.TH "dlaic1.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
dlaic1.f \- 
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdlaic1\fP (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)"
.br
.RI "\fI\fBDLAIC1\fP applies one step of incremental condition estimation\&. \fP"
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dlaic1 (integerJOB, integerJ, double precision, dimension( j )X, double precisionSEST, double precision, dimension( j )W, double precisionGAMMA, double precisionSESTPR, double precisionS, double precisionC)"

.PP
\fBDLAIC1\fP applies one step of incremental condition estimation\&.  
.PP
\fBPurpose: \fP
.RS 4

.PP
.nf
 DLAIC1 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 DLAIC1 computes sestpr, s, c such that
 the vector
                 [ s*x ]
          xhat = [  c  ]
 is an approximate singular vector of
                 [ L       0  ]
          Lhat = [ w**T 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]**T and sestpr**2 is an eigenpair of the system

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

 where  alpha =  x**T*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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (J)
          The j-vector w.
.fi
.PP
.br
\fIGAMMA\fP 
.PP
.nf
          GAMMA is DOUBLE PRECISION
          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 DOUBLE PRECISION
          Sine needed in forming xhat.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION
          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 135 of file dlaic1\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.