1
       2
       3
       4
       5
       6
       7
       8
       9
      10
      11
      12
      13
      14
      15
      16
      17
      18
      19
      20
      21
      22
      23
      24
      25
      26
      27
      28
      29
      30
      31
      32
      33
      34
      35
      36
      37
      38
      39
      40
      41
      42
      43
      44
      45
      46
      47
      48
      49
      50
      51
      52
      53
      54
      55
      56
      57
      58
      59
      60
      61
      62
      63
      64
      65
      66
      67
      68
      69
      70
      71
      72
      73
      74
      75
      76
      77
      78
      79
      80
      81
      82
      83
      84
      85
      86
      87
      88
      89
      90
      91
      92
      93
      94
      95
      96
      97
      98
      99
     100
     101
     102
     103
     104
     105
     106
     107
     108
     109
     110
     111
     112
     113
     114
     115
     116
     117
     118
     119
     120
     121
     122
     123
     124
     125
     126
     127
     128
     129
     130
     131
     132
     133
     134
     135
     136
     137
     138
     139
     140
     141
     142
     143
     144
     145
     146
     147
     148
     149
     150
     151
     152
     153
     154
     155
     156
     157
     158
     159
     160
     161
     162
     163
      SUBROUTINE DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK,
     $                   INFO )
*
*  -- LAPACK routine (version 3.3.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*  -- April 2011                                                      --
*
*     Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, N
      DOUBLE PRECISION   ANORM, RCOND
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * ), IWORK( * )
      DOUBLE PRECISION   AP( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  DSPCON estimates the reciprocal of the condition number (in the
*  1-norm) of a real symmetric packed matrix A using the factorization
*  A = U*D*U**T or A = L*D*L**T computed by DSPTRF.
*
*  An estimate is obtained for norm(inv(A)), and the reciprocal of the
*  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the details of the factorization are stored
*          as an upper or lower triangular matrix.
*          = 'U':  Upper triangular, form is A = U*D*U**T;
*          = 'L':  Lower triangular, form is A = L*D*L**T.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
*          The block diagonal matrix D and the multipliers used to
*          obtain the factor U or L as computed by DSPTRF, stored as a
*          packed triangular matrix.
*
*  IPIV    (input) INTEGER array, dimension (N)
*          Details of the interchanges and the block structure of D
*          as determined by DSPTRF.
*
*  ANORM   (input) DOUBLE PRECISION
*          The 1-norm of the original matrix A.
*
*  RCOND   (output) DOUBLE PRECISION
*          The reciprocal of the condition number of the matrix A,
*          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
*          estimate of the 1-norm of inv(A) computed in this routine.
*
*  WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)
*
*  IWORK   (workspace) INTEGER array, dimension (N)
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, IP, KASE
      DOUBLE PRECISION   AINVNM
*     ..
*     .. Local Arrays ..
      INTEGER            ISAVE( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLACN2, DSPTRS, XERBLA
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      UPPER = LSAME( UPLO, 'U' )
      IF.NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( ANORM.LT.ZERO ) THEN
         INFO = -5
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DSPCON'-INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      RCOND = ZERO
      IF( N.EQ.0 ) THEN
         RCOND = ONE
         RETURN
      ELSE IF( ANORM.LE.ZERO ) THEN
         RETURN
      END IF
*
*     Check that the diagonal matrix D is nonsingular.
*
      IF( UPPER ) THEN
*
*        Upper triangular storage: examine D from bottom to top
*
         IP = N*( N+1 ) / 2
         DO 10 I = N, 1-1
            IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
     $         RETURN
            IP = IP - I
   10    CONTINUE
      ELSE
*
*        Lower triangular storage: examine D from top to bottom.
*
         IP = 1
         DO 20 I = 1, N
            IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
     $         RETURN
            IP = IP + N - I + 1
   20    CONTINUE
      END IF
*
*     Estimate the 1-norm of the inverse.
*
      KASE = 0
   30 CONTINUE
      CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
      IF( KASE.NE.0 ) THEN
*
*        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
*
         CALL DSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
         GO TO 30
      END IF
*
*     Compute the estimate of the reciprocal condition number.
*
      IF( AINVNM.NE.ZERO )
     $   RCOND = ( ONE / AINVNM ) / ANORM
*
      RETURN
*
*     End of DSPCON
*
      END