APPLICATION OF DETECTION FILTER THEORY TO
LONGITUDINAL CONTROL OF GUIDEWAY VEHICLES
by
Jean-Pierre Augustin Gerard
Ingenieur, Ecole Centrale de Paris
(1977)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June, 1978
Signature of Author
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Aeronautics and Astronautics
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2
APPLICATION OF DETECTION FILTER THEORY TO
LONGITUDINAL CONTROL OF GUIDEWAY VEHICLES
by
Jean-Pierre Augustin Gerard
Submitted to the Department of
Aeronautics and Astronautics on June 30, 1978
in partial fulfillment of the requirements for
the degree of Master of Science
ABSTRACT
This paper recalls briefly the main results of the
detection filter theory, which, through sophisticated data
processing, allows in certain circumstances to detect and
identify component failures in a system, by assigning unidirectional or bidirectional error outputs to each failure.
The algorithm of a computer program developed to help the
design of a detection filter is then detailed. An application of it in the content of longitudinal control of a
guideway vehicle was then made to investigate what practical
results could be expected.
Thesis Supervisor:
Title:
Wallace E. VanderVelde
Professor of
Aeronautics and
Astronautics
3
ACKNOWLEDGEMENT
I want to express my gratitude to Professor W.E.
VanderVelde for his guidance and good advice all along
during this study.
tion.
I enjoyed working under his direc-
Special thanks go to Michael Dyment, a fellow
graduate student, who did not hesitate to work long hours
before he left to make sure that the interface between
his guideway vehicle simulation program and a reference
model program worked, and that I understood how to use
it.
Last, but not least, I thank Mrs. Barbara Marks for
her patience in the typing of my difficult manuscript.
My financial support was a fellowship of Jean Gaillard
Memorial Foundation during the school year, and a research
assistantship in June.
4
TABLE OF CONTENTS
Page No.
Chapter No.
1
Introduction
5
2
Theoretical Background
8
3
Detection Filter Design Algorithm
22
4
Guideway Vehicle Simulation and
Detection Filter Design
43
5
Experimental Results
68
6
Conclusions
85
Appendices
A
Listing of Detection Filter Design
Program
A-1
B
Listing of Longitudinal Guideway
Vehicle Simulation
B-1
C
A Problem Met in Detection Filter
Design
C-1
D
Orthogonal Reduction Procedure
D-1
References
86
5
CHAPTER
1
INTRODUCTION
With the decreasing price trend in computation capability
and the increasing price trend in hardware components, it will
make more and more economic sense to try to achieve high levels
of reliability in control systems with less redundancy in
material parts, at the expense of more computation.
Thus, even
on guideway vehicles where weight is not a dominant problem,
sophisticated data processing can be envisioned as a way to
achieve the required reliability of the longitudinal control
system.
For a complex system without any redundancy, a failure in
any element entails a failure of the whole system.
Redundancy,
on the contrary, allows certain component failures without preventing the system as a whole to function.
One of the simplest
kinds of redundancy is what might be called "standby redundancy."
Two or more components which perform the same functions are
set in parallel, and in case of failure of the operating component, the system switches to the backup one.
The problem is
to know which component of the chain is faulting, when the system as a whole fails.
This can be done by majority rule with
three components in parallel.
A detection filter, under certain
circumstances, can detect which component is faulting and requires then only two components in parallel.
There are some
other advantages in the use of detection filters, not discussed
6
in this paper, such as their use as suboptimal filters which
could provide partial state estimation for failed systems.
The detection filter theory was first presented by Beard
(ref. 1) and was further developed by Jones (ref. 2).
This
study was made to investigate whether detection filters would
be of practical value in longitudinal control of guideway
vehicles:
detection filter theory assumes a linear time in-
variant model, which is not the case for a guideway vehicle,
subjected to nonlinear forces such as the aerodynamic force.
Furthermore, some inputs of the real system would be difficult
to indicate, such as the grade of the track, and some components of the control system would be noisy.
To assess the
relative values of these effects compared to the effects of
failures in the system, a simulation of a representative vehicle
was set up and tests were made to evaluate the practical value
of a detection filter processing the difference between a real
system output and a simplified linearized reference model output.
The detection filter was designed with a computer program
which was developed, applying algorithms derived from reference 2.
Chapter 2 recalls the theoretical results necessary to
understand the application, chapter 3 details the algorithm of
the detection filter design program, chapter 4 presents the
guideway vehicle simulation, the reference model for the detection filter, and the detection filter which was computed,
chapter 5 gives the experimental results, and chapter 6 states
the conclusions.
Appendix A gives the listing of the detection
filter design program, Appendix B the listing of the guideway
vehicle simulation together with the reference model simulation, Appendix C presents some problems met in the practical
design, and Appendix D the orthogonal reduction procedure used
repeatedly in the algorithm.
8
CHAPTER
2
THEORETICAL BACKGROUND
The concept of the detection filter was first presented by
Beard (ref. 1) and was further explored by Jones (ref. 2).
a brief summary is given here.
Only
The aim of this chapter is just
to present the results necessary to understand the application;
for more details see reference 1 and reference 2.
The detection filter theory assumes that the plant dynamics
can be represented by a linear, time invariant set of differential equations.
Let x be the state vector (n dimensioned)
u be the input vector (q dimensioned)
y be the output vector On dimensioned)
The system equations are
x =Ax
+ B u
y=c 5
where
A is a n x n matrix
B is a n x q matrix
C is a m x n matrix
From the comparison between y, the output of the system
measured by means of sensors, and
m, the output of a simula-
tion run in parallel (real time) with the system, with the
same equations, A, B, C having their unfailed values, the detection filter theory allows to detect which component of the
9
system has failed, under certain circumstances.
The general reference model is the following:
f)
General Reference Model
x
Equations are
A x+B u
y =Cx
x(O) given
Xm
x + Bm-u + D(y - y
in = Amin-m
-in )
K
= C
Yi
i
(x (0) is necessary
x (O) given
--m
to start the simulation,
but as (A - DC)
is designed to have no positive real part eigenvalues, x (0)
does not need to be equal to x(O) for x(t) and x (t) to be equal
in steady state).
---in
In the absence of failure A - A
m
B
Introducing the error vector
- x
x - x
-
=
(A -
DC)
-i
- DC (x -m)
(0) = x(0) -
Cm - C.
we have
= A(x - x ) - D(y - ym )
= A(x - x)
c
= x
B
m
m(0)
10
The output error E
Y-mthen follows the equation
In the event of a failure in the physical system, some
values of parameters in A, B, C change (may become time varying).
The usefulness of the detection filter theory comes from
the fact that very often failures can bemodelized according to
one of the two following ways:
- controller failure model
x = A x + B u + bi ni(t)
y= C x
- sensor failure model
x =Ax
+ B u
y = C x + em' nci(t)
where bi and em i are two time-invarying vectors, even if the
failures introduce time variations in the matrices.
Example
Consider the simple case below
AL:5
____
__
_n
Equation
Using the phase variable x
equations
2
= z, x2 = z, we have the state
11
(4)
'
(1
y (
<;
d)X1)
)()2)
If K 1 fails and becomes K1
x =
x + B u +
1) (k1 (t)
in this case b
-
1
*
kl(t), the model becomes
1)
= /
v
1
K1
)
U
n i(t)
= [kl (t) - 1] K 1 u
If K 2 fails and becomes K 2 · k 2 (t), the model becomes
x
= Ax
+ B u
y = C x + ()
(K2)
=
In this case em
[k2 (t) - 1] x1
1
nci(t) = K 2
1
[k2(t) - 1] x 1
- -=
In case of failure, the error differential equations become then:
- controller failure model _
+ b.
i n i (t)
= (A - DC)
sensor
(Afailure
DC) model d
sensor failure model
=
(A-DC)
C
+e
-
(t)
nc (t)
nc (t)
where d. is the ith column of the matrix D.
The detection filter theory allows the detection of the
faulting component of a system because of three features:
under certain circumstances, it allows to find a D such that:
12
a -
eigenvalues of A - DC can be almost arbitrarily assignable
b -
outputs associated with a bi (controller failure model)
can be constrained to be unidirectional
c -
outputs associated with a nci (sensor failure model) can be
constrained to a plane.
More precisely: definition (Beard)
The event associated with the vector b is detectable if
there exists a matrix D such that
(1) C E maintains a fixed direction in the output space, where
£ (t) is
the settled out solution
(2) at the same time all eigenvalues of A - DC can be specified
almost arbitrarily.
It can be shown that the solution to
£=
(A - DC) e + b n(t)
with A - DC matrix negative definite is, after the vanishing of
the transient terms
and this solution lies in the space spanned by the columns of
Wb = [b, (A - DC) b,...,
That is to say,
_
(A - DC)
b] .
may be expressed in the form
6(t) = Wb (t)
(t) depending
on n(t)
Then
C (t)
= C W
(t)
Beard showed that condition (1) of the definition is
equivalent to the fact that C Wb has rank 1.
The most useful property of direction filters, however, is
13
their property, under certain circumstances, to detect without
ambiguity several failures at a time.
If there are n independent
sensors in a n-order plant, it seems intuitive, and it can be
shown, that no ambiguity is left in monitoring failures of the
plant.
If there is only one sensor, on the contrary, it seems
obvious that no discrimination between eventual failures can
be performed.
The following concepts are necessary to under-
stand how the case where there are less than n independent sensors
is handled.
O
null space:
the null space of an operator A is the largest sub-
space of the space where A is defined, whose image under A is
the zero space.
o
It is denoted
(A).
detection equivalent events (Jones)
Two events bl and b2 associated with failures in a system
are said to be detection equivalent if
(a) every detection
filter for b1 is a detection
filter
for b2
(b) the unidirectional output error generated by the failure
associated with b2 is in the same output direction as that
associated with b1 .
o
detection space of an event
The detection space of bl contains all events which are detection equivalent to b 1 .
(a)
Vector space definition (Jones).
Let bl be an event vector associated with a failure.
that C b1
~
0.
the direct sum
Assume
Detection space for b1 is denoted by R1 and is
14
R1 = -
where R 1 C Rn is the largest subspace
R1
satisfying the three conditions
(1)
R
(M)
c
R 1 =C
(2)
R1 C
(3)
AR 1 c R1
AS b 1
A
' (C)
where M =
CAn-l
f(M), condition
(1) ensures
that %f =
1
4
R 1 is an
observable subspace for (A,B,C). Condition (2) ensures that for
every vector of R1i,{-
where
i
C
Then every vector of R1 has the same output direction as bl
1
(b) Matrix notation (Beard)
R 1 can be shown to be the null space of
-
--
Al _
f
,
L-
T
/ )A
I (C )
-r-L I ' c
---
(
,L4Ar7($
-(cA)
where Em is the identity matrix in a m dimension space.
Note:
If C
1 = 0, just replace bl by A
smallest integer such that CA
b
b
where /
is the
is not zero, in the above
definition.
o
detection generator
It is possible to show that the detection space R bl is
15
cyclic invariant, and that there exists a unique vector g in
Rb
such that the vectors
1
y _
g are a basis for Rbl
g, A g,..., A
CA
g=C
Vector definition (Jones)
Let d(Rb ) =
(1)
Akg
(2)
CA
b; g is
if
<
Rb
abl9
the detection generator of %1
=
Cb
Beard showed that if the ~bl eigenvalues of A - DC associated
with the controllable subspace of b 1 are given by the roots of
'Ybl
S
+ p
s
I9bl-l
+ ...
+ P2 s + P1 = 0
b1
where the Pi are scalars (which implies that if a desired eigenvalue of Rbl is complex, its conjugate must be selected too,
hence the almost arbitrarily assignability concept), then
D
must
be a solution of
DCA
o
bl-l
P+
P2A g+ ... + p
b1l-l
A
g +A
g
Mutually detectable set of events (Jones)
Given the inhomogeneous error equations
£=
(A - DC)
+ bi ni(t)
i =
E C ao
The failures associated with the events bl,...,b r are mutually
16
detectable by a single failure detection system if
(1) the output generated by each of b
nl(t),..., br nr(t)
maintains a fixed direction in the output space, and
(2) the eigenvalues of A - DC can be specified almost arbitrarily by a proper choice of D.
This definition says nothing about the output directions
From a practical point of view, however, one case can
C bi
be immediately examined:
C bl is parallel
(1) If b2
if two events b
and b 2 are such that
to C b2 , there are 2 possibilities:
Rl' then b2 and bl are detection
equivalent,
and a
detection filter cannot distinguish between failures associated with these two events.
(2) If b2
1 it can be shown that if Cbl //Cb
2
a failure de-
tection system which detects failures associated with b1
cannot simultaneously detect failures associated with b2 .
The output error for the second failure cannot be constrained
to a single direction.
This can be generalized to the case where one output direction C bi can be expressed
as a linear combination
of others.
In
that case, to have unidirectional outputs, it can be shown that
eigenvalues for each detection space can no longer be arbitrarily
assigned.
o
Hence the new concept.
Output separability
Vectors i,...,
-l
[C b..,
C br]
]
br
are output separable if the rank of
r
= r.
It can be shown that output separability is sufficient to
17
guarantee that a D can be found for which failures associated
with b,...,
br produce unidirectional output errors.
dimension of R i is denoted by
9i'
Is =
C
If the
Vi eigenvalues
of
A - DC can be almost arbitrarily assigned by the choice of D.
Output separability, unfortunately, does not imply mutual
detectability:
it may happen that eigenvalues of each Ri can
be almost arbitrarily assigned, when the bi are output separable,
but that some eigenvalues of A - DC are determined, and cannot be
changed.
More precisely:
° Let S be the space spanned by [,...,
detection space for S
R
0
S
R
where R
= R
such that
We can define a
(Jones)
is the largest subspace which satisfies
(1) (M) n R
=O
(2)
Rd
C
'
(3)
AR
C
Ra
(C)
C
Rs can be shown to be the null space of
I
A-
2
where
D S = AB[(CB)(cB)- (B)
C=
b].
)
-js
i]
C
T
- -l
-T
[Em - CB [(CB) (CB)]
(CB) ] C
and B is the matrix [bl,...,r].
R s is a direct extension of Ri defined formerly.
In a sense,
it is the set of events which are detection equivalent to the
set of bi, i = l,...,r.
If the bi'S are output separable, we have
18
R1
2
Let us define
" ..
=
RrC Rs
+ ...
s= dimension
+
where
i = dim of Ri
of RX
If D is chosen such that it makes outputs associated with
bl,...,brunidirectional, only Us of the eigenvalues associated
with R s can be almost arbitrarily assignable, the remaining
-s
- s are unassignable.
Therefore
R1,...,Rr are mutually detectable<-,i=zr
i
s
The preceding concepts are sufficient to understand the
basic structure of the algorithm written to help the designer
develop a detection filter.
What follows is necessary to under-
stand how the program can help the designer to find the values
of the unassignable eigenvalues if the bi's are not mutually
detectable, and a detectable subset if these eigenvalues are not
acceptable.
o
Excess subspace.
If bl,...,b are not mutually detectable,
-r
the excess subspace of R
is any subspace Ro C
satisfies
R Rr
R=
=.
1
In general, it is not unique.
(C) which
o
However, it can be shown that the
Vo eigenvalues of A-DC associated with R
(which are the
unassignable eigenvalues of A-DC for a given set of b's)
independent of the choice of D.
o
are
The algorithm used will deter-
mine a basis of the unique subspace Rog defined by:
19
Rog excess subspace of RX
ARog C
Rog
a
gr
...
It can be shown that Rog is the null space of the matrix
o
_LX Iog
_
I
subs
I
V'_
A
matrix
[(CB)T (CB)]
1 (CB) C
C:)
_- (/I
° D
jC2
:2
where the c.1 's are the rows of the
o
OS- 9-fi
IL
-'Em'4 _ c
Y.PC7
B matrix
gl
(CB)-]
[b1 ,..,
(CB)
b r]
I
Let us call Rog this basis.
ARog C Rog
= AB[(CB)
Once it is determined, as
... ''gr , we have with G = [gl,'.. gr ]
ARog = Rog 71- + G
it can be shown that the rows of e
i1 =
..= (A
1
As A, Rog,
- D S C)
C)
are known, 7
are equal to
Ro
R og for i ==
...
(2-1)
can be computed, and the unassignable
eigenvalues of A - DC associated with B are the eigenvalues of77 .
o
Property of Rog:
suppose we have a set of events bl,...,br
which are not mutually detectable for a system (A,C) .
fine Rogk = excess subspace associated with
fork =Jones
1,...,r,
showed that-r
for k = l,...,r, Jones showed that
If we de-
20
(a) Rogk C Rog
for all k
(b) The excess subspace associated with the set of events b
where bj and bk have been extracted is
R
=R
og i
(R
ogi
og k
The program written uses this property to help the designer
to find a subset of the b.'swith acceptable unassignable eigenvalues:
(it is an option)
o
for each event bi it computes the set ~i of unassignable eigenvalues associated with b...,bi -1-1
1'
_
o
the designer
-ii+l'''
knows that if he eliminates
of events, the unassignable
b
-n
bi, for i
J of the set
eigenvalues of the set of events,
bj, jc [(l,...,r) - J] will be
n Ai
ie J
In particular, if
f)
. =
, the remaining events once
the
the events
events b1
i' i~ J~have been extracted are mutually detectable.
o
Output stationarity (Reference 2)
Assume
'',...,
bk are output separable, and let D* be the
class of operators such that for every D
D* the output gene-
rated by each of b1,..., bk with respect to (A - DC, C) is unidirectional.
The subspace
can be made output stationary with
b1 ,..., bk if there exists a D' 6 D* such that the output from
every element
C
i (or CA f
i
if C
/
for
(A - D'C, C) is unidirectional
along
i = O,etc).
The cost of using output stationarity to increase the number
21
of failures which can be detected by a single failure detection
system is that certain eigenvalues of A - DC may have to be
assigned a multiplicity greater than one.
Suppose we want to make h. output stationary with bl,...,br
where
b
bl'...,b
r
...,,h
b
is a set of output
separable
are not output separable.
is the smallest subset of bl,
C FC
uL
and
This implies that C h.
is a linear combination of C bl,...,C br.
bl,..., b
vectors,
Suppose that
b
such that
i C hi
C
has a solution where
and
'' '
,
L
=
FL
=
' T1 T[1'''
[b 1 ,..., be]
are a set of nonzero coefficients. If b1 ...,
b
are mutually detectable, it can be demonstrated that h. can be
made output stationary with bl,..., br if there exists a solution to RL
= Si where
C
RL
and where
=
[R1
--,· Re]
S i1 = [h
-1i
:
S i1 ], detection space of hi.
22
CHAPTER
3
DETECTION FILTER DESIGN ALGORITHM
A - Principle of the algorithm
There are two basic steps in the algorithm:
During the first part, the designer has to find an acceptable
set of events, either output separable and mutually detectablethat is to say without unassignable eigenvalues--or output
separable and with acceptable unassignable eigenvalues.
The
program first tests the output separability of the events, and,
if the events are output separable, goes on to compute the detection space RX associated with the whole set of events, and
the detection space Ri associated with each bi.
it computes the detection generator
If
table.
~Ri
t4R
=
),
gi
In the process,
associated with each Ri.
the events are mutually detec-
Then a detection filter D can be designed such that all
the eigenvalues of A - DC are almost arbitrarily assignable.
If ()
r(Ri),
there are x(R)-
i
)
(Ri
S
i
unassignable eigenvalues in A - DC, independently of the choice
of D.
values.
The program goes on to compute these unassignable eigenThree possibilities are then offered to the designer:
o
accept the unassignable eigenvalues, and go to the next step;
O
find a subset of the b's
with no unassignable eigenvalues.
To do this, the program computes for each bi the set
Ai
of un-
assignable eigenvalues associated with the events
(b1'''
i-l' bi+l.'''' r )
events bj, j
The designer then takes out the
I, I a set of indices,
(I C [l,..,r]) such that
23
.I
j
. contains only acceptable unassignable eigenvalues.
I
3
If, for example, one of the A i's, assume A 1 ,
is the null set,
the designers know that the events b2,'''' br are mutually detectable.
o
increase the dimension of state space.
he has to go back to the beginning
(Not yet operational,
with the new A, B, C, and the
new set of events B).
Once the designer has an acceptable set of events, the
program goes on to compute the detection filter with the desired
eigenvalues.
This is done in base normal canonical form (Jones).
The transformation matrix from the given coordinate system to
base normal canonical form is defined to be T 1.
structure
for T
-1
is
iT~i
where
the
The general
-
(3-1)
,_vAA
i's are the detection generators of the Ri's
i is the dimension
of Ri
To is a matrix such that T is nonsingular.
made for T
The choice
is:
74
W-tfl)--y(S-95
/-=t3,,ffi
, (A!C)
AJ
d
where
X
1'
detectable, R
''Yo is a basis
for Ro
has dimension 0).
?
1--
(If the events are mutually
24
The wr+l...,w
are chosen so that the vectors
97i- *I
(A
g
o.
m
the
set
q-t~iL/~
-
complete the set
-7
-
-.
to form a basis in Rn.
If RS
.
is already of dimension n, where
n is the state space dimension, there is no need for the vectors
,.....w . The set
-r+l
· ' -- m -
xv-
w
_
Y44
a basis of R~ ,is
also a basis
for Rn.
More precisely, the wi are the auxiliary vectors associated
with C' (A - D
i
C)
in the orthogonal
reduction
of
starting with the identity matrix
cs (-
'g
)
where
C'i is a row of C's
;i
5
/'V
L~
-
C`~3
Gec·~
~s
qi is the largest integer such that
all of C' ,...,C' (A - D C)
have a nonzero auxiliary vector
(See appendix D on orthogonal reduction procedure for the definition of auxiliary vectors).
All but m of the vectors of the right hand side of (3-1)
are in the null space of C.
These m columns are used to define
a transformation of the output space compatible with T- 1 .
I
V-C
,T~~~~
|
-'
L_
-L
T
_
l
5
'it i
/
bL
..
a
v:
transforms the state vector to base normal form and T transforms
it back to the original coordinate system.
We have the relations
25
Base normal form
original base
^A
T
-1 AT
B=
T
B
=Tm
CT
-i
n-1
^
-1
Zm= Tm
Xm
This transformation is used because the design of the detection filter in the canonical basis is straightforward:
due to
the two relations
Dc
-SUts. ~~~~a-ie~y
4
. A
Drn
Aj~~~+kr A -cJI-]/
where the
are the coefficients of the polynomial
LP
(
7
of the eigenvalues
of Ri-,
)
(3-2)
+
-A
4
t-+i
t
and
ARog = Rog 7 + 6 e
, we have:
(3-3)
A is of the form
Al
f
where
where
Chapter
.
'"
=
V0o
x
4
matrices with only one nonzero row, defined in
matrices with only one nonzero row, defined in
2, equation
/T is a
A 2
(2-1)
o matrix
associated
with
Rog, given by rela-
26
tion
(3-3)
/%A,/so=
U =;
°L
-<-o
,
/o
/^/
A-,
1[-
o-
wi
_
a i
j7is
is a V.
j
matrix
*
15
for
matrix,
i
j
(3-4)
1
C rA /is of; 5'r the form
o
-L
r
)
AoJ
ol--
=57
where
In order for D to be a detection
vector
is a
filter for
[bl,..., br],
each space R i has to be invariant for A - DC, or, equivalently,
are the coefficients of the desired
If the ~
for A - DC.
wher
-<-ARLL
set of eigenvalues
of Ri, A - DC is equal to
A, o- - o
o
°
A4 0
-h
rj.
0.
z
>
^9-
Ld
_;?
-7 r
If a D is selected
associated with each
o
rF
i
so that ~ -
DC is of this form, outputs
will be unidirectional and the eigenvalues
27
associated with each Ri can be chosen (if the dimension
less than n, the state space dimension, n A - D
C will be the same as those of A.
too, but the program does not do it.
of
is
eigenvalues of
They could be selected
See Ref. 2 for more details).
To set A - DC in the desired form, D is selected to be the
sum of two terms
D = DFR + Dv
with
-_
F.
I
~
0O
9-
CL^
-
-
0
-6/-
.
-
-
--_
O/
0 .- .
with
0-
cA-
Ira arz
I
-
o
--f'2 -- -
I-r,
I_
ICAR
c-
Zr-a
-
C,
c;
_
*- .'!L 0o
.o
. ..~
~~.
i = l,...,r with the
cdz
Pil ,...piyi defined in (3-4).
'1
Finally, the program computes
D= T ^DTm-1
28
B - Algorithm of the detection filter program
BA)
Reading of data
Step 1.
Enter A,B,C,
bi
dimensions A(n,n), B(n,q), C(m,n),
B(n,r)
Step 2.
Compute rank of C.
Step 3.
If there are more than rank C events to be detected,
divide the bi into groups of no more than rank C vectors
in a
group.
BB)
Output separability
Step 4.
Test each group for output separability.
C b
group b1 ,..., br
-r compute
1''''
are linearly independent.
BC)
---Cb r and check whether they
If not, the group has to be changed.
Mutual detectability
Step 5.
For each group of events selected, mutual detectability
will be investigated.
computed,
5.a
Given a
as well as
For each group, I ,
R1, R 2, ..,R
will be
1''' 'r'
Apply orthogonal reduction to C, starting withJ(l)
= En.
Let %c be the terminating matrix.
5.b
Compute
Compute
C-
-
i
Apply orthogonal reduction to M D-starting with
A-
iZC'
29
Let
-d
be the terminating matrix,
V
=/
(
).
(Note: an option allows to start the orthogonal reduction with
the identity matrix to compute the w i needed in the final steps,
and the integers qi, such that
C (
_
c)
'
has a nonzero auxiliary vector, qi largest integer for which
this is true).
5.c
For each b
i i=
,r
-
Compute
c-
(c Asc
Ad 1 LL LC= LIA4;
)IT( )T J
c
Reduce
CI"
I
c (A - 4 C)
Mig -
starting
with JZ -A
I
Let
terminating
matrix
i bethe
LetJ9-i be the terminating matrix
5.d
Compute
'7- . isA.
C
Apply orthogonal reduction to M, starting with each J2_
, i
i = l,...,r.
Each reduction ends on a zero matrix.
The last
vector to be removed from the range space of JZi is a multiple
of the detection generator
i'
30
5.e
=
Compute
ii =
'
+ r
s = dimension
+ 1 for all i = l,...,r.
Check whether
V
=
of Rs
= dimension
of Ri.
pi
i=l,r
4
If equality holds, the events are mutually detectable, go to Step
6.
If not go to step 5.f.
5.f
(determines
total of
excess
subspace
Rog).
og
If
0
==i=l,r
s -
ioa
i'
o eigenvalues of A - DC are unassignable; they will
be computed.
o
Compute
[(C B)T
(C B)]
=
(C B)
(partly done in step 5.b)
o
Compute
I
pi Z -
O
Apply orthogonal reduction to M
Jo
2
o
be the terminating matrix
Define Rog = ]1E'.. .
starting with J2.
!(i
J
)
where the
Let
= Vis
ji's are VO linearly
independent columns of Jog
o
Compute
i
=
Ci
(A - D s C)
Rog
Form matrix & whose rows are the
o
o
Compute
where
o
//=
[R T R1 -l
= [Rog
og
og R
= [
1'y
T
og
ogR
r] ''
matrix
Compute eigenvalues of
for i =,...,r
.'s
RogT
og
]
of the generators.
I7 which are the unassignable eigen-
values associated with the set of events.
31
5.g
Three options open:
o
accept the eigenvalues of
o
find a subset of b,...,
eigenvalues
j
77-
b
;
go to step 6
with acceptable unassignable
go to step 5h
increase dimension of state space ;
o
5.h
go to step 1.
(indicate unassignable eigenvalues associated with each bi).
For each i, i = l,r compute
Gi =
6
with the ith column deleted ( & defined in step 5f)
Hi = & with the ith row deleted (
defined in step 5f)
= ith row of
C.Tr
1
o -l
Apply orthogonal reduction to Moi.
Let ~i be the terminating
matrix.
Find a matrixatrix
i whose columns span the column space
of I,'.
Find a matrix
Moi. Form [~ -
L
whose columns span the row space of
]i
Compute
Let A i be this set.
Find eigenvalues of 7i.
A i is the
set of unassignable eigenvalues associated with
[1''''
5.i
i-l'
i+l'''
r]·
Test for output stationarity:
determine whether it is
possible to make an event -a
b output stationary with b,...,
1
br
Z-
32
o
compute
5a'
the detection space associated with ba (same
computation as in 5.c except that orthogonal reduction of MD
associated with b
-a starts with identity matrix)
O
find the subset of b ,..., br of which
bination.
is a linear com-
Call J the set of indices of b. such that
b
-a =b
= Ad
-a
< k
k -kk
=
° Form matrix R.
-J C [l,...,r]
[.. Rig..]for
~(a), '
.
E
will be possible if there exists some
If Va =
b
-
Output stationarity
such that
eigenvalues associated with each Ri, i
are equal to the eigenvalues selected for Ra.
i,.Ri) =
i >
a'
i
-
a
,
If, for some
eigenvaluesof Ra are
unassignable.
Note:
the step 5.i is only partly
implemented
in the program,
as it is in June 78, and not fully tested out.
BD)
Filter design
Step 6.Let
6.a
Use R
bi) i = l,...,r be the set of events at this point.
og
defined
in step 5.f.
Use results
of step 5.b:
w i and qi'. Form the matrix
T
-LVt47 } jRC
(5
6.b
rC'
p.)3
Form the matrix
-
.i-
C
I~~~~~~~~~~~~~~~~~~~~~~~~~~~zt
_ f
"zt
-
?
-
Vr
1
33
-, A -jf -1"
T_=L 34
I
K
7u
Compute T -1
L
Form Tm =
/
2·1·I9
3 (/'
, -rPC v ) --".'
z c,
% cI
-:1
-LrL/Is
-,ZOi
d
Compute Tm
6.c
A
Compute A = T
-1
~-1 B, /C
A
AT, B = T
= T
-1
m
CT
A is of the form
At
,r
with
9-FF
.r
A
-
1VIA
matri
-|"'
A ,
/ rr
r
rr (, -J-)
(n)
- .
4
=
s) matrix
/
L= J
only one nonzero row
0U0'ijO j
matrix for
1
i
I
A
Aii
= -
i -.
•2
-
,-Y
Vi
matrix
fr ii Zj
'vi matrix
34
Compute
6.d
- 0
Ct
-6?4,'T--
-2
On
C
i
'-
DFR =
R
-
(?
'
I
i
^
,L-
0
Enter the desired
a--
A'il''''
ii'..., .ixiy
C7
(eigenvalue$for
Compute
Y(A) ( 1 ) -1O AI. ,
(,
Ir, "
I
i -'
I
j.
-+ ,Vi
Compute
.Lf .4',
'
_
- Ci.
r4'
,
(U'8t
'1
t-
7
Compute
C
i,
a
-
6?
cI
'Il-
o
•ct
0
Compute
D = D
qt~
0
Compute
A
D = T D T
-1
m
0
C)
P.{'
J
R.i) ,
1
i = 1,r
35
C - Examples
The following examples are pure mathematical transformations
of matrices, described here just in order to illustrate the theoNo physical background is to
retical notions introduced earlier.
be searched for the A, B, C matrices used in this part.
