.TH "laic1" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
laic1 \- laic1: condition estimate, step in gelsy
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.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\&. "
.ti -1c
.RI "subroutine \fBdlaic1\fP (job, j, x, sest, w, gamma, sestpr, s, c)"
.br
.RI "\fBDLAIC1\fP applies one step of incremental condition estimation\&. "
.ti -1c
.RI "subroutine \fBslaic1\fP (job, j, x, sest, w, gamma, sestpr, s, c)"
.br
.RI "\fBSLAIC1\fP applies one step of incremental condition estimation\&. "
.ti -1c
.RI "subroutine \fBzlaic1\fP (job, j, x, sest, w, gamma, sestpr, s, c)"
.br
.RI "\fBZLAIC1\fP applies one step of incremental condition estimation\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function 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\&.  
.PP
\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
.PP
.br
\fIJ\fP 
.PP
.nf
!>          J is INTEGER
!>          Length of X and W
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is COMPLEX array, dimension (J)
!>          The j-vector x\&.
!> 
.fi
.PP
.br
\fISEST\fP 
.PP
.nf
!>          SEST is REAL
!>          Estimated singular value of j by j matrix L
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          W is COMPLEX array, dimension (J)
!>          The j-vector w\&.
!> 
.fi
.PP
.br
\fIGAMMA\fP 
.PP
.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 
.PP
.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 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB134\fP of file \fBclaic1\&.f\fP\&.
.SS "subroutine dlaic1 (integer job, integer j, double precision, dimension( j ) x, double precision sest, double precision, dimension( j ) w, double precision gamma, double precision sestpr, double precision s, double precision c)"

.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

.PP
Definition at line \fB133\fP of file \fBdlaic1\&.f\fP\&.
.SS "subroutine slaic1 (integer job, integer j, real, dimension( j ) x, real sest, real, dimension( j ) w, real gamma, real sestpr, real s, real c)"

.PP
\fBSLAIC1\fP applies one step of incremental condition estimation\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SLAIC1 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 SLAIC1 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 REAL array, dimension (J)
!>          The j-vector x\&.
!> 
.fi
.PP
.br
\fISEST\fP 
.PP
.nf
!>          SEST is REAL
!>          Estimated singular value of j by j matrix L
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          W is REAL array, dimension (J)
!>          The j-vector w\&.
!> 
.fi
.PP
.br
\fIGAMMA\fP 
.PP
.nf
!>          GAMMA is REAL
!>          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 
.PP
.nf
!>          S is REAL
!>          Sine needed in forming xhat\&.
!> 
.fi
.PP
.br
\fIC\fP 
.PP
.nf
!>          C is REAL
!>          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

.PP
Definition at line \fB133\fP of file \fBslaic1\&.f\fP\&.
.SS "subroutine zlaic1 (integer job, integer j, complex*16, dimension( j ) x, double precision sest, complex*16, dimension( j ) w, complex*16 gamma, double precision sestpr, complex*16 s, complex*16 c)"

.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

.PP
Definition at line \fB134\fP of file \fBzlaic1\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.