Man page - laic1(3)

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Manual

laic1

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine claic1 (integer job, integer j, complex, dimension( j ) x, realsest, complex, dimension( j ) w, complex gamma, real sestpr, complex s,complex c)
subroutine dlaic1 (integer job, integer j, double precision, dimension( j )x, double precision sest, double precision, dimension( j ) w, doubleprecision gamma, double precision sestpr, double precision s, doubleprecision c)
subroutine slaic1 (integer job, integer j, real, dimension( j ) x, realsest, real, dimension( j ) w, real gamma, real sestpr, real s, real c)
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)
Author

NAME

laic1 - laic1: condition estimate, step in gelsy

SYNOPSIS

Functions

subroutine claic1 (job, j, x, sest, w, gamma, sestpr, s, c)
CLAIC1 applies one step of incremental condition estimation.
subroutine dlaic1 (job, j, x, sest, w, gamma, sestpr, s, c)
DLAIC1 applies one step of incremental condition estimation.
subroutine slaic1 (job, j, x, sest, w, gamma, sestpr, s, c)
SLAIC1 applies one step of incremental condition estimation.
subroutine zlaic1 (job, j, x, sest, w, gamma, sestpr, s, c)
ZLAIC1 applies one step of incremental condition estimation.

Detailed Description

Function Documentation

subroutine claic1 (integer job, integer j, complex, dimension( j ) x, realsest, complex, dimension( j ) w, complex gamma, real sestpr, complex s,complex c)

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

Univ. of Colorado Denver

NAG Ltd.

subroutine dlaic1 (integer job, integer j, double precision, dimension( j )x, double precision sest, double precision, dimension( j ) w, doubleprecision gamma, double precision sestpr, double precision s, doubleprecision c)

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

Univ. of Colorado Denver

NAG Ltd.

subroutine slaic1 (integer job, integer j, real, dimension( j ) x, realsest, real, dimension( j ) w, real gamma, real sestpr, real s, real c)

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

Univ. of Colorado Denver

NAG Ltd.

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)

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

Univ. of Colorado Denver

NAG Ltd.

Author

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