LAPACK: SRC/zpocon.f Source File

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00001       SUBROUTINE ZPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK,
00002      $                   INFO )
00003 *
00004 *  -- LAPACK routine (version 3.2) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *     November 2006
00008 *
00009 *     Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
00010 *
00011 *     .. Scalar Arguments ..
00012       CHARACTER          UPLO
00013       INTEGER            INFO, LDA, N
00014       DOUBLE PRECISION   ANORM, RCOND
00015 *     ..
00016 *     .. Array Arguments ..
00017       DOUBLE PRECISION   RWORK( * )
00018       COMPLEX*16         A( LDA, * ), WORK( * )
00019 *     ..
00020 *
00021 *  Purpose
00022 *  =======
00023 *
00024 *  ZPOCON estimates the reciprocal of the condition number (in the
00025 *  1-norm) of a complex Hermitian positive definite matrix using the
00026 *  Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.
00027 *
00028 *  An estimate is obtained for norm(inv(A)), and the reciprocal of the
00029 *  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
00030 *
00031 *  Arguments
00032 *  =========
00033 *
00034 *  UPLO    (input) CHARACTER*1
00035 *          = 'U':  Upper triangle of A is stored;
00036 *          = 'L':  Lower triangle of A is stored.
00037 *
00038 *  N       (input) INTEGER
00039 *          The order of the matrix A.  N >= 0.
00040 *
00041 *  A       (input) COMPLEX*16 array, dimension (LDA,N)
00042 *          The triangular factor U or L from the Cholesky factorization
00043 *          A = U**H*U or A = L*L**H, as computed by ZPOTRF.
00044 *
00045 *  LDA     (input) INTEGER
00046 *          The leading dimension of the array A.  LDA >= max(1,N).
00047 *
00048 *  ANORM   (input) DOUBLE PRECISION
00049 *          The 1-norm (or infinity-norm) of the Hermitian matrix A.
00050 *
00051 *  RCOND   (output) DOUBLE PRECISION
00052 *          The reciprocal of the condition number of the matrix A,
00053 *          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
00054 *          estimate of the 1-norm of inv(A) computed in this routine.
00055 *
00056 *  WORK    (workspace) COMPLEX*16 array, dimension (2*N)
00057 *
00058 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
00059 *
00060 *  INFO    (output) INTEGER
00061 *          = 0:  successful exit
00062 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00063 *
00064 *  =====================================================================
00065 *
00066 *     .. Parameters ..
00067       DOUBLE PRECISION   ONE, ZERO
00068       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00069 *     ..
00070 *     .. Local Scalars ..
00071       LOGICAL            UPPER
00072       CHARACTER          NORMIN
00073       INTEGER            IX, KASE
00074       DOUBLE PRECISION   AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
00075       COMPLEX*16         ZDUM
00076 *     ..
00077 *     .. Local Arrays ..
00078       INTEGER            ISAVE( 3 )
00079 *     ..
00080 *     .. External Functions ..
00081       LOGICAL            LSAME
00082       INTEGER            IZAMAX
00083       DOUBLE PRECISION   DLAMCH
00084       EXTERNAL           LSAME, IZAMAX, DLAMCH
00085 *     ..
00086 *     .. External Subroutines ..
00087       EXTERNAL           XERBLA, ZDRSCL, ZLACN2, ZLATRS
00088 *     ..
00089 *     .. Intrinsic Functions ..
00090       INTRINSIC          ABS, DBLE, DIMAG, MAX
00091 *     ..
00092 *     .. Statement Functions ..
00093       DOUBLE PRECISION   CABS1
00094 *     ..
00095 *     .. Statement Function definitions ..
00096       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00097 *     ..
00098 *     .. Executable Statements ..
00099 *
00100 *     Test the input parameters.
00101 *
00102       INFO = 0
00103       UPPER = LSAME( UPLO, 'U' )
00104       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00105          INFO = -1
00106       ELSE IF( N.LT.0 ) THEN
00107          INFO = -2
00108       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00109          INFO = -4
00110       ELSE IF( ANORM.LT.ZERO ) THEN
00111          INFO = -5
00112       END IF
00113       IF( INFO.NE.0 ) THEN
00114          CALL XERBLA( 'ZPOCON', -INFO )
00115          RETURN
00116       END IF
00117 *
00118 *     Quick return if possible
00119 *
00120       RCOND = ZERO
00121       IF( N.EQ.0 ) THEN
00122          RCOND = ONE
00123          RETURN
00124       ELSE IF( ANORM.EQ.ZERO ) THEN
00125          RETURN
00126       END IF
00127 *
00128       SMLNUM = DLAMCH( 'Safe minimum' )
00129 *
00130 *     Estimate the 1-norm of inv(A).
00131 *
00132       KASE = 0
00133       NORMIN = 'N'
00134    10 CONTINUE
00135       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00136       IF( KASE.NE.0 ) THEN
00137          IF( UPPER ) THEN
00138 *
00139 *           Multiply by inv(U').
00140 *
00141             CALL ZLATRS( 'Upper', 'Conjugate transpose', 'Non-unit',
00142      $                   NORMIN, N, A, LDA, WORK, SCALEL, RWORK, INFO )
00143             NORMIN = 'Y'
00144 *
00145 *           Multiply by inv(U).
00146 *
00147             CALL ZLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
00148      $                   A, LDA, WORK, SCALEU, RWORK, INFO )
00149          ELSE
00150 *
00151 *           Multiply by inv(L).
00152 *
00153             CALL ZLATRS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
00154      $                   A, LDA, WORK, SCALEL, RWORK, INFO )
00155             NORMIN = 'Y'
00156 *
00157 *           Multiply by inv(L').
00158 *
00159             CALL ZLATRS( 'Lower', 'Conjugate transpose', 'Non-unit',
00160      $                   NORMIN, N, A, LDA, WORK, SCALEU, RWORK, INFO )
00161          END IF
00162 *
00163 *        Multiply by 1/SCALE if doing so will not cause overflow.
00164 *
00165          SCALE = SCALEL*SCALEU
00166          IF( SCALE.NE.ONE ) THEN
00167             IX = IZAMAX( N, WORK, 1 )
00168             IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
00169      $         GO TO 20
00170             CALL ZDRSCL( N, SCALE, WORK, 1 )
00171          END IF
00172          GO TO 10
00173       END IF
00174 *
00175 *     Compute the estimate of the reciprocal condition number.
00176 *
00177       IF( AINVNM.NE.ZERO )
00178      $   RCOND = ( ONE / AINVNM ) / ANORM
00179 *
00180    20 CONTINUE
00181       RETURN
00182 *
00183 *     End of ZPOCON
00184 *
00185       END