LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cpbcon.f
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00001 *> \brief \b CPBCON
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CPBCON + 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 CPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
00022 *                          RWORK, INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          UPLO
00026 *       INTEGER            INFO, KD, LDAB, N
00027 *       REAL               ANORM, RCOND
00028 *       ..
00029 *       .. Array Arguments ..
00030 *       REAL               RWORK( * )
00031 *       COMPLEX            AB( LDAB, * ), WORK( * )
00032 *       ..
00033 *  
00034 *
00035 *> \par Purpose:
00036 *  =============
00037 *>
00038 *> \verbatim
00039 *>
00040 *> CPBCON estimates the reciprocal of the condition number (in the
00041 *> 1-norm) of a complex Hermitian positive definite band matrix using
00042 *> the Cholesky factorization A = U**H*U or A = L*L**H computed by
00043 *> CPBTRF.
00044 *>
00045 *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
00046 *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
00047 *> \endverbatim
00048 *
00049 *  Arguments:
00050 *  ==========
00051 *
00052 *> \param[in] UPLO
00053 *> \verbatim
00054 *>          UPLO is CHARACTER*1
00055 *>          = 'U':  Upper triangular factor stored in AB;
00056 *>          = 'L':  Lower triangular factor stored in AB.
00057 *> \endverbatim
00058 *>
00059 *> \param[in] N
00060 *> \verbatim
00061 *>          N is INTEGER
00062 *>          The order of the matrix A.  N >= 0.
00063 *> \endverbatim
00064 *>
00065 *> \param[in] KD
00066 *> \verbatim
00067 *>          KD is INTEGER
00068 *>          The number of superdiagonals of the matrix A if UPLO = 'U',
00069 *>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
00070 *> \endverbatim
00071 *>
00072 *> \param[in] AB
00073 *> \verbatim
00074 *>          AB is COMPLEX array, dimension (LDAB,N)
00075 *>          The triangular factor U or L from the Cholesky factorization
00076 *>          A = U**H*U or A = L*L**H of the band matrix A, stored in the
00077 *>          first KD+1 rows of the array.  The j-th column of U or L is
00078 *>          stored in the j-th column of the array AB as follows:
00079 *>          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
00080 *>          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
00081 *> \endverbatim
00082 *>
00083 *> \param[in] LDAB
00084 *> \verbatim
00085 *>          LDAB is INTEGER
00086 *>          The leading dimension of the array AB.  LDAB >= KD+1.
00087 *> \endverbatim
00088 *>
00089 *> \param[in] ANORM
00090 *> \verbatim
00091 *>          ANORM is REAL
00092 *>          The 1-norm (or infinity-norm) of the Hermitian band matrix A.
00093 *> \endverbatim
00094 *>
00095 *> \param[out] RCOND
00096 *> \verbatim
00097 *>          RCOND is REAL
00098 *>          The reciprocal of the condition number of the matrix A,
00099 *>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
00100 *>          estimate of the 1-norm of inv(A) computed in this routine.
00101 *> \endverbatim
00102 *>
00103 *> \param[out] WORK
00104 *> \verbatim
00105 *>          WORK is COMPLEX array, dimension (2*N)
00106 *> \endverbatim
00107 *>
00108 *> \param[out] RWORK
00109 *> \verbatim
00110 *>          RWORK is REAL array, dimension (N)
00111 *> \endverbatim
00112 *>
00113 *> \param[out] INFO
00114 *> \verbatim
00115 *>          INFO is INTEGER
00116 *>          = 0:  successful exit
00117 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00118 *> \endverbatim
00119 *
00120 *  Authors:
00121 *  ========
00122 *
00123 *> \author Univ. of Tennessee 
00124 *> \author Univ. of California Berkeley 
00125 *> \author Univ. of Colorado Denver 
00126 *> \author NAG Ltd. 
00127 *
00128 *> \date November 2011
00129 *
00130 *> \ingroup complexOTHERcomputational
00131 *
00132 *  =====================================================================
00133       SUBROUTINE CPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
00134      $                   RWORK, INFO )
00135 *
00136 *  -- LAPACK computational routine (version 3.4.0) --
00137 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00138 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00139 *     November 2011
00140 *
00141 *     .. Scalar Arguments ..
00142       CHARACTER          UPLO
00143       INTEGER            INFO, KD, LDAB, N
00144       REAL               ANORM, RCOND
00145 *     ..
00146 *     .. Array Arguments ..
00147       REAL               RWORK( * )
00148       COMPLEX            AB( LDAB, * ), WORK( * )
00149 *     ..
