public interface laic1
LAIC1 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(Lx) = sest
Then LAIC1 computes sestpr, s, c such that
the vector
[ sx ]
xhat = [ c ]
is an approximate singular vector of
[ L 0 ]
Lhat = [ wH 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 sestpr2 is an eigenpair of the system
diag(sest*sest, 0) + [alpha gamma] * [ conjg(alpha) ]
[ conjg(gamma) ]
where alpha = xH*w.
Subroutines
Arguments
| Type |
Intent | Optional | Attributes |
|
Name |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
job |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
j |
|
|
complex(kind=sp),
|
intent(in) |
|
|
:: |
x(j) |
|
|
real(kind=sp),
|
intent(in) |
|
|
:: |
sest |
|
|
complex(kind=sp),
|
intent(in) |
|
|
:: |
w(j) |
|
|
complex(kind=sp),
|
intent(in) |
|
|
:: |
gamma |
|
|
real(kind=sp),
|
intent(out) |
|
|
:: |
sestpr |
|
|
complex(kind=sp),
|
intent(out) |
|
|
:: |
s |
|
|
complex(kind=sp),
|
intent(out) |
|
|
:: |
c |
|
Arguments
| Type |
Intent | Optional | Attributes |
|
Name |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
job |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
j |
|
|
real(kind=dp),
|
intent(in) |
|
|
:: |
x(j) |
|
|
real(kind=dp),
|
intent(in) |
|
|
:: |
sest |
|
|
real(kind=dp),
|
intent(in) |
|
|
:: |
w(j) |
|
|
real(kind=dp),
|
intent(in) |
|
|
:: |
gamma |
|
|
real(kind=dp),
|
intent(out) |
|
|
:: |
sestpr |
|
|
real(kind=dp),
|
intent(out) |
|
|
:: |
s |
|
|
real(kind=dp),
|
intent(out) |
|
|
:: |
c |
|
Arguments
| Type |
Intent | Optional | Attributes |
|
Name |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
job |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
j |
|
|
real(kind=sp),
|
intent(in) |
|
|
:: |
x(j) |
|
|
real(kind=sp),
|
intent(in) |
|
|
:: |
sest |
|
|
real(kind=sp),
|
intent(in) |
|
|
:: |
w(j) |
|
|
real(kind=sp),
|
intent(in) |
|
|
:: |
gamma |
|
|
real(kind=sp),
|
intent(out) |
|
|
:: |
sestpr |
|
|
real(kind=sp),
|
intent(out) |
|
|
:: |
s |
|
|
real(kind=sp),
|
intent(out) |
|
|
:: |
c |
|
Arguments
| Type |
Intent | Optional | Attributes |
|
Name |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
job |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
j |
|
|
complex(kind=dp),
|
intent(in) |
|
|
:: |
x(j) |
|
|
real(kind=dp),
|
intent(in) |
|
|
:: |
sest |
|
|
complex(kind=dp),
|
intent(in) |
|
|
:: |
w(j) |
|
|
complex(kind=dp),
|
intent(in) |
|
|
:: |
gamma |
|
|
real(kind=dp),
|
intent(out) |
|
|
:: |
sestpr |
|
|
complex(kind=dp),
|
intent(out) |
|
|
:: |
s |
|
|
complex(kind=dp),
|
intent(out) |
|
|
:: |
c |
|
Module Procedures