LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zppcon.f
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00001 *> \brief \b ZPPCON
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZPPCON + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZPPCON( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          UPLO
00025 *       INTEGER            INFO, N
00026 *       DOUBLE PRECISION   ANORM, RCOND
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       DOUBLE PRECISION   RWORK( * )
00030 *       COMPLEX*16         AP( * ), WORK( * )
00031 *       ..
00032 *  
00033 *
00034 *> \par Purpose:
00035 *  =============
00036 *>
00037 *> \verbatim
00038 *>
00039 *> ZPPCON estimates the reciprocal of the condition number (in the
00040 *> 1-norm) of a complex Hermitian positive definite packed matrix using
00041 *> the Cholesky factorization A = U**H*U or A = L*L**H computed by
00042 *> ZPPTRF.
00043 *>
00044 *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
00045 *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
00046 *> \endverbatim
00047 *
00048 *  Arguments:
00049 *  ==========
00050 *
00051 *> \param[in] UPLO
00052 *> \verbatim
00053 *>          UPLO is CHARACTER*1
00054 *>          = 'U':  Upper triangle of A is stored;
00055 *>          = 'L':  Lower triangle of A is stored.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] N
00059 *> \verbatim
00060 *>          N is INTEGER
00061 *>          The order of the matrix A.  N >= 0.
00062 *> \endverbatim
00063 *>
00064 *> \param[in] AP
00065 *> \verbatim
00066 *>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
00067 *>          The triangular factor U or L from the Cholesky factorization
00068 *>          A = U**H*U or A = L*L**H, packed columnwise in a linear
00069 *>          array.  The j-th column of U or L is stored in the array AP
00070 *>          as follows:
00071 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
00072 *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
00073 *> \endverbatim
00074 *>
00075 *> \param[in] ANORM
00076 *> \verbatim
00077 *>          ANORM is DOUBLE PRECISION
00078 *>          The 1-norm (or infinity-norm) of the Hermitian matrix A.
00079 *> \endverbatim
00080 *>
00081 *> \param[out] RCOND
00082 *> \verbatim
00083 *>          RCOND is DOUBLE PRECISION
00084 *>          The reciprocal of the condition number of the matrix A,
00085 *>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
00086 *>          estimate of the 1-norm of inv(A) computed in this routine.
00087 *> \endverbatim
00088 *>
00089 *> \param[out] WORK
00090 *> \verbatim
00091 *>          WORK is COMPLEX*16 array, dimension (2*N)
00092 *> \endverbatim
00093 *>
00094 *> \param[out] RWORK
00095 *> \verbatim
00096 *>          RWORK is DOUBLE PRECISION array, dimension (N)
00097 *> \endverbatim
00098 *>
00099 *> \param[out] INFO
00100 *> \verbatim
00101 *>          INFO is INTEGER
00102 *>          = 0:  successful exit
00103 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00104 *> \endverbatim
00105 *
00106 *  Authors:
00107 *  ========
00108 *
00109 *> \author Univ. of Tennessee 
00110 *> \author Univ. of California Berkeley 
00111 *> \author Univ. of Colorado Denver 
00112 *> \author NAG Ltd. 
00113 *
00114 *> \date November 2011
00115 *
00116 *> \ingroup complex16OTHERcomputational
00117 *
00118 *  =====================================================================
00119       SUBROUTINE ZPPCON( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
00120 *
00121 *  -- LAPACK computational routine (version 3.4.0) --
00122 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00123 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00124 *     November 2011
00125 *
00126 *     .. Scalar Arguments ..
00127       CHARACTER          UPLO
00128       INTEGER            INFO, N
00129       DOUBLE PRECISION   ANORM, RCOND
00130 *     ..
00131 *     .. Array Arguments ..
00132       DOUBLE PRECISION   RWORK( * )
00133       COMPLEX*16         AP( * ), WORK( * )
00134 *     ..
00135 *
00136 *  =====================================================================
00137 *
00138 *     .. Parameters ..
00139       DOUBLE PRECISION   ONE, ZERO
00140       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00141 *     ..
00142 *     .. Local Scalars ..