Example
1.
I
6
0O
7
O
- 1
>7)
:
-A
O
-f
,_
-3
C
,_tz1
0
-4
o
?
J
?P
-2
-3 I
'15
0
J
0
C
4
0
0
C?
C =
C
i
- ' (
1 )
7)
-i
'5C
o
cC
C
-J
Running the program, we find:
o
dimension
of R
o
dimension
of R1 is
O
dimension
of R2
Then, dimension
I
O
is 1
J
= 3 (as R
0
C,I
is 0
of R
CZ
=
[b
dimension
of R1 = 1 (as R1
=
bl G
dimension
of R2 = 1 (as R2
=
b2
b2]
R 1)
, R 2)
,
R )
36
we have
>2 + 2
~
and
There is one unassignable eigenvalue.
2)
1
1
The program checks its
value, which is - 1.
The designer accepts this value, and goes on.
The vectors
Wi obtained in the orthogonal reduction of MD, starting with the
identity matrix (step 5b of the algorithm) turn out to be
I
Then
C
-4
o
C)
0
0
1
o
4
6
V
,-
C
C-
C)
O
()
-c
0
1I
0
I=
oj
-J
T
C
7
O
c
a
1
C
-j
Li
C·
4
C
.
C
C,
-1J
C,
C
0-
O
C,(s
C'J
C
'-9
A=
-?
C
-
c
-2
-1
C)
C
o
....
"
0
7
-"
1
37
-0
0.
9
-f
C) )
0
Then
-3
0 I
'z
o
2
-
o_
If the designer wants the eigenvalue -8 associated with R1
and -9 associated with R2 )
0
C)
O
C
"
0C>
C2
01Y
0
9
0
0
&;
0
0
0
Then
I
O
p =-
c)
C
9
0
-
6
-3
L-
1,
C-
cY
£
I.;>-
0,
0o
(o
I?
.
-Z
e
-G
,3
-
L's
As a further check
_- f
A
-
0
_c-
0
0
We see that
(A - DC)j 1 = -8
(A - DC)
2
)
-9
1
_ ,
2
C.
GC
6
7
6
7
-
4)~~'
.
C)7
I
38
Example
2.
Same matrices A, B, C
O
-
_Lm
-2
"
-
,
-G
o
-3
71
6
D
|>
.3.-
U
V
/I
- r-)2- - - '~'-4'g
-
I
-I
C
IC
C
C
C
C
C
,
I
(
C.;
c,
j
O I4.
eL
But, we shall use the events
0
U
o
(.2
I
-
,7
¢/
/
C
i
-3
'I
\
c,'
(d
/o
C)i
C
/
C)
19~~~~~~j'
Running the program, we find
o
dimension
of R
is 1
o
dimension
of R 1 is 0
o
dimension
of R 2 is 0
o
dimension
of R 3 is 0
O
dimension
of R4
is 0
I
I
0
39
C,
o
II
I
I
--
i/
c
4C,
-3
-2.
C?
_I1
(D
/
C,
t
''
-I
Then dimension of R
= 5
dimension
of R 1 = 1
dimension
of R2
dimension
of R3 = 1
dimension
of R4 = 1
=
1
We have
2 +
1 +
and
3 +
4
4)
= 1
and
- (
1+
t2 +
3 +
There is one unassignable eigenvalue, the program checks its
value, which
is 0.
The designer accepts this eigenvalue and goes on.
$R= 5 = 4
is no wi in this case (I
i~~~~~~~~-
oO
c
of state space).
C-
I
1
0
0
O
--.
C
(2
0
C-
1
TFi
L
Cl
C?
0,
:L
v
There
40
-0
I
-
r0
-/
co~
o
-
I
C)
o
0O
C
-4-
I
C-/
-3
C
7
6
C
0
C.
C,C
C
Then
(i
C)
-3
--
-2·
0
1'~~~~~~~~.1
7
0
&
0
0"
4-I
C)
d)
If the designer wants the eigenvalue -7 associated with R1,
-8 associated with R 2, -9 associated with R3, -10 associated
with R4 )
0,C
C--
G0
C
74
0
C
8
Then
O
o
C
0i
o
-I
0
C.
41
o
6
-3 -.
7
-
-1
7
&
c
O
_
_4
C
C
And
C
C
C
-_
/
I
cJ
n
0'"
-
7
=
-o
7
6
.2
acheck2
further
.As
71
O
0
I
As a further check
C
-I
o
0
We see that
(A - DC)
1 = -7 1
(A -
DC)
2
(A - DC)
3=
(A - DC)
4
=
8
-9
=
-I
- S
C,
C
0
0
,O
o-
O
-'7
o
o
_8
2
3
-10
4
If the designer had decided not to accept the unassignable
eigenvalue, the program can help him in selecting the subset of
bi ' s , in computing the
A
1
=
0)
i associated with each b.
A2O0=
A3
=
In this case
42
which means that
° with the set
b2 , b3 , b)
o with the set(b 1
b3 , b4
, the unassignable eigenvalue is 0
, the unassignable eigenvalue is 0
O
with the set b 3 , b4
the unassignable eigenvalue is
O
the sets of events
, b 2,
1b
Jb3'
b, b2'
1
j4
have no unassignable eigenvalues associated with them.
have no unassignable eigenvalues associated with them.
O,
43
CHAPTER IV
GUIDEWAY VEHICLE SIMULATION AND
DETECTION FILTER DESIGN
(A) Background
It was determined that a study of the applicability of detection filter theory to guideway vehicle control would be most
useful if it were done in the context of a typical guideway
vehicle rather than in the context of any specific system.
different approaches are possible:
Two
one where the spacing of
different vehicles on the guideway is monitored by a wayside
controller and one where each vehicle has an onboard spacing
sensor which measures the distance from the vehicle ahead.
Figure 4.1 and Fig. 4.2 show the block diagrams of the control
systems with a spacing sensor and with a wayside controller.
The velocity profiler and the velocity control loop are
common to both cases.
To achieve a high level of reliability,
it is preferable to implement a detection filter on board the
vehicle, so that the filter could be used even in the case of
a failure occurring in the communications between the wayside
and the vehicle.
In the case of a control system with a way-
side controller, information on the spacing between the vehicle
and the vehicle ahead is not available onboard if one does not
wish to implement a special communication link for the detection filter only.
Hence, it would not be possible to design
a detection filter to monitor failures on the whole system.
44
-
0
Ql
b Xl
-3 1-
-
-
-
I
o)
E
a)
3o
rl
0
I
,)
rl
UJ
r-I
45
I
-
I
r-
J
0
0
U
3
"
a)
-)
JIV
U
a
a)
a,
a
0r
C\N
tT~
rT4
46
Only failures occurring in the velocity control loop could be
monitored
as the velocity profiler, whose function is to limit
the jerk and the acceleration commanded to the vehicle within
bounds compatible with passenger comfort, is essentially nonlinear and could not be accurately modeled in the linear reference
model of the detection filter.
In the case of an autonomous vehicle-follower system, the
position of the vehicle ahead is not available as a signal.
whole system cannot then be monitored by a detection filter.
The
The
velocity command profiler and the position loop controller would
very likely be implemented in a digital computer, and the velocity
command loop could be thought of as implemented with analog equipment in a preliminary feasibility study.
In this case too, then,
a detection filter would be designed only for the velocity control
loop.
Figure 4.3 shows the velocity command loop, common to both
systems; it is the part of the system for which a detection filter
would be designed.
(B) Generic system parameters
We shall deal only with the components describing the velocity
command loop.
Figure 4.4 shows the component dynamics.
The generic
system parameters used were those found in a contractor documentation.
(1) Velocity indicator:
onboard indication of vehicle velocity.
No data given on noise.
We used the following model:
47
00
o
,--i
.--
0
4J
0
0
>1
--
0
0
,
co
.H
¥4
48
llcl
c
li
ZN
'A
00o
o
,,-
0
s4
0r,
0
4-
C
.)
0
0
cd
r.
49
(Appendix C shows why a
value of 1 is not advisVind = K 4 [xv + n(t)] able for the detection
filter design).
K4 = 1.2
t ^
(2) Vehicle dynamics
m
G + FA
A
G
=Fp + p C
where
F
= propulsion
system force = T
Fc = Coulomb friction force = -100
=-
f
sgn(Xv)lbs
sgn
(Xv)
FG = grade force
=-mg
grade lbs, up to 6%
100
F A = aerodynamic forces
= -(0.03) (-v ww ) XvVI
V
wI
lbs = -caero (Xv Vw)iX
Vw
with VW = wind velocity in ft/sec
(3) Compensator:
proportional + integral
K1 + K2/S with K
K2 = 1000
= 1500
(Units lbs ft sec)
(4) Propulsion system
The propulsion system is modeled with a 3rd order dynamics
transfer function.
T
T
1___·~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
comm
(1 +
1.5
13.5
)
2
(.)s
(1 + 2(
7)s
s
3(l+302
30
We shall use the form
T = a2 T + a3 T + a4 T + K3 Tcomm
with
a 2 = -55.5
a4
a 3 = -1467
K:3 = 12150
= -12150
50
(5) Acceleration feedforward
The commanded acceleration is fed forward through a gain mv,
which should be equal to the mass of the vehicle.
are not equal, but close
cally, in this simulation, m and m
mv = 350
m = 373
numbers:
More realisti-
(slugs)
(C) System equations
The variables used are:
T:
realized
T,
thrust,
xv:
vehicle position
xv:
vehicle velocity
z:
T,
input to the compensator
(z = vc
vind)
-
The inputs are
ac
acceleration command
(x-Vw)
Xv-Vwl where Vw is the wind velocity
g sine
grade effect
n(t)
noise
The outputs (later compared with those of the filter simulation) are
Tc (commanded thrust)
These were the only physically
accessible signals
ind
We have the relations
(1)
(X V )
(2)
(xv)
c
= XV
, T
where
(3)
(T)=T
(4)
(T) = T
-
-i
c 'v
m XvI
aero
x
v
is the grade
T = a2 T + a3 T + a4 T + K 3 T c
w
w
I
51
But
T
T
c
+m
e
=K
a
v
c
+ K2 z + mvac
1
=K(V c -
K1 (Vc
Vin d) + K2 z + mvac
K4 (xv+
-
n (t))
+ K2 z + mv ac
Then
(5) T=-
K1K 3K 4 Xv + aT + a3T + aT + K2K3 z
K1K3 V + K3mva
K1K 3 K 4 n (t)
(6) z = V
(7)
V
= Vc - K4 Xv - K4 n(t)
Vind
(2
a
In = matrix
form this gives
In matrix form this gives
I.
)I
O
0
O/
00
x-V
VI
lr
0
.T-
t'
_ k0
~?
c,
L)
l<
i-,
c
-1
CLQ c
Y0e
-·e-
C
Li
V
0
,
%,,
0
O \
o
o
o
0
c-,
U
.1.
/,
/-
71
I ,I
tC;
C)
r
-C
0
(
&
CV.
J
x
"CC
C
O
o
~
,,(~L~V1
jik")
&
o
W0
3
a
o Co
/
0
C0
L
6'
v'
/,I
52
(8) T
-K1 K 4 X v + K 2
(9) Vin d
=
mva c
+ KlV c
K 1K
4
n(t)
K 4 Xv + K 4 n(t)
In matrix form
T
l
).
ri1nA
i
O
0
a
a
O
o
c3
O
(
\
0)
;I
I2
Figure 4.5 shows the action of the velocity profiler on a wayside velocity command, to keep the jerk and the acceleration under
values compatible with passenger comfort.
Figure 4.6 shows the response of the system in velocity regulation mode, plotting the velocity error versus time, Vc given by
Fig. 4.5.
(D) Reference model of the system for the detection filter
The elements whose failures were to be monitored by a detection
filter were: (see Fig. 4.3)
o
the controller
o
the velocity indicator
I the propulsion system.
53
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55
The two first elements, on a real system, would be duplicated,
and the system would switch to the backup component in case of a
failure indicated by the detection filter.
The propulsion system
would be made of two parallel modules; in case of a failure, the
vehicle would continue with half of its propulsion capability.
The
velocity control loop functional block diagram would be in fact
the one indicated by Fig. 4.7
The detection filter works only on a linear model.
To derive the matrices A
We have
Bm, Cm for the reference model of
the detection filter, all the nonlinearities were neglected in the
system, the grade component was ignored, and the simplified model
of Fig. 4.8 was used (notice that the Coulomb frinction was modeled
in the reference
model
as a bias).
The states selected are XV, T, T, T, Te, Vc
(vehicle velocity, thrust, first and second derivatives of thrust,
compensator output and velocity command)
The outputs are T c and Vin d
We have the relations
56
vIj
..'
0
0
'N
0
Ar
L)
.,A
a
.-I
00
0
0>1
0,11
U)
*,l
01)
.qU)
(a
.
rT4
57
04
4A
-4
jl
m
I
-Z-
1-
0)
f
0)
II
Cr
a)
uo
0
.,,a)
4,
v
C)
a)
4J
0)
o
-,
1U
58
T
= T
C
+ma
C
V
~
0
T
Te
a
.
f
d)
+ K2 (V-Vind)
( a c- K 4Xv)
+ K2 (VC-v in d )
= K 1 (V-V.
cindi
= Kl
+ K2Vc
TF
1c
m+K1K 4
K1K4
(Xv ) = m
m
2c
coul
_T
m
(T) = T
(T) = T
T
=
(T)
K
+
.
+ a3T + a4T
= K3TC + a2T
= K3 T + K3mvaC+ a2T + a3T + a 4T
C
(Vc ) = a C
In matrix form
,)
O
j
7
o
v
T
0
i:F /
C?
C
0
-'I
I
&
C)
-
C
\
c)
C
a
6rn
(C
r-.
C)
C
"I
(2
C,
0
C)
o
C,
~
4i
K, K
C,
"
/
1
y(
0
0
0
(9
v
0/
V
I
-(1J
59
This is not of the form
x
-m
m
= A
+ B
x
-n-m
m
u
Ym = C
m-
There is a matrix E
x
-m
=
=
m such that
A n--mn
x + B
u
x + E u
-
The system configuration, with the filter, is in fact
We have then the equations
x
=
Ax+
y = Cx+ Eu
Bu
Xm = AmXm + B
+ D(y - Y-m)
In the absence of failures, A-
Ym = Cnxm
B
B
in
C.C
+
EU
m
Then
=
Then
- DC)
_A
5 = (A - DC)E
in the absence
of failure.
in the absence of failure.
So long -asE
So long as
the failures considered entail no variation in the E matrix, the
turns DE 4 and DEm
simplify out in the equation of
, and the
theory of the detection filter, as it was presented in Chapter 2,
60
is applicable without modification to this case.
It would be
applicable too in the case where, even if a failure caused a
modification in E, it could be modeled as a sensor failure.
In this case,
Em =
[
As a failure in m v is not to be monitored, this problem does not
arise.
Note:
In fact, even in the absence of failures, we do not have
A =- A .-
B
Bm
C
Cm because the simulation of the system,
represented by Am , Bm
Cm is linearized, and because the grade
component is ignored.
This study was partly made to check that
the neglected nonlinearities and the grade component produced outputs along the C b'is associated with the failures to be monitored
much smaller than the failure outputs.
(E) Detection filter design
The first step in the detection filter design is to derive the
event vectors associated with the failures to be monitored.
Failures
in compensator, motor, tachometer, can be modeled as failures in
K 1 , K2, K 3, K 4.
Event associated with a failure in K1 .
If K1 fails and becomes arbitrarily time-varying, Kkl(t)
being its new value, the system equations become
61
Tkv F^
)
X
&
e
/-
-ac x
-,-_
Ecewl)I
I-)_
I )
4<_
+t
I
I 6
The event associated with a failure in K1 is then
We have
e
(=
/)
Ce
Event associated with a failure in K2 .
If K2 fails and becomes
arbitrarily time-varying, its new value being K2 k2 (t), the system
equations become
/
x _ ~x + -=t ~ -(_~ ' /) /dt) 2
The event associated
with a failure
in K2
is
Event associated with a failure in K3.
5
If K3 fails and becomes
arbitrarily time-varying, its new value being K3 k3 (t), the system
equations become
A
)fX
The event associated with a failure in K3 is
J-i
--y
I0
Io
62
C e
t4
But,
In this case, we shall use the first vector of the series
A e 64
A2 e6 4 ,..., An
for which C A i
.0
Cs
CA e
Z-
64
1
0
o00
C
-"4
I e
4 0
o
a
2-Z
/A 3 6- ~_
2.
2
C-"j
0
I
En
2.
t-I '<
The event associated with K 3 is then
t a2
t kk~
, g4
-I k,,
\'
63
Events associated with a failure in K4 .
If K4 fails and be-
comes arbitrarily time-varying, its new value being K 4 k4 (t), the
r-)
system equations become o
S~~
°J
I
- JE'tt",
'Cj
(C'
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~L
Let us call
/
-22
-US
'/
d~~~~-
0
n 5 (t) = (-K2 xxv
nc2(t) =
-
-
K1
1
T
1 coul
+
K 1 m
K(
) (k
4
(t )
- 11) K 4
v(k 4 (t) - 1) k 4
The system equations, after failure in K4, can be rewritten
x = A x + B u + n 5 (t) e65
y = C x + E u + nc2(t)
e22
The error equations will then be
= (AE = C
-
~~c
DC)
+ n(t)
e65 -
2 nc2 (t)
+ nc2(t) e2
-22
where d2 is the 2nd column
of the filter D
64
e
22
corresponds
to a variation
-22
~~
~
~
~
in C.
~
~
Then
~
(see ref 2 page
~
~ ~ 2
193-194), the error output of a failure associated with e22 can
where F is
only be contained to the plane spanned by (PcA)
such that C -
.e
If
we notice that
(-)
-6
-22
A failure in K4 cannot be modeled under a controller failure
model or a sensor model failure, because it involves variations in
C and in A.
It can be seen as the superposition
of a sensor
failure and a controller failure.
The controller failure will be represented by the event e65'
The sensor failure will be represented by the couple of events
(e61' A e61).
However
0
P°
-=
o0
A e 6 1 is parallel
to e65
In short, we have
o
event associated with failure in K1 is e65 = b
0
event associated
with failure in K 2 is t65 = b
then
65
/I
o
event associated
with failure in K
is b
-2
,
=
P
P
3 l
/'
V
o
events associated with failure in K4 are e5 and e6 1
It appears that
o
failures in K1 and K2 are detection equivalent.
A filter cannot
be designed which will distinguish between the two failures.
At
most, it would allow to determine if the compensator has failed, but
not which part of the compensator has failed.
o
A failure in K4 cannot be constrained to generate unidirectional
outputs.
plane
In this case, error output can only be constrained to the
spanned by (C
65' C e 6 1 ).
C is of dimension
2; this means
that a failure in K4 will span the whole output space (C e5
C
and
61 are independent).
It was decided to design a detection filter for the events b
and b2 .
A failure in K1 or K2 would generate outputs along Cb_
1, a
failure in K3 along Cb2 , a failure in K4 along Cb1 and Cb2 .
This
way, a filter could distinguish among failures in the three elements
to be monitored
(Using more logic, it is possible
to distinguish
be-
tween failures in K4 and other failures which would generate outputs
along C
and Cb2 :
both tachometers could be used in parallel, with
only the output of one fed back to the velocity controller.
The
two outputs would be compared, a failure would be declared if the
difference between the two did not stay in an allowable margin.
The
66
detection filter could then identify the faulting tachometer.)
The system for which the filter is to be designed is represented by
.2
W,
~ig6y
&2
O
C)
0
C
&
CI
O
0o
0
.
0
/ )
A
C
0
C)
- 1Zl50,
,2Q
-/4166 -5-
-_26A'
0
0
.f O0 /
O
C)
&
~
v
Q3
C,
01
v9
~~~C)
V
_
'1
C)
o
2
C)
C)
4V 6
iSSV
.1
/,
0C
-2
I_ S
C
x _/0
- 1 /3 7oC.0~
-
Ce32237
.1
_ -. 72U
0
o
/
I
C))
67
Using the computer program developed from the algorithm presented in Chapter 3, it was found that:
R~g
has
R1
has a dimension
1
R2
has a dimension
3
Then
'~1
+
a dimension
4
R
has a dimension
6
R1
has a dimension
2
R2
has a dimension
4
~2 = ~
The events
1 and b2 are mutually detectable.
We assigned the eigenvalues - 10 and - 10 to R1 , - 10, - 10, - 10,
- 10 to R 2
01
_ 4oZ./
66
6)
C)
The filter computed was
'O
_~~7o
10-f
4 6,& '2 5SZi
S52
4c iS
23,/
22 80629
68
CHAPTER
5
EXPERIMENTAL RESULTS
According to the detection filter theory, a failure in K1 ,
K2 , or K3 should produce unidirectional outputs along Cl
and Cb 2,
is the event associated with a failure in K 1 or K 2 , and
where
b2 an event associated with a failure in K3 .
From the comparison between the outputs of the guideway
vehicle simulation and of the guideway vehicle reference model,
one has access to
Tc
whose two components are respectively
-
Tcm and Vind - Vind.
-
expressed in the basis
(
C 22
This vector of the output space is
).
(I
In this basis, C
has the value
. It is necessary to change the
(and 74
basis of the output space to measure the error outputs along CL
and Cb2.
The new basis
along the old one.
{ <
(
C6)
= P
We have then x
-new
IHence
3- 2, 7x4 -/
In the following plots,
along
_
Cl
p
2 = [P-1(-Y)]2
1[
2 -
,--C c
=
e
=
_
x
with
-old w
-1/^{
- +.82
P=
0
has the components (4
(-M)]l
3io.
is the error output
is the error output along C
2
One first series of tests was made to determine the order of
magnitude of the outputs due to the unmodeled effects and nonlinearities.
Figure 5.1 shows the outputs when the simulation is run with no
69
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70
grade effect, and with all the nonlinearities equal to zero, except
for the coulomb friction which is modeled in the reference model.
As the coulomb friction component is the same in the simulation and
the reference model, the error outputs should be identically equal
to zero.
What appears is then just the results of numerical pre-
cision loss.
It is the numerical difference of the outputs of two
physically equivalent systems modeled in different ways, integrated
with a finite difference method, with a time interval of 0.02s.
It appears that an output along 1
of less than 0.1 in absolute
value is not significant, and that an output along
0.15 in absolute value is not significant.
2
of less than
2
As one would expect,
these values are smaller than the output errors due to the nonlinearities and due to the failures.
Figure 5.2 shows the error outputs when the simulation is run
with the grade effect only (no noise, no aerodynamic forces, no
Coulomb friction).
nificant.
It appears that the output along
There is only an output along 2
at its maximum value along the test track.
the value of g sin
1
is not sig-
of magnitude 1
103
The third plot shows
, the projection of gravity along the track.
The assigned wayside velocity command changes 3 times during the
test period without any particular effect.
It makes physical sense
that the unmodeled grade effect results in error output along the
channel associated with a failure in the propulsion system:
the
grade effect is equivalent to a change of response of the propulsion system.
Figure 5.3 shows the error outputs when the simulation
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73
is run with the aerodynamic force effect only, with no wind gust
(no noise, no Coulomb friction, no grade effect).
It appears that
the output along ~1 is not significant; there is an output along
2 of magnitude less than 100 at its maximum value during the test.
The assigned wayside velocity command changes 3 times during the
test, resulting in changes of
2 associated
with a velocity
error associated
2'
At steady state, the error along
of 30 ft/sec
with a velocity
is equal to -23, the
of 50 ft/sec is equal
to -63.
It
makes physical sense that the aerodynamic force effect results
only in an error output along the channel associated with a failure
in the propulsion system; the aerodynamic force is equivalent to a
change of response in the propulsion system.
Figure 5.4 shows the error outputs when the simulation is
run with noise in the tachometer output only (no Coulomb friction;
no grade component, no aerodynamic force effect).
It appears that
with a gaussian zero mean noise of standard deviation 0.01 ft/sec
in the tachometer, there is an output along 1 whose maximum value
21
happened to be .68, and an output along e2' whose maximum value
happened to be 13.
The assigned wayside velocity command changes
3 times during the test without any particular effect.
In summary, the main neglected effect in the reference model
is the grade effect, which produces an output along E2 only, whose
maximum value is roughly 6103 times greater than the residue due to
numerical precision loss.
The only neglected effect in the reference
model which produces an output along 1
is the noise in the tachom-
74
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75
eter, whose maximum value is roughly 7 times greater than the
residue due to numerical precision loss.
A test was then conducted to check the transient response
of the outputs due to incorrect initial conditions when there is
no failure, no nonlinearity or neglected effect, i.e., when the
reference model and the vehicle simulation are physically equivalent.
The error on ~1 was initialized to 3000; the error on
was initialized to 622.
issued.
2
No change in wayside velocity command was
Figure 5.5 shows the error decay as a function of time.
As the eigenvalues assigned with R1 are -10 and -10, and the eigenvalues assigned with R2 are -10, -10, -10, -10, the initial errors
should decay in several tenths of a second.
Fig. 5.5,
sec and
1 decays
As can be seen from
to 5 per cent of its initial value within
2 does within
0.7 sec.
It appears
that even if
0.2
is
not initialized in the reference model with the initial values
of x, i.e., Xm(0)
x(0), afterlsec the error outputs will be less
than 1/300 of their initial values.
A third series of tests was finally conducted to investigate
the effects of failures
in K1 , K 2,
K 3, K 4 .
Figure
5.6 shows the
headwind
of 30 ft/sec
specifications of this test:
0
a wind gust, between t = 6 and t = 14 s,
°
a variation of the grade.
The second plot of Fig. 6 shows
the value of g sin 9 , the component of gravity along the track
0
3 changes in wayside velocity command.
t =
wayside
velocity
command
0 - 4
30
4 - 8
50
8 - 12
30
We have
12 - 20
50
(sec)
(ft/sec)
76
Fig. 5.5
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o
tachometer noise was input into the simulation
o
Coulomb friction was taken into account in both the simulation
and the reference model.
In this series of tests, the worst case was considered with all
the nonlinearities and neglected effects running up.
Figure 5.7 shows the outputs along both channels in the absence
of failure
Figure
5.8 shows the outputs
in case of a failure in K1
Figure 5.9 shows the outputs in case of a failure in K2
Figure 5.10 shows the outputs in case of a failure in K3
Figure 5.11 shows the outputs in case of a failure in K4
A "failure" in each case means that the gain changed, the new
gain being equal to half of its initial value.
arbitrary failure mode to simulate.
This is a completely
It should be recalled that the
detection filter does not depend on the manner in which components
fail; the filter simply recognizes that the modeled function is no
longer being performed.
If a total failure were simulated, in the
sense that the gain was set to zero rather than half its nominal
value, the detection filter outputs signifying failure would be even
larger.
It appears (1) that outputs generated by failures can easily be
distinguished from outputs due to neglected effects or nonlinearities:
failure outputs along
residual outputs along
are roughly 10 times larger than
without failures; failure outputs along
~2 are roughly 5 times larger than residual outputs along e2
without failures;
79
(2) that simulation shows that the detection filter performs
accordingly to theory.
Failures in K 1 and K2 generate unidirec-
tional outputs along 1' failures in K3 along 2'
along
and
2'
failures in K4
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CHAPTER
6
CONCLUSIONS
This study has shown the applicability of detection filter
theory to the detection of failures in longitudinal control systems
for guideway vehicles.
Even though the detection filter theory was
developed in the context of a linear time invariant system (prior
to failures), the first tests have shown that error outputs due to
nonlinearities, or noise, or neglected effects in the reference
model can be easily distinguished from error outputs due to component failures.
It was further shown that it is easy to distinguish
between the three kinds of failures most likely to occur in the
velocity control loop.
This feature allows to achieve high levels
of reliability with less hardware redundancy.
To detect which element
is failing, it is not needed to triplicate every component susceptible of failure, as it would be if majority rule were the detection
law.
This study, however, has not addressed the problem of the detection law.
It was just shown that for a particular choice of
filter eigenvalues, the problem can be solved, but no attempt was
made to determine an optimal choice of eiganvalues with respect to
the differentiation between normal error outputs and failure outputs,
and with respect to the time delay before a failure can be detected.
This would be the object of a further study.
86
REFERENCES
1.
Beard, Richard V., "Failure Accommodation in Linear Systems
through Self-Reorganization," PhD Thesis, Department of
Aeronautics and Astronautics, Massachusetts Institute of
Technology, February 1971; also Man-Vehicle Laboratory Report MVT-71-1.
2.
Jones, Harold L., "Failure Detection in Linear Systems,"
PhD Thesis, Department of Aeronautics and Astronautics,
Massachusetts Institute of Technology, August 1973; also
C.S. Draper Laboratory Report T-608.
A-i
APPENDIX A
LISTING OF DETECTION FILTER DESIGN PROGRAM
A-2
~OMMON/MAN1I2/ARCB3T,C3I ,,PQ P,IECRE-PSBUJFF
nIMENSION A(12912),B3(12,12),C(12,12),31(12,12)
;IMENSION C(12,12),3t1FF(12,12)
INTEGER PR
FALL MAIN1
;ECR=O
;ALL MAIN2
iECR=O
rALL MAIN3
ICCR=O
;ALL MAIN4
;ECR=0
FALL MAINS
TECR=3
cALL MAIN6
TECR=O
?ALL MAIN7
IFCR=O
CALL MAIN8
IFCR=6
CALL MAIN9
CALL MAIN9C
CALL MAIN9D
mAIOOOlO
mATOnO2O
4AIOnO30
MAI00040
qAI00050
uAI00060
MAIOO070
MATI0080
4AIOO090
mAIOnlO0
MAIOnllO
MAIO0120
MAIO0130
MAI 00140
MA10150
.A100160
MA I00170
MAI00180
MAIOO190
MA100200
YAI00210
AI100220
MA I00230
TOP
MAT00240
END
MAI00250
A-3
SiBROUTINE MAINlI
uAI0OlO
rOMMON/MA1I2/A,8,CIC3IN,9P,RI-CREPS,BUFF
MA00020
rOMMON/MA413/IROW.ICOL
rOMMON/MAJI4/OMEGCDSCS
C([2,12)9I(121f2),CBI(IP912)
6IMENSION A(12912)98(1292),
DTMENSION UFF(1212)
rIMENSION IROW(12).ICOL(12)
nIMENSION OMEGC(12,12),3S(12,12),CS(12,12)
TNTEGER P,OR
l
MAIOO030
MAI0ono40
MAI00050
MAT00060
MAI00070
MAInoOBO
mAI00090
wRITE(6lnO,100)
100
MAIOOlOO
cO0RMAT(lX,#WRITE
NPQR.IECRICWH7RE
18,I(NtR),IECR
WITING IDEXTYPICAL
A(N,),B(N,0),C(P,N),
MAOOlT00110.
