LAPACK 3.3.1
Linear Algebra PACKage

zhecon.f

Go to the documentation of this file.
00001       SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
00002      $                   INFO )
00003 *
00004 *  -- LAPACK routine (version 3.3.1) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *  -- April 2011                                                      --
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       INTEGER            IPIV( * )
00018       COMPLEX*16         A( LDA, * ), WORK( * )
00019 *     ..
00020 *
00021 *  Purpose
00022 *  =======
00023 *
00024 *  ZHECON estimates the reciprocal of the condition number of a complex
00025 *  Hermitian matrix A using the factorization A = U*D*U**H or
00026 *  A = L*D*L**H computed by ZHETRF.
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 *          Specifies whether the details of the factorization are stored
00036 *          as an upper or lower triangular matrix.
00037 *          = 'U':  Upper triangular, form is A = U*D*U**H;
00038 *          = 'L':  Lower triangular, form is A = L*D*L**H.
00039 *
00040 *  N       (input) INTEGER
00041 *          The order of the matrix A.  N >= 0.
00042 *
00043 *  A       (input) COMPLEX*16 array, dimension (LDA,N)
00044 *          The block diagonal matrix D and the multipliers used to
00045 *          obtain the factor U or L as computed by ZHETRF.
00046 *
00047 *  LDA     (input) INTEGER
00048 *          The leading dimension of the array A.  LDA >= max(1,N).
00049 *
00050 *  IPIV    (input) INTEGER array, dimension (N)
00051 *          Details of the interchanges and the block structure of D
00052 *          as determined by ZHETRF.
00053 *
00054 *  ANORM   (input) DOUBLE PRECISION
00055 *          The 1-norm of the original matrix A.
00056 *
00057 *  RCOND   (output) DOUBLE PRECISION
00058 *          The reciprocal of the condition number of the matrix A,
00059 *          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
00060 *          estimate of the 1-norm of inv(A) computed in this routine.
00061 *
00062 *  WORK    (workspace) COMPLEX*16 array, dimension (2*N)
00063 *
00064 *  INFO    (output) INTEGER
00065 *          = 0:  successful exit
00066 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00067 *
00068 *  =====================================================================
00069 *
00070 *     .. Parameters ..
00071       DOUBLE PRECISION   ONE, ZERO
00072       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00073 *     ..
00074 *     .. Local Scalars ..
00075       LOGICAL            UPPER
00076       INTEGER            I, KASE
00077       DOUBLE PRECISION   AINVNM
00078 *     ..
00079 *     .. Local Arrays ..
00080       INTEGER            ISAVE( 3 )
00081 *     ..
00082 *     .. External Functions ..
00083       LOGICAL            LSAME
00084       EXTERNAL           LSAME
00085 *     ..
00086 *     .. External Subroutines ..
00087       EXTERNAL           XERBLA, ZHETRS, ZLACN2
00088 *     ..
00089 *     .. Intrinsic Functions ..
00090       INTRINSIC          MAX
00091 *     ..
00092 *     .. Executable Statements ..
00093 *
00094 *     Test the input parameters.
00095 *
00096       INFO = 0
00097       UPPER = LSAME( UPLO, 'U' )
00098       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00099          INFO = -1
00100       ELSE IF( N.LT.0 ) THEN
00101          INFO = -2
00102       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00103          INFO = -4
00104       ELSE IF( ANORM.LT.ZERO ) THEN
00105          INFO = -6
00106       END IF
00107       IF( INFO.NE.0 ) THEN
00108          CALL XERBLA( 'ZHECON', -INFO )
00109          RETURN
00110       END IF
00111 *
00112 *     Quick return if possible
00113 *
00114       RCOND = ZERO
00115       IF( N.EQ.0 ) THEN
00116          RCOND = ONE
00117          RETURN
00118       ELSE IF( ANORM.LE.ZERO ) THEN
00119          RETURN
00120       END IF
00121 *
00122 *     Check that the diagonal matrix D is nonsingular.
00123 *
00124       IF( UPPER ) THEN
00125 *
00126 *        Upper triangular storage: examine D from bottom to top
00127 *
00128          DO 10 I = N, 1, -1
00129             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
00130      $         RETURN
00131    10    CONTINUE
00132       ELSE
00133 *
00134 *        Lower triangular storage: examine D from top to bottom.
00135 *
00136          DO 20 I = 1, N
00137             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
00138      $         RETURN
00139    20    CONTINUE
00140       END IF
00141 *
00142 *     Estimate the 1-norm of the inverse.
00143 *
00144       KASE = 0
00145    30 CONTINUE
00146       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00147       IF( KASE.NE.0 ) THEN
00148 *
00149 *        Multiply by inv(L*D*L**H) or inv(U*D*U**H).
00150 *
00151          CALL ZHETRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
00152          GO TO 30
00153       END IF
00154 *
00155 *     Compute the estimate of the reciprocal condition number.
00156 *
00157       IF( AINVNM.NE.ZERO )
00158      $   RCOND = ( ONE / AINVNM ) / ANORM
00159 *
00160       RETURN
00161 *
00162 *     End of ZHECON
00163 *
00164       END
 All Files Functions