LAPACK 3.3.0

dsyt01.f

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00001       SUBROUTINE DSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
00002      $                   RWORK, 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, LDAFAC, LDC, N
00011       DOUBLE PRECISION   RESID
00012 *     ..
00013 *     .. Array Arguments ..
00014       INTEGER            IPIV( * )
00015       DOUBLE PRECISION   A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
00016      $                   RWORK( * )
00017 *     ..
00018 *
00019 *  Purpose
00020 *  =======
00021 *
00022 *  DSYT01 reconstructs a symmetric indefinite matrix A from its
00023 *  block L*D*L' or U*D*U' factorization and computes the residual
00024 *     norm( C - A ) / ( N * norm(A) * EPS ),
00025 *  where C is the reconstructed matrix and EPS is the machine epsilon.
00026 *
00027 *  Arguments
00028 *  ==========
00029 *
00030 *  UPLO    (input) CHARACTER*1
00031 *          Specifies whether the upper or lower triangular part of the
00032 *          symmetric matrix A is stored:
00033 *          = 'U':  Upper triangular
00034 *          = 'L':  Lower triangular
00035 *
00036 *  N       (input) INTEGER
00037 *          The number of rows and columns of the matrix A.  N >= 0.
00038 *
00039 *  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
00040 *          The original symmetric matrix A.
00041 *
00042 *  LDA     (input) INTEGER
00043 *          The leading dimension of the array A.  LDA >= max(1,N)
00044 *
00045 *  AFAC    (input) DOUBLE PRECISION array, dimension (LDAFAC,N)
00046 *          The factored form of the matrix A.  AFAC contains the block
00047 *          diagonal matrix D and the multipliers used to obtain the
00048 *          factor L or U from the block L*D*L' or U*D*U' factorization
00049 *          as computed by DSYTRF.
00050 *
00051 *  LDAFAC  (input) INTEGER
00052 *          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
00053 *
00054 *  IPIV    (input) INTEGER array, dimension (N)
00055 *          The pivot indices from DSYTRF.
00056 *
00057 *  C       (workspace) DOUBLE PRECISION array, dimension (LDC,N)
00058 *
00059 *  LDC     (integer) INTEGER
00060 *          The leading dimension of the array C.  LDC >= max(1,N).
00061 *
00062 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
00063 *
00064 *  RESID   (output) DOUBLE PRECISION
00065 *          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
00066 *          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
00067 *
00068 *  =====================================================================
00069 *
00070 *     .. Parameters ..
00071       DOUBLE PRECISION   ZERO, ONE
00072       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00073 *     ..
00074 *     .. Local Scalars ..
00075       INTEGER            I, INFO, J
00076       DOUBLE PRECISION   ANORM, EPS
00077 *     ..
00078 *     .. External Functions ..
00079       LOGICAL            LSAME
00080       DOUBLE PRECISION   DLAMCH, DLANSY
00081       EXTERNAL           LSAME, DLAMCH, DLANSY
00082 *     ..
00083 *     .. External Subroutines ..
00084       EXTERNAL           DLASET, DLAVSY
00085 *     ..
00086 *     .. Intrinsic Functions ..
00087       INTRINSIC          DBLE
00088 *     ..
00089 *     .. Executable Statements ..
00090 *
00091 *     Quick exit if N = 0.
00092 *
00093       IF( N.LE.0 ) THEN
00094          RESID = ZERO
00095          RETURN
00096       END IF
00097 *
00098 *     Determine EPS and the norm of A.
00099 *
00100       EPS = DLAMCH( 'Epsilon' )
00101       ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
00102 *
00103 *     Initialize C to the identity matrix.
00104 *
00105       CALL DLASET( 'Full', N, N, ZERO, ONE, C, LDC )
00106 *
00107 *     Call DLAVSY to form the product D * U' (or D * L' ).
00108 *
00109       CALL DLAVSY( UPLO, 'Transpose', 'Non-unit', N, N, AFAC, LDAFAC,
00110      $             IPIV, C, LDC, INFO )
00111 *
00112 *     Call DLAVSY again to multiply by U (or L ).
00113 *
00114       CALL DLAVSY( UPLO, 'No transpose', 'Unit', N, N, AFAC, LDAFAC,
00115      $             IPIV, C, LDC, INFO )
00116 *
00117 *     Compute the difference  C - A .
00118 *
00119       IF( LSAME( UPLO, 'U' ) ) THEN
00120          DO 20 J = 1, N
00121             DO 10 I = 1, J
00122                C( I, J ) = C( I, J ) - A( I, J )
00123    10       CONTINUE
00124    20    CONTINUE
00125       ELSE
00126          DO 40 J = 1, N
00127             DO 30 I = J, N
00128                C( I, J ) = C( I, J ) - A( I, J )
00129    30       CONTINUE
00130    40    CONTINUE
00131       END IF
00132 *
00133 *     Compute norm( C - A ) / ( N * norm(A) * EPS )
00134 *
00135       RESID = DLANSY( '1', UPLO, N, C, LDC, RWORK )
00136 *
00137       IF( ANORM.LE.ZERO ) THEN
00138          IF( RESID.NE.ZERO )
00139      $      RESID = ONE / EPS
00140       ELSE
00141          RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
00142       END IF
00143 *
00144       RETURN
00145 *
00146 *     End of DSYT01
00147 *
00148       END
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