dlaic1.f(3) [centos man page]

```dlaic1.f(3)							      LAPACK							       dlaic1.f(3)

NAME
dlaic1.f -

SYNOPSIS
Functions/Subroutines
subroutine dlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
DLAIC1 applies one step of incremental condition estimation.

Function/Subroutine Documentation
subroutine dlaic1 (integerJOB, integerJ, double precision, dimension( j )X, double precisionSEST, double precision, dimension( j )W, double
precisionGAMMA, double precisionSESTPR, double precisionS, double precisionC)
DLAIC1 applies one step of incremental condition estimation.

Purpose:

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.

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 DOUBLE PRECISION array, dimension (J)
The j-vector x.

SEST

SEST is DOUBLE PRECISION
Estimated singular value of j by j matrix L

W

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

GAMMA

GAMMA is DOUBLE PRECISION
The diagonal element gamma.

SESTPR

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

S

S is DOUBLE PRECISION
Sine needed in forming xhat.

C

C is DOUBLE PRECISION
Cosine needed in forming xhat.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
September 2012

Definition at line 135 of file dlaic1.f.

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

Version 3.4.2							  Tue Sep 25 2012						       dlaic1.f(3)```

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```zlaic1.f(3)							      LAPACK							       zlaic1.f(3)

NAME
zlaic1.f -

SYNOPSIS
Functions/Subroutines
subroutine zlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
ZLAIC1 applies one step of incremental condition estimation.

Function/Subroutine Documentation
subroutine zlaic1 (integerJOB, integerJ, complex*16, dimension( j )X, double precisionSEST, complex*16, dimension( j )W, complex*16GAMMA,
double precisionSESTPR, complex*16S, complex*16C)
ZLAIC1 applies one step of incremental condition estimation.

Purpose:

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.

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*16 array, dimension (J)
The j-vector x.

SEST

SEST is DOUBLE PRECISION
Estimated singular value of j by j matrix L

W

W is COMPLEX*16 array, dimension (J)
The j-vector w.

GAMMA

GAMMA is COMPLEX*16
The diagonal element gamma.

SESTPR

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

S

S is COMPLEX*16
Sine needed in forming xhat.

C

C is COMPLEX*16
Cosine needed in forming xhat.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
September 2012

Definition at line 136 of file zlaic1.f.

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

Version 3.4.2							  Tue Sep 25 2012						       zlaic1.f(3)```
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