.TH "zlaic1.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
zlaic1.f \- 
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzlaic1\fP (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)"
.br
.RI "\fI\fBZLAIC1\fP applies one step of incremental condition estimation\&. \fP"
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zlaic1 (integerJOB, integerJ, complex*16, dimension( j )X, double precisionSEST, complex*16, dimension( j )W, complex*16GAMMA, double precisionSESTPR, complex*16S, complex*16C)"

.PP
\fBZLAIC1\fP applies one step of incremental condition estimation\&.  
.PP
\fBPurpose: \fP
.RS 4

.PP
.nf
 ZLAIC1 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 ZLAIC1 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
.PP
.br
\fIJ\fP 
.PP
.nf
          J is INTEGER
          Length of X and W
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is COMPLEX*16 array, dimension (J)
          The j-vector x.
.fi
.PP
.br
\fISEST\fP 
.PP
.nf
          SEST is DOUBLE PRECISION
          Estimated singular value of j by j matrix L
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is COMPLEX*16 array, dimension (J)
          The j-vector w.
.fi
.PP
.br
\fIGAMMA\fP 
.PP
.nf
          GAMMA is COMPLEX*16
          The diagonal element gamma.
.fi
.PP
.br
\fISESTPR\fP 
.PP
.nf
          SESTPR is DOUBLE PRECISION
          Estimated singular value of (j+1) by (j+1) matrix Lhat.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is COMPLEX*16
          Sine needed in forming xhat.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is COMPLEX*16
          Cosine needed in forming xhat.
.fi
.PP
 
.RE
.PP
\fBAuthor:\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBDate:\fP
.RS 4
September 2012 
.RE
.PP

.PP
Definition at line 136 of file zlaic1\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.