table of contents
| laic1(3) | LAPACK | laic1(3) |
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, real sest, 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, double precision gamma, double precision sestpr, double precision s, double precision 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, real sest, 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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