ECR IS 099./9,IC
OMENqIONl MAI012O
2, tOF DECLAQED COLUMNOF C6131)
PEAO(5, 1000)N.P9',Q,IEC~,[C
1000
FORMAT(613)
uAI00130
uAIOO1140
MA100150
wRITE(6100)NP 1R.IECRIC
MAI00160
101
WRITE(6.101)
rORMAT(lX,eIF DATA ARE CORRECTLY ENTEREDTYPElI.ELSETYPF0Of)
PEAD(,51001)ISIGNI
MAI00170
MAIOOlBO
MAI00190
1001
"ORMAT(12)
MA00200
TF(IECR.GT.5)WRTITE(6,lOO1)ISIGNI
TF(ISIGN1.EQ.O)GO TO 1
2
wRITE(69102)
102
EORMAT(IX,IWRITE EPSPRECISION FOR THE COMPUTATION OF THE
1,,RANK OF CTYPICAL EPS IS 0.0001')
oEADO(5,1002)EPS
1002
MA100260
.
rORMAT(Flo.4)
MA1002?0
wRITE(6,o1002)EPS
wRITE(6o101)
MAIOO1280
MAI00290
oEAD(5,1001)ISIGN2
OAI00300
TF(IECP.GT.5)WPITE(5,1001) ISIGN2
MA100310
TF(ISIGN2.EQ.0)
LAIo00320
GO TO 2
rALL LEOFA(AN.TIECR)
PALL LEOF9(BNqO*IECR)
3
MA100330
MA10n340
rALL LEOFC(CNOIECR)
4AI00350
iO 3 =1,o
r"O 3 J=19
MA100360
MAIO0370
-nUFF(IJ)=C(IJ)
MAI00380O
cALL MFGR(CTrCPN,IRAN(,IROW-.ICOLEPSIEQ)
104
wRITE(6,104) IE4
FORMAT(lX,'ERROR CODE
1,9
I16)
;
4
105
COMPUTATIOn OF RANK OF C IS IER'
4 I=1,
MTA100430
OAI00 4 40
uAI00450
MA100460
MAI00470
mAI00480
MA100490
MATOOSbO
4MAIOO510
TNTEGER PR
MA00520
nO
MAI00530
MATIOO540
I CI(IJ)=0.EO
n
2 I=1,P
0 a J=lQ
nO 2 =1,'
100
MAI00390
uAI00400
MA100410
MA100420
nO 4 J=1N
r(IJ)=BUrF(IJ)
iRITE(69105)IRANK
rORMAT(1Xg#RANK OF C IS'I14)
QETURN
FND
¢UIROUTINE PROCBI(CFICBIN.PRIECR)
nIMENSION C(12t12),81(1212),CBI(12P12)
1 I=1,P
nO 1 J=1R
2
'
MA100210
mAI00220
MA100230
AI00240
MAI00250
PBI(IJ)=CBI(IJ)+C(IK)*8I(KJ)
?F(IECP.GT.3) WRITE(69100)((CBI(TJ),J=1,R),I=lP)
iORMAT(SE10.4)
AI00550
MA100560
MAIO0570
MAI00580
MAI00590
MATIO0600
MAI00610
A-4
101
twRITE (6101)
-OPMAT(IlX,tTHF
PRODUCT
OF C AND
)
1.,PUT IN MATRIX CBI(PR) tIAIO00640
BI
AS BEEN COMPUTED
AND,
MAI100620
MA00630
mETURN
qAIOn650
rND
MAI006560
A-5
qUFOOOlO
SiiBPOUTINE LEOFA(AN,IECR)
DTMENSION A(12,lE)
INITEGER P,,R
RUFOGnO20
Buroho30
BUFOnO0O
1
WRITE(6,100)
100
FnRMAT(1X,'TYPE ((A(I,J),J=1,N),I=I,NFREE
FORMAT')
qluronoso
RrAD(5*)((A(IIJlqJ=1,N)9I=1N)
WPITE(6,101)
101
102
103
FnRMAT(1X,'A=)
RUFOOO80
WOITE(6,*)((A(IJ)J=1,N),1=1,N)
RUF00090
RUFO 100
WoITE(6t102)
FORMAT(1X,'IF SATISFIED,TYPE 11.OTHERWISETYPE
RFAD(5,103)ISIGN
FoRMAT(I2)
IF(ISIGN.E3.O)
RKTURN
EDD
00')
RUFOO 140
RUFOO150
GO TO
RUFOO160
StRROUTINE
LEOFB(8,N,0,IE-CR)
DTMENSION
(12,12)
BUFOO 170
RIJFO 180
P,R
INJTEGER
RUfOO190
Rur0200
1
Ir:=O
WoITE(6,100)
100
FnRMAT(1X,'TYPF 3(I,J),J=1,Q,I=l,N,FREE
RUFO02 10
t
FORMAT )
RrAD(5S,*)(((IJ),J=1,IQ),I=1IN)
RUFOf220
pUFO 0230
'WRITE(6,101)
qtJF00240
101
FnRMAT(IX,'B=')
102
WDITE(6,102)
FnRMAT(IX,'IF SATISFIFDTYPE
RFAD(5O103)ISIGN
103
RUFOo250
WcITE(6t*)((B(TJ)tJ=lg[~)t=1.N)
FoRMAT(I2)
IFr(ISIGN.E3.O)
RF TURN
E~,D
RU00260
00')
1l.OTHERWISEtTYPE
BUF00300
UF00310
nUFOO320
GO TO 1
RUO0330
SBRROUTINE LEOFC(C,NPIECR)
RUFOo0340
OTMENSION C(12,12)
9UP00350
RUFOO0360
RUv00370
1
Io=P
WQITE(6.100)
100
FnRMAT(lX,TYPE((C(IJ)J=1,N).I=,P),FREE
R(JFO0380
FORMAT')
RCAD(5,*)((C(IJ),J=1IN),I=1iIP)
WoITE(6,101)
FoRMAT(1X,'C=
m
103
WDITE(6,10?)
FoRMAT(1X*'IF SATISFIEDTYPE
RFAD(5,103)ISIGN
FnRMAT(12)
IF(ISIGN.El.O)
11.OTHE2wISETYPE
00')
RLJF00500
BUFOO510
RU00520
IJTEGER P,tR
IO=R
WPITE(6,100)
FoRMAT(1X,'TYPF((I(I,J),J=1,R),I=1,9J),FREF
RFAD(5,*)((BI(IJ),J=1,1),I=I,N)
WPITE(6,101)
101
FoRMAT(IX,'BI=')
WoITE(6,*)((BI(I,J),J=1,IR),I=1,N)
WoITE(6,102)
RU'00430
BUFOn440
RUFOO450
RUF00460
RUFO0470
BUm 0480
UFO0490
GO TO
RrTURN
EoD
StRiROUTINE LEOFBI(RINRIECR)
DTMENSION I(12,12)
1
100
RUFO0390
PuC'0o4on
RUFOO410
RtJF00410
RUF0020
)
WOITE(6,*)((C(IJ),J=1N),I=1,IP)
102
RUPO0270
RUFO0280
RUF0290
ImTEGER
PR
101
RUFOO 10
RUFOO120
RUFOO130
RUFO o.530
RUJFO 540
RIJF00550
FORMAT')
RUFO0560
qUFOOS T570
00580
RUFO
RUFO00590
RU00600
pUFOO610
A-6
102 FnRMAT(1X,IF SATISFIED,TYPE11.3THEIRISETYPE 00')
RFAD(5.103)ISIGN
E'D
BUrO0630
0540
103 FARMAT(T2)
12IJcO
IF(ISIGN.E3.O)
RFTURN
RUFOO6O20
GO TO 1
BUF00650
RtJF00660
BUFOO670
A-7
SBROUTINE
Ma00IOlO
AIN2
MAIOO020
CnMMON/MAN12/A.BCRICBINPQRIECREPSSUFF
rOMMON/MAVI3/I3W,ICOL
MAIOnO30
DTMENSION a(1212),B()2,12),C(!2912),~I(12,12),CBI(12912)*IROWI12)wAIONO4O
MAIOOO O
DTMENSION ICOL(12),RUFF(12,1l2)
MAI0O060
ImITEGER P,t,R
WtITE(6,100)
MAIOO70
FRMAT(lX,gIF THE NUMREP OF EVENTS IS GREATER THAN RANK OF C/
le'OU HAVE TO DIVIDE THE 3I IN SETS Or NO MOPE THAN RANKC VECTORQs
·1o'IlN A GOUP.IF THIS IS THE CASE TYPE O0,ELSE TYPE 11')
RFAD(5,1000) ISIGNI
1000
ORMAT(12)
TF(IECR.GTS.5) WITE(641000) ISIGNI
100
Ir(IISIGN1.NE.O)GO
1
101
1001
102
TO 1
MA00140
STOP
WoITE(6,101)
FmRMAT(lXtTYPE THE NW VALUE OF R,13 t )
PFAD(5,1001) R
FnRMAT(13)
WoITE(6,1001)R
W:ITE(6,102)
FnRMAT(IlXtIF THE DATA AE CORRETLY ENTERED,TYPE
MAI00150
MAIOO16O
MAI00170
MAIOO8BO
MAIo00190
UAI00200
MAI00210
11,ELSE TYPE On' MA10220
MA100230
1)
ISIGN2
RcAD(51000)
Ir(IECR.GT.5) WRITE(6.1000) ISIGN2
Ir(ISIGN2,rO.oO) GO TO
I(lIECR.GT.5)WRITE(6,loOl)N
C~LL LEOFBT(BINqRIECR)
C^LL PROCBI(C,BICfIlNPRIECR)
IrBI=12
nO 2 =1,'
n 2 J=1,q
2
BiiFF(IJ)=O.EO
AO 3 I=19
rO 3 J=lq
3
qlUFF(IJ)=CBI(IJ)
cALL MFGR(BUFFTICRIPRIRANKIROW,ICOLERS,IER)
WoITE(6,103) IERIPANK
103 FnRMAT(1X,'ERPOR CODE IN THE COMPUTATION OF CBI RANK IS1,T3,/,
11PANK OF CI IS.14)
104
105
MAIOnOBO
MAIOnO9O
MAIOOo100
MAlOOllO
AIOnl2O
uAI0130
MAIO024O
MAI00250
MAI00260
MA1O0270
1A100280
MAIO029O
MAI00300
MAIO0310
.MAIOo320
MA100330
mAI00340
MAIO0350
MAYO0360
MAI00370
MAIOO380
MA00390
MAIO0400
WoITE(6,104)(IROW(I),I=l,N),(ICOL(I),I=l,N)
MAI004O
FORMAT(lX,'IROW=',I3.'IC3L=',13, 1=',13)
WoITE(6,103)
FnRMAT(1XtIF
THE ANK OF C
MATPIX IS NOT EQUAL TO THE
MAI00420O
MAI00430
MA100440
1,,NUMBER
O
EVENTS
I,YOJ
HAVE TO CHANGE TE
3,,THISENTFR 00.ON THE CNTRARY,IF
4,D,'9ENTgEJTEQ 11')
RPAD(5,1002)
'/
GROUP OF BI.TO
O0',/ MAIO00450
TIE CBI ARE LINEARLY INDEPEN-' MA100460
MA100470
ISIGN3
1002 FnRMAT(I2)
IF(IECR.GT.5) WRITE(6olO02) ISIGN3
IF(ISIGN3.-O.0) GO TO 1
WoITE(6,1003)
1003 FnRMAT(1X,A
DETECTION FILTER WILL BE DESIGNED FOR THE EVENTS',/
1,,BI YOU HAVE KEYED IN A THIS POINT')
MA1004 80
MAT00490
MATOO500
mAIOOSlO
MAIO05?0
MAI00530
MAI0540O
RFTURN
MAIOOss550
EmD
MAIO0560
A-8
SiBPOUTINE MAIN3
MAIOOO10
CoMMON/MANI2/AB,C.RI.CTIN,P,Q,R,IECR,EPS,BUFF
COMMON/MAJI4/OMEGCDSCS
MAIOnO20
MAIOnO3O
CnMMON/MANT6/BUFF1
MAIOnO4O
CnMMON/TRASH2/CBVECoCRVIV
4AIOOO50
DTMENSION A(1?.12),(12,12)*C(12,12),BT(12,12),CBI(12,12)
DTMENSION UFF(12,12),3BUFl(12l12)
DTMENSION 9MEGC(12,12),C3VEC(78),CBVIV(78),DS(12,12),CS(12,]2)
IP.TEGEP PR
IF(IECR.GT.2)WRITE(6,1000)
1000 FnRMAT(IXfSU9ROUTINE
MAIN3)
C**COMPTTATION O OMFGC
EDoSI1= 1.E-9
Dn 11 I=1,9
D
1
J=19.4
MAIOO140
.MAIOO15O
12
OMEGC(IJ)=O.
11
Ok4EGC(I,I)1=I.EO
EO
MAIOO16O
MAIOO170
tC= 12
CALL ORTRED(C,OMEGC,P,NICEPSII,IECR)
IF(IECR.GT.3)WRITE(6,100)
((OMEGC(IJ)*J=19).I=1IN)
100 FoRMAT(4(1X,'OMEGC=',E10.4))
C**COMPfiTATION O C8IT*CBI
Do 1 1=19R
D
1 J=1,R
BiIFF(I.J)=O.
I
EO
*
2 J=1*R
?
Do 2 K=1*P
BItFF(IJ)=;UFF(IJ).CRI(<I)*CRI(KJ)
Ir(IER.GT.5)WITE(6,?200)((BUFF(IJ)J=1,R),I=1,R)
200
FnPMAT(4(1YX,
CBIT*CRI=I
C**TPANcITION TO SYMMETRIC
,E-10.4))
TO4AGE
Io=12
CALL
30A FoRMnAT(5(lxtCRVEC=,.F10.
))
C**COMP)iTATION0O INVEPSE OF C3IT*CRI
CALL LINVID(CBVECP.CRVIVPIOGTDlO2,IER)
Ir(IECP.GT.5)WPITE(6.400)
400 FnOPMAT(4(lXqCPVTV= .Fl.4))
(C3VIV(I) ,I=1,10)
C** TRANSITION TO FULL MODE (C3IT*CRI)-l=BJFF
CALL VCVTSr(CRVIVRB~IFFI8)
IF(IECR.GT.5)WPITE(6,0OO)((3UFF(IJ),J=1,RQ),I1=1,R)
FnRMAT(4(1x, 'C-l='
ElO.4))
COMDUTATION OF BI*(CRIT*CBI)-1*CIRTT=BUPF
qO0
Do 3 I=1*R
Do 3 J=1,P
3
RiFFl(IJ)=0O. EO
Dn 4 I=1,R
Do 4 J=1*P
D 4 =1*R
4
RiBFFI(IJ)=BUFF(IK)*CBI(J,<)+F3UFF1(IJ)
C**
**********'****v~vv§§***
**
UF'1l=(CBIT*CBI)-l*C8IT
IN CONJMON MANI6
C***********************
TcI(IECR.GT.5)WPITE(6,600)((UFFl1(IJ),J=1),I=ItR)
600 FoRMAT(4(lx,'UFFl=1,F10.4))
Dn 5 I=1N
D
5
MA0I0260
MA100270
MAIOO2O
MAIno290
MAIO0300
A0310
MAI00320
MAI00330
VCVTFq(BltJFFRIB*CRVEC)
IF(IECP.GT.S)WPITE(6,00)(C3VEC(I),IIlO0)
4
C*
MAIOO180
MAIOO190
AI00200
MAIOO2 1O
MAIO220
AIT00230
MA00240
MAI00250
Dm 2 I=19R
D
MAIOO06O
MATOO7O
AIOnO80O
MAIOOO90
MAIOO100
MAIOO110
MAIOO12O
MA0I0130
AI00360
MAT00370
MAI00380
MAT00390
MAI004 00
MAT004 10
MAT00420
MAI00
4
30
MAIOn440
4
MA100 50
MAT00460
AI00470
MAI00480
MA1004 90
UAIO500
AI00510
AI100520
MAIOO0530
uA100540
MAY0550
MAI00560
MAI00570
MAT00580
5 JP
8BFF(I,J)=n.
On 6 I=19N
AI00340
MAI00350
MAIO0590
EO
4AIOO600
MAIO610
A-9
MAI00620
On 6 J=IP
D 6 K=1,R
6
RBiFF(ITJ)=3I(TK)*81)FFI((,J)+RUFF(I.J)
Ir(IECR.GT.5)WPITE(69700)((~3UFF(IJ)tJ=9P),I=lN)
700 FoRMAT(4(1X,'RC8TCB-lCBT=,E10l.4))
F nS
C** COMDUTATION
7
DOn 7 I=IN
7 J=19P
D
D-(IJ)=O.
D
S
EO
8 I=lN
800
mAI00670
AI006bO80
MA100690
MAI00700
MAI00710
DO 8 J=1P
MAI00720
DO 8 K=19N
Dc (IJ)=DS(IJ)*+A(I*K)*BJFF(K*J)
MAI00730
4AIOn740
IF(IECR.GT.4)WDITE(69OO)((DS(I9J)gJ=19P)I=lN)
900
FnRMAT(4(1Xq'DS='vF1O.4))
C ** CO-APUTATION OF CS
D
9 =1tP
D 9 J=1,P
EO
9
C'(IJ)=O.
DO, 10 I=1,D
Dn 10 J=l,D
10
MAI00630
MAT00640
MAT00650
MAI00b60
On 10 K=lN
rS(IJ)=CS(I,J)+C(IK)*3UFF(KJ)
Ir(IECR.GT.5)WQITF(6,ROO)((CS(KJ),J=lP),K=1,P)
FoRMAT(4(1X,'CS=',E10.4))
PCTURN
END
4AI00750
4AI0n760
MATOO 7 70
AIT007BO
AI00790
MAIOO800
AIOO810O
MAI00820
MAI00830
MAIOO840
MAO0850
MAI00860
4MAIT00870
MAIOO8BO
A-]
SiBROUT INE
AIN4
AIOlOnlO
,BCRI ,CBINtPQq, IE-REPSBUFF
CrnMMON/MANT2/A
cOMMON/MA 1I3/ IRW. ICnL
MA0In0030
MA10004O
-OMMON/MAN4/OMEGCDSCS
C^MMON/MANT5/INU.INUS,
INJ0O
CoMMON/MANI6A/ADSC
CoMMON/TRAH2/X40oRIJFF I3UFF2 BUFF3
C(12912) I(12,12t.CBI(12t12)
DTMENSION a (I12.)B(12,12)
DTMENSION lUFF(12* P1)
DTMENSION RUFF1(12,12) XD(1l44,12),CS(12912),DS(12912)
DTMENSIONqUr;?)
l, 2)
DTMENSION .UFF3(12912),IOW(12)9ICOL(12),OlEGC(12912)
DIMENSION TNU(12),ADSC(12,12)
PR
I~,TEGER
MAIOOlO0
MAIOOllO
4AI00120
MAIOO130
MATB00180
Do 3 K=1.P
MA100190
MAI00200
MAIOO210
MA100220
MAI00230
MA100240
MAI00250
MA!00260
MA100270
MA100280
Cc(IJ)=CS(19J)*RUFF1(I(<)C(KJ)
MA00290g
EDSIL=1.E-4
MAI0030n
MAI00310
1 J=1IP
D
BijFFI(IJ)=-CS(1,J)
On 2
=19P
BiiFFt(II)=1.E08+UFFI (II)
100
It'(IECR.GT.6)WPITE(69100)((BUFF1(I1J) 9J=1D) 9I=1P)
FnRMAT(4(1X9'UFFI=mE1O.4))
O
D
3 I1=,P
3 J=19N
C¢(IJ)=0.F0
on 17 I=19D
On
MAIO00320
4A100330
17 J=1,9
IF (ABS(CS(IJ)).LT.EPSIL)CS(IJ)=0.
17
M4A100O80
MAIOO090
MA00170
2
3
MA100050
MAI00060
4&I00070
MA0I0140
MAI00150
MAI00160
Ir(IECR.GT.2)WPITE(6, 100)
1100 FRMAT(1X,'SURPOUTINE MAIN4)
C**COMPtITATION O CS (CONTINUED)
Do I=1,P
1
MAIOnO20
CoNTINUE
Ir(IEC.GT.5)WRITE(6,?on00)((CS(TJ),J=1,N),I=I9P)
?00 FoRMAT(4(1XvCS=,E10.4))
C**COMPtJTATION Or A-OS*C
"A100340
MAI00 3 50
MA 100360
4
B!FF2(19J) =RUFF2(I.J)*DS(I 9K)*C(KgJ)
MAI00370
mAT00380
MAI00390
MA1004 00
MAI00410
MA1004 20
Ir(IEC..GT.6)WPITE(69300)((BUFF2(IJ),J=19N)I=1,N)
mAYO0430
300
FnRMAT(4(1W'DSC=',El0.4))
MAI00440
MA100450
MAIo0060
DO 4
Dn 4
BiFF2
DOn 4
I=1N
J=1,N
(I .J) =O.EO
K=1,P
Do S I1,N
Do 5 J=19N
S
BiFF1 (I J)=A(1,J)-BI)FF2(I9J)
On 55 I=1,
MA IO0470
MAI00480
Dn 55 J=1,·
55
ArnSC(IJ)=9UFFlI1,J)
IF(IECR.GT.S)WRITE(6,400)((BUFFI(IJ)J=19)
400
rORMAT(4(1XAm-OS*C=1,El0.4))
OF XMD=MO4
C**COMPIiTATION
On 6 I=lP
6
Dn 6 J=1N
XvD(IJ) =CS(I J)
On 7 I=1,P
DO 7 J=1.N
7
8tiFF3(IJ)=CS(I,J)
N =N-1
IF(NN.EQ.O0)
GO TO 11
1=1N)
mAIO0 4 90
MAIO0500
mAI00510
MA I00520
MAI00530
MAI0050
MAI00550
MA100560
MA10O570
MAIO0580
MAIo00590
MA100600
MAI00610
A-]
On 11 L 19
N.1=LLP
N
MAI00620
MA100630
MAIOOb4O
On 8 I=IP
DO 8 J=19N
MA0060
BtIFF2(IJ)=O.EO
MAI005660
On 8 K=1,N
A
BFF2(IJ)=RUFF2(IJ)+BUFF3(IK)*RUFr1(KJ)
MAO670
Ic¢IECR.GT.7)WPITE(69,500)((RUFF3(1.J)J=1l9)I=1,P)
500 FRMAT(4(XtRUFF3=',ElO.4))
~~~~~
DO 9 I=1,P
MA100720
MAIO0730
DO 10 I=1lP
MAI0740
nO 10 J=1N
TI=I+L*P
10
MAT00750
MAI00 7 6
YMD(IIJ)=RUFF2(-J)
Ir(IECR.GT.7)WQITE(6,600)((3UFF2(ITJ),J=1I,),I=,P)
600 FoRMAT(4(X,'BIJFF2=,FO.4))
11
CoNTINUE
N=N*P
IF(IECR.GT.3)WRITE(6,700)(XMD(IJ),J=19,N),I=1,NP)
700
FRMAT(4(lX,'XMD='E]0.4))
C** ORTOGONAL
IyMD=144
IF YOU
MAI00850
11 IF YOJ
WANT
TO DESIGNTHE
FILTER,',/1X,
DO NOT')
1101 FaaMAT(12)
CALL ORTRED(XMD,OMEGC,NPNIXMDEPSI1,IECR)
15
Irt
IECR.GT.
1WRITE
6,0)(
(OMEGC
IJ) JlNJ=
l,1N}
F',XPMAT(4(lxqmEEGS=',Fj.4))
I(ISIGN.Eo.11
) O TO 15
Go TO 16
CoNTINUE
Do
Do
13
14
MATOObOO8
MAIOO810
MA00820
MAIOO840
PAD(5,1101)ISIGN
P00
AAI00770
'A00780
U400790
MA00830
REDUCTION OF MD'=XMD
EDSI1I=1.E-9
?100 WoITE(6,2100)
FRMAT(X,TYPE
l'nO
MA00700
%AI00710
Dn 9 J=1,N
BtFF3(IJ)=RUFF2(IJ)
9
MA10060
'4~~~~~~~~~~~AIOO6B
MAI00690
MAI00860
MA100870
MA00880
MAI0900
MAI00900
MAI0091O
MAI0920
4AIOn930
A~
n3
4A1I0940
MAn00950
IA100960
0AT0O977
14 I=1,9
13 J=,4
AI00990
MAI100990
8'iFF2(I,J)=O.E0
MAI0 00
iFF2(I,
I
)=1.EO
RI=4
CALL ORTRE(XMMOUFF2,NPNIXMDEPSI1,ICRI)
MAI IQ0 1
MAI0102
MAIO03
Ir(IECP.GT.1)WPITE(6,?101)((8UFF2(1,J),J=1,N)I=1,)
IMA01040
x
2101 FnRMAT(4(
16
CnNTINUE
C**COMPnTATION
Do
OME GSP=' ,ElO.4))
RANKOMEGS AN) LINEAR DEP£NDENCY
12 I=11, '
FF2(IJ)=OMEGC
(IJ )
InMEGC12
900
1000
MAI0107
\4A4 I 001
o 12,40
JJ1=
12 Bt,
MATI050
MA10 60
CALL MFGP(RUFF2,IOMEGCNNIRANK,
IRO.,ICOL,EPS,IER)
Ir(IECR.GT.1)W RITE(690 ) IER
FnRMAT(1X,, ERROR CODE IN COMPUTATION
O OMEGS ANK IS'.13)
WoITE(6,1l0nO)
I
PANK
FnRMAT(IX,, RANK OF OMFGS IS',I 13)
I !US=IRANK
WnITE(6,1003)
1003 FORMAT(IX,(IF YOU WANT TO OVECO
ME
1 IVEN Y UTOMATIC CMPJTATIONCYPE T-HE RANK OF OMEGS',/,PX,
0.OTHERWISETYPE
11')
RrAD(5,1004) ISIGN
1004 FnRMAT(12)
AIO1090
mA
1 100
AIOl
0110
MA10120
I130
mAI
MAT1140
AIl0150
AI01160
MAIO1170
MAIOl180
MAA01190
MAIO1200
MAIOI21O
MA01220
A-12
I'(ISIGN.NE.O)
WolTE(6,1005)
G
TO 18
1005 FRMAT(IX,'TYPE THE RANK OF OGS')
NUS
ROAD(5,*)
WoITE(6,*)
18
INUS
CnNTINUE
It(IECQ.GT.O)WRITE(6,1001)(IROW(I)ICOL(I),I=lN)
1001 FnRMAT(2(1X,,IPOW=,I3,ICOL=,,I3))
I6(IECR.GT.O)WRITE(6,1002)((BUFF2(IJ),J-1,N),I=1,)
1002 FnRMAT(4(1X,'BUFF2=,F10.4))
RrTURN
EsO
MA!01230
MA101240
MAI01250
MAI01250
4AIO1270
MAI01280
MAIO1290
M4AI01300
MAI01310
MAI01320
MA101330
MAI01340
A-13
cURROUTINE
AI 00010
MATN5
rOMMON/MAI12/AgCRIC3INPQR.IeCaEPSBUFF
MA100020
rOMMON/MAV13/IROW. ICOL
'-OMMON/MAI 4/0MEGC.DSCS
MAIOOO30
MA10O040
CnMON/MANT5/INU.INUS,INJO
CnMmON/MA4NT5A/GG
MAI N00050
MA100060O
CnMMON/TRAS12/XMOXMD2,BJFF1 ,BUFF2,RJFF3
MAIn00070
~IMENSION
A(llZ2),B(1212),C(lZ,12),9I(12912),CBItl?121
DTMFNSION
UFF(12912)
CS(12.12),nsl(12,12),O0MEGC(12,12)*IOW(12),TCOL(l2)
nIMENSION
DTMENSION VECRUIJ(12),UFF1(12,12),BUFr2(12,12),BFF3(12?,12)
DTMENSION YWD(144,12),X432(144,12)
DTMENSION INU(12),GG(12,12)
C**COMPIaTATION Or M
1
100
FARMAT(1X,(CBITCBI)-l='E10O.4,'FOR
MA100200
qAI0O210
MAI00220
MATOo230
MAIOo240
I =I3)
IMAI00270
2
Om 2 K=1.N
VrCBU(I)=VECBU(I)+A(1I,K)*BI(K,JJ)
I(IECR.GT.8)WRITE(6,?0O)(VECBU(I),I=1,N)
200
FnRMAT(4(1X,'VECBU=',F10.4))
MAI00280
MAI00290
MAI00300
4AI003 10
nt 3 I=1,N
DO 3 J=1,P
4AIO0320
MAIO0330
PFF(IJ)=VECRII(I)*C8T(J'JJ)*CC
Ir(IECR.GT.5)WRITE(6,30)((3UFF(IJ).J=1,P),I=1,N)
FnRMAT(4(IXtDORI=',E1O.4))
MAIo0340
C**COMP/iTATION
O
C'
DOn4
=1,P
D 4 J=1P
4
MAI0f250
MAO00260
VFC8U(I)=0.
300
MAi00130
MA100140
MAIOOl8o0
MAIOO190
on 2 I=1,N
3.
MAIOO120
MAIO0160
MAIo?100170
On i5 JJ=1i.R
COMD'UTATION OF OBI
C~=O.
On 1 I=1,P
C=CC+CBI (TJJ)**2
C,'=1./CC
Ir(IECR.GT.6) WRITE(6,100)CCJJ
qAIOOO90
wAIOOo100
MA0011O
MAri150
rALL MAINS(XMD2)
IiTEGER P,,R
C**COMPi'TATION FOR FACH BII=1R
C* e
MAooo80
BFF1(1,J)=-CI(I,JJ)*CRI(JJJ)*CC
D
5
I=1,P
MAI00350
MAI00360
MAIOO370
MAI00380
MAI00390
A100400
MA100410
5
B,FFI(1I,I)=1.*+UFFI(1I.)
MAI00 4 20
I(IECR.GT.8)WPITE(6,4On)((BUFFl(IJ),J=1P)I=1,P)
'4AIO030
400
FNRMAT(4(1x,BUIJFFI= '.E1O.4))
O
6 I=1P
MAI004 40
MATIO04 50
6
BFF2(IJ)=BUFF2(IJ)+BtUrFl(I,K)*C(KJ)
MAIO0 4 60
MA100470
MAI00480
MA100 4 90
500
I(IECR.GT.S)WRITE(6on)((BUFF2(ITJ),J=1,N),I=IP)
FnRMAT(4(1X*'CPRIME=*.E1O.4))
MA00500
4AI00510
DO 6 J=1,N
B,'FF2(I ,J)=0.
O- 6 K=1,P
C** COMrUTATION OF A-DBI*C
Dn 7 I=1N
Dn 7 J=1*N
BtFF3(I,J)=0.
Dn 7 K=1,P
7
Bi'iFF3(IJ)=BUFF3(I,J)+BUFF(I,K)*C(KJ)
600
MAIO0520
MA100530
4MA'0540
MAI00550
MA100560
MAI00570
Ip(IECR.GT.8)WRITE(6,600)((BUFF3(1,J),J=l,),I=1,N)
MA0I058O
FnRMAT(4(IXtRUFF3=',E104))
MA100590
OD 8 I=1tN
On 8 J=1N
MAIO0O600
MAIOO610
A-14
8
,'FFl(IJ)=A(I.J)-BLJFF3(I.J)
WAIlon620
Ir(IECR.GT.5)WRITF(697O0)((BuFF1(IJ),J=1,4),I=1,N)
700 FnRMAT(4(1X,'A-D9I*C=',E1.4))
C*# COMOUTATION OF XMD=MO'
D
q
10
800
9
=1,P
MA100660
Dn 9 J=1N
XvD(IvJ)=BUFF2(IoJ)
BtFF3(IJ)=BUFF2(IJ)
NY=N-1
D' 13 L=19,N
N'1=L#P
MAI00670
mAT00680
Mh100690
4AI007 00
MAI00710
mAI00720
OD 10 I=1,
On 10 J=1,4
B,'FF2(I,J)=O.