00150 *
00151 *  =====================================================================
00152 *
00153 *     .. Parameters ..
00154       REAL               ONE, ZERO
00155       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00156 *     ..
00157 *     .. Local Scalars ..
00158       LOGICAL            UPPER
00159       CHARACTER          NORMIN
00160       INTEGER            IX, KASE
00161       REAL               AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
00162       COMPLEX            ZDUM
00163 *     ..
00164 *     .. Local Arrays ..
00165       INTEGER            ISAVE( 3 )
00166 *     ..
00167 *     .. External Functions ..
00168       LOGICAL            LSAME
00169       INTEGER            ICAMAX
00170       REAL               SLAMCH
00171       EXTERNAL           LSAME, ICAMAX, SLAMCH
00172 *     ..
00173 *     .. External Subroutines ..
00174       EXTERNAL           CLACN2, CLATBS, CSRSCL, XERBLA
00175 *     ..
00176 *     .. Intrinsic Functions ..
00177       INTRINSIC          ABS, AIMAG, REAL
00178 *     ..
00179 *     .. Statement Functions ..
00180       REAL               CABS1
00181 *     ..
00182 *     .. Statement Function definitions ..
00183       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
00184 *     ..
00185 *     .. Executable Statements ..
00186 *
00187 *     Test the input parameters.
00188 *
00189       INFO = 0
00190       UPPER = LSAME( UPLO, 'U' )
00191       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00192          INFO = -1
00193       ELSE IF( N.LT.0 ) THEN
00194          INFO = -2
00195       ELSE IF( KD.LT.0 ) THEN
00196          INFO = -3
00197       ELSE IF( LDAB.LT.KD+1 ) THEN
00198          INFO = -5
00199       ELSE IF( ANORM.LT.ZERO ) THEN
00200          INFO = -6
00201       END IF
00202       IF( INFO.NE.0 ) THEN
00203          CALL XERBLA( 'CPBCON', -INFO )
00204          RETURN
00205       END IF
00206 *
00207 *     Quick return if possible
00208 *
00209       RCOND = ZERO
00210       IF( N.EQ.0 ) THEN
00211          RCOND = ONE
00212          RETURN
00213       ELSE IF( ANORM.EQ.ZERO ) THEN
00214          RETURN
00215       END IF
00216 *
00217       SMLNUM = SLAMCH( 'Safe minimum' )
00218 *
00219 *     Estimate the 1-norm of the inverse.
00220 *
00221       KASE = 0
00222       NORMIN = 'N'
00223    10 CONTINUE
00224       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00225       IF( KASE.NE.0 ) THEN
00226          IF( UPPER ) THEN
00227 *
00228 *           Multiply by inv(U**H).
00229 *
00230             CALL CLATBS( 'Upper', 'Conjugate transpose', 'Non-unit',
00231      $                   NORMIN, N, KD, AB, LDAB, WORK, SCALEL, RWORK,
00232      $                   INFO )
00233             NORMIN = 'Y'
00234 *
00235 *           Multiply by inv(U).
00236 *
00237             CALL CLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
00238      $                   KD, AB, LDAB, WORK, SCALEU, RWORK, INFO )
00239          ELSE
00240 *
00241 *           Multiply by inv(L).
00242 *
00243             CALL CLATBS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
00244      $                   KD, AB, LDAB, WORK, SCALEL, RWORK, INFO )
00245             NORMIN = 'Y'
00246 *
00247 *           Multiply by inv(L**H).
00248 *
00249             CALL CLATBS( 'Lower', 'Conjugate transpose', 'Non-unit',
00250      $                   NORMIN, N, KD, AB, LDAB, WORK, SCALEU, RWORK,
00251      $                   INFO )
00252          END IF
00253 *
00254 *        Multiply by 1/SCALE if doing so will not cause overflow.
00255 *
00256          SCALE = SCALEL*SCALEU
00257          IF( SCALE.NE.ONE ) THEN
00258             IX = ICAMAX( N, WORK, 1 )
00259             IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
00260      $         GO TO 20
00261             CALL CSRSCL( N, SCALE, WORK, 1 )
00262          END IF
00263          GO TO 10
00264       END IF
00265 *
00266 *     Compute the estimate of the reciprocal condition number.
00267 *
00268       IF( AINVNM.NE.ZERO )
00269      $   RCOND = ( ONE / AINVNM ) / ANORM
00270 *
00271    20 CONTINUE
00272 *
00273       RETURN
00274 *
00275 *     End of CPBCON
00276 *
00277       END
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