LAPACK 3.3.1 Linear Algebra PACKage

# chpcon.f

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00001       SUBROUTINE CHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
00002 *
00003 *  -- LAPACK routine (version 3.3.1) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *  -- April 2011                                                      --
00007 *
00008 *     Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH.
00009 *
00010 *     .. Scalar Arguments ..
00011       CHARACTER          UPLO
00012       INTEGER            INFO, N
00013       REAL               ANORM, RCOND
00014 *     ..
00015 *     .. Array Arguments ..
00016       INTEGER            IPIV( * )
00017       COMPLEX            AP( * ), WORK( * )
00018 *     ..
00019 *
00020 *  Purpose
00021 *  =======
00022 *
00023 *  CHPCON estimates the reciprocal of the condition number of a complex
00024 *  Hermitian packed matrix A using the factorization A = U*D*U**H or
00025 *  A = L*D*L**H computed by CHPTRF.
00026 *
00027 *  An estimate is obtained for norm(inv(A)), and the reciprocal of the
00028 *  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
00029 *
00030 *  Arguments
00031 *  =========
00032 *
00033 *  UPLO    (input) CHARACTER*1
00034 *          Specifies whether the details of the factorization are stored
00035 *          as an upper or lower triangular matrix.
00036 *          = 'U':  Upper triangular, form is A = U*D*U**H;
00037 *          = 'L':  Lower triangular, form is A = L*D*L**H.
00038 *
00039 *  N       (input) INTEGER
00040 *          The order of the matrix A.  N >= 0.
00041 *
00042 *  AP      (input) COMPLEX array, dimension (N*(N+1)/2)
00043 *          The block diagonal matrix D and the multipliers used to
00044 *          obtain the factor U or L as computed by CHPTRF, stored as a
00045 *          packed triangular matrix.
00046 *
00047 *  IPIV    (input) INTEGER array, dimension (N)
00048 *          Details of the interchanges and the block structure of D
00049 *          as determined by CHPTRF.
00050 *
00051 *  ANORM   (input) REAL
00052 *          The 1-norm of the original matrix A.
00053 *
00054 *  RCOND   (output) REAL
00055 *          The reciprocal of the condition number of the matrix A,
00056 *          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
00057 *          estimate of the 1-norm of inv(A) computed in this routine.
00058 *
00059 *  WORK    (workspace) COMPLEX array, dimension (2*N)
00060 *
00061 *  INFO    (output) INTEGER
00062 *          = 0:  successful exit
00063 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00064 *
00065 *  =====================================================================
00066 *
00067 *     .. Parameters ..
00068       REAL               ONE, ZERO
00069       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00070 *     ..
00071 *     .. Local Scalars ..
00072       LOGICAL            UPPER
00073       INTEGER            I, IP, KASE
00074       REAL               AINVNM
00075 *     ..
00076 *     .. Local Arrays ..
00077       INTEGER            ISAVE( 3 )
00078 *     ..
00079 *     .. External Functions ..
00080       LOGICAL            LSAME
00081       EXTERNAL           LSAME
00082 *     ..
00083 *     .. External Subroutines ..
00084       EXTERNAL           CHPTRS, CLACN2, XERBLA
00085 *     ..
00086 *     .. Executable Statements ..
00087 *
00088 *     Test the input parameters.
00089 *
00090       INFO = 0
00091       UPPER = LSAME( UPLO, 'U' )
00092       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00093          INFO = -1
00094       ELSE IF( N.LT.0 ) THEN
00095          INFO = -2
00096       ELSE IF( ANORM.LT.ZERO ) THEN
00097          INFO = -5
00098       END IF
00099       IF( INFO.NE.0 ) THEN
00100          CALL XERBLA( 'CHPCON', -INFO )
00101          RETURN
00102       END IF
00103 *
00104 *     Quick return if possible
00105 *
00106       RCOND = ZERO
00107       IF( N.EQ.0 ) THEN
00108          RCOND = ONE
00109          RETURN
00110       ELSE IF( ANORM.LE.ZERO ) THEN
00111          RETURN
00112       END IF
00113 *
00114 *     Check that the diagonal matrix D is nonsingular.
00115 *
00116       IF( UPPER ) THEN
00117 *
00118 *        Upper triangular storage: examine D from bottom to top
00119 *
00120          IP = N*( N+1 ) / 2
00121          DO 10 I = N, 1, -1
00122             IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
00123      \$         RETURN
00124             IP = IP - I
00125    10    CONTINUE
00126       ELSE
00127 *
00128 *        Lower triangular storage: examine D from top to bottom.
00129 *
00130          IP = 1
00131          DO 20 I = 1, N
00132             IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
00133      \$         RETURN
00134             IP = IP + N - I + 1
00135    20    CONTINUE
00136       END IF
00137 *
00138 *     Estimate the 1-norm of the inverse.
00139 *
00140       KASE = 0
00141    30 CONTINUE
00142       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00143       IF( KASE.NE.0 ) THEN
00144 *
00145 *        Multiply by inv(L*D*L**H) or inv(U*D*U**H).
00146 *
00147          CALL CHPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
00148          GO TO 30
00149       END IF
00150 *
00151 *     Compute the estimate of the reciprocal condition number.
00152 *
00153       IF( AINVNM.NE.ZERO )
00154      \$   RCOND = ( ONE / AINVNM ) / ANORM
00155 *
00156       RETURN
00157 *
00158 *     End of CHPCON
00159 *
00160       END