00143       LOGICAL            UPPER
00144       CHARACTER          NORMIN
00145       INTEGER            IX, KASE
00146       DOUBLE PRECISION   AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
00147       COMPLEX*16         ZDUM
00148 *     ..
00149 *     .. Local Arrays ..
00150       INTEGER            ISAVE( 3 )
00151 *     ..
00152 *     .. External Functions ..
00153       LOGICAL            LSAME
00154       INTEGER            IZAMAX
00155       DOUBLE PRECISION   DLAMCH
00156       EXTERNAL           LSAME, IZAMAX, DLAMCH
00157 *     ..
00158 *     .. External Subroutines ..
00159       EXTERNAL           XERBLA, ZDRSCL, ZLACN2, ZLATPS
00160 *     ..
00161 *     .. Intrinsic Functions ..
00162       INTRINSIC          ABS, DBLE, DIMAG
00163 *     ..
00164 *     .. Statement Functions ..
00165       DOUBLE PRECISION   CABS1
00166 *     ..
00167 *     .. Statement Function definitions ..
00168       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00169 *     ..
00170 *     .. Executable Statements ..
00171 *
00172 *     Test the input parameters.
00173 *
00174       INFO = 0
00175       UPPER = LSAME( UPLO, 'U' )
00176       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00177          INFO = -1
00178       ELSE IF( N.LT.0 ) THEN
00179          INFO = -2
00180       ELSE IF( ANORM.LT.ZERO ) THEN
00181          INFO = -4
00182       END IF
00183       IF( INFO.NE.0 ) THEN
00184          CALL XERBLA( 'ZPPCON', -INFO )
00185          RETURN
00186       END IF
00187 *
00188 *     Quick return if possible
00189 *
00190       RCOND = ZERO
00191       IF( N.EQ.0 ) THEN
00192          RCOND = ONE
00193          RETURN
00194       ELSE IF( ANORM.EQ.ZERO ) THEN
00195          RETURN
00196       END IF
00197 *
00198       SMLNUM = DLAMCH( 'Safe minimum' )
00199 *
00200 *     Estimate the 1-norm of the inverse.
00201 *
00202       KASE = 0
00203       NORMIN = 'N'
00204    10 CONTINUE
00205       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00206       IF( KASE.NE.0 ) THEN
00207          IF( UPPER ) THEN
00208 *
00209 *           Multiply by inv(U**H).
00210 *
00211             CALL ZLATPS( 'Upper', 'Conjugate transpose', 'Non-unit',
00212      $                   NORMIN, N, AP, WORK, SCALEL, RWORK, INFO )
00213             NORMIN = 'Y'
00214 *
00215 *           Multiply by inv(U).
00216 *
00217             CALL ZLATPS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
00218      $                   AP, WORK, SCALEU, RWORK, INFO )
00219          ELSE
00220 *
00221 *           Multiply by inv(L).
00222 *
00223             CALL ZLATPS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
00224      $                   AP, WORK, SCALEL, RWORK, INFO )
00225             NORMIN = 'Y'
00226 *
00227 *           Multiply by inv(L**H).
00228 *
00229             CALL ZLATPS( 'Lower', 'Conjugate transpose', 'Non-unit',
00230      $                   NORMIN, N, AP, WORK, SCALEU, RWORK, INFO )
00231          END IF
00232 *
00233 *        Multiply by 1/SCALE if doing so will not cause overflow.
00234 *
00235          SCALE = SCALEL*SCALEU
00236          IF( SCALE.NE.ONE ) THEN
00237             IX = IZAMAX( N, WORK, 1 )
00238             IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
00239      $         GO TO 20
00240             CALL ZDRSCL( N, SCALE, WORK, 1 )
00241          END IF
00242          GO TO 10
00243       END IF
00244 *
00245 *     Compute the estimate of the reciprocal condition number.
00246 *
00247       IF( AINVNM.NE.ZERO )
00248      $   RCOND = ( ONE / AINVNM ) / ANORM
00249 *
00250    20 CONTINUE
00251       RETURN
00252 *
00253 *     End of ZPPCON
00254 *
00255       END
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