# claic1.f(3) [centos man page]

```claic1.f(3)							      LAPACK							       claic1.f(3)

NAME
claic1.f -

SYNOPSIS
Functions/Subroutines
subroutine claic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
CLAIC1 applies one step of incremental condition estimation.

Function/Subroutine Documentation
subroutine claic1 (integerJOB, integerJ, complex, dimension( j )X, realSEST, complex, dimension( j )W, complexGAMMA, realSESTPR, complexS,
complexC)
CLAIC1 applies one step of incremental condition estimation.

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.

Parameters:
JOB

JOB is INTEGER
= 1: an estimate for the largest singular value is computed.
= 2: an estimate for the smallest singular value is computed.

J

J is INTEGER
Length of X and W

X

X is COMPLEX array, dimension (J)
The j-vector x.

SEST

SEST is REAL
Estimated singular value of j by j matrix L

W

W is COMPLEX array, dimension (J)
The j-vector w.

GAMMA

GAMMA is COMPLEX
The diagonal element gamma.

SESTPR

SESTPR is REAL
Estimated singular value of (j+1) by (j+1) matrix Lhat.

S

S is COMPLEX
Sine needed in forming xhat.

C

C is COMPLEX
Cosine needed in forming xhat.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
September 2012

Definition at line 136 of file claic1.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       claic1.f(3)```

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```slaic1.f(3)							      LAPACK							       slaic1.f(3)

NAME
slaic1.f -

SYNOPSIS
Functions/Subroutines
subroutine slaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
SLAIC1 applies one step of incremental condition estimation.

Function/Subroutine Documentation
subroutine slaic1 (integerJOB, integerJ, real, dimension( j )X, realSEST, real, dimension( j )W, realGAMMA, realSESTPR, realS, realC)
SLAIC1 applies one step of incremental condition estimation.

Purpose:

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.

Parameters:
JOB

JOB is INTEGER
= 1: an estimate for the largest singular value is computed.
= 2: an estimate for the smallest singular value is computed.

J

J is INTEGER
Length of X and W

X

X is REAL array, dimension (J)
The j-vector x.

SEST

SEST is REAL
Estimated singular value of j by j matrix L

W

W is REAL array, dimension (J)
The j-vector w.

GAMMA

GAMMA is REAL
The diagonal element gamma.

SESTPR

SESTPR is REAL
Estimated singular value of (j+1) by (j+1) matrix Lhat.

S

S is REAL
Sine needed in forming xhat.

C

C is REAL
Cosine needed in forming xhat.

Author:
Univ. of Tennessee

Univ. of California Berkeley