Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3 - applies 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 )

```

#### 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**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.

```

#### 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.

LAPACK auxiliary routine (version 3.3.1)   April 2011                            CLAIC1(3lapack)
```