KC )
00185             CALL SSCAL( N-K+1, T, AFAC( KC ), 1 )
00186 *
00187             KC = KC - ( N-K+2 )
00188    20    CONTINUE
00189       END IF
00190 *
00191 *     Compute the difference  L*L' - A (or U'*U - A).
00192 *
00193       NPP = N*( N+1 ) / 2
00194       DO 30 I = 1, NPP
00195          AFAC( I ) = AFAC( I ) - A( I )
00196    30 CONTINUE
00197 *
00198 *     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
00199 *
00200       RESID = SLANSP( '1', UPLO, N, AFAC, RWORK )
00201 *
00202       RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS
00203 *
00204       RETURN
00205 *
00206 *     End of SPPT01
00207 *
00208       END
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