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claic1 (3)
  • >> claic1 (3) ( Solaris man: Библиотечные вызовы )
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    NAME
         claic1 - apply one step of incremental condition  estimation
         in its simplest version
    
    SYNOPSIS
         SUBROUTINE CLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
    
         INTEGER J, JOB
    
         REAL SEST, SESTPR
    
         COMPLEX C, GAMMA, S
    
         COMPLEX W( J ), X( J )
    
    
    
         #include <sunperf.h>
    
         void claic1(int job, int j, complex *cx, float sest, complex
                   *w,  complex  *gamma,  float  *sestpr, complex *s,
                   complex *c) ;
    
    PURPOSE
         CLAIC1 applies one step of incremental condition  estimation
         in its simplest version:
    
         Let x, twonorm(x) = 1, be an approximate singular vector  of
         an j-by-j lower triangular matrix L, such that
                  twonorm(L*x) = sest
         Then CLAIC1 computes sestpr, s, c such that
         the vector
                         [ s*x ]
                  xhat = [  c  ]
         is an approximate singular vector of
                         [ L     0  ]
                  Lhat = [ w' gamma ]
         in the sense that
                  twonorm(Lhat*xhat) = sestpr.
    
         Depending on JOB, an estimate for the  largest  or  smallest
         singular value is computed.
    
         Note that [s c]' and sestpr**2 is an eigenpair of the system
    
             diag(sest*sest, 0) + [alpha  gamma] * [ conjg(alpha) ]
                                                   [ conjg(gamma) ]
    
         where  alpha =  conjg(x)'*w.
    
    
    
    ARGUMENTS
         JOB       (input) INTEGER
                   = 1: an estimate for the largest singular value is
                   computed.
                   = 2: an estimate for the smallest  singular  value
                   is computed.
    
         J         (input) INTEGER
                   Length of X and W
    
         X         (input) COMPLEX array, dimension (J)
                   The j-vector x.
    
         SEST      (input) REAL
                   Estimated singular value of j by j matrix L
    
         W         (input) COMPLEX array, dimension (J)
                   The j-vector w.
    
         GAMMA     (input) COMPLEX
                   The diagonal element gamma.
    
         SESTPR    (output) REAL
                   Estimated singular value of (j+1) by (j+1)  matrix
                   Lhat.
    
         S         (output) COMPLEX
                   Sine needed in forming xhat.
    
         C         (output) COMPLEX
                   Cosine needed in forming xhat.
    
    
    
    


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