.TH "claic1.f" 3 "Tue Nov 14 2017" "Version 3.8.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
claic1.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBclaic1\fP (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)"
.br
.RI "\fBCLAIC1\fP applies one step of incremental condition estimation\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine claic1 (integer JOB, integer J, complex, dimension( j ) X, real SEST, complex, dimension( j ) W, complex GAMMA, real SESTPR, complex S, complex C)"

.PP
\fBCLAIC1\fP applies one step of incremental condition estimation\&.  
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\fBPurpose: \fP
.RS 4

.PP
.nf
 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**H 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]**H and sestpr**2 is an eigenpair of the system

     diag(sest*sest, 0) + [alpha  gamma] * [ conjg(alpha) ]
                                           [ conjg(gamma) ]

 where  alpha =  x**H*w.
.fi
.PP
 
.RE
.PP
\fBParameters:\fP
.RS 4
\fIJOB\fP 
.PP
.nf
          JOB is INTEGER
          = 1: an estimate for the largest singular value is computed.
          = 2: an estimate for the smallest singular value is computed.
.fi
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.br
\fIJ\fP 
.PP
.nf
          J is INTEGER
          Length of X and W
.fi
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.br
\fIX\fP 
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          X is COMPLEX array, dimension (J)
          The j-vector x.
.fi
.PP
.br
\fISEST\fP 
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.nf
          SEST is REAL
          Estimated singular value of j by j matrix L
.fi
.PP
.br
\fIW\fP 
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.nf
          W is COMPLEX array, dimension (J)
          The j-vector w.
.fi
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.br
\fIGAMMA\fP 
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.nf
          GAMMA is COMPLEX
          The diagonal element gamma.
.fi
.PP
.br
\fISESTPR\fP 
.PP
.nf
          SESTPR is REAL
          Estimated singular value of (j+1) by (j+1) matrix Lhat.
.fi
.PP
.br
\fIS\fP 
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.nf
          S is COMPLEX
          Sine needed in forming xhat.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is COMPLEX
          Cosine needed in forming xhat.
.fi
.PP
 
.RE
.PP
\fBAuthor:\fP
.RS 4
Univ\&. of Tennessee 
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Univ\&. of California Berkeley 
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Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
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\fBDate:\fP
.RS 4
December 2016 
.RE
.PP

.PP
Definition at line 137 of file claic1\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.
