csycon.f.html

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      SUBROUTINE <a name="CSYCON.1"></a><a href="csycon.f.html#CSYCON.1">CSYCON</a>( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
     $                   INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Modified to call <a name="CLACN2.8"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</a> in place of <a name="CLACON.8"></a><a href="clacon.f.html#CLACON.1">CLACON</a>, 10 Feb 03, SJH.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          UPLO
      INTEGER            INFO, LDA, N
      REAL               ANORM, RCOND
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IPIV( * )
      COMPLEX            A( LDA, * ), WORK( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="CSYCON.23"></a><a href="csycon.f.html#CSYCON.1">CSYCON</a> estimates the reciprocal of the condition number (in the
</span><span class="comment">*</span><span class="comment">  1-norm) of a complex symmetric matrix A using the factorization
</span><span class="comment">*</span><span class="comment">  A = U*D*U**T or A = L*D*L**T computed by <a name="CSYTRF.25"></a><a href="csytrf.f.html#CSYTRF.1">CSYTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  An estimate is obtained for norm(inv(A)), and the reciprocal of the
</span><span class="comment">*</span><span class="comment">  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies whether the details of the factorization are stored
</span><span class="comment">*</span><span class="comment">          as an upper or lower triangular matrix.
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangular, form is A = U*D*U**T;
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangular, form is A = L*D*L**T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input) COMPLEX array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          The block diagonal matrix D and the multipliers used to
</span><span class="comment">*</span><span class="comment">          obtain the factor U or L as computed by <a name="CSYTRF.44"></a><a href="csytrf.f.html#CSYTRF.1">CSYTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.  LDA &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IPIV    (input) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment">          Details of the interchanges and the block structure of D
</span><span class="comment">*</span><span class="comment">          as determined by <a name="CSYTRF.51"></a><a href="csytrf.f.html#CSYTRF.1">CSYTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ANORM   (input) REAL
</span><span class="comment">*</span><span class="comment">          The 1-norm of the original matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RCOND   (output) REAL
</span><span class="comment">*</span><span class="comment">          The reciprocal of the condition number of the matrix A,
</span><span class="comment">*</span><span class="comment">          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
</span><span class="comment">*</span><span class="comment">          estimate of the 1-norm of inv(A) computed in this routine.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) COMPLEX array, dimension (2*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            UPPER
      INTEGER            I, KASE
      REAL               AINVNM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      INTEGER            ISAVE( 3 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.82"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.83"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="CLACN2.86"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</a>, <a name="CSYTRS.86"></a><a href="csytrs.f.html#CSYTRS.1">CSYTRS</a>, <a name="XERBLA.86"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      UPPER = <a name="LSAME.96"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.97"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -4
      ELSE IF( ANORM.LT.ZERO ) THEN
         INFO = -6
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.107"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CSYCON.107"></a><a href="csycon.f.html#CSYCON.1">CSYCON</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      RCOND = ZERO
      IF( N.EQ.0 ) THEN
         RCOND = ONE
         RETURN
      ELSE IF( ANORM.LE.ZERO ) THEN
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Check that the diagonal matrix D is nonsingular.
</span><span class="comment">*</span><span class="comment">
</span>      IF( UPPER ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Upper triangular storage: examine D from bottom to top
</span><span class="comment">*</span><span class="comment">
</span>         DO 10 I = N, 1, -1
            IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
     $         RETURN
   10    CONTINUE
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Lower triangular storage: examine D from top to bottom.
</span><span class="comment">*</span><span class="comment">
</span>         DO 20 I = 1, N
            IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
     $         RETURN
   20    CONTINUE
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Estimate the 1-norm of the inverse.
</span><span class="comment">*</span><span class="comment">
</span>      KASE = 0
   30 CONTINUE
      CALL <a name="CLACN2.145"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</a>( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
      IF( KASE.NE.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Multiply by inv(L*D*L') or inv(U*D*U').
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="CSYTRS.150"></a><a href="csytrs.f.html#CSYTRS.1">CSYTRS</a>( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
         GO TO 30
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute the estimate of the reciprocal condition number.
</span><span class="comment">*</span><span class="comment">
</span>      IF( AINVNM.NE.ZERO )
     $   RCOND = ( ONE / AINVNM ) / ANORM
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="CSYCON.161"></a><a href="csycon.f.html#CSYCON.1">CSYCON</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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