On 10 K=1,
m10IO0730
MAI00740
4bAI00750
MAI100750
RFF2(I,J)=BUFF21IJ)+BUrF3(I,K)*8UF1l(KJ)
MAI00770
I(IECQ.GT.B)WRI.E(6ROO){(3UFF3{IJ),J=19,),I=1,P)
qAI00780
MA4I00790
FnRMAT(4(1XlBUFF3=',EO.4))
DO
11=10
OD 11 J=1,
11
12
900
13
WAI00800
B,'FF3(IJ)=3UFF2(IJ)
MAI00810
4AI00820
On 12 I=1,P
On 12 J=l,9
MAI00830
MAI00840
I=I*+L*P
MAI00850
XYD(IIJ)=:UFF2(IJ)
Irl(IECR.GT.8)WRITE(6900)((UFF2(IJ),J=1,4),I=1,P)
FnRMAT4(1X,'RIJFF2=',F10.4))
CmNTINUE
No=N*P
MAO00860
MA100870
MAI00880
MAI00890
MAI00900
Ir(IECR.GT.3)WPTTE(6,901)(iXMDIJ),J=1,N),I=1INP)
MAI0910
q901 FnRMAT(4(lX,'XMD=1,ElO.4))
C* OTOGONAL
REDUCTION OF MO=Xq4O
IvMO=144
E~SII=1.E-3
DO 14 I=1,q
On 14 J=1,4
B,'iFF(IJ)=jMEGC(IJ)
C;LL ORTRED(XM0,9UFFNPJIX0NEPSIIIECR)
16IECR.GT.1)WQITE(6,QO)((C9UFF(I.J),J=1,N),I=1,N)
902 FnRMAT(4(1X*.'OMEGI=',r1O.4))
C** COMoUJTATION F ANKOMEG! AD LINEAR OE'ENDENCY
;O 16 I=1,N
RO
003
904
905
16 J=1.
M4A01040
MAI01050
MAI01060
CALL .MFGR(RUFFIOMEGI,N,',IRANK,IROWICOLEPSIER)
MAI1070
IT(1ECR.GT.1)WPITE(6,903)IER
FnRMAT(1XERPOR
CODE IN COMPUTATION OF RANK OF OMEGI IS',I3)
WoITE(6,904)IRANK
FnRMAT(X,PANK
OF OMEGI IS',I3)
IU(JJ)=IRANK
Ih(IECR.GT.2)WRITE(6.905)(IROW(I),ICOL(I),I=1,N)
FnRMAT(4(1X 'XIOW=',I3,'ICOL=',I3))
MA101080
MAIOI09O
MAI01100
MAI,01'110
MAI01120
MAI01130
MAI01140
Ir(IECR.GT.2)WPITE(6.QO6)((BUFF(IJ)J=lN)I=IN)
MA101150
EORMAT(lX,,COMPUTATION
IRI=4
uAI01160
MA101170
MAI0l180
wRITF(6,907)
15
MAI00980
MAI00990
MAI01000
MAI0101O
MAI01020
4AI01030
aUFFI(IJ)=BUFF(IJ)
InMEGI=12
906 FnRMAT(4(1X,'8tlFF=',E0l.4))
C**COMPi,'TATIONO THE GENERATOR
907
MAI00920
4AI00930
MAI00940
%AI00950
AT00960
4AI00970
14
16
AIO0n630
AIOn640
4AIo0650
OF THE GENERATOR Gjjm}
fALL ORTREOD(XMD2,RUFF1,4PNIXMDEPSIIICRI)
CnNTINUE
MAIO]19O
MAIO1200
uAIo1210o
MA101220
A-15
mAI01230
WoITE (6,90)
908
FPMAT(1X,'IF
yOiJ WANT T OVERCOM T
RAN<S OF OEGI',/,IxK,
IrnIVEN BY UTOMATIC COMPJTATION,TYPE O.OT-4ERwISETYPEIll)
RcAD(6O1000)ISIGN
1000 FnRMAT(I2)
909
Ic(TSIGN.E).11)
GO TO
WVITE(6,909)
F^RMAT(X,'TYPE
17
THE RANKS O
OMEGI,=1,R')
RrAD(5*)(INU(I),I=1IP)
W~ITE(6,*)(INU(I),I=1IR)
17
WrITE(6,910)
FnRMAT(1X,'IF SATISFIFDTYPE
PrAD(5,1000)ISIGN
Ir(ISIGN.EO.O)
CnNTINUE
GO TO
11.IF NT
TYPE 00')
15
BALL MAIN5A
RrTURN
MAIO1420
MA101430
S'tBROUTINE MAINSA
C** BUIiDS THE MTRIX GG OF THE GENERATORS
CnMMON/MANISA/GG
MAI01450
DTMENSION (12,12),8(12,12).C(12912),dI(12.12),CBI(12.12)
MAIO01460
DTMENSION
MAT01470
AI01 4 80
MAT01490
MAI01500
UFF(12,1l),GG(12,12)
100
FnRMAT(1X,,SUBROUTINE
I
C^NTINUE
DOn 3 II=1,9N
2
WITE(6,10])Iy
MAINSA,)
UAIO01510
101 FnRMAT(IX,WRITE GG(I.J),J=lIPI=I3'FREE
FORMAT')
I r>=R
RrAD(5,*)($G(IIJ),J:IrI)
W'ITE(6,*)(GG(TIJ),J=1,IR)
W ITE(6,102)
3
FnRMAT(lX,,IF SATISFIEDTYPE
RrAD(5,103)ISIGN
FoRMAT(I2)
I(ISIGN.EO.O) GO TO
ll.IF N3TTYPE
CnNTINUE
WoITE(69104)((G(IfJ),J=IIR),I=1,N)
104
AI 01440
CoMMON/MANT?/ABCBICRINtPQRIECREPS,RUFF
IT!TEGER P,9,R
rIc(IECR.GT.2) WRITE(6,100)
103
MAIO1300
MAI01310
MA101320
MAI01330
MA101340
MAI01350
MAI01350
MAT01370
m4TO1390
MAI01390
MAT01400
4
AIT01 10
ED
102
MAI01250
'AI01260
MAI01270
MAT01280
4AI012 90
Io=R
910
MA I01240
F-RMAT(4(1x,'GG=',El0.4))
WrITE(6,102)
RcAD(5,103)ISIGN
I(ISIGN.ED.O)
RFTURN
END
GO TO 1
00')
MA101520
MAT01530
MAI0 1540
MAI01550
MAI01560
MAI01570
MAI01590
MAITO01590
MAIO1600
MAI01610
MAI01620
MAI01630
MAI01640
qAIO1650
MAI01660
AIO1670
MAI01680
UA101690
A Il700
A-16
/*EOJJ
USERID r.ERARDJPCLASS A NAMf 4AINSP
FORTPAN
:READ ,AIN5P
FORTRAN Al GERARD 5/17/78
11:23
SBROUTINE
AIN5D(XMD?)
CnMMON/TRASH2/RUFFI
DTMENSION A(12,12),B(12912),C(12912),8I(12912),CBI(12,12)
DTMENSION UFF(12,12)
DTMENSION xMD2(144,12),BJFFl(12,12)
MA100030
qAI00040
MAIOO05O
MA10060
IC(IECR.GT.2)WRITE(6,99)
FnRMAT(lX,'SU8POUTINE
AIN5P')
XmD2(IJ)=C(I,J)
B,',FF(I,J)=C(I,J)
NY=N-1
Dr 5 L=1NN
N'I=L*P
DO 2 I1=lP
DO 2 J=1N
?
100
3
4
5
200
4AIOO001o
MAI0nf20
C**COMPiTATION
OF M
D
1 I=1rP
On 1 J=1IN
1
20:33:39
CrMMON/MANI2/A,8,CBI,CBINPORIEC*,EPSBUFF
ITEGER PR
99
06/27/78
MAIOO070
MAIOO080
MAIOOO90
MAIOOlOO
MAIOOllO
MAI00120
MAI00130
MAI00140
MAI00150
MAIOO160
MAI00170
MAI00180
MAI00190
B,'FFl(IJ)=0.EO
MAI00200
DO 2 K=1'N
MAI00210
RiFFI(ITJ)=BUFFl(IJ)+BUFF(I,K)*A(K,J)
It(IECR.GT.8)WRITE(6,100)((BUFFl(IJ),J=lN),I=l9P)
FnRMAT(4(1X,'B8UFFl=1,El0.4))
MAI00220
MAIO0230
MAI00240
DO 3 I=1,P
MAI00250
Dn 3 J=1tN
BtFF(IJ)=g3UFFl(,J)
MA100260
MA100270
D 4 I=,P
DO 4 J=lrN
mAI00280
MAI00290
It=I+L*P
XvD2(IIJ)=BUFF(IJ)
CnNTINUE
N¢=N*P
I&(IECR.GT.3)WPITE(6,200)((XMD2(IJ),J=lN),I=lNP)
FnRMAT(4(1X,'XMD2=',E1O.4))
RcTURN
MAI00300
4AI00310
MA00320
MAI00330
MAI00340O
MAI00350
MAI00360
EitO
MAI00370
A17
S,'iRROUTINE
MAIOOnO1O
A[46
MAIO0020
C~MMON/MANT/ABCBICBINPQRtIECREPS,RUFF
CnMMON/MANIS/INUINUS*INJO
DTMENSION INU(12)
.DTMENSION A(12,l2),(12,12),C(I2,12),CBI(12,12),BUrF(12,12)
DyTMENSION I(12,12)
I,'TEGER
P,,R
MAIOO70
C** CHErK WHETHE~ SUM NUI=NUJS
C** COMOUTATION OF DETECTION SACE
D
MAIOO030
MAIOOO40
MAIO0050
MAIOOO6O
MAIOO080
MAIOOO9O
DIMENSIDN
1I =1,R
MAI00100
1
TNU(I)=INV(I)#I
I)
R,r=,R)
I
M(IECRGT.)WRITE(6,S)n(IIN
SPACE OF RI3
HAS A DIMENSION '.I3)
100 FnRMAT(lXtETECTION
I,US=INUS+*
Ir-(IECR.GT.1)WPlTE(6,?OO)INUS
PACE ASSOCIATED WITH THE ST OF I '.1/,
700
FnRMAT(1X,,DETECTION
1IY,'SELECTED HAS A DIMENSION,I3)
IeUM=o
MAIOO110
MAIOO120
MAIOO30
MAIOO14O
MAIOOI50
MA0I0160
MAIOO170O
UAIOOlBO
DO 2 I=1,R
MAIOO190
2
IcUM=ISUM+INU(I)
W6ITE(6 9 201)ISUM
MAIOO200
MAI00210
201
FnRMAT(1X91SUM
OF NUI
LAI00220
IS',I3)
MAIOn0230
I;UO=INUS-ISUM
MA1002IOOZ40
3
W~ITE(6,20?)
202 FmRMAT(1X,'IF THE SUM OF THE NIJI IS EUAL TO NUS-DIMENSION',/,lX, MAI00250
1'nF THE ETECTION SPACE ASSOCIATED WITH THE SET OF RI-THESE't/,lXMA100260
1,IS ARE MUTUALLY DETFCTABLE.A DETECTION FILTER CAM BE ',/,IX
MA100270
MAI00280
1,ESIGNED
OR THIS SET WITH ASSIGNARlE EIGENVALUES.I,/,1Xo
l'rF IT IS NJOT.A TOTAL
OF NUS-(SUM
OF NUI)
EGENVALUES
ARE,/1X,
MA100290
MAI00300
IttNASSIRNA3LETIF YOU WANT TO CHECK TEIR VALUETYPEI1,',/,IX,
MAIO0310
1',THERWISE TYPE 00')
PrAD(5,10)ISIGN
uAIO0320
WoITE(5,10)ISIGN
MA100330
10
F~RMAT(I2)
MA100340
Ir(ISIGN.NE.ll) GO TO 4
MAI00350
WnITE(6,203)
MAI00360
POGRAM WILL PROCEED ON COMPUTING THE UNASclGN.,./,MAI00370
203 FnRMAT(1XTHE
llyt'EIGENVALUES.IF OIU MADE A MISTAKE IN SELECTING THE OPTION,/, MAI00380
1ly, TYPE On.OTHERWISE TY'E 11'.)
MA100390
RcAO(D5,10)ISIGNI
MAI00400
WnIolTE(6,10)ISIGNI
MAI00410
Ic(ISIGN1.Q.o0)GO TO-3
MAI00420
CALL MAIN6A
MAI00430
RmTURN
MA100440
4
WDITE(6,204)'
MA100450
204 FnRMAT(IX,'THE PROGRAM WILL NOT COMPJTE THE UNASSIGN.',/,lXe
MA100460
l'rIGENVALUES IF YOU MADE A MISTAKE IN SELECTING THE OPTION TYPEO0 MAI00470O
I;/,IX,'OTH-ERWISE TYPE 11')
4AI004 80
mA100490
PRAD(5,10)ISIGNI
WDITE(6,lO)ISIGNI
MAI0500
Ic(ISIGN1.E.0)
MAI00510
RrTURN
E~O
GO TO 3
MAI00520
MAIO0530
A-18
S6,BROUTINE MATN6A
MAIOOO10
CnMMON/MANI2/ABCRI,CBINPORIECREPS,RUFF
A4IOOO20
CnMMON/MANI4/OMEGC.DS.CS
wIA0n030
C-MMON/MANIS/INIJINUS.INJO
MAIOO40
CnMMON/MANT6/PUFF1
C** UFl=(CBIT*C8I)-I*CBIT
C** COMCS FROM MIN3
MA100050
MAIOWO60
MAIOO070
CnMMON/MANT6A/ADSC
MAIOO80
CnMMON/MANI6B/XMOIND
MAI0009O
CnMMN/TRASH2/PuF3
MAI0100
D'MENSION a(12,12),B(12,12),C(12912),~I(12,12),CB[I12,12)
DTMENSION MEGC(l2,l2),DS(12912)*CS(12.12).RUFFl(12,12)
4AIOOlO
4AT00120
DOTENSION 3UFF(12,12),ADC(12,12),XM3(12912),BUFF3(12,12),INU(12)
MAI00130
IFTEGER PR
Ir(IECR.GT.2)WRITE(6*OO1)
100
rORMAT(1X, SURROUTINF MAIN6A')
C** COMnUTATION
F (CBIT*CBI)-l*CBIT*C=CI
DO
1=1R
MAIOO10
MAI00190
Bi ,FF (I ,J)=O.EO
MAIO00200
On 1 K=1,P
MAIOo210
MA100220
MAI00230
MAI00240
MAI00250
B,'IFF(IJ)=BUFF(I,J)+BIIFFl(IK)*C(K,J)
101
Ic(IECR.GT.5)WRITE(6101)((BUFF(IJ),J=1,N),I=l,R)
FnRMAT(4(1X'CI=',E1lO.4))
Ir(IECR.GT.8)WQITE(6,20n)((BUFF1(IJ),J=l~),I1l=R)
200
201
?
3
O0RMAT(4(1XtUFFl=',El0%4))
COtPUTATION
OF MO=XMO
S
6
4AIoo250
4AI00270
I=(IECR.GT.8)WPITE(6.P01)((ADSC(IJ)*J=1,N),I=1,N)
CORMAT(4(X,A-DS*C=vE1l0.4))
IC.0=I
D 9 II=1l.
IiU1=INU(TII)-2
D 2 J=1N
XMO(INDJ)=SUFF(IIJ)
DO 3 I=1N
DO 3 J=1,N
B,FFl(IJ)=ADSC(I,J)
MAIO0280
AI00290
jAI00300
mAI00310
MAo100320
AI00330
4AIo00340
MAI0350
MAT00350
M4AI00370
ID=IND+I
MAI00380
I tU2--INU1
TF(INU2.El.1)
On 4 J=1N
MAI0o390
MAIO0 4 00
GO TO 9
4AI00410
XuO(IND,J)=O.EO
4
MAI00160
MAI00170
On 1 J=1,N
1
C**
MAIOO140
MAIOO150
-aT00420
On 4 K=1N
MA100430
XvO(INDJ)=XMO(INDJ)+BUrF(IIK)*PUF71(KJ)
I<iD=IND+l
MA100440
baIO0450
,F(INU2.E3.0)
On 8 JJ=1,INUl
MAIO460
AIO0470
GO
TO 9
C. 5 I=1N
On
J=1,N
BFF3(I,J)=O.EO
~AIO0480
MAIO0490
MAI00500
On 5 K=1N
MAIOO5LO
B,FF3(IJ)=BUFF3(I.J)+BUFF1(IK)*AOSC(K<,J)
4AI00520
On 6 J=1,N
XAO(INDJ)=0.EO
On 6 K=1,N
MAI005O40
MAIOOS50
XO(INDJ)=XMO(IND,J)+BuFF(I,K)*BUFF3(K,J)
ID=IND+
4AIOn560
MAI00570
On 7 I=1N
On 7 J1:N
A100530
7
Bt,FFL(IJ)=BUFF3(I.J)
MAIO058OO
4AI00590
AIT00600'
8
CnNTINUE
MAI00610
A-19
9
300
CNTINUE
Ir(IECR.GT.5)WRITE(6,0)((XMO(I,J),J=1,N),I=1,IND)
FnRMAT(4(1XM90=,E10.4))
DO 10 I=Ig
Do 10 J=1,
1.0 Bi'FFltIJ)=BUFF(I,J)
C** 9UF'1=CI IN COMMON MANI6
-
A10062O
ma100630
MA100640
MAT0o 6 50
MA1400660
MAI00670
4AT00680
A-20
C;LL MAIN64
RcTURN
S.,8BOUTINE MAIN6A
CnMMON/MAN2/ABCBICRINP.QRIECREPSRUFF
CmMMON/MANT4/OMEGC,DSeCS
C^MMON/MANIS/INU.,INUS.INJO
C^MMON/MANT6/BUFF1
C** BJF'=(CBIT*CBI)-1*C8IT
C** COMrcS FROM MAIN3
CiMMON/MANT6A/ADSC
CmMMON/MANT6B/XMOINO
Cr.MMON/TRASH2/PUFF3
DTMENSION A(91,2),R(12,12),C(12,12),8I(12,12),CBI(1212)
DIMENSION OMEGC(1212),DS(12,12),CS(12,12),BUFF1(1212)
'AI00690
MaI00700
MAJOnol0
MAIOOOlO
MAIOnO30
MAIOOnO403
MAIOO50
MAIOO060
MAI00070
AIOO080
MAIOn090
MAIOOIOO
MArOOllO
MAl00120
UFF(12912),ADSC(12,12),XM3(1212),BUFF3(12912)*INUJ(12?) MA100130
MAI00140
I.TEGER P2,R
Ir(IECR.GT.2)WRITE(6,100)'
MAI00150
MAI0O160
100
cORMAT(lX,'SURROUTINF MAIN6A)
C** COMaUTATION F (CIT*CBI)-l1*C3IT*C=CI
MAIOOI70
DTMENSION
D
D
I
101
MAIOO190
B'iFF(I.J)=O.EO
D^ 1 K=19P
MA 00200
FI(IK)*C(KJ)
Bi'FF(1IJ)=UFF(IJ)*BIFl
MAI00220
IE(IECR.GT.5)WRITE(69101)((BUFF(I,J),J=1,N),I=lR)
FnRMAT(4(iXCI=tElO.4))
MAIO0230
MAI00240
Ir(IECR.GT.8)WRITE(6,P00)((BUFFI(IJ)gJ=1P),1=1R)
MAI00250
MA100210
CRMAT(4(1X,'UFF1=',ElO.4))
200
C**
MAI001O
1=1,R
1 J=1,N
CO,.PUTATION
OF MO=XMO
Ir(TECR.GT.8)WRITE(6,?O1)((ADSC(1IJ)*J=lN)tI1=1N)
201
iORMAT(4(]XtA-DS*C=,,ElX%4))
I,Ul=INU(II)-2
3
MA100330
MAI00340
MA100350
MA I00360
IkD=IND*1
IKU2=-INU1
Dnn 4 J=1.N
X-AO(INDJ)=O.EO
D 4 K=19N
XvO(IND,J)=XMO(IND.J)+BUFF(IK)*BUFFI(KJ)
MAI00380
MAI00390
qA I00400
MAI00410
4A 0420
MAY 00430
MAY 00440
I!D=IND*l
MA00450
ODi 8
D
GO TO 9
JJ=1,INU1
5 T=1,N
D0 5 J=1,N
Bt)FF3(IJ)=O.EO
On 5 K=1,N
3'8IFF3(IJ)=BUFF3(IJ)+BUFFI(I,K)*ADSC(KJ)
Dn 6 J=19N
XvO( INDtJ)=O.EO
DO 6 K=1,N
6
MA100290
MA100o320
vF(INU2.El.O) GO TO 9
5
MAI00290
DOn 2 J=1N
XuO(INDJ)=BUFF(II,J)
DO 3 I=1.N
D 3 J=1,N
BtFF1(I,J)=AOSC(IvJ)
TF(INU2.EO.1)
4
MA IOOZ70
mA100300
MAT00310
I'ID=1
DO 9 II=1o
2
MAIO0260
X'O(IND,J)=XMO(INDtJ) +BUFF(1IK)*BUFF3(KJ)
INID=IND41
D
7 I=1NOn 7 J=1N
iA100370
MA 100460
'AI00470
MAIOO4O
MAI00490
MAI00500
MAI.005 10
MA100520
MAO00530
MAIOn540
MA 100550
MAIOOS6O
MAIo0560
MAI00570
MA I00580
MAr0o0590
A-21
7
8
Bt'iFF1(IJ)=BUFF3(IJ)
CnNTINUE
MAI00600
ohI00610
9
C',NTINUE
maI00620
I-(IECR.GT.5)WPITE(6,300)((XMO(IJ)J=1,N),I=lIND)
MA100630
300
10
FnRMAT(4(lX,'MO=',ElO.4))
MAIO0640
DOn 10 I=1,
Dn 10 J,
MA100650
MAlIOn660
i,',FF1(IJ)=BUFF(TIJ)
C*o 8UF:-l=CI
IN
COMMON MANI6
MAT00670
AI0O0680
CALL MAIN63
RrTURN
MAI00690
MAIO0700
E;,D
1AI00710
A-22
S,BROUTINE MAIN68
4AI00010
CnMMON/MAN2/A,8,C,RICBIN,DPQR,OIECREPS,BUFF
MAIOo2O
CnMMON/MANT3/IROWICOL
CnMMON/MANT4/OMEGC.DSCS
CnMMON/MAN6B/XMOIND
CnMMON/MANT6C/BUFFI
D;MENSION XMO(12,12),OMESC(12,12).DS(12,12),CS(12,12)
MA100030
4AIOn04O
MAln0050
MAIOOO60
MAI0f070
DTMENSION UFF(12,12),A(12,12),B(1212)C(12912)*BI(12,12)
DYMENSION CI(I1212)PUFr1(12,12),ICOL(12),IRPOW(12)
I.TEGER P,O,R
I-(IECR.GT.2)WPITE(6.100)
100 FnRMAT(1XSURROUTINE
MAIN6B)
C** ORTWOGONAL REDUCTION F XM3=MO
DOn 1 I1N
MAIOOO90
MA1OO100
MAI00110
MAIO0120
MAIOO130
MAI0140
D 1 J=19N
I.
MAIOO150
B,FF(IJ)=OMEGC(IJ)
MAI00160
I)UFF=12
ErSI1=1 .IE-Q
CALL
*MAIO170
MAIOO180
ORTRED(XMORUFFIND.NIBUFFEPSI1,IECR)
MAIOO19O
I~(IECR.GTo2)WQITE(6101)(()UFF(IJ),J=19N),I=1,N)
101 FmRMAT(4(1x°'OMEGOG='.E1lO.4))
C* COM;UTATION OF THE LINEAR EPENDENCY O
D
Or
2
300
400
MAIO0200
THE COLUMNS OF OMEGOG
2 I=19N
FnRMAT(IX,ERROR
CODE
MA100240
MA100250
MAIO00260
MAI00270
ICOLEPSI1I ,IER)
IN COMPUTATION
OF RANK
OF OMEGOG
IS',I13)
Ic(IECR.GT.2)WPITE(6,30O)IRANK
F^RMAT(lX*RANK OF OMFGOG IS'I'3)
Ir(IECR.GT.2)WPITE(6,400)(IQOW(I),ICDL(I),I=1,N)
FnRMAT(lXIROW=',I3'IC3L='I13)
Ir(IECR.GT.2)WQITE(6,~OO)((UFF(IJ)J=lN)I=1N)
500. FnRMAT(4(Ix,'DEP OF OMEG3GlElO4))
CLL MAIN6C
RI-TURN
MAI00330
mA00340
MAI00350
MA100370
MAI00380
S,,9ROUTINE AIN6C
CnMMON/MANT2/ABCRI.CBIoNPORIECREPSBUFF
CnMMON/MANI5/INU,INUSINJO
AI00390
MAI00400
CnMMON/MANI6D/ROG
AIo00420
MA00430
CnMMON/MANI6C/RUFFl
1AIOO410
CnMMON/TRASH1/IZ
C**IN CnMMON MANI6CRUFF1=OMEGOGCOMES
FOM MAIN68
DYMENSION (12,12),B(12,12),C(12,12),8!(12,12),CBI(12,12)
DvMENSION UFF(12,12),BUFFI(12,12),IZ(12),ROG(12,l12)
DIMENSION INU(l2)
ILTEGER P,O,R
IC(IECR.GT.2) WRTITE(699)
99
FRMAT(1X,'SURPOUTINE
MAIN6Cl)
C** SELrCTION
OF ROG
MA100440
MAI00450
4AI00460
MATO00470
"A100480
MA00490
MAI00500
MAT00510
WPITE(6,100)
FnRMAT(1X,'IDENTIFY WHICH COLUMNS OF OMEGOG YOU WISH TO,/,1X
It,EEP
Y TYPING THEIR
lly,'INDICATE
WHAT AE
NUMBERS IN FORAT
I3.IF
THE NUO FIRST
INEARLY
1',OLUMNS.Or OMEGOG')
NUO=NUS-(SUM NI),/,MAfO050
INDEPENDENT',/lX,
MAIOO5SSO
M4AIO00570
1000 FRMAT(1213)
4AT00580
WITE(6ln0)(IZ(I)I=,INUO)
W-ITE(6,101)
FnRMAT(1X,'IF DATA ARE ICORECTLY
MAT00520
MAI100530
MA00560
RA(5,1000)(I7(I),=11,UO)
101
MAIO00280
MAIO00290
MA100300
MA100310
MAI00320
MA100360
~~~El'-,.~~~~~~~~~D
I
100
MAI00210
MA0I0220
MA100230
2 J=1,N
I'FF1(I9J)=BUFF(IJ)
CLL MFGR(~UFF,IBUFF,NN,IRANKIROW,
IC(IECR.GT.2)WQITE(6,200)IER
200
MAIOO80
MA00590
ETEREDTYPE
MA100600
OO.OTHERWISEI,/.9xMAIO0610
A-23
1,,TYPE
MAI00620
MATI00630
11')
PcAD(5,1001)ISIGN
MAI00640
1001 FnRMAT(I2)
2
Ir(ISIGN.E).O) GO TO
MATI00650
Dn 2 J=1INUO
Jr'=IZ(I)
Dr 2 I=1,N
MAI 00660
RnG(IJ)=BUJFF1(IJJ)
MAI00690
MAIO0700
MAI00 7 10
MaIOO720
MAI00730
MA100740
MAI 00750
MAI00760
MA 100670
MA 00680
Ir(IECR.GT.2)WPITE(6,?O0)((ROG(I,J)J=INJO),1I=1,N)
FnRMAT(4(1X,9ROG=',EO1.4))
?00
IS A (N*INUO)
C*# ROG
MATRIX
CALL MAIN61
RErTURN
EoD
SiBROUTINE MAIN6D
CMMON/MAN2/BCBICBI,NPQRIECREPSBUFF
MATI00770
CnMMON/MANI6/CI
mAIo00780
MA1007 90
CnMON/MANT15/INU,
INUS. INJO
CmMMON/MAN I 6D/ROG
C**
CI JJAS BEEN
COMPUTED
MATI
00800
IN MAIN6A(WAS
BUFF1)
CnmMON/MANI6A/ADSC
CnMON/MANT6E/TETA
DyMENSION (12.12),8(12.12),C(12o,12),*NI(12,12).CBI(12.12)
DTMENSION C(12,12),RUFF(12,12)vlINLJ(12),ROG(12,12).TETA(12,12)
DTMENSION DSC(12912)
ITEGER P,t9R
C**
COMPUTATION
F TETA MATRIX
TF(IECR.GT.2)WRITE(6,99)
99
FmRMAT(1XtSUBRROUTINE MAIN6D')
Ir (IECR.GT.8)WRITE(6998)((CI(ITJ),J=I,9),I=1,R)
98
97
MA1I00880
MATI00890
MAIOO900
MATOO910
MI0o0920
I-(IECP.GT.B)WPITE(6.7)((ADSC(IJ),J=lN),I=1,N)
MATIOn930
FnRMAT(4(1X,'ADSC=',ElO.4))
MAI 00940
MIA00950
MAI00960
MAI00970
N,'I=INU(II)-1
Dn
2
MAI00 8 30
MAT00840
MAIO0850
MAI00860
MAI00870
FnRMAT(4(1X.'CI=',E1O.4))
On 6 II=1,
1
MAIO081O
MAI00820
1 J=1,N
TcTA(II,J)=O.EO
MATI0090
K=1.N
On
TrTA(IIJ)=TETA(TI,J)+CI(IIK)*ADSC(<,J)
D
2 J=1,N
BFF(II,J)=TETA(IIJ)
I(NUI.EQ.n) GO TO 6
D 5 JJ=194UI
On 3 J=1.N
MA100990
MAI 01000
T-TA(IIJ)=O.EO
On 3 K=1N
MA 01010
AI 01020
MAT01030
MAIO1040
MATI01050
MATI01060
A101070
MAIOlO8O
4
TrTA(IIJ)=TETA(TIJ)+BUrF(IIK)*ADSC(KJ)
On 4 K=1,N
8tFF(I,K)=TETA(II,K)
5
6
CnNTINUE
CnNTINUE
MAIOllO 10
I'(IECR.GT.8)WPITE(6,l00)((TETA(I,J),J=lN),I=lR)
MAIOI 130
FnRMAT(4(1X,'TET=',E1O.4)
MAITOl1140
MAIO1 150
3
100
7
8
Or 7 I=1,R
0n 7 J=1IINUO
B!tFF(I,J)=n.EO
On 7 K=1,N
B!'FF(IJ)=3UFF(IJ)+TETA(IK)*ROG(K,J)
On 8 I=1,R
DOn8 J=1IUO
T&TA(IJ)=UFF(IJ)
MAI01090
MAIO 100
MAI01120
MAI0l160
MAI01170
MAIO l180
MAIO1 190
MAIO1200
MAIO1210
MAIO1220
A-24
C**TETA IS A (R*TJUO)
ATRIX
I~(IECR.GT.5)WRITE(6,?0O
PO0o
MAI01230
((TETA(1IJ) ,J=lINuJO),I=lR)
FnRMAT(4(1 X, 'TETA=' ,ElO.4))
MAI01250
AI01250
CALL MAIN6E
RrTURN
MAIO)1260
MAI01270
ED
MhA01280
A-25
S,'BROUTINE MAIN6E
MAIOO010
CMMON/MANT2/A,B,C,BI,CINPORIECNEPSBRUFF
MAI00020
CnMMON/MANI5/INU.INUS.INJO
MAI0n030
CnMMON/MANISA/GG
MAIOAnOO40
CmMMON/MANT60/ROG
CnMMON/MANT6E/TETA
CnMMON/MANTI6F/XPI
MAIOOO50
MhATOO60
MAIOOO70
CnMMON/TRASH2/CBVEC,CRVIVBUFF1,BUFF2,9UFF3
MAI0080
DTMENSION (12,12),8(12,12),C(12912),6I(12,12)tCBI(12,12)
DyMENSION UFF(12,12?),RO3(12I2),GG(1,12),TETA(12.12)
DTMENSION XPI(12,12),TNLJ(12)CRVEC(7),CBVIV(78),BUFFI(12,12)
DTMENSION UFF?(12,12),BJFF3(12,12)
I.TEGER P.R
I(IECR.GT.2)WPITE(6,9100)
100 FnRMAT(IX,,SUBROUTINE MAIN6E)
C** COMOUTATION OF MATRIX XPI=-I
C** COMnUTATION OF (ROGT*POG)
Dn 1 I1,IYUO
MAIonlBO
Dn 1 J=1,INUO
Bi'FF(IJ)=0.EO
MAIOO190
MAIOO200
Dn
MA1On210
MAIO0220
1 K=1N
1
Bi',FF(1
,J)=qUFF(I ,J)+ROG(<,I)*ROG(KJ)
C** COMOUTATION F (ROGT*ROG)-1
C** TRAMSITION TO SYMMETRIC STORAGE
I1=12
TF(IECR.GT.5)WRITE(6,99)INUJO
99
cQ0RMAT(lX,'INUO=',I3)
Ic(INUO.EQ.1)
101
GO TO 11
MAI00230
MA100240
MAI00250
MAIO0260
MAIO0270
MAI00280
MAI00290
CTLL VCVTFS(BUFF*INUO.IRCBVEC)
Ir(IECR.GT.B)WRITE(6,IO1)((BUFF(IJ),J=1IINUO),I=1,INUO)
MAIOO30n
FnRMAT(4(1X,'BUFF=',EIO.4))
MAIO00310
I-(IECp.GT.8)WPITE(6.O)(CRVEC(I),I=1,12)
102 FnRMAT(4(1X,'C9VEC=',Fl0.4))
C** COMnUTATION nF INVERSE OF CVEC
CALL LINV1 (CRVECINUN,C3V'IVIOGTDlED2,,IER)
Ir(IECR.GT.8)WPITE(6.103)(CBVIV(I),I=112)
103 FnRMAT(4(1X,'CBVIV=',F10.4))
C** COMSUTATION Of (ROGT*ROG)-l
C;LL VCVTS7(CBVIV,INUORJFF,IR)
MAI00320
MA100330
MAI00340
MAI00350
mAI00360
MAI00370
MAI00380
MAIO0390
MAI00400
MAIO0O410
Gn TO 12
CNTINUE
11
MAIOO090
4AI00100
MAIOO110
MAIOO120
MAIOO13O
MAIOO140O
4MA100150
4AI00160
MAIOO170
8,FF(1,1)=I./BUFF(1,1)
CmNTINUE
I~(IECR.GT.5)WRITE(6,104) ((BUFF(IJ),J=1,INUO)tI=,INUO)
='EIO.4))
104 FnRMAT(4(XIROGT*ROG-1
C** COMSUTATION F (ROGT*ROG)-l*ROGT
12
MA100420
MA100430
MAI00440
mAI00450
AI00460
D
2 I=,INUO
DOr 2 J=1 9 N
MAI00470
MAI00480
B,':FF1(IJ)=O.FO
MAI00490
OD' 2 K=l1IMUO
4AIO500
2
B,FF1(IJ)=BUFFI(I.J)+BIJuF(IK)*RO6(JK)
MAIOO51O
Ii(IECR.GT.)WRITE(6105)((UFF(IJ)J=19),I=1,INUO)
MA0I0520
105
FnRMAT(4(1X,'RBUFFl=',F10.4))
C**
4I00530
AIO00540
MAT0055O
OF A*ROG
COMnUTATION
Dn 3 I=1N
Dn 3 J=1,IJUO
MAI00560
MAI00570
MAI00580
8BFF2(IJ)=O.FO
o 3 K=1IN
,J) +A (I ,K) *POG(KJ)
3
B'FF2(I ,J)=BUFF2(I
106
Ic(IECR.GT.8)WPITE(6,106)((3UFF2(IJ)*J=,INUO),I=1,N)
FoRMAT(4(lX,'A*ROG=',E10.4))
MAIS00590
MAIO00600
MAI0o610
A-26
C** COMrUTATION
MAI0n620
F G*TETA
DrO 4 I=1,N
D 4 J=1INUO
MA100630
MAI00640
B,FF(I*J)=O.EO
MA100650
D
MA100660
4 K1,R
BtFF(IJ)=RUFF(IJ)+*G(,(I,K)*TETA(K,J)
Ir(IECR.GT.)WPITE(6,107)((BUFF(IJ),J=1,INUO),I=1,N)
107
rORMAT(4(lXtG*TFTA=FE10.4))
C*" COM5UTATION F AMRA-G06TETA
DO 5 I=1N
'n 5 J=1II1UO
5
B,FF3(I,J)=3UFF2(I.J)-BIJFF(I,J)
MAT00670
MAI0O6BO
MA0I0690
MAI00700
4AI00710
7
OF XPI
C** COMIUTATION
C** XPI IS A INUO*IN(JO MATRIX
Dn 6 I=1,INUO
Do 6 J=l1INUO
"AI00740
MAIOf750
qAI00760
AI00770
4
MAI00
XoI (IJ)=0O.EO
Ma100780
iaI00790
Do 6 K=1,N
6
MAI0800
XI(I,J)=XI(I,J)+RUFFI(IK)*RJFF3(KJ)
uAI00810
MAI00820
MAIO0830
MA1OO84O
mAI00850
MAIO0860
MAI00870
Ir(IECR.GT.S)WPITE(6,o108)((XPI(I,J),J=1,INUo),I=1,INUO)
108 FnRMAT(4(X,'XPI=*',ElO.4))
EIGENVALUES
C** COM5UTATION 9F X
CALL MAIN67
ReTURN
ELD
SiBROUTINE MAIN6F
C'MMON/MANI2/ABCBICBINPQRIE'CREPSRUFF
mAI00f80
CnMMON/MANT5/INU, INUSINJO
C^MMON/MANT6F/XPI
MAI00890
MAIOO900
C^MMON/MANI66/W
MAIOO0910
MA100920
MAITOO930
I100940
MAI00950
MA100960
uAIOO970O
VAI00990
UAI00990
MAIO1000
CnMMON/TRAqH2/BUJFF
OTMENSION XI(12,12),TNU(12),BUJFF(12t12),Z(1,1)
DTMENSION a(12,12),B(12,12),C(12,12),BtI(12,12),Ct(12,12)
OTMENSION LIFFl(12,12)
CmMPLEX W(12)
INTEGER P,,R
Ib (IECR.GT.2)WRITE(6,99)
MAIN6F')
FnRMAT(1XSURROUTINE
99
C** COMoUTATION 9FXPI EIGENVAUES
D
1
100
I
MAIOO110
=INUO
MAI01020
MAI01030
On 1 J=,INUO
B,FF1(IJ)=XPI(I,J)
I'iOB=O
4AT01040
KK=13
MAIO1050
IiUFF=12
MAI01060
I;=l
MAI01070
CALL EIGRF(3UFFl,INUOIPJFFIJOBWZIZKWKIER)
W6ITE(6,100)IER
FnRMAT(1X,,ERPOR CODE IN COMPUTATION OF XPI EGENVALUES
MAIOIOBO
MAI01090
MaIOI101
FnRMAT(1X,,IF IER IS
1
REATER THAN 128BEIGE4VALUES ARE NOT CORPECTMAIO1llo
1)
WiITE(6,10?)(W(I),I=l.INJO)
102
I',I3)
MAO.0 1
WRITE(6,101)
101
20
MAIO0730
MAIOll30
MA1l14O
FnRMAT(IX,UNASS.EIGENV.',2(E10.4.2XElO.4))
MAIOll$O
RrTURN
EktO
MAIOl 1650
MAI01170
A-27
uAIOOl00
S,,BRROUTINEMAIN7
MAI00020
I"ITEGER P,,R
4AIO030
C** STEc 5G
MAIOO040
WOITE(6l10nO)
MAIOO050
1000 FRMAT(1X,'THRFE POSSTBILITIES ARE o=EN NOW:t,/,lX,
1j'ACCEPTTHE UNASSIGNAqLE EIGENVALUES OF THE DETECTION FILTEP GOTN."AI00060
MAI00070
1. ,lX,WIT4 THIS SET OF VENTS',/l1X.
SUBSET OF THE ACTUAL BIS HICH DOES NOT YIELO UNASST.'MAIOnOB0
l'iOOK FOR
I/
X 'EIGENJVALUES'
/,1X
1,vNCREASE THE DIMENSION
MAIOOO9O
F THE REFERENCE MODEL')
4ATOOlO1
WnITE(6,1001)
LAST POSSIBILITY IS NOT YET OPERATIONAL,)
1001 FRMAT(IX,THE
1
W;ITE(6,1002)
1002 rORMAT(lX'IF YOU WANT TO FIND A SU3SET OF THE ACTUAL 8IS',/,lX,
00')
EI3ENVALUEStTY-E 11.OTHERWISETYPE
l,.wITHNO UASSIGNABLE
100
mAIOOlSO6
FnRMAT(I2)
MATOO170
Ir(ISIGN.N.Ill)
3
GO TO 3
cORMAT(lX,*THF PROGRAM dILL LOOK FO A SU3SET OF THE BIS',/tlX.
1',wITHNO UNASS. EIGENVALJES.IF YOUJ MADE A MISTAKE IN',/,1X9
1'cELECTING THE OTIONTYaE
0o.OTHERWISEtTYPE 11t )
PrAD(5,100) ISIG41
WITE(6,100)ISIGNI
I,(ISIGN1.EQO.O0)GO TO
CiLL MAIN7A
RrTURN
WMITE(6,1006)
11 e )
GO TO
MAI100290
MAIO0300
mA100310
'AI00320
MAIOln330
RcAD(5,100)ISIGN2
WrITE(6,100)ISIGN2
I
MA100340
RrTURN
E;D
S,'RPOIJTINEMAIN7A
C'MMON/MANI2/AB,CBI9,CBI,N,POtRtIECR,EPSFUFF
CnMMON/MANT3/IPOWICOL
MA100350
MATO0360
hAI00370
MAIOO380
mAI00390
CMMON/MANIS/INUINUSINJO
MAIO0400
CnMMON/MANI6E/TETA
C'MMON/MANI6F/XPI
CeMMON/TRASH2/RUFF19gFF2tX4OI
OTMENSION a(12,12),8(12,12),C(12,12),tbI(12,12),CBI(12,12)
DTMENSION IU(12),BUFF(12,12),TETA(12,12),XPI(12,12)8UFFl(12,1?)
DOMFNSION UFF2(12,12),XIOI(12,12),IOW(12),ICOL(12)
IWTEGER P) 9 R
Ir (IECR.GT.2)WRITE(6,99)
FnRMAT(2X,'SUBROUTINE MAIN7A')
MAIOo410
MAI00420
MAI00430
MAIOn440O
MAI00450
MAI00460
MAI00470
MAI00480
4AIO04 90
C* # STEA
H
MAI00500
C** COM5UTATION FOR ALL 8IS
98
MAI00200
MA100210
MAIO0220
MA100230
MAI00240
MAI00250
MA100260
4AIO'0270
MAI00280
19lXv'OTHERWISE.TYPE
Ir(ISIGN2.rQ.O)
MAI00180
MAIOO190
WILL DESIGN A FILTER WITH THE RIS',/91X
POGRAM
1006 FRMAT(X,'THE
0
leiS EVENTS.IF YOU MADF A MISTAKE IN SELECTING THE OPTIONTYPE
99
MA100120
'AI00130
MAIL00140
MAIOO150
PrAD(5,100)ISIGN
W'ITE(691003)
1003
UAI00100
MAI00510
01
1 =1,R
W-ITE(6,98)II
AI00520
MAI00530
FnRMAT(1X,,COMPUTATION OF THE EIGENVALUES ASSOCIATED WITH B',12)
MAIO05O40
I;,D=I
C** COM.UTATION
OF MOI
MA100550
MAI00560
Ni'I=INUO-1
MAI00570
DOn 1 J=1,IUO
MAI00580
Xk'OI(INDqJ)=TETA(IItJ)
MAI00590
BiFF(1,J)=-TETA(IIJ)
IH(NUI.EO.O)
GO TO 4
MAIOb00600
MAI0610
A-28
D
4
J=19UI
MA0IO0620
11O=INDl
MAIO0630
Dn 2 J=1IINUO
B'FFl(IND,J)=0.EO
2
3
33
4
MA100640
MAA00650
D 2 K=1,INUO
B,FFI(INDJ)=RUFF1(INnJ)*BUFF(1,K)*XPI(KJ)
D 3 J,INUO
MA00660
MAI100670
4AT00680
Bt'FF(1,J)=UFFl(INDJ)
Dn 33 J=1IINUO
XuOI(INDJ)=BUFFl(INDJ)
CnNTINUE
MA100690
MAI00700
MATOn7lO
MAI00720
IE(IECR.GT.S)WITE(69lOO)((XMOI(IJ)J=lINUO)I=INUO)
100 FARMAT(4(lX,*MOI=,E10.4))
C** OTWOGONAL REDUCTION OF MOI
5
Dn 6 I=1IIjUO
MAI00760
Dn S J=1,IUO
BFF(IJ)=).E0
A00770
MA100780
6
101
Ir(IECR.GT.12)WRITE(6,101)((BUFF(IJ)J=1,INUO),1=l1,INUO)
FnRMAT(4(lX,'RUFF=',E0.4))
IMOI=12
E;SII=0.001
EO
C;LL ORTRED(XMOIBUFFINJOINUOI1XMOIEPSIIIECR)
I(IECR.GT.5)WRITE(6,1O2)((3UFF(IJ),J=-lINUO),I=1,INUO)
102
rORMAT(4(lXtBUFF=
C** COMUTATION
F BETA
FlO0.4))
MA100910
104
FnRMAT(X,'IROW=',I3'ICL=tI3)
Ir(IECR.GT.2)WPITE(6105)((BUFF1(IJ),J=1,INUO)tI=1INUjO)
105 FRMAT(4(IX#DEP
OF BFTA'E0.4))
On TO 666
Ic(IECR.GT.2)WITE(6,l103)IRANK
OF BETAP IS',I3)
GO TO 77
CLL MAN7AA(IRANK)
CnNTINUE
C** RETP=RUFF
I(IECR.GT.12)WRITE(6,106)((BUF(IJ),J=1lIRANK)I=1,INUO)
106 FnRMAT(4(1X,'BETA=,EO.4))
D
8 I=IINUO
DO 8 J1.IPANK
8BfF2(IJ)=BUFF(IJ)
C** BET=BUFF2
C** COMMUTATION OF DELTA
Dn 9 =1'I4UO
On 9 J=1,IUO
9
,A100960
MA100970
I00980
MAI00990
MAI01000
'4101030
IANK=
CnNTINUE
Il(IRANK.E3.0)
MA100950
MA01020
I(ABS(BUFl(11l)).LT.EPSI)
FnRMAT(1X,RANK
MAI00930
AI00940
MAIO]010
CNTINUE
IoANK1
A
mAI00890
A100900
uA100920
GO TO 66
Ir(IECP.GT.2)WITE(6,19)IER
77
MA!00840
MAI00850
Ir(INUO.EQ.)
FnRMAT(1X,ERROR CODE IN COMPUTATTON OF RANK OF BETAP IS,I3)
I&(IECR.GT.2)WRITE(6,104)(IROw(I)tICOL(I),I=l1,INUO)
103
MA100820
4A00830
I&(IECR.GTR)WPITE(6,97)INUO
192
666
MAIOObOO
MA.Oo8lO
MAI00880
On 7 J=lIIUO
BFFI(IJ)=BUFF(IJ)
I1UFF=12
CILL MFGR[BUFF1IXMOIINJOINUOIRAN<,IROWICOLEPSI1,IER)
66
MFF(II)=1E0
AI00790
MA100860
MAI00870
DO 7 I=lI9UO
7
MA100730
MAI0n740
MAI00750
B,'FF(IJ)=XMOI(I*J)
Bi'FFl(IJ)=XMOI(IJ)
uAIOlo4o
4A01050
MA01060
MAI01070
MA101080
MA10190
MAI011O
MA10110
MAI01120
AI01130
MAI-01140
MAI01150
MA101160
MATOI170
MAI01180
MAI1190
MA01200
MA101210
MAT1220
A-29
97
TF(IECP.Gr.8)WRITE(6.97)INUO
rORMAT(lX,,INJO=,I3)
I-(INUO.EO.l)
107
109
110
88
888
108
GO
MAI01230
4AI01240
TO 8
AIO1250
CALL MFGR(3qUFFI,IXMOIINJO,INUO,IPAN<1,IROWICOLEPSIlIEP)
Ir(IECR.GT.2)WQITE(6,107)IER
FnRMAT(1X,ERPOR CODE IN COMPUTATION OF RANK OF XMOI IS'-13)
I{-IECR.GT.2)WQITE(6,109)(IROW(I),ICDL(I),!=1,INUO)
FDRMAT(1X,,IROW=',13,'ICDL='tI3)
MAI01260
MAIO1270
MAI01280
MAIO12gO
4AIO1300
T'(IECR.GT.2)WQlTE(6,110)({UFF1(IJ),J=lINUO),I=lINUO)
MAI01310
F'nMAT(4(IXn'OEP OF DELTA IS',E10.4))
Go TO 88
CmNTINUE
ITANKI=1
Ic(ABS(BUFFI(,*-l)).LT.EPSII) IANK1=0
CnNTINUE
IT(IECR.GT.2)WPITE(6,108)IRANKI
MA101320
MAI01330
MAI01340
MAI01350
MAI01360
AI01370
MAI01380
FnPMAT(1X,,QANK
MI01390
oF XMOI
IS',I3)
Ir(IRANK1.EQ.0) GO TO 999
C.LL MAN7AB(IRANK1)
,
999 CnNTINUF
C** DEL;A=BUFF
IA(IECR.GT.12)WRITF(6,111)((8UFF(IJ),J=lIRANK1),I=l,INUO)
111
FnRMAT(4(1X,'DELTA=
t',E10O.4))
MA101450
TO 10
MAIO01470
IcUM=IRANKIRANKJ
Ic(ISUM.EQ.INJO)
MAI01460
GO
WoITE(6112)
FnRMAT(IX,IRANK+IRANK1.E.INUO
STOP
10
CnNTINUE
C** FORmATION OF DELTA:BETA
112
C** OEL;A:BETA
11
MAI01400
AI01410
MAE01420
MAI01430
qAIOl44O
IS A INUO*INt!O
THERE IS A MISTAKE')
4ATRIX
MA1I01480
MAIO1490
MAI01500
MAI01510
MAI01520
AI01530
Dn 11 I=I,NUO
MAI01340
I6(IRANK.E).0)
GO TO 1110
DO 11 J=1,IRANK
MAI01530
MAIOI5650
J'"=IRANKI+J
B'FF(IJJ)=BUFF2(I,J)
AIO1570
MA101580
Gn TO 1130
1110 CnNTINUE
1130 CnNTINUE
Ii(IECR.GT.5)WRITE(6,l13)((BUFF(IJ),J=,INUO)I=1,INUO)
113 FnRMAT(4(1X,'DELTA:RETA='Elo0.4))
C** COMPUTATION OF THE SETS LAMBOAI
C'LL MAN7AC(IRANK)
12
CrNTINUE
CALL MAIN79
qAI01590
MAI01600
MA101610
MAIO1520
MAn01630
MA101640
%AI01650
uAI01660
MAIO1670
RC-TURN
MAI01680
ELn
MA101690
A-30
S,BROUTINE AN7AA(IRANK)
C*' SELECTION OF BETA FROM THE COLUMNSOF BUFF=BETAP
C** BUF' COMES FOM MAIN7A
uA70n010
MA700020
MA700030
CnMMON/MANI/ABCeRI.CBINP.OQRIECREPSRUFF
MA700040
CMMON/MANI5SNUNUNUSINJO
CnMMON/TRASHI/IZ
C'MMON/TRASH42/BUFFI
D;MENSION A(12,12),R(12,12),C(12,12),BI(12,12),CBI(12.12)
DIMENSION UFF(l2,i2),BU'Fl(1212),IZ(12),INU(12)
I!TEGER P,R
MA7000O50
MA700060
MA700070
MA7000O80
MA700090
MA700100
D
DO
MA700110
mA700120
1 I=1*IUO
1 J=lIlUO
MA700130
B,FFl(IJ)=BUFF(IJ)
MA700140
Ir(IECR.GT.12)WRITE(6,100)((BUFF(IJ),J=1,INUO),I=1,INUO)
MA700150
100 FmRMAT(4(1X,'BUFFl=',ElO.4))
MA700160
Ic(IECR.GT.2)WRITE(6,101)
MA700170
MAI'N7AA')
101 FnRMAT(lXpSUBROUTINE
MA70010O
2
W'ITE(6,102)
WHICH COLUMNS OF ETAP YOU WISH TO KErP',/.1X.MA700190
102 FnPMAT(lXtIDENTIFY
3.YOU MUST KEEP RANK OF BETAP COL')MA700200
t1'YPE THEIR NUMBERS IN FRMAT
RcAD(5,1000)(IZ(I),I=jIgjANK)
MA700210
MA700220
1000 FRMAT(1213)
W-ITE(6,lOn0O)(IZ(I),I=1,IRANK)
MA700230
MA700240
WnITE(6,103)
103 FRMAT(1X,9IF
DATA ARE INCORRECTLY ETERED,TYPE
0',/,1X.
MA700250
MA700260
1'THERWISE TYPE 11')
MA700270
RrAD(5,1001) ISIGN
MA700280
1001 F'RMAT(12)
MA700290
Ic(ISIGNoE).0) GO.TO 2
MA700300
D^ 3 J=1,IQANK
1
3
J"=IZ(J)
MA700310
D
3 I=1,IUO
B,'iFF(I,J)=3BUFFl(IJJ)
'AA700320
MA700330
I~(IECR.GT.5)WRITE(6,104)((BUFF(IJ),J=1,IRANK),I=1,INUO)
104 FmRMAT(4(lX,'RETA=,EO.'4))
R-TURN
EUZ
S'BROUTINE MAN7AB(IRANK1)
C** SELrCTION OF DELTA FOM THE COLUMNS OF BUFF
'
; COMES FOM MAIN7A
C* RIJF
MA700340
4A700350
MA700360
MA700370
MA700380
MA700390
MA700400
C'MMON/MANI2/ABCRIeCBI.NPORIECREPSBUFF
MA700410
CrMMON/MANIS/INU,INUSINJO
CnMMON/TRASHI/IZ
CnMMON/TRASH2/BUFF1
O;MENSION A(12.12),8(12,12),C(12,12),BI12,12).CBI(12.12)
I;,TEGER P,,R
Dn I =IINUO
DO I J=1,IJUO
MA700420
MA700430
MA700440
MA700450
MA700460
MA700470
uA700480
MA700490
R,1 FFI(I,J)=BUFF(I,J)
MA700500
Ir(IECR.GT.12)WRITE(6,100)((BUFF(IJ),J=1I1NUO)I=1,INUO)
MA700510
100
FnRMAT(4(lXtBUFF1=',FlO.4))
MA7005O20
15(IECR.GT.2)WRITE(6,101)
MA7.00530
101
FnRMAT(2X,SUBROUTINE
MA700540
DOMENSION
1
2
102
RUFF(12.12).BUFFI(12.12),IZ(12),INU(12)
AIN7A8B)
MA700550
WoITE(6,10?)
FTRMAT(1X.,'IDENTIFY WHICI COLUMNS OF XMOI YOU WISH TO KEEP',/,lX, MA700560
MA700570
13.YOU MUST KEEP K OF XMOI COL')
1ITYPE THEIP NUMBERS IN FRMAT
RrAD(5100O)(I7(I).I=ltIRANKl)
1000
WiITE(6,100o)
WnITE(6,103)
MA70580
MA700590
FnRMAT(12I3)
(IZ(I) ,I=1,IRANK1)
MA700600
MA700610
A-31
]03
FnRMAT(IX,,IF DATA ARF ICORRECTLY
19,THERWISE TYPE 11')
ETERED,TYPE
O0',/,1X,
PrAD(5,1001) ISIN
"A7Ob40
1001 FARMAT(I2)
A700650
I~(ISIGN.EO.0)
DO 3 JI9ANKI
JI'=IZ(J)
D
3 I=19IVUO
3
104
GO TO 2
A700660
MA700670
MA700680
4A700690
Bi'iFF(IJ)=3UFF1(IJJ)
I(IECR.GT.5)WPITE(6,104)((3UFF(IJ)tJ=1,IPANK1),I=lINUO)
FmRMAT(4(1X,'ETA=9EIO0.4))
RrTURN
~
EF-10sD~~~~~~~~~
COM5UTES THE SETS
MA7007 50
MA700760
OF LAMBDAI
CrNMMON/MANT?/A.B,C,BI,CBINP,O,R,IECR,EPSBUFF
MA700770
C** BUF'=DELTA:BETA COMES FROM MAIN7A
CAMMON/MANI5/INU, INUSINJO
C'MHON/MANI6F/XPI
MA700780
MA700790
MA7007 90
MA700800
CfMMON/TRASH2/BUFFIBJFF2
A700810
CMPLEX WI(2)
DTMENSION A(12,1?),B(]2,12),C(12,12),SI(12,12),CBI(1212)
DTMENSION 7(1,1)BUFF(12912),XOT(12,12),SU8Fl(12,12),RUFF2(12,1?)
DTMENSION INU(12)
I-TEGER P9,R
C** COMUTES THE INVERSE OF DELTA:BETA
IC-(IECR.GT.2)WRITE(6,100)
100 FnRMAT(IX,SUBPOUTINE
AIN7AC')
I-(IECR.GT.9)WRITE(6,lO1)((BUFF(IJ),J=1,INUO),=1,INUO)
101 FMRMAT(4(1X,9iFF=1E10.4))
DO 1 I=191I4UO
Dn 1
1
J=1,I1'UO
1B',F1(IJ)=BUFF(IJ)
I,UFF1=12
102
C=LL LINVrF(gJFF1,INUO,I3UFF1,3UFF2,IDGTWKAREA,IER)
I(IECR.GT.2)WRITE(6,99)IER
FnRMAT(1X,ERQOR CODE IN COMPUTATION OF D:3-1 IS ',13)
IE(IECR.GT.5)WPITE(6,102)((BUFF2(I,J),J=1,INUO)I=,INUO)
FRMAT(4(1X,'fRIJFF2=',F10.4))
MA701070
MA701080
B!,FF1(IJ)=BUFFI(IJ)+BUFF2(IK)*XPI(KJ)
Ir-(IECR.GT.9)WPITE(6103)((BUFF1(I,J),J=1,INUO),I=1,INUO)
103
FnRMAT{4(1X,
RUFF=1 ,EIO0.4))
C** COn4UTATION OF BFF1*DELTA:BETA
O 3 =1INUO
OF THE LAST
TRANK
COLUMNS
OF
MA7I140
MA701150
4A701160
MA701170
UFF2
I i(IECP.GT.5)WPITE(6O104)((BtJFF2(IJ),J=1,INUO),I=
104 FRMAT(4(IXP0O=,Elf.4))
N'=INUO-IRANK
A701090
MA701100
4A70110
MA701120
'0A701130
Dn 3 J=1tINUO
B,'FF2(IJ)=0.EO
Dn 3 K=1IqJUO
B'IFF2(IJ)=BUFF2(I,J)*BUFF1(I,K)*BUFF(KJ)
I1(IRANK.EO.0)
MA7009B0
MA700990
MA7010 00
MA701010
mA701050
mA70100
D'n 2 K=1IJUO
IS MADE
'MA700960
MA700970
!A701040
8,,FF(I,J)=O.E0
3
MA700920
MA700930
MA701030
Dr 2 IlI'J0O
D
2 J=19,INUO
C** XPI"
MA700830
,A700840
4A700850
MA700860
MA700870
MA700880
MA700890
4A700900
MA7009 10
MA701020
C** (OETA:BETA)IS 9UFF2
C** COMUTATION OF BUFF2*XP
2
MA700820
MA700940
MA700950
IGT=4
WAREA=12
99
MA7007 00
MA700710
MA700720
MA700730
MA700740
S 'BROUTINE MAN7AC(IRANK)
C**
MA700620
'A700630
MA701180
IINUO)
MA701190
MA701200
MA701210
GO TO 5
MA701220
A-32
DO 4 I=IIANK
MA701230
D
MA701240
4 J=1IANK
I=NN.I
J=NN+J
uA701250
MA701260
4
B,'FF(IJ)=QUFF2(IIJJ)
I~(IECR.GT.5)WRITE(6,105)((BUFF(I,J),J=IIRANK),I=1,1RANK)
105 F'RMAT(4(lX1XPI=',E10.4))
C** COM UTATION OF XPI EIGENVALUES
I;OB=O
*A701270
MA701280
MA701290
MA701300
MA701310
IUFF=12
MA701320
I =1
MA701330
KiK=13
C~LL EIGRF(BUFFIRANK.IPJFFIJo8oWIZIZKWK9IER)
WrITE(6.106)IER106 FmRMAT(IX,'ERPOR CODE IN COMPUTATION OF XPIT EIG.NV* IS'I13)
WnTE(69107)(WI(T)9I=I9IANK)
107 FeRMAT(1XLAMBDAI
AEt'2(ElO.4tlX 9 El0.4))
RcTURN
5
C'NTINUE
WnITE(69108)
108 F'RMAT(XgtTHE
SET OF LAMBDA! ASSOCIATED WITH THIS BI IS'9/9 1X*
ltHE NUL SET)
RrTURN
-MA701460
EiD
SIBROUTINE MAIN78
#
C*
SELECTS THE 4IS TO BE RETAINED
BUFF
CMMON/MANI2/A,8BCBICBIoNPOiRIECREPS
CAMMON/TRASH1/IZ
CnMMON/MANIO/IFLAG
OTMENSION A(12.12),B(12,12),C(12,12)BI(1'212),CBI(12,12)
D MENSION RUFF(12,12),IZ(12)
MA701340
mA701350
*A701360
MA701 3 70
MA701380
MA701390
MA701400
MA701410
MA701420
MA701430
MA701440
MA701450
MA700010
MA700020
MA700030
MA700040
MA700050
MA700060
MA700070
I;.TEGEP POR
M700080
100
I&(IECR.GT.2)WRITE(69100)
F RMAT(IX,'SUBROUTINE MAIN78')
MA700090
MA700100
I
W ITE(69101)
4A700110
FnRMAT(lXtIF YOU WANT TO CHANGE THE Si:T OF BIBTYPE oo00t/,1X
lt'THERWISETYPE 11')
RrAD51000)
ISIGN
1000 FRMAT(I2)
101
I;(ISIGN.NE.11)
GO TO 2
MA700120
MA700130
MA700140
MA700150
MA700160
W5ITE(6-9102)
102 F RMAT(1X,THE POGRAM WILL NOT ALLC4 YOU'TO CHANGETHE SET19/1X,
1'rF BIS.IF YOU MADE A MISTAKE IN SE..ECTING THIS OPTIN'/lX,
1ITYPE 00o*OTHEPWISETYPE 11')
RcAD(5,1000)ISIGNI
I~(ISIGN1.O.O) GO TO 1
RrTURN
MA700170
MA700180
MA700190
MA700200
MA700210
MA700220
MA700230
?
UA700240
103
W3-ITE(69103)
FnRMAT(1XtTHE
POGRAM WILL ASS'"4E YOU WANT TO SUBSTRACT',/1IXP
1'cOME RIS FROM THE SET oF EVENT.IF
YOU MADE A MISTAKE IN 'e/91Xp
1'eELECTING THIS OPTIONoTYPE 00';1T4ERWISE9TYPE 111)
RrAD(5O1000)ISIGN1
I~(ISIGNI.Q.O0)
3
104
GO TO
1
W-ITE(69104)
F^RMAT(lXqTYPE THE NUMBER OF EVENTS YOU WANT TO RETAIN')
RCAD(5,*)I:I
WoITE(6,*)IPI
W~ITE(6,105)
IN TYPING THE ATA TYPEOO./.lX,
105 F^RMAT(1X9'IF YOUMMADE A M.TAKE
1',THERWISEoTYPE 11')
RrAD(5O1000)ISIGN
.
MA700250
MA700260
MA7002 70
MA700280
MA7.00290
MA700300
MA700310
MA700320
MA700330
MA700340
MA700350
MA700360
MA700370
A-33
4
106
Ir(ISIGN.EO.O)GO TO 3
WoITE(6,106)
THE INDEXES OF THE BIS YOU WANT TO RETAIN')
FRPMAT(XTYPE
MA700380
mA700390
MA700 4 00
RrAD(5,*)(IZ(1I),I=lIPI)
MA700410
W5 ITE(6,*)(IZ(I),I=1,IRI)
WrITE(6.105)
RrAD(5,1000)ISIGN
MA700420
MA7004 30
I (ISIGN.El.0)
GO O
MA700440
mA7004 50
4
MA7004 60
MA700470
MA700480
MA700490
MA70050O
C** FOR;ATION OF THE NEW MATRIX BI
Dn 5 I1=,N
Dr 5 J=1,IQI
J= IZ(J)
5
B!"FF(I*J)=Bl(IJJ)
6
107
D
6 I=1N
Dm 6 J=1tIqI
MA700510
uA700520
Bt(IJ)=BUrF(IJ)
I'(IECR.GT.2)WPITE(6lO7)'((8I(IJ),J=1,IRI),I=1.N)
F^RMAT(4(1X,'I=',EIO.4))
RIRI
IrLAG=l
RITURN
MA700530
ED
MA700590
MA700540
MA700550
MA700560
MA700570
MA700580
MA700600
mA700610
MA700620
MA700630
DIMENSTON A(12,12)9R(12,12)oC(12912),~I(12912),CBI(12,12)
MA700 6 40
DTMENSION 3UFF(12,12)
MA700650
IF-TEGER P),R
MA700 6 60
IH(IECR.GT.2)WITE(6,100)
MA700670
FmRMAT(1X,'SUBROUTINE MAIN8')
MA700680
WAITE(6,101)
YOU WISH TO TEST AN EVENT FOR OUTPUT STATIOt,/olXMA700690
FmRMAT(IXWOULD
S,,BROUTINE MAIN8
TEcT FOR OUTPUT STATIONIARITY
CrMMON/MANI2/AB*CBRICBINPORIECREPSBUFF
C**
100
1
101
1'JAPITY?IFYESTYPE
MA7007 00
11,IF NOTYPE 00no')
PcAD(6,1000)ISIGN
1000 FnPMAT(I2)
WnITE(6,1000)ISIGN
Ir(ISIGN.N-.11)GO TO 2
WAITE(6,10?)
102 FnRMAT(1X,THE
PROGRAM WILL :POCEFO N TESTING AN EVENT',/1X,
1'-OR OUTPUT STATIONARQITY.IF YOU MADE A MISTAKE IN SELECTING'/,lX
1,THE OPTION,TYPE 00.OTH-RWISE,TYPE 11')
RcAD(6,1000)ISIGN
I (ISIGN.El.0) GO TO
C)LL MAIN8A
R~TURN
W-ITE(6,103)
2
103 FnRMAT(1X,,THE POGRAM WILL NOT TEST EVENTS FOR OUTPUT',/.lX,
1,'TATIONARITY.IF YOU MAD A MISTAKE IN SELECTING THIS't,/9 1X.
1imPTIONTYDE 00.OTHERWISEtTYPE 11')
P-AD(S,1000) ISIGN
W6ITE(6,1000)ISIGN
GO
REAIS
MA700790
MA700810
MA700 8 20
MA700830
MA700840
MA700850
MA700860
MA700870
MA700~80
MA700890
MA7.00900
TO 1
MA700910
MA700920
MA700930
RrTURN
E,D
S,,8BOUTINE MAIN8A
C**
'4A7007B0
MA700800
WiITE(610no) ISIGN
Ir(ISIGN.EO.0)
MA700710
MA700720
MA700730
MA700740
MA700750
MA700760
MA700770
THE EVENT 8A FOR WHICH OUTPUT STATIONARITY
IS
TO BE TESTED
CcMMON/MANT8A/RA
MA700940
MA7009 50
CrMMON/MAN2/A,BCRI*CRINtPORIECR,EPS,BUFF
MA700950
212)CB(2 ,(12C(12
DTMENSION (1
UFF(12,12)qBA(12)
DTENSION
MA700970
MA700980
12)I(,2)CBI(1?12)
A-34
100
I
101
I, TEGER PR
I (IECR.GT.2) WITE(6, 100)
M4A700990
MA701000
MAIN8A')
FnRMAT(l1XSURPOUTINE
WITE(6,101)
FnRMAT(1X,WRITE BA(I),I,4,IN
MA701010
MA701020
MA701030
FREE FORMAT')
MA701040O
RrAD(5,*)(9A(I),1=1,N)
WAITE(6,*)(BA(I) I=1,N)
WnITE(6,10?)
102 FnRMAT(X,,IF YOU MADE A MISTAKE IN TYPING
1,'THERWISE TYPE 11')
RCAD(5,1000) ISIGN
1000 FnRMAT(I2)
WAITE(6,1000) ISIGN
GO TO
Ir(ISIGN.E.0)
CALL MAIN89
R TURN
ED
A
TYPE 00,/,lX,
4A701 050
MA701060
MIA701070
MA701080
MA701090
MA701100
MA701110
MA701120
MA70 130
MA70 1140
MA701 150
A-35
St',BROUTINE
AIN89
C** COM;UTATION OF THE DETECTIDN SPACE OF 3A
C** SUB0OUTINE SIMILAR TO MAINS
C~MMON/MANI?/ABCBICBINtPORIECREPSRUFF
CnMMON/MANISA/BA
CnMMON/TRASH2/RUjFFRIJFF2,UFF3,XMD
DYMENSION A(1?,12),B(12,12),C(12,12)fI(12,12),CBI(12,12)
DTMENSION UFF(1?,12),B3A(12)B.RUFF1(12,12),3UlFF2(12,12)
DTMENSION UJFF3(12,12),XAD(144,12)
DTMENSION IROW(12),ICOL(12)
ItTEGEPR
C*
COMRUTATION OF C*BA
Dr 1 I=1IP
R',FF(
I,1)=O.EO
O 1 J1N
BI'FF(I,1)=UFF(I,1)+C(I,J)*3A(J)
Ir(IECR.GT.9)WRITE(6,10o0)(BUFF(I1)I=IP)
100
C**
FnRMAT(4(lX'qCBA=',F10.4))
COMrUTATION
OF DBA
C'-=0.
C''=O .
OD 2 I=1,P
2
CC=CC+BUFF(I,1)**2
101
Ir(IECR.GT.6)WRITE(6,101)CC
FnRMAT(1X.(CBAT*CBA)-1=IElO.4)
C=1 . /CC
Dn 3 I=19N
B,'FF(I,2)=0.EO
3
D
3 J=I1N
B'FF(I2)=:UFF(I,2)+A(I.J)*3A(J)
102
Ir(IECR.GT.8)WRITE(6,lo02)(BJFF(I,2),1I=lN)
FnRMAT(4(1XA*BA=tE1lO.4))
D 4 I=1N
D~ 4 J=1,P
4
B'IFF1(IJ)=BUFF(I,?)*PUF"(J,1)*CC
103
FIRMAT(4(1X,'D=',E1lO.4))
C**
I(IECR.GT.5)WRITE(6,103)((BUFF1(I,J),J=1,D)
,IlN)
COM UTATION
D
OF C'
5 I=1,P
Dr 5 J1
9
P
S
8"FF2(I
6
B'FF2(1,I)=1.+BUFF2(II)
104
FnRMAT(4(lXv9UFF2=mFIO.
D
9 J)=-BUFF(I,4)*BUFF(J*l)*CC
6 J=1,P
Ir(IECR.GT.8)WRITE(6,104)((BUFF2(IJ)tJ=1),I=1,P)
4
))
D' 7 I=1P
D' 7 J=1N
BFF(ITJ)=0.EO
7
D 7 K=1,P
Ri'tFF(IJ)=3UFF(I.J)+RIJFF2(1
,K) *C(KJ)
I(IECR.GT.5)WRITE(6,10OS)(BUFF(IJ),J=lN)I=l1,P)
105
FnRMAT(4(1X,'CPRIME=',E10.4))
C* * COMrUTATION
OF A-0DBA*C
D^ 8 I=1*N
Dn 8 JN
BFF2( I ,J) =0O.EO
Dr 8 K=1,P
8
B'FF2(I,J)=BUFF2(I,J)+BUF1(IK)*C(KJ)
I5(IECR.GT.8)WPITE(6,106)((BUFF2(TJ)J=ltN)I=1IN)
106
F6RMAT(4(1X,6DBA*C=',F10.4))
Dn 9 I=1N
Dn 9 J=1N
A-36
9
BFFI (I ,J) =A(I,J)-BUFF2(IJ)
I (IECR.GT.5)WRITE(6,107)((3UFF(1IJ),J=1N),I=1,N)
F RMAT(4(lx,'A-D8A*C=,.El0.4))
107
F XMD=MD'
C** COMIUTATION
DO
10 =1,'
ODn 10 J=194
X.D(IJ)=BJFF(IJ)
10
B,FF2(IJ)=BUFF(IJ)
NV=N-1
Dn 14 L1,9N
N' I=L*P
DO 11 I=1,0
DM 11 J,9
B.',FF3(I ,J)=O.EO
OD
11
11 K=1,
Bi',FF3 (I ,J)=BUFF3(
DO
I ,J)+BUF2
(I ,K) *BUF;
(KJ)
12 I=1,
DOn12 J=1.J
12
B,',FF2(I,J)=BUFF3(IJ)
DOn 13 =1,P
Dn 13 J=19,N
I=I*L*P
13
14
XmD(IIJ)=RUFF3(IJ)
CmNTINUE
N?=N*P
Ir(IECR.GT.3)WPITE(6,108)('(XMD(IJ),J=1,N)91=1,NP)
108 FnRMAT(4(lX,'XMD=',ElO.4))
C~* ORTHOGONAL REDUCTION OF XMD
IvMD=144
ESII=0.0001
%n 15 I=1,
D'
15 J=1l,
B!'FF(IJ)=O.EO
15
B.FF(II)=l.E0
C-LL ORTRED(XMDUFFNP,'4,IXMD.EPSIIIECR)
I~(IECR.GT.1)WPITE(6,9O9)((3UFF(IJ),J=,N),I=1N)
109 FnRMAT(4(lx,'OPEGA=',ElO.4))
C** COMrUTATION OF RK OMEGA AND LINEAR DEP
D'
D
16
16 I=1,4
16 J=1,
8,'FF1(I,J)=BUFF(IJ)
InMEG=12
CiLL MFGR(BUFFIOMEGNNIRANK,IROW,ICOLEPSIER)
110
Ir(IECR.GT.1)WRITE(6,110)IER
FnRMAT(1X,*IER=:I3)
WEITE(6,111)IPANK
111
FnRMAT(lX,'*K
OEGA=*I3)
WoITE(69112)(IROW(I),ICOk(I),IPlN)
112
FrRMAT(X,tIROW=,I3,ICOL=:,T3)
WAITE(6,113)((3UFF(IJ),J=1,N),=l,N)
113
FnPMAT(4(1X,'DEP OF SA IS',ElO.4))
CALL MAIN8C(IRANK)
R TURN
S,)BROUTINE MAINBC(IRANK)
C*.
COMDUTATION
OF
THE SUBSET
F EVENTS
I FROM
WHICH
*
BI
IS
C * OUTGUT STATIONARY
CAMMON/MANT2/ABC,BI
.CI ,NPOQRIECREPSRUFF
CnMMON/MANTI8A/RA
CnMON/TRAH2/UPF1
DtMENSION A(12,1?),R(12,12),BT(12,12)*CBI(12,12),C(12,12)
A-37
DTMENSION ;JFF(12,12),*A(12),BLJFFl(12,12)
DTMENSION TROW(12),ICOL(12)
PR
I'TEGER
I' (IECR.GT.2)WPTTE(6,100)
100 FnRMAT(1X,'SI8ROUTINE MAIN8CO)
C** COM;UTATION OF C*BA
2 I=IP
D
BtFF(I1)=O0.EO
Dn 2 J1N
2
C*
BtFF(I ,1)=:3UFF(I,1)+C(IJ)*9A(J)
COM-UTATION OF LINEAR DFPEDENCY OF CBA..CBI
C**
SURPOUTINE
IF n=11,THIS
TO 3
I(R.NE.11)GO
101
wONIT WORKt
W5ITE(6,101)
CANJDT TEST OUTPJT STATIONARITY WITH THIS',/,
FRMAT(1X,'R=1lYOU
llyt,'SUBROUTINE.C'4ECK OURCE')
S OP
CmNTINUE
3
I6I=R+I
o
CpI
DI
DO
4
4 I=1:P
I(, IRI)=BUFF
5 I=1,P
S J=1IQI
(I, 1)
BiFF(IJ)=C8I(IJ)
s
IMUFF=12
ErSIt=0.0001 EO
C;LL MFGR(RUFFIBUFFPIRItIRANK1,IROWICOLEPSI,IER)
102
IF(IECR.GT.2)WRITE(6,102)IER
FrnRMAT(1XERRORQ CODE IN RANK OF BUFF IS'*I3)
Ir(IECR.GT.2)WRITE(L,103)IRANKI
103
F'RMAT(1X.RANK
Ir(IECR.GT.2)
OF CA
..CBI
I
*,I3)
WITE(6,104)(IROW(I),ICOL(I)tI=1,P)
104
FnRMAT(lX,'IROW='EFIO.4,'ICOL=',E0.4)
105
FnRMAT(4(1X,RJUFF=',E]O.4))
IF(IECR.GT.2)WPITE(6105)((BUFF(I,J),J=19II),I=1,P)
Ic(IECR.GT.2)WITE(6,105)
106
FOP LINEAR DEPENDENCY IN PRECEDING,/1,X,
FnRMAT(1XOSOLVING
lt,.ATRIXYOJ KNOW THE ELATION ETWEEN CBA AND OTHER CRI',/,lX,
1,FBA CAN BE MADE OUTPUT SEPERARLE WITH THE CBI FROM WHICH',/,IX,
,
T IS DEPENDENT.SEE
1 DVISABLE TO DO SO')
RrTURN
EGO
RULES
OF THUMB
TO SEE
IF IT IS
,/,1X,
ai
A-38
C*
e
MAIOnO10
S,8ROUTINE MAIN9
COM~UTATION
F THE MATPIX
TO
MAIO0O20
(STEP 6 A)
MAIOO30
CnMMON/MANT2/ABCRICBIN,PQ,R,IECREPS,RUFF
MAIOOO40
MAIOOO5O
CnMMON/MANI5/INU, INJS, INJO
CrMMON/MAN I 6A/AOSC
CnMMON/MANI6C/TO,
IRANK, II
UAI100060
CnMMON/M ANT6D/ROG
MAIOO70
CnMMON/MANI3/IROWICOL
MAIo00080
MAIOOO90
CnMMON/TRASH2/WSBUFF2
OF N INTEREST FROM NOW ON
C** WHAi WAS EFnRE N MANIAC,3MEGOGTS
WTMENSION A(12912),R(12912),C(12912),6I(12912),CBI(1212)
MAIOOlO0
MAIOOllO
DTMENSION UFF(12,12),W(1212),IZ(12),TO(121?),ADSC(12912)
MAIOO120
DiMENSION INU(12),POG(12,12l,BUFF2(1?12),IROW(12),ICOL(12)
MAIOO130
PR
ITEGER
MAIOO1l40
100
Ir(IECR.GT.2)WQITE(6,100)
FnRMAT(IX,'SUBROUTINE MAIN9')
1
2
C NTINUE
WC-ITE(6,101)
101
FnRMAT(1X,,TYPE THE NMBER
OF
MAI0150
MAIOO160
MAT00170
MAo00180
ANKS
MAIOO190O
F CS WHICH HAVE A',/,1X,
MAI00200
MAI00210
MAI00220
MAI00230
1, ON-ZERO AUXILIARY VCT3R IN THE ORTHOG REDUCTION OF XMD',/,
11Y,'STARTI1GWITH THE IDENTITY MATRIX')
C*
ENTPRING THE NUMBEQ OF WR
RrAD(5,")II
WnITE(6,102)II
102 F'RMAT(I3)
MAI00240
MA1I00250
MAI00260
WMITE (6, 103)
103
FnRMAT(1X,'IF DATA ARE CRRECTLY
PrAD(5,102)ISIGN
I(ISIGNoEO0°)
I(II.EO.)
3
ENTEREDTYPE11.OTHERWISE.TYPE
MA100290
MAI00300
GO. TO 2
GO TO
MAI00310
MAI00320
CnNTINUE
D
5
MA100330
MAI00340
I1IN
WrITE(6,104)III
FnRMAT(IX9,TYPE WI(19I3),FOR
RFAD(5,*)(W(IJ) ,J=IITI)
I=1,'*I3)
WrITE(6*) (W(IJ),J=1,II)
WnITE(6,103)
RrAO(5,102)ISIGN
IF(ISIGN.E.0) GOTO4
105
CnNTINUE
W'ITE(6, 105) ( (W(IJ) J=19 II) , I=1,N)
FnRMAT(4(1X,'W=',E10.4))
WAITE(6,103)
RrAD(5,102)ISIGN
IF(ISIGN-.E.0)
GO TO 3
C** ENTrRING THE EXPONENT ASSOCIATED WITH THE WR
6
WllITE(6,106)
THE EXPONIENTS 0I ASS3CIATED WITH THE WIt)
106 FnRMAT(IX9TYPE
107
4AI00350
MAJ00360
MA100370
MA100380
MA100390
MA100400
MAI00410O
MA100420
MAI00430
MAI 00440
MAIO0450
MAI00460
MA100470
MA100480
M4AI00490
RrAD(5* (IZ(I),I=1IT)
WcITE(6,107)(IZ(I),I=1,II)
MAI00500
MAI00510
FnRMAT(1213)
MA I 00520
WITE(6,103)
MA I.00530
4AI00540
MAIO0550
MA100560
MA100570
PrAD(5.102)ISIGN
IF(ISIGN.E).O) GO TO 6
C** COM6UTATION 9F ((A-DS*C)**IZ(I-1))*W(.I)
CALL MAIN9A(AOSCIZWJ,3UFFII)
C** COMmUTATION
OF TO
IeUM=O
7
MAI00270
MAI00280
C** ENTrRING THE WR
4
104
0)
On 7 I=1II
IcUM=ISUM*IZ(I)
MAIOO590
MA100590
MAI00600
MAI00610
A-39
C**
D
8
%AI00620
MAT00630
SUu IS THE COLUMN DIMENSION OF W
Do 8 =1N
4 100640
MATOD650
MA1I00660
8 J=1tISUM
B?,FF2(IJ)=W(IlJ)
I =12
EDS=0.0001FO
MAIO0670
C~LL MFGR(wIWNISUMIRANKIROWICOL.EPSIER)
MAI00680O
112
WcITE(6,112) .IER
FnRMAT(IX,,FRROR CODE IN COMPUTATION OF RK OF W IS9,I3)
IF (IECR.GT. 1 )WRI TE(6,113)IRANK
MAI00690
UAT 00700
113
FnRMAT(lX,'K
114
I6r( IECR,.GT . 1) WITE(f6,f1 1 4) (I ;OW(tI ),*ICOL(tI ),*I =,NS)
FnRMAT(1X' IRO=' t3,' IC3L=' 1I3)
IY(IECR.GT.1)WRITE(6,111)((W(IoJ)*J=1 ISUM),I=1IN)
OF ADSCW
IS',I3)
CoNTINUE
C** TEST TO CHECK THAT BUFF2 HS N-NUS COLJMNS
I( IECR.GT.12)WRITE(6 108)INUO
108 FoRMAT(1X, 'INUO=' I3)
IF(IECR.GT.12)WRITE(6,109)INUS
FnRMAT(lX,'INUS=',I3)
I (II .EQ.0) IRANK=0
InIM=IRANK+INUS
Iv(IDIM.EQ.N)
GO TO
14
MAI00750
MAI00870
14
WDITE(6,110)
110 FnRMAT(X,'TO DOES NOT HAVE N-INUS CLUMNS.YOU
1'
MISTAKECHECK THE USER GUIDE')
MA I00740
MA700770
MA100780
MAIO 0790
MA100800
MAT00810
MAI008 20
uAIO0830
MAI00840
UAT00850
MA100860
CALL MAIN98(BIJFF?,NIPANKIECR)
109
MAI00 20
MAI00730
MAI 00760
OF W IS',EIO.4))
111
FnRMAT(4(1X,'DEP
C** SELcCTION OF IND COLUMNS O
W
9
MAIO710
7
MAI 00880
MADE1,/,1X,
MA100890
MAI0900
MAO00910
GO TO 1
CnNTINUE
Ir(INUO.EQ.0) GO TO 11
AA100940
Do 10 I=lq
Dn 10 J=1,INUO
10
Tn(IJ)=RO(I,J)
11
CnNTINUE
GO TO
Ir(II.EQ.0)
Do 12 I=1,N
Do 12 J=1,ITRANK
MAI00920
MAI 00930
MAI 00950
MA100960
uAI00970
13
uaAI00980
MAI 00990
AAIOO1000
12
J'=INUO+J
Tn(IJJ)=BUFF2(I.J)
13
CONTINUE
UA101OlO
uA1O1020
MAI01030
L=IRANK+INJO
MAT01]O40
FoRMAT(4(1X,'TO=',EIO.4))
RrTURN
MAI01050
MAY01060
MAI01 0 70
E~.D
MAI 01080
IF(IECR.GT.9)WPITE(611)((TO(ItJ).J=1,L),1=1,N)
115
S:jBROUTINE MAIN9A(ADSCIZWNvUFFtlI)
C** COMnUTES
((A-OS*C)**IZ(tr-I)*W()
CnMMON/MANT6£/9UFF1
C** IN ANI6E WAS TETA,OF NO ITEREST FROM NOW ON
C**WE SWALL USE RUFFI AS A WOR<ING AEA
DTMENSION DSC(12912),IZ(12),W(12912),qUFF(12912),9UFFI(12,12)
100
MAYO1 100
MAIOrl lO0
MAI01 120
MAI01 130
MAI01 140
I,TEGER PO,R
MA01 150
IF(IECR.GT.2) WRITE(6,100)
FoRMAT(1X,'SURROUTINE MAIN9A')
MAY01160
MAI01 170
MAI01lBO
MAI01 190
,=1lN)
IF(IECR.GT.12)WRITE(6,101I)((ADSC(IJ),J=1l,)
101
MAI01090
FnRMAT(4(1X,'ADSC='.EIo0.))
I !C= I
Do 4 IND=1.II
DO
1 I=1N
MATl0120n
MAY01210
MAI01220
A-40
I
BniFF1(IINC)=W(IINOD)
9,BFF(IIND)=W(IIN0)
MAIOl230
IiC=INC*1
MA1240
MAT01250
K-=IZ(INO)-l
Ir(KK.EOQ.O)
Do 4 K=1K(
D 2 =1N
-MAI01260
GO TO 4
MA101270
MA101280
MAI01290
W¢I,IND)=0.EO
Dn 2 JN
?
T01300
MAI01310
uA101320
AI01330
W IIND)=W(IIND)*ADSC(ItJ)*BUrF(JIJD)
Do 3 I=19N
3
B,',FFl(IINC)=W(IIND)
8,'FF(I,IND)=W(IIND)
4
CnNTINUE
MA101370
Do 5 I=1,N
Dn S J=1II
MAI01380
MAI01390
ImiC=INC+1
5
6
102
MA101340
MA01350
.MAI01360
8,FF(I,J)=W(IJ)
4A01400
Dn 6 I=1N
MA01410
DO 6 J=1,INC
MA01420
W¢IJ)=BUFr1(I,J)
AT01430
I~(IECR.GT.5)WQITE(69102)((W(IJ),J=1I*NC)I=1.N)
FnRMAT(4(1XOADSC**IZ(I)*W=,EIO4))
C** RUF?=((A-DSC)**(IZ(
1)-I) *wl (A-DSC)*(IZ(2)-I)-l*W2.*
C** W=(i1,(A-OSC)*Wl,..,(A-nSC)**(IZ(U)-I)*Wl,W2,..
MA0140
E'dD
MA101490
SUBROUTINE MAIN9B(UFF29,IRANKIECR)
C** SELCTION
OF INOEPENDENT
COLUMNS OF W
CMMON/MANT3/ICOL
MAIO
01500
MAI01510
LAI01520
CMMON/MANI6E/BUFF
MAT01530
DMENSION
UFF2(12,12),BJFF(12,12),ICOL(12)
I.!TEGERPO*R
MA101540
MAT01550
Ic(IECR.GT.2)WRITE(6100)
FRMAT(1X,SUBROUTINE
MAIN98t)
W"TE(6,101)
FPRMAT(lX9TYPE THE INDEXES OF THE COLUMNS OF W YOU WANT,/.*IX,
1,+0 KEEP.YU MUST KEEP IANK COLUMNS')
RFAD(5*)(lCOL(I)I=1qIRANK)
102
103
FoRMAT(1X,IFDATA
AE
ICORRECTLY ETEREDTYPE
1,,TYPE 11')
RrAD(5,104)ISIGN
104 FnRMAT(2)
?
3
105
GO
MA01560
MAT01570
MArO150
AI101590
MAIO1600
MA01610
WroITE(6,10?)(ICOL(T),I=1,IRANK)
FRMAT(1513)
WrITE(6,103)
Ir(ISIGN.E.o.0)
Dn 2
1,N
WAI01460
MAI101470
RrTURN
100
1
101
MAI01440
MA101450
MA101620
MA101630
MA101640
O0.OTHERWISEt,/,1XMATO1650
MA101660
MAI0167
MAT01680
TO I
MAI01690
MAI101700
Dn 2 J=1,IRANK
J'"=ICOL(J)
BFF(I,J)=UFF2(IJJ)
MA0171
MA101720
MAi01730
Do I=1,N
3
Do 3 J=1,IQANK
4A101740
mATI?50
BtFF2(IJ)=BUFF(IJ)
I(IECR.GT.5)WRITE(6,105)((BUFF2(I,J)J=,IRANK)I=1,N)
FRMAT(4(1x,'BlJFF2=,E1O*4))
RSTURN
Ei.
MA101760
MAO1770
MA017BO
MA101790
MAIOrI0
o
A-41
Si'BROUTINE AIN9C
C** COM6UTES AD T-l (STEP 63)
.CBI
CnMMON/MANT2/A,BCBl
CoMMON/MANI 6C/TO, IRANK,II
NPe,0R IEZREPSBUFF
MAIOOS100050
CnMMON/MANIS/INU INUS*INJO
CnMMON/MAN19C/TTTTMTTM
CoMMON/TRASH2/BUFF1,BIJFF2,BUFF3,BUFF 4
MAIOnO60
MA100070
YAIOOO80
MAI00090
DTMENSION UFF(I212),TO(I2,12),GG(i2,12),BUFF1(12.12)
DYMENSION aUFF2(12,12)TNU(12),OMEGC(12,12),CS(12,12)
DTMENSION )S(12,12)TM(12,12),TTM(1212)
DTMENSION T(12.12),TT(12,12),BUFF4(12*12)
IITEGERP,R
Ir(IECR.GT.2)WQITE(6,100)
100 FnRMAT(1X,'SUBROUTINE MAIN9C9)
FOR ALL GI
C** COMPUTES GI,..,A**(INU(T)-1
CALL MAgCA(AINU,NIECR,GBUFF1,BUFF2,BUFF3,R)
C** 9UF1=(G1
AG1
1)-1)*G1 ,G2,AG2
..A**( TINLIU(
C** BUF2=(A**(INU(I)-)*GlA*(INU(2)-)*32,
FoRMAT(1XgtlISUM='.13)
DO 2 J=1IISUM
2 I=1,N
D
TtIJ)=BUFF1(lJ)
L=IRANK+INJO
STOP
CnNTINUE
IrOT=ISUM+.RANK
ITOT=ITOT+INUO
IF(ITOT.EQ.N) GO TO 6
WnITE(6,103)
103 FmRMAT(1X,'T DOES NOT HAVE N COLUMNS,/,I1X,
1,1HERE IS A MISTAKE.CHEC< THE USER GJIDE')
STOP
CnNTINUE
IF(IECR.GT.S)WRITE(6,104)((T(IJ),J=1N),I=1IN)
104 FnRMAT(4(1X,'T=',EIO.&))
C** COMoUTATION.OF T-1=TT
1r-12
WWAREA=12
Dn 66
66
MAIool5o
MAITOO1O
MAITOO170
mAT 00180
MAIOO190
MATI00200
MAI00240O
J'~=ISUM+J
T¢IJJ)=TO(1IJ)
3
4
CnNTINUE
C** TEST TO CHECK THAT T HAS N COLUMNS
INUA=INUS-INUO
Ir(ISUM.EQ.INUA) GO TO 5
WOITE(6, 102)
102 FRMAT(1X,'BUFF1 DOES NOT HAVE INUA COLUMNS!,/,1X,
MISTAKE.CHEC( THE SER GJIDE')
1,v-HERE IS
6
MAIOO110
MAIOO120
MA100130
~AIOOl4O
IUM=ISUM*INU(I)
Ir(L.EQ.0)
GO TO 4
DO 3 J1L
On 3 1=1IN
¶5
MAIOO1l00
On 1 IIR
C** ISUM NUMBER OF COLUMNS OF 3UFF1
Ir(IECR.GT.9)WRITE(6,101)ISUM
2
12,12)
MAI00210
MAI00220
MA100230
IcUMlH=O
101
MAIOO040
CoMMON/MAN T5A/GG
CnMMON/MANT 4/OMEGC ,DS .CS
(12?,12),R(12,12),C(12,12),I(31212),CBI(
DTMENSION
I
MA100I010
MAIOOO20
MAIOOnO30
I=1,9
DO 66 J=19tq
B,!FF4(IJ)=T(IJ)
MAI00250
MAI00260
MAI00270
MAIOO2O80
MA100290
MAI00300
MATIO0310
MAI00320
MAI00330
MAIO0340
MAI00350
UAIO0360
'A100370
MAI 00380
MAI00390
MAT100400
MAIOO41O
MA100420
MA100430
MAIO0440
MAIOO450
MA100460
MAIO0470
AI0480
MAIO0490
MAIO0500
MAIO0510
MAIOO520
MAIO530
MAIO5O40
MAIO0550
MAIOOS6O
MAIQ057O
MAIO580
MAIO59O
MAIOO600
MAIO00610
A-42
67
105
106
CtLL LINV2r(TNITTTID3TWKAREA,IEi)
On 67 I=1N'
MA100620
MAI00630
On 67 J=1,
MA100650
Tf,J)=RUFr4(IJ)
Ir(IECR.GT.1)WPITE(6,105)IER,IDGT
FoRMAT(1X,'EPROR CODE IN COMPUTATION OF T-l',I3,'I0GT=',I3)
Ic(IECR.GT.5)WPITE(6l106)((TT(IJ),J=,N),TI=1,N)
MAI00650
4AI00660
MAI00670
MA1006 80
FoRMAT(4(1X,'T-l=
ElnO.4))
MAI00690
ITOT=II+R
MA100700
Ir(ITOT.EO.P)
109
7
C**
GO TO 7
WDITE(6,109)
FoRMAT(1X,9TTM
IS NOT P*P.CHECK THE
MAIOO
SER GUIDE')
STOP
CoNTINUIJE
COMPUTATION
OF TM
7
1O
MA100720
MA100730
MA100740
MA100750
MAT00760
CALL MA9CB(C,P,N-BUFFPRCSBUFFII,3UFF1,BUFF3,TMIECR)
MAI00770
C** COMoUTATION
OF TM-1
D
77 I=1,P
MAIO780
MA! 00790
77
78
107
108
Dr 77 J=1,P
MA00800
B'IFF4(IJ)=TM(IJ)
CALL LINV2F(TM,PITTTMIDGT,WKAREA,IER)
mAI00810
MAI00820
DO 78 I=1,9
Do 78 J=1,
MA100830
MA00840
T4(I,J)=BUrF4(IJ)
IF(IECR.GT.l)WPITE(6,107)IER,IDGT
FoRMAT(1X,ERROR
CODE FO? T-1 COMPUTATIONT,13,9IDGT=,I3)
Ir(IECR.GT.5)WRITE(6,108)((TTM(IJ),J=,P),I=1,P)
FoRMAT(4(lX,'TTM=,Eln.4))
RrTURN
MA100850
MAI00860
MA100870
MAI00880
MAI00890
MAI00900
E;,D
MAI00
SUBROUTINE MA9CA(A.INUNIECRGGBUFF1,BUFF2,BUFF3,R)
C** COMoUTES GI,..,A**(INU(I)-1) FOR ALL GI
DTMENSION A(12,12),INU(12),GG(1212)BUFFl(12,l12),BUFF2(12,12)
DTMENSION UFF3(12,12)
ITEGE
100
1
P,R
MAI00960
MA100970
MAI00980
MAI00990
IlD=1
mAIOlO00
O
O
MAIO101010
MAIO1OO
6 II=1,9Q
I I=1N
8!'FF1 (I,IND)=GG(III)
B,'FF2(III)=GG(III)
MAI01030
MAI01040
IkiD=IND.l
Ic(KK.EQ.0)
Do 5 K=1IKK
3
10
MA100920
MAI00930
MAI00940
MAI00950
Ir(IECR.GT.2)WPITE(6.100)
FoRMAT(1X,,SUPROUTINE MA9CA')
IF(IECR.GT.12)WRITE(6,101) (INU(I),I=19R)
MAI01050
Kt=INU(II)-l
2
9
MAI01060
GO TO S
uAIO1070
MA01080
Dn 2 I=1N
B,'FF3(I,II)=BUFF2(I,IT)
MA0I1090
MAIOl100
Do 3 I=1N
Bti'FF2(III)=0.EO
On 3 J=I1N
mAI0112O0
BiFF2(I,II)=BUFF2(I,II)+A(IJ)*BUFF3(JII)
MAI.O140
Dn 4 I=1IN
MAIOl150
4AI0l110
MAI)1130
4
8'FFI(IIND)=BUFF2(I.II)
MAIl160
5
6
IjD=IND+1
CoNTINUE
CoNTINUE
MAI01170
MAI01180
MAI01190
101
FORMAT(8(lx,'INU=',I3))
IF(IECR.GT.5)WRITE(6102)((BUFF2(IJ)J=)
102
FnRMAT(4(1X'BUFF2=,EI.4))
M4AI01200
,=lN)
MAI01210
MAI01220
A-43
I D=IND-1
IF(IECR.GT.5)WQITE(6,103)((3UFFI(I,.J),J=lIND),I=1,N)
103 FnRMAT(4(lXv'RFFlI=tr F0.4))
C** BUFl=(Gl,A*Gl ,..,A**(INU(J)-l)*Gl,G2,A*52
C** UFY2=(A**(INU(U)-l)*Gl.A**(INJU(I)-l)*$2
RFTURN
EktD
MAI01230
MA101240
MAI01250
MA101260
MAI01270
.AqI01280
MA101290
SUIJBROUTINEMA9CS(C,P.N,BJFF2,P,CS,BUFF,IIBUFF1,BUFF3,TM,TECR)
MAIOI300
C** COMpUTES TM
MAI01310
DTMENSION C(12912),AUrF2(12912)tCS(12,12),3UFF(12912),BUFrl(12,12)MAI01320
OTMENSION PUFF3(12,12)9T4(12,12)
MAI01330
I,TEGER PO,R
MA101340
Ir(IECR.GT.2)WPITE(6,100)
MAIO1350
100 FnRMAT(lX,'SUBROUTINE MA9CB')
MAI01360
C** UF 2=(A**(I\U(U))-l)*GlA**(INU(I)-l)*32..
MAI01370
C**
UFY=(A-DSC)**(I7(Ll)-l)*Wl,(A-DSC)**(IZ(T)-I)*W2,.o
IF(IECR.GT.12)WRITE(6,101.)((BUFF2(TJ),J=1,R),I=:.N)
101 FnRMAT(4(1Xt'BIJFF2='tF10.4 ))
Ir(IECR.GT.12)WRITE(6,102)((BUFF(IJ),J=1,IT),I=1,N)
102 FnRMAT(4(1X,9'8UFF=',EI0.4))
Ir(IECR.GT.I2)WRITE(6,103)((CS(I,J),J=1IN),I=1,P)
103 FnRMAT(4(1X,'CS=',E1O.4))
C** T=C*BUFF?:CS*BUFF
Dn 1 I P
DP 1 J=1,R
Tm(IJ)=O.EO
)
uAIO1380
MAT01390
MAI014 00
MAIO1410
MAIO1420
MAI01430
aT01440
MAI01450
MAI01460
MAI01470
MAI01480
Dn 1 K1,N
MAI01490
T*A(IJ)=TM(IJ)+C(IK)*BJFF2(KJ)
MAI0150ISO0
IF(II.EO.O)
D
2 II1P
MAI01510
MAIO1S20
GO TO 4
On 2 J=1,II
B,iFFI(TJ)=O.EO
On 2 K=1.N
MAT01530
A101540
MAIO1550
2
BIiFF1(1IJ)=BUF1(1,J)+CS(IK)*BUFF(KJ)
MA0IO1560
104
Ir(IECR.GT.9)WQITE(6,104)((TM(IJ),J=1,R),I=1,P)
FnRMAT(4(1X,'TM1=,E1O.4))
MAIO1570
MA101580
IF(IECR.GT.9)WPITE(6,105)((BUFF1(IJ),J=1IT),I=Im)
MAIO1590
FnRMAT(4(lX,
D 3 I=1P
DOn 3 J=1lII
J'i=II+J
MAIO1600
105
'TM2=',EIO.4))
MAO01610
MA101620
MA)01630
3
4
TM(IJJ)=BUFFI(IJ)
CONTINUE
J'=II+R
MAIO1640
MA101650
MAI01660
I(FIECR.GT.5)WRITE(6106)((TM(IJ)J=1lJJ)I=1,P)
MAIO1670
106
FnRMAT(4(lX,'TM='El0.4))
MAIO1690
A-44
RrTURN
END
SUBROUTINE MAIN9D
C** COMPUTES AHjH,CHDH,(STEP
MAI01690
MAI01700
MAIOnOlO
60)
CnMMON/MANT2/A,8BC,BICBINP,QOR,IECREPSBUFF
CnMMON/MANI9C/T,TT,TM,TT-
CnMMON/MAN14/AHgHgCH
F N INTEREST FRO4 NOW ON
C** IN ANI4 WERE OMEGC,DCS,
DTMENSION A(12,I?),B(12,I2),.C(12,12),BI(12,12),CBI(12.12)
DTMENSION PUFF(12,12),T(12,12),TT(12,12),T4(12,12),TTM(12,12)
DOMENSION AH(12,12),B9H(1212),CH(12,12)
IiTEGER P.Q,R
C** COMPUTATION aF AH
Ir(IECR.GT.2)WRITE(6,100)
MAIN9D1)
100 FnRMAT(1XSUBROUTINE
IE(IECR.GT.12)WRITE(6.101)((T(IJ),J=lN)I=1,N)
101
FnRMAT(4(X,'T=,E10.&))
102
FoRMAT(4Q(X,'TT=',E1lO.4))
Ir(IECR.GT.12)WRITE(6,103)((A(IJ),J=1,N)1I=1,N)
FnRMAT(4(1XtA=',E1O.4))
MAIOO02O
uAI0030
MAIOOO40O
mAlOnO5O
uMAITOO60
MA100070
uAlOn030
MATIOOO90
mAI00090
MAIOOlGO
MAI00120
MAIOO130
MAI00140
Iv(IECR.GT.12)WRITEF(6,102)((TT(IJ),J=lN),I=1,N)
103
On
I=1N
J=1,N
On
BIFF(I,J)=O.EO
On
I
Dn 2 I=1N
Dn 2 J=19N
AC(ItJ)=O.EO
On 2 K=1,N
104
AW(IJ)=AH(I,J)+TT(I,K)*3UFF(K,J)
IF(lECR.GT.O)WRITE(6, 104)
FnRMAT(1X,'A HAT= )
Ir(IECR.GT.O)WRITE(69*)((AH(IJ)J=1N)gI=1N)
C**
COMPUTATION
105
OF BH
MA I00330
MA1 00o340
FoRMAT(4(X,'B=,E1O.4))
MA100350
Dn 3 I=1N
On 3 J=lQ
MAJ o00360
MAI 00370
MA100380
MA100390
Dn 3 K=1N
Bf4 (IJ)=BHfIJ)+TT(I,K)*3(KJ)
MA! 00400
Ir(IECR.GT.O)WRITE(6,106)
106
FnRMAT(1X,'B
m
HAT= )
I-(IECR.GT.O)WRITE(6,*)((BH(IJ),J=1,I),1I=1*N)
C*
COMoUTATION OF CH
I -(IECR.GT.12)WRITE(6,107)((TTM(I,J),J=1,P)I=lN)
107
FnRMAT(4(1X,'TTM=',El0.4))
Ir(IECR.GT.12)WRITE(6,108)((C(IJ),J=1N)
108
FnRMAT(4(1XlC=,ElO.4))
On 4 I=1P
MAI 0 0470
1=19P)
uAI004BO
MA100490
MA!00500
qAI00510
MAI00520
Dn 4 K=1,N
MA100530
MAI00540
MAI00550
MAI00560
MAI00570
Bt,'iFF(IJ)=9UFF(IJ) +C(II)*T(KJ)
DO 5 I=1*P
On 5 J=1,N
CW(IJ)=O.EO
5
MAIO0410
mAI004 20
uAI00430
MAIOn440
MAI00450
MA100460
On 4 J=1N
8'FF(IJ)=O.EO
4
MA100230
MA100240
MAI00250
MA100260
MAI00270
MAIO02BO
MA100290
MAI00300
MAI00310
MA100320
IF(IECR.GT.12)WRITE(6,105)((B(IJ),J=1Q),I=1N)
B4(IJ)=0.EO
3
MAI00190
mAI00200
MA!00210
MATI00220
1 K=1,N
B~iFF(IJ)=9UFF(I,J)+A(I,<),*T(K,J)
2
MAIOOlS0
AO100150
*AA1.0o160
MATI00170
MAI00180
On 5 K=1,N
C,(IJ)=CH(IJ)+TTM(IK)*BUFF(KJ)
M4AI00580
MAI00590
A-45
109
IF(IECR.GT.0) WITE(6,109)
MAIOO600
FoRMAT(1X,C
Ip=P
MAI00610
MAI00620
HAT=)
Ir(IECR.GT.O)WRITE(6,*)((CH(IJ)tJ=1N)*I=IIP)
CALL
MAIN9E
MAIO00640
RFTURN
MAT00650
ED
MAIO00660
StiBPOUTINE MAIN9E
C** COMoUTES DFR
CrMMON/MANI 4/AH,8H, CH
MA100670
MAI00680
MAI00690
CnMMON/MANI?/ABC,8I ,CBINPORIECREPSBUFF
CnMMON/MANT5/INU INUS INJO
CnMMON/MANTSA/DFR
C** IN AANISA WAS GOF
NO INTE-REST FROM NW ON
D!MENSION a(12,l2),R(12,12),C(12912),8I(12,12),CBI(12,12)
DYMENSION RUFF(l1;,12),INJ(12),DFR(1212) ,AH(12912)
DTMENSION R4H(12q.2) CH(12,12)
ITEGER PtR
101
102
1
2
3
FnRMAT(1X,'SU9ROUTINF
6
103
AIN9E,)
MA100790
FnRMAT(4(lX,'AH=',l10.4))
MAI00810
I ( IECR.GT.12)WRITE(6,102)(INU(I) ,tI=1R)
FnRMAT(lX,8('INU=',1I3))
OD 5 JJ=1,t
J=O
MAIt00820
4AI0n830
MA100840O
MAI00850
Dn
MAI00860
1 K=1JJ
JJJ+INU(K)
Dn 2 I=1,N
DrR(IJJ)=aH(I,J)
MAI00870
MAI00880
MA100890
JiJ=JJ-I1
MAIOO900
JO
DO 3 K=1,JJJ
MAIOn910
MAIOO920
J-J+INU(K)
Ir(JJJ.EO.O) J=O
MAI00930
MAIO0940O
J=J+INU(JJ)
J=J*1
'A100950
MAI009 60
I=JJ
MA1I00970
DOR(IJJ)=O.EO
CoNTINUE
IcUM=O
MAIOO990
MAI00990
MAIOIOOO
Dn 6 J=19R
IcUM=ISUM+INU(J)
MAIO101O
MATIOlO2O
IcUM=ISUM+1
Dn 7 J=ISUM,P
MAIO1030
MAIO1040
I=1*N
MAT01050
DR(IJ)=0.EO
7
MAIOI060
Ir(IECR.GT.9)WRITE(6,103)
MI01070
FnRMAT(lX,DFR=')
IP=P
MAI01090
MAIOlO9O
Ir(IECQ.GT.9)WRITE(6,*)((OFR(IJ),J=1IP)9I=I.N)
CALL MAIN9F
R TURN
E;,O
SiRROUTINE MAIN9F
C**
MAI00780
MAI00900
D
7
4aIO0710
4AIV0720
MATO0730
MAI00740
UA100750
MAI00760
Ir(IECR.GT.12)WRITE(69101)((AH(ItJ)tJ=tN)
I=1N)
On 4
4
5
MAI00700
MA100770
Ic( IECR.GT.2)WRITE(6100)
100
MAIO0630
COMOUJTES THE POL COEFF
MAIO100
MAI01110
MAI,01120
MAI01130
MAI01140
MAIO1150
CoMMON/MANT2/A,B,C,BI,C8INP,O,R,IECR,EPS,BUFF
CnMMON/MANI5/INUINUS, INUJO
CnMMON/MANI6A/XP
MAI01160
MAI01170
MAI 01180
CnMMON/TRASH2/BUFF!
MAI 01 190
C** IN 4ANI6A WAS ADSC OF NO.INTEREST FROM NOW O4
MAIO1 2 00
A-46
DTMENSION A(12.12Bi(12.12)*C12,12),
3
I(12,12),CBI(12,12)
C** REAnS
100
THE EIGENVALUES
DSIRED
FOR EACH DETECTION
SPACE
MA101250
Dn 8 II=1,R
AI01270
mA101280
4A01260
MAIN9FI)
FmRMAT(1XeSUBROUTINE
1
WoITE(6,101)NI
101
FnRMAT(IX,'TYPE THE DESIQREDI13,EIGENVALUES
FOR THE,/,1X,
DATA ARE C3RRECTLY ENTEREDTYPE
102
FnRMAT(1X,IF
103
PrAD(5,103)ISIGN
FRMAT(I2)
MA101350
MAT01370
MAIO13O
MA01390
mAI01400
GO TO 2
MA101410
W!ITE(6, 104)
FmRMAT(1XOTHE
POGRAM
DOES NOT ALLO0
SOURCESUBROUTINEMAIN9FI)
1,,/1X'SEE
THAN 4MAI101420
MAI01430
4
A1I01 60
3 I=INI,4
HAE01470
B,FFl(I)=O.E0
X6(1,II)=O.EO
Dn 4 I=1,1I
4
Xo(1,1I)=X0(1,I)+8UFF(I)
MA101480
MA'101490
XO(III)=-XP(1,II)
MA101500
MI11
MA101510
mAI01520
MAI01530
Xp(2,II)=0.EO
Dn 5 =294
S
XD(291I)=X(2TII)*BUFFI(1)*BUFFI(I)
Dr 6 =34
6
Xo(2,II)=XO(2II)+BUFF1(2)*8UFFI(I)
Xn(2II)=XD(2,II)*8UFFI(3)*BUFFI(4)
X=BUFF1 (1) *BUFFI(2)
mAI01540
MAI101550
mAI01560
MA101570
MA101580
M4101590
X.,A=X*BUFF1(3)
X',B=X*BUFF (4)
MA101600
mAI01610
Y=BUFF1(3) *BUFFl (4)
Y'A=Y*BUFFI(1)
Y4B=Y*BUFFI (2)
X6(3I1) =XXA*XXB
MA01620
XD(3,II)=X(3,II)+*YYB
X(3vII)=-XP(3vII)
MA01660
MAO1670
AIO01680
MAI01630
MAI01640
1 1650
MA1~~~~~~~~~~~~~01650
=X3(Ii)yAXi
X(3tII)
Xm(4,II)=1.E0
D 7 I=14
9
GREATER
4I101450
I ININ+l
3
7
MULTIPLICITY
MA1I101440
CnNTINUE
On
00
lI.OTHERWIDETYPEOt)MA01350
GO TOI
I(ISIGN.E0O0)
C** COMoUTES THE POL COEFF
IC(NI.LE.4)
MAI101290
3
MA101
MA01310
A01320
MA101330
MA101340
II,'DETECTON SPACE.FREEFORMAT')
RrAD(69*)(8UFFl(I),I=NI)
WDITE(6,*)(BUFFlI(I),I=1,4I)
WOITE(6,102)
2
A11240
I(IECR.GT.2)WPITE(6,100)
N=INU(II)
104
MAI01210
MA01220
MA101230
DTMENSION UFF12,12),INJ(12),XP(12,12),BUFFI(12)
I;'TEGER P,R
MA1IO1690
X6(4,II)=X0(4,II)*BUFF
Don 9 I1*NI
(I)
J"=2*NI.1-I
XP(JJII)=XP(ItII)
AI01750
7 60
MAIO01
-
X6(IqII)=X0(JJtII)
10
CnNTINUE
;ONTINUE
105
FnRMAT(lX,POL
MAIO1710
MA101720
mAJ41730
4AI01740
ONTINUE
Don 10 I=l11NI
J=I+N1
MA
101700
IF( IECR.GT.S)WRITE(6,105)
COEF ARE$)
M4TO1770
MA101780
MA101790
MA 01800
MA101810
A-47
Io=R
MAI01820
Ir(IECR.GT.5)WPITE(6,*)((XP(IJ),J=1,IR),I=1,N)
CALL MAIN9
IA101830
MAIO1840O
RF-TURN
END
mAT01850
MA1I01860
A-48
Si'BROUTINE MAIN9G
C**
COMPUTES
mAIOOOl0
PSI
MAI00020
CnMMON/MANI2/A,B,C,BI,CBIN,P,Q,RIECREPS,BUFF
MAIOOO30
CnMMON/MANI4/AH,9H,CH
MAIOn040
CnMMON/MANI6A/XP
MAI00050S
JJ=JJ-1
MAI00060
MATOOO70
4ATOfOBO
MAT0009O
MAIOO100
mAI00110
MAIOO120
MAIOO130
MAIOO140
MAIOO150
mAIOOI60
MAIOO170
~~MAI00180
MAIOOT190
D 2 =1JJJ
IA=IA+INU(I)
MATIO0200
MAIOO210O
CoMMON/MANI68/OPSI
CnMMON/MANT5/INU,TNIJSINJO
C** IN ANI6R WEQE XOTETA,OF
NO INTEREST FROM NOW ON
DTMENSION A(12,12),R(12,12),C(12,12),t6I(12,12),CBI(12,l2)
DTMENSTON RUFF(12.12),AH(12,12),BH(12,12),CH(12,12)
DTMENSION XP(12q12),DPSI(12q12),INU(12)
I1,TEGERP,O,R
Ir(IECR.GT.2)WRITE(6,100)
100 FoRMAT(1XSURROUTINE
AIN9G)
D
4 JJ=1,qR
Dn 1 1=1N
1
DCSI(IJJ)=O.EO
~~~I~:S~~~~~~~O
2
IT=IA+1
C**
MATOO220
I&(JJJ.EQ.O)IA=1
IA TS THE ROW WHERE
PI REGINS(STEP
6E)
IR=IA+INU(JJ)
In=IB-1
MA100250
MAIOO260
O
MAIO0270
3 I=IA,9IB
I:=I-IA
3
4
S
101
MAIT00230
MAIO0240
MAT00280
I=II,1l
MAIOO290
DSI(IJJ)=XP(II,JJ)+AH(II8)
CONTINUE
MAI00300
MAT00310
J-=R+l
MAT00320
On 5 J=JJD
D 5
1*N
MAI00330
MAI00340
D0SI(IT,J)=O.E0
IF(IECR.GT.5)WRIrE(6,101)
MA00350
FnRMAT(1X,'DPSI=')
MAI00360
MAT00370
Io=P
MAI00380
Ir(IECR.GT.5)WRITE(6,*)((DPSI(IJ)J=1,IP),I1=1,N)
CALL MAIN94H
MAIO03 90
MAI00400
RFTURN
MATI004 10
ED
MAI00420
S6BROUTINE
MAI N9H
MAI00
C** COMPUTES H=DPSI+DFR
C** COMPUTES D=T*DH*TTM
CnMMON/MANI2/ABCBICBINP,O,R,IECREPSRUFF
CnMMON/MANI9C/TTT ,TMTTM
4
30
mAI00440
MAI00450
MAI00460
ATI00470
CnMMON/MANI5A/OFR
MAT00480
CoMMON/MANI4/AHBHCH
MAT00490
CoMMON/MANI6B/DPSI
MATOO500
CoMMON/TRASH2/DDHBUFF1
MAI00510
OTMENSION
DTMENSTON
MAIOO520
MAI-00530
(12,12),B(12,12),BI(12,12),C(12,12),CBT(12.12)
UFF(12,1?2)*T(12,12),TT(121?),TM(12,12),TT(12,12)
DTMENSION DFR(12912),OPSI(12912),D(12912)*DH(12912)*Bl)FF1(1212)
ODTMENSION H(12,12),BH(12,12),CH(12,1 2 )
I?-TEGERP,8,R
MAI00540
Ir ( ECR.GT.2)WRITE(6,
100)
uAIQ0570
100
FnRMAT(1X,SUBROUTINE
1
DOn 1 I=1,N
DO 1 J=l1P'
DW(IJ)=DFR(IJ)*DPSI(I,J)
MAIN9Ht)
mAI00550
MAI0O560
MAI00580
MAI00590
MA100600
MAIOOblO
A-49
I (IECR.GT.0) WQITE(6,101)
FnRMAT(lX,D HAT=')
I:P
Ir(IECR.GT.O)WQITE(6,*)((DH(IJ),J=lIP),I=1,N)
C** CHE-K :COMPUTES AH-DH*CH
101
Ir(IECR.LE.3)
MA100670
GO TO 4
Dn 2 I=1N
mA100680
D
2 J1N
8,'iFF(I,J)=O.EO
Dn 2 K=1,P
MAI00690
MAI00700
MAI00710
B!i'FF(IJ)=UFF(IJ)
?
+DH(I ,K)*CH(KJ)
3 BiFFI(IIJ)=AH(IIJ)-BUFF(1,J)
W6ITE(6910?)
102 FnRMAT(1X,,AH-lH*CH#)
WtITE(6*)((BUFFI(IPJ)gJ=1~N)
MAI00750
MAI00760
'AI00770
*I=1N)
DI 5 I=1,N
n 5 J=1 9 P
MAI00910
MAI00320
BIFF(IJ)=O.EO
On K=1P
MAI00830
MA00840
B('FF(IJ)=gUFF(I,J)+DH(IK)*TTM(K,J)
MA100850
On 6
MAI00860
I=1N
,
On 6 J=1P
D1I,J)=O.EO
103
O 6 K=1,N
Dt I,J)=D(I.J)
T (I ,K)*RUF
(K,J)
104
MAI00890
MAO1900
MAI00910
MA100920
WoITE(6,*)((D(IJ),J=l),I=1,N)
MAI00930
Dn 7 I=1N
On 7 J=1N
8
MAI00870
MAI00880
W-ITE(6,103)
FnRMAT(I1X'D=')
C**CHEC;:COMPUTES A-D*C
Ir(IECR.LE.3)RETURN
7
4AI0070
MAI00790
MA10O0800
C~NTINUE
4
C** COMoUTEs D=T*DH*TTM
6
MAI00720
MAI00730
7
MA100 40
DO 3 I=19N
Dn 3 J=1N
5
MAI00620
MAI00630
MA
100640
MAI00650
MAIO0660
MA100 9 40
MAI00950
MA100960
MAI00970
B,'FF(IJ)=0.EO
MA100980
Dn 7 K=1,P
MA0Ioo0990o
BiFF(1I,J)=UFF(I,J)+DO(I,<)*C(K,J)
On 8 I=IN
MAIO1000
MATIO10
O
MAIO1020
8 J=1N
8,,BFFI(IJ)=A(I,J)-BUFF(IJ)
MAI01030
WoITE(6.104)
uAI01040
FnRMAT(1XgtA-D*C)
I=1lN)
WITE(6,*)((BUFF1(IJ),J=lt~),
RrTURN
ED
;UBROUTINE MFGR(AIAMq4,IAN<,IROWICOLEPSIER)
nIMENSION A(1) ,IPOW(1) ,ICOL(1)
nOUBLE PRECISION SAVF,HOLDWORKF1;2
TNDER=IER
MAI01050
MAIO1060
MAI01070
MATI01080
AJ00010
PANOO020
QAOnO30
A'on040
RANOOO50
TER=O
1
,F(M)
tF(N)
2
TER=1000
PANOOOBO
r.0 TO 44
PAN0090
3
4
TF(IA)4,2,5
TRA=-IA
RAOOl400100
RANOOIlO
TCA=1
RANOO120
5
r,0 TO 6
TRA1
RANOO130
RANOO14O
292.1
292,3
PANOO060
RAN00070
A-50
6
PAO00150
PA900160
TCA=IA
nIV-=O.E0
TC=l
~~~~~~~~~~~~
PANOO180
TC1
., 9 J=1.4
PA00190
TCOL{(J)}=J
iP=IC
RAN00200
8 I=1.4
CEEK=A( IR)
PAN00210
RAN00220
PAN00230
RAN00240
PAN00250
a
7
TF(ABS(SEEK)-ARS(PIV))8,8,7
FIV=SEEK
iC=d
,R=I
8
RANO00260
QA400270
TR=IR+IRA
9
TC=IC+ICA
10
~0 10 I=1.M
TROW(I)=I
TOL=ABS(EDS*PlV;
RANOO280
PAN00290
RANO0300
-
RAN00310
RANO00320
RAN0O0330
jRANK=O
TDA:IRA+ICA
'~OsD~~~~~~~~~=l~
Jt=1
11
12
13
]4
J= 1
i'IM=M
TF(M-N) 12,12,11
i IM=N
r.O 27 J=I,LIM
28,?8,13
TF(ABS(PIV)-TOL)
iRANK=J
TF(NR-!RANK)16,16,14
16
17
RAN00400
PAN0O410
PAN00420
RAN00430
PAN00460
pAN00470
PAN00480
QAN00490
PANOO500
TM=IM+ICA
TN=IROW(NR)
TROW(NR)=ITROW(IRANK)
IRAN<)=IN
TROW(t
TF(NC-IRANK)19,19,17
M=JC
TNC=ICA*(NC-1)+1
cEEKA ( IM4)
(IM)=A(MC)
(MC)=SEEK
TM=IM+IRA
RN00450
ANS00510
RAN00520
PAOO0530
RAN0050
RAN00550
QAN00560
RAN57
PAN00580
RANOO590
PAJ00600
QANOO610
PAN00620
RAN00630
PA400640
IC=MC+IRA
QANOO650
TN=ICOL(NC)
TCOL(NC)=TCOL ( IRANK)
TCOL (IRAN<)=IN
eAVE=PIV
6IV=O.EO
RAN00660
RA4N00670
RAN00690
RAN00690
RAN00700
'jl=J+1
RAN00710
TR=JO
TC=JD+ICA
PAN00720
PAN00730
TF(I-M) 21,26,26
RAN00750
T=j
20
RAN00390
TM=JR
R= I NR
60 15 I=I,N
cEEK=A ( IM)
(PIM)=A(Ma)
(MR)=SEEK
,C=INC
18 I=I,M
19
PAN00360
RAN00370
QAN00380
RAN00440
;O
18
RAN00350
tNR=(NR-1)*IRA1
%R=MR+ICA
15
1RAK00340
RAN00740
A-51
21
22
23
24
?5
=I*+1
TR=IR*IRA
RAN00760
QPANOO770
;OLD=A(IR)
WOLD=HOLD/SAVE
(IR)=HOLD
WRC=IR+ICA
-C=IC
~~~~~~~=~~j~~~
TF(K-N)23,20,20
=K+1
r1=A(KRC)
r2=A(KC)
;,ORK=F1-F2HOLO
A(KRC)=WOQK
TF(DABS(WIPK)-ARS(PIV))25,25,24
PIV=WORK
kR=I
PAN00780
RqAN00790
RAN00800
q9A00810
RAN00820
~
~~RAN00830
RAN00840
RAN00850
RAN00860
PAN00870
PA0O0880
PAN00890
PAN00900
RAN00910
PAN00920
NC=K
RAN0O0930
WRC=KRC+ICA
VC=KC+ICA
RAN00940
RAN00950
,,0 TO 22
AqN00960
iC=JC.ICA
iR=JR*IRA
jD=JD*IDA
yF(IRANK-4)29,34,34
PAN00970
9AN00980
RAN00990
RAN0100
=IRANK-1
,Rl=IRANK+l
PANOlOlO
PAN401020
iC=JD-IDA
iR=JD-ICA
RAN01030
QAN01040
30
,F(J)34,34,31
RANO01050
31
TR=JR
TC=JC-ICA
TJ=JC+IRA
RA401060
RANO1070
RAN01080
'jl=J+l
°O 33
=IqlM
RAN01090
ANOlO100
IR=IR
WC=JC
.,ORK=O.EO
aO 32 K=J1,IRANK
wORK=WORK+A(KR)*A(KC)
WR=KR-ICA
KC=KC-IRA
TR=IR*IRA
(IJ)=A(IJ)-WOPK
PAN01l10
PAN01120
PANOl13O
QAN01140
RAN01150
ANO 1160
PANOl170
PAN01180
PAN01190
26
27
28
29
32
J=IJ+IRA
33
34
35
PANO1210
v0 TO 30
RAN01220
yF(IRANK-4) 35,43,43
=IRANK
36
37
PAQ4O1200
'i=J-l
TR1=IRANK+l
jR=JD-IDA
C=JD-IRA
yF(J)43,43t37
,C=JC
iI=JR+ICA
jD=JD-IDA
n0 42 I=IR1,N
RAN01230
9AO0L240
PAN01250
PAN01260
PAN01270
RAN01280
RAN01290
PAN01300
RAN01310
RAN01320
KR=JR
PAN0O1330
~C=IC
RAN01340
;,IORK=0.EO
RAN01350
K=J
RAN01360
A-52
39
40
41
42
TF(K-IRANK)40,41,41
rl=A(KR)
C2=A(KC)
RANQ01390
W4ORK=WORK*Fl*F2
WC=KC-ICA
;R=KR-IRA
K=K*l
PAN01400
PAN01410
RAN01420
RANO1430
nO TO 39
RAN01440
TC=IC+ICA
;(JI)=-(A(JI)*WORK)/A(J))
il=JI+ICA
'R=JR-IRA
PQN01450
RAN014650
RAN01470
RAJ01480
I=J-l
43
44
45
46
oAN01370
RA'013!0
QPA01490
AO TO 36
PANO1500
;ONTINUE
rONTINUE
~ONTINUE
oETURN
vND
PAN01510
PAN01520
RAN01530
RAN01540
RANO1550
A-53
CUBROUTINE ORTRED(DEPI,4RRNPPIME,NEALIDEP1,EPSIIIECR)
MIMENSION DEPl(1),DEP(1'4,12),APR(12,12),WRED(12)
DTHENSION WW(12,12)
CnMMON/TRASH2/WW
I,=IDEPI*NqEAL
TF(IECR.GT.12)WPITE(6,1004)(DEP1(I).1=1,N)
1004 rOPMAT(5(1X,'OEP1=',E1O.4))
~O 0 K1,N
TI=(K-i)/IDEPI
'=:II1
T=K-II*IDEP1
1005
10
,F(IECR.GT.12)WPITE(A,10OOS)IJ
rORMAT(lX. I=',13, J=' I3)
nEP(IJ)=DEP1(K)
I (IECR.GT.8)WRITE(6,1003)((DEP(IJ),J=1,NREAL),I=1,NPRIME)
1003
CORMAT(4(1XlDE0=',EO.4))
Ic(IECR.GT.O)WRITE(6t10)
100
IORMAT(1X.'COMPUTATION DF ORTHOGONAL PEDUCTIONWITH
1PrECISION OF EPSI1')
TNDEX=O
rO 9 J=1,PRIME
TSIGN=O
O0 1 K=1,N4REAL
1
WoED(K)=O.EO
ORTOOO10
ORTOOO2O
OPTOnO30
ORTOOO40
ORTOO50
OPTOO506
ORTOOO70
ORTOOO8O
ORT00090
OTOO10n
OroTO1lO
ORTOO120
ORT00130
ORT00140
OrTOO150O
OQTOO16O
ORTOO170O
ORTOOO80
ORTOOl9O
ORT0O20n
ORT00210
ORT00220
ORT00230
ORTOO24O
nO 3 K=1,JREAL
ORT00250
2
-, 2 L=19IREAL
wPED(K)=WREDK)+APR(KL)*DEP(JL)
ORT00260
ORT00270
ORT00280
3
;ONTINUE
TF(ABS(WRED(K)).GT.EPSII)ISIGN=1
'F(ISIGN.OQ.1) GO TO 4
IF(IECR.GT.n)WPITE(6,101)J
101
CORMAT(1X,'VECTOR DEP(',1I3,'..) IS LREADY OPTHOGONAL TO
1 6RR AT THIS POINT')
rO TO 8
4
W;J=O.EO
Ir(IECR.GT.3)WRITE(6,I1000)(WREO(K)
,K=1,NREAL)
1000 FmRMAT(4(1X,'WRED=',ElO.4))
MO 5 I=1,NREAL
S
wVJ=WVJ*WED(I)*DEP(J,I)
TF(IECR.GT.3) WRITE (6,1001)WVJ
nO 6
6
12
I=1,NREAL
gO 6 L=IiREAL
.lW(IL)=WQED(T)*WRED(L)/WVJ
OPT00290O
OPTO0300
OQRT00310
ORT00320
ORT00330
ORT00340
ORT00350
ORT00360
ORT00370
ORT0O380
ORT00390
ORT00400
ORTOO41O
OPT00420
ORT00430
DOn 12 =1IREAL
DOn 12 L=19,REAL
OPT00440
OTO0450
Ic(ABS(WW(IL)).LE.EPSII)WW(IL)=O.
CnNTINUE
TF(IECR.GT.5)WRITE(6.1002)((WW(IL),L=1,NEAL),I=1,NQEAL)
!NDEX=INDEX+1
nO 7 I=1,f9EAL
ORT00460
ORT00470
ORT00480
0RT00490
ORTOO500
0 7 L1,NPEAL
7
8
APR(IL)=ARPR(IL)-WW(IL)
CnNTINUE
Ir(IECR.GT.O)WRITE(6,102)INDEX
102
rORMAT(1X,
1In,'ALTERATIONS TO A
HVE BEEN PERfORMED)
ONTINUE
1001
O0PMAT(1XtWVJ=4,E1O.4)
1002 FORMAT(1X,5 E10.4)
Dn 11 I=1,NREAL
On
11 J1,NREAL
ORT00510O
ORTOO520
ORTO0530
ORTOOS40
ORTO0550
ORT00560
ORTOO57O
OPTO580
ORTOOS90
ORT0o600
ORTOO61O
A-54
IF(ABS(ARR(IJ)).LE.EPSI1)
11
ARR(IJ)=O.
ORToo620
C'nNTINUE
ORTO0630
DETURN
ORT00640
rND
ORTO0650
B-1
APPENDIX
B
LISTING OF LONGITUDINAL GUIDEWAY VEHICLE SIMULATION
B-2
:PE)O
C
:rOTDAN
TEST
Al
ITCA
6/2?/7B
17:39
TES00010
TES00020
SIMULaTIOJ D0OGAM
C
- LCV DETECTION FILTEP
STUDY
TES00030
TESOO140
TESOOO5O
C
TESOn060
E-4AL*4(A-H.0-Z)
IMPLICIT
DI'ENSION C(3,7),D(3,S)
TESOnO 70
T (,I) ,'VC9* 1)CHT(9,1),V4IND(g,1)
DI'MENSlTN
7,1)
[EN'%,IOIN AtD-)I( 7.1).A
,Y ('A. ) X)(7)
>,9(7,1)
>.XMF(6),Y,,'-ES(P)XINI(6)
> .(X
EPSI(2)
(3, 1) D l(3.1)
ALL
TESO110
TESO0 150
,CC(?4)
UST RE INPT
FT - L - SEC
.,JITS
IN FPS STAND4RO SYSTEM
TES00160
TESO0170
TES001O0
TES00190
SPECTFY SYSTEM CONSTAnTS
EXTE.INALFT
N=7
TOL=O. I
I'ID=1
TESOo0210
TESOo0220
TESO00230
TESO00230
AD 5,201)IP1
aHVEST=350.OEO
G=32.2EO
TA IL=10000.
I COm =0
OEO
A'J=373.
,1= 1500 .0 00
AK2=looo1000.or
Ar3= 1?150
TES00200
TES00240
WPITE(6,10?)
c
TESOnlon
TES00130
TES00140
PEAL*R
c
C
C
C
c
c
TESOO90
TESO0 120
CO-'MOtN/Al/ A(7.7),8(7,5),U(5,1)
DT, rT
WA(7.9)
DTMEFNSIGf's
TESOOO80
OEO
AK4=1.OEO
AK4-1.2EO
Ai=l150.OCO
A2=-5S.SEO
A3=-1466.5;O
A4=-12150.OEO
Cv=100.E0
0
AJ"AA=6.44
AMAX=8 .OSEO
TES00250
TES00270
TES00280
TESO0290
TESO0300
TES00310
TE S00320
TESO0330
TESO0340
TEso0330
TES003SO
TESO0370
TES00380
TESO0390
TESOO400
TES00410
TFS0042O
TES00430
TES00440
TESOO 4 50
IF L=U
I-La53=0
vw=O . OEO
TFSO00450
I nil
IM y=o
TES004800
C
WT=7.333333EO
TES00490
C
C
SEED FOR NOISE
TFS00470
TES00500
C
C
C
TESO0O510
TESO00520
ISEE0=3141 no
TES00530
AFPOC=0.0370
TES005O40
BW=AEROC
DN=I.OEO
TES00550
TES00550
TESO0570
INITIAL CJDITIONS
WPITE(6,103)
TES0050
TESO0590
TESOObOO
B-3
TESO00610
PErD (5,20O)XX
TESO062o
TES00630
TESO064O
wPITE (. 104)
PFal)(5,202)VC
WRiTL (b. 10.)
TESOOb530
TESOOA60
PFa0(5,201)ICHV
TO 12
IF(ICHV.EO.O)GO
WPITE(6 , 10')
DO 12 J=1*ICHV
12
PEAD(5i*)CT(Jol)q`VCM(J,1)
TFSO0670
TES00680
TES00690
CONTINUE
WqITE (6.107)
TFS00710
TES00720
F4D (5,*) DTr
IF(DT.EO.O.)DT=O.1D0O
TESO 730
TESO00740
W~ITE(6,10R)
TESO0750
TES00760
TFS00770
RPFAD(5201)ICHW
TO 13
IF(ICHW.EO.O)GO
W4QITE(6.109)
13
DC 13 J=1,ICHW
1) VWIND(J *1)
T(J
PPFAD(5E*)C
CONTINUE
WITE(69216,)
IC(OMP
FAD(59*)
TO 16
IF(ICOMP.El.O)rO
WOITE (6,217) ICOM:
PFAD (.*) T AIL,FAILVL
1A
CONJTINUE
4PlTE(#aIln)
ITL-(f6.110n)
jIU
READ(5,*) IMP
PRINT
C
C
IF(ICHV.EQ.O)Gn
DO 15 J=1,TC!V
IN-4OR4ATITON
TO
5
WPITE(6.21?)J.CT(J.l),VCA(J91)
CONT INUJE
CONTINIJE
X(1,1)=XX
X(2,1)=VC/A(4
X(7,1)=VC
VOL)=0.
V2COMM=10O.EO
TESO020
TESOOR30
TESO0840
TESO0850
TES0f850
TESO 0870
TESOO890
TES0090n
TFSO0910
TESO0920
TES00930
TES00940
TESO 0950
TES009,O0
TES00980
TESO0990
TESOl o000
TES01010
TESO 1020
TESOlUO60
TESO1O7O
TESOIOO
TFSO 1.090
TESO 110on
TTTM=TTM+OT
INITIALI7E DFTECTION STATE XES(6*1)
C
(1)=VC/K<4
TESOI 110
TESO1120
TES 130
TESOl 140
xiNI (2)=O.-EO
rESol 150
XINI (3)=O.0O
XINI (4) =V:
TESOI 150
TESO 1170
x N I (6)=VC
TES01lB0
TES01190
XIJI(5)=O.;O
C
C
TESOO010
TESO1040
TESO 1030
TTM=O.EO
xIJI
TESOO00
TESO 1030
T=O.000
C
TESOO790
TES00970
wITE(6,.21I)DT
TO 14
IF(ICHW.E0.0)GO
n 1 J=1,TCHW
,VIIND (J I)
'WV;ITE(6,21 4)J'C HT(Jo)
14
TES0O70
TESOORBO
TF 3008 80
ACK THIS
WCITE (6,21n)XX
WPITE(6,211) VC
1S
TESOo7tOO
LEAD VEHICLE
DYNAMICS
TESO 12o00
TESO01210
B-4
TES01220
xvH=loon.O
TES01230
TE01240
vvH=20.0
VvH*FST=10.n
TESO01
Dx=XVH-X (1.1)
C
FORA
TES01260
DETFCTION
OD-L DESIGN
ATICES
CALL SOLUT(5)
CALL MODEL(AMV.AMVEST.A
*A3,A4,AK1,A•2,AK3,AK4)
~~~c~~~~~~~~~~ ~~~~TESO0
COWP'JTE
C
A %4ATIY
~~~~~~~~~~~C
no 1 J=1 9 7
DO 1 rK=19,7
I
17
TES01360
COJTINUE
CONTINUE
n
A (1, ) =l.
A(2,3)=1.0-F0/A4V
TES01370
TES01380
TES01390
TESO01400
A(3,4)=1.00
TES014 10
A (5,*2)=-AK1*AK4*AK3
A(5 ,3)=tA4
A (D,.3)
=A4
A(5.4)=43
TESO 1430
TES01440
~~~~~~~~~~~~~~TES
14,0
TES01420
4
5
4)
^3
fol5
TESO1450
TES014 60
TES014 70
TES01 4 3O
TES01490
A (5,7)=AK1*AK3
=-AK4
A (6,)
TESOlSOn
A(6,7) =1.00
TESO01510
C
COMPJTE R MATRIX
TESO1520
TES01530
TESO01540
TESO 1550
C
fDO 2 J=1,7
2 K=I 5
r
°TFS01560
(JK)=O.OE
CONTINUE
TESO1570
P (2.1)=-CV/AMV
TES015O80
R(2,3)=-./AMV
TESO1590
B (2.4) =-1 .OEO
TESO1600
P (5,2)=AMVST*AK3
TES01610
B (5,5) =-AK] *AK3*ON*A!<4
TFSOL620
B3(6,5) =-AK*DN
COMPITE
TESO16 30
TES016I0
B(7,2) =ON
C
C
310
TES0132-0
1330
A(J.K) =0.00
A(5,D)=A2
A(3,b)=AN2*AK3
2
~~~~TESO0
TESO1290
TESO13 00
TES01340
TEso]35(O
(4. 5) = .070
C
TESO1270
TFS01280
C
C
ATrPIX
TES01650
TESO1b60
TES0 1670
DO 3 J=l,3
DO 3 K=197
C(JK) =0.O0O
3
CONTINUE
C (12)=-A<1*AK4
C (1 .o)=AK2
C (1.1)=AK 1
C(2,2)=AK4
C(3 T1)=1.Eo
TESO1700
TES01710
TES01720
TESO1730
7
TES01 40O
TESO1 7 50
TES01760
TESO1
C
C
TES01680
TES01690
CO-PUJTE 0 MATQIX
7
70
TFS01780
DO 4 J=1l3
TES01790
TESO 1800
DO 4 K=1,5
TES01810
C
D(JK) =O.0O
TES01820
B-5
4
Y(Jo1)=OOO
TES0 1830
CONTINUE
D (! *2) =AMV-S
D(1 ,)=-AKI*
TESO 1840
TESO 1850
TESO 1860
TESO1870
TESO1&BO
TESO1890
TESO1900
TESO1910
TESO1920
TESO1930
TFSO1940
TESO1950
D(2.5)=AK4
IF (IPI1 .FU. ) WPTTE'(6,?218)
IF(IP.FQ0. I) CALL 'A)tJMP(A,77)
o.1) WPITEi(6,219)
IF(IPl.E
1F ( 121 *EQ, ) CALL M)UMD(P,7,5)
IF (IPI .. 7) WPTT-(Sq220)
CALL MO!ikDo(C,3,7)
4PITE(6,?? )
IF(IPl.EQ.o)
IF (IP1 .Q.
C
C
C
100
C
C
C
C
C
MJD(D,3,95)
t) CAL
TESO01960
TFSO01970
NAVISATION LOOP
TES01980
CONT INLIUE
TESO01990
COMPJTE
NEW
INPIJT TO
FOLLqWEP '40DE SNS)R
TES02000
TESO?010
TESO2020
TESO?030
TESO?040
O0N-LINFAR SYSTEM
COMmUTATIDNS
TESO?2050
DXP=OX
XV"=XVr+VVA*DT
DX=XVN-X(1
OX = 1 0 0 0 .
C
C
C
TES02060
TES02070
.1)
VARIA3LE
G
GrAI
AJU FOLLOWEQ
COMAND
VELOCITY
Gl=0.2
V2COMM=Gl *X
C
C
C
VELOCITY POFILFR
IF(ICHV.EQ. 0.AI.TM.,LI.DT*.) 1COMm=VC
IF(ICHv.EQ.0.ANOl.TM.LTflr-.3)GO
TO 22
O) 22 J=1,ICHV
IF(DA~S (TM-CT(Jl 1) ) .LF.nT*.5)VlCOM=VCM(J,1)
P?
C
CONTINUE
C
TESO 220
TE 0?230
TAKE SALLER
VELOCITY
C
IF(VlCOrM..
T.V?COM.4) VrOm1=Vl1COrM
IF(V1COMM. -,F. VC3MM)VCOM4=V2COnA4
IF(A6S(VCO'"4i-VOL).GT.0.01)IFL=0
IF(V2COMM.! .V1COMM) IFL=2
I9 ITM/1I~)
>y;AFS
1)
*IDMP) FI.ITA) RTTE(692?2)
YM-S (2) ,EPStI(1)
,PSI
lFSlJ)
9*J=l96)
(2)
CLL PPOFLL(VCOMMAMAYAJMAXOTACVCXXIFL,
IMO)
VOLD=VCOMM
C
C
C
TES02080
TFSO?090
TESO?100
TES?211O
TESO?120
TESO?130
TESO2140
TESO?150
TESO2160
TESO2170
TESO?1BO
TESOP190
TESO?200
TESO?210
WIND
GUST 4OFL
IF(ICH4.EO.O)VW=O.OEO
IF(ICHW.EQ.l)GO
TO 20
IF(ICHw.EQ.1)VW=VWIND(l,(11)
IF(ICH*!.EQ.1)GO TO ?0
K=ICHW-1
DO 20 J=1,<
TESO0240
TESO2?50
TESO?260
TESO2?70
TESO?280
TES02290
TES02300
TES502310
TESO2320
TESO?330
TESO?340
TESO2350
TESO?360
TES02370
TES02390
TESO2390
TESO?400
TFSO?410
TESO?420
TES02430
B-6
.. fLT.CHT(J+.1
T(j,1).AN
IF(TM.GT.C
))V=V',IND(Jol)
4
TES070
$0
TES0? 4 70
TESO?
4
TESO? 90
TRAC' SL(PET MODL
I
CALL TSTTP<(X(I,1),GN,SL3PE9G)
~~~~~~~~~~~~~~~~
C
DSTRIRJTION
FTjrpTO-GuS144
C PANO0'- NqR
TES07520
TES02530
WT=,oNOF( IRqFED)/100.
c
TES02530
INPUT VFCTOR U
~~
c~~~~~~~~~~~~~~~~~~~~~~~~~
TES05250
TFSO? 5 60
5 70
TEF502
C
IF(X(2,1).'.0.0)U(1,1)=0.0E
0
TESO25B0
TE029
tl(2,1)=AC
TES?0600
TES02610
TFSO?620
Uj(4,1 ) =GNJ*SLOPF
C
NOISE INPUT
U(5,1)=WT
C
WT=O.
TESO?650
+WT)
(X(2,1)
i(( ,v1)0-=O.EnTFSO2680
C
j(5,1)0.70
J(4.1)
IS GRAVITY
TFSO?660
TES0270
TFSO?680
TES0?2690
INPUT
U(4,1)=0.En
C
C
TES02630
TES02630
TFSO?&40
VINDAN4
C
S AERD INPUT
U(3,1)
FQ.ITM)WPITE(.213)TtMX(11)9X(291)VC
If(((IIM/Im)A?)*IDMP)
1 J(4t1),U(3,I)=0).ACgVC(1MMVIN)E¢(lo
C
S)OLUTION TO STATE
r
C
TES02O500
TES0?50
TES02510
EAN -VAIANCE 1./100.
C ZERO
TES02440
IFL9InTINn
-QUATION
vfFPP=X (2'*1))-VC
CALL FITJDI (Ao7..T5,X.T,JTtA1(AD2)
TES02730
TES02740
TES02750
7
TFSO? 60
TESO770
7
TESO? 80
TES02 7 90
xn) 2D 1=1 7 )*TES02800
C
UT
CON
TES0O820
UTINuY
ST
XDTTT
*IN)7CCN1WWiER)
C * 3TOL
CALL DvERK(NNFCTTT
C
C
?'3
no3 23
UI(i.=191,7
X(IL
,)XD(T)
CLL
TES028 50
TESO2860
CONTINUE
O T
C
C
TEFC.TES02870
n
SYSTE
FICOPUTE
OUTPT
Y,
~~~~TES02890
T9=TM4>DTC~~~~~~~
CALL MMULD( CXCX?397qI)
ICTLLMjLDDqiqm.J,3,5,l)
CAL-L MADDO (CX, ftiY,
C
C
C
3ol)
OTI N0E
DETECTIL\
TES02830
8
TES02 40
INTETOLFACEC
CALL FILTE~)(6.XmE~SYMFS,IFLAG3,XINITrliTTTMTOL9YU
TESO?8 80
TES029 00
TES02910
TES02
20
TES0230
TES02930
TESO950
TES02 9 60
TES02
TMT TTM
9
9
70
TES0?90
TTTM=TTTM+ITTS29
TESO3000
TES03010
TES03020
Tm=TM+DT
*
ITM=I TM~l
TSTOP=20. 0;0
C ,P1
TM2ESF
TO~97
T~c)LEM;7*jTATI04TES03040
FAILRE
TES03030
B-7
C
IF(ICOfP.E'l.O)GO TO 30
rTIFMP=Tr
T (A.c.(TATL-TTETP).oT.OT*.5)O
T
TES03050
TEs03060
TES03070
TEFS03080
3
TES03090
1) AMVEST=FAI _VL
IF (ICP.E.
TES03100
A;V=FATI VL
IF (ICOIP.E3.2)
IF(ICOnaP.FE'.3)Kl=FAILVL
IF(ICOAP.El.4)AK?=FAILVL
TES03110
TES03120
AK=FAILVL
TES03130
IF(ICOP.E').5)
TESO31 4O
TES03150
TES03160
!F(ICOP.E).6) K4=FAILVL
F (ICOMP.E3.7)a< 1=FATLV_
IF ( ICOMP.E').8),A<2=FAT LV_
3r
AA<3=F4TLVIF ( ICOP.E').9)
TES03170
IF (ICCM!P.E). 10) AAK4=FAILVL
1 l)C1 =FAiT. VL
IF ( ICOMP·E.
IF ( ICO'D.E'. 12)C, -FAI VL
)SD1I =%aIL VL
IF(ICO'P.EF).
TES03140
TES03190
TES03200
TES03210
1'I4)SDP=FAILVL
IF (ICOMPE.
wPITE(6,21) IC0)M¥4F ILVLTM
TES03220
TES03230
GO TO 17
TES03240
CONTINUE
TES03250
IF(TM.LT.TqTOP)GO TO 10n
7)
E). 1) C"ALLMDUMP(A,7,
IF ( IPI.
TES03260
TFS03270
IF ( IPI .EQ.I ) CALL moiJAP(l,7,5)
.EQ. 1 CAil m)tIJMP(C,3,1 7)
IF(IP
.EO.I 1) CtLL MOUMP(D; 395)
IF(IPI
TES032BO
TES03290
TES03300
IF ( IP1. F.Q ] ) CALL '4lJMP (X 7,1 )
)CALL MOUMP(U,5,1)
IF(IP1.)Q.1
TES0310
TES03320
FORMAT STATEMENTS
TES0335n
IF(IP1.FO.1
C
)CALL MOIliM(Y3t1)
TES03330
TES03340
C
1,2
FORMAT(,
1n3
104
105
FORMAT(, INITIAL TACK POSITIONl )
FORMAT(' INITIAL ELOrITY (T/SEC)')
FOQPMAT(t WaYSI)E COMVAND VELOCITY CHNSJGES (I1)')
106
FOPMAT(,
107
1nA
FORMAT(, SAMLIN5 INCDEMENT (DT=.1
)
FORMAT(' WIND cIJSTS (T1)
109
FORMAT($
110
210
X.Y,II
JMP (NO. OF 3tS),)
FORMAT(, I'TEGF
F ORMAT(
IN!ITIAL POSITION' F12.3,/)
211
FOR'.AT(, I\JITIAL VFL-OCTY'F'1.3,/)
TESO+70
212
213
214
?0?
201
215
FORkAT(' VELOCITY CHAMK!E TIME, NEW vCO0MAN3D ,I3,2F8.2)
FOPRAT(' TT"E ',10(FR.2,1X),3I4)
FORMAT(' WIND LEVEL CHAN3E TIME, NEW VELOCIFY',I3,2F8.2)
FOkhMAT(F12.S)
FOR4AT( I 1 )
VALUE =',
FORMAT(/,' FATLUPE OF DEV1CE 'I32X,'NEW
TESO34SO
TFSO3490
TES03500
TFS03510
TFSO3520
TES03530
>Fl0.4.2X,'T
nJ;.'P
DESIG!4 MATPIY
EM.TEP CANGE
217
TME OF FAILURE
FORMAT(
IS5)
FORMAT(/,'
A ATR:IX',/)
F RIMAT(/,'
MAT'IX,/)
4
10
TES03420
TES03430
TES03440
(+=HEAOWIND)')
TES03450
TES03450
TES035+O
,FO10.4,//)
FORHAT(
2?0
P21
222
TE.03
DEFAULT),)
AND VWIND
CuPONF.NT FATLIJE
216
218
21Q
TES033q0
TFSO390
TES03400
AND VCOAMM')
TE
ENTER CHANGE TIiE
=
TES03360
TES03370
(I=YES)')
N0.
TESO3550
(ZERO IF NO FAIL)')
AND NEW COM:UNENT
GAIN
FOR NO.
'
TES03560
TF03570
TES03580
TES03590
FORMAT(/, C ATiIXt/)
FORMAT(/, D MaTIXt,/)
FORMAT(' FILT OUT',1OG10.2)
STOP
TES03S00
TES03610
TESO3b20
TES03630
END.
TES03640
B-8
:PEAD
FILE1
cOQTPAJ al1DISCA
S/26/76
SutJROUTINE FCT( N\4,Tr.xxPRIE)
20:23
FILOO010
COMMOr/A1/ A(7.7),h(7,5)vU(5,1)
FILn0O20
9IMENSION Y'ImTE('7).X(7)t,1(7.1)*x2(7,1),A~(7,1)
CaLL MMlJLD(.R*U.X1 J
DO 1 =1.7
X?(Il1)=AX(Tl)
I
rILoO030
1.)
rILOnO40
FILo0O5o
FIL00060
CONTINUE
FILOnO70
CALL MJLD(A. , XPNN,N1)
FILo0O0O
Dn 2
rILOnO90
=1*7
xRiNF(I)=yPl(I.1)+X1(I1)
CNTINJE
FILOO100
FILOOLIO
RFTURN
FILOO120
EliN
FILOO130
FJHCTION S5S3(X)
FIL0O140
1 .FO
IF(X.GE.O.FO)SGJN=1.EO
FIL00160
QFTURtLRi
FIL0170
EnD
SUBROuTINE FI'r)IF(ANJ.B,mXUDTAD1,D2)
FILO1BO
FILOO19O
IPLICIT R:AL*4(A-HO-Z)
FILO0200
IF (X.LT..0)SGN-
i)IMENSION
RFAL*p
FTLOO15O
(NNJ).B(N),X(N,1).U(M,1),ADI(\.1),AD2(N,1)
FIL00210
T*TCOUNT
FILO0220
CALL i'1ULD(AXaD1.NN,1)
CaLL MMULD(3qUJA22,Nqm1)
FIL00230
rIL00240
DO 1 J=1N
'
FILOO250
X(J,.I)=X(Jl)+(Ai(J.I)+41)2(Jl))*OT
l
rILO0260
CONTINUE
FIL00270
R TURN
E._J)
FILOO280
FIL00290
SUwPOUTTTNE TSTTR<(XGh,S-OPEG)
FIL00300
~~~~~~~~~~~~C
C
TsTTRK
- LO\IITHDTINAL
P.TOILE
SLOPE AND GAVITY
C
INPUT
C
C
C
C
.
OF AGRT
TEST
TPACK,
IFORMATION
- X-
LONGITUDINAL
GNJ -
O4TINaL GPAVITY
.FIL00370
OSITIaN
FIL00330
(FT)
(FT/sFC**2)
FTILOO360
OUTPUT - SLqDE - TEST TRACK SLOPE a' X (AD)
G - GVITY
CO-nONENT DAPALLEL TO TRACK (FT/SEC**2)
FILO0o3O
FIL00390
FIL00400
LRV DTECTION
C
MARCH 10,
FILTER SIMlILATION - USOOT
1978
...
qICH-AEL J. DYMENT
rIL00430
..............
FIL00440
I4PLICIT RAL*4(A-HO-Z)
C
FIL00410
FIL00420
C9
.FIL00450
C
TQACK CONSTANTS
TRACK
LENGT
FILO0460
= TL
FIL00470
F1L00480
XL=6000.EO
x1=1550.EO
x2=1850.EO
FIL00490
FIL0050n
FIL00510
x3=2150.EO
x4=2350.Eo
FILOO520
FIL00530
x5=2650.EO
FIL00540
X6=2950.EO
RESET POSITION IF VEHICLE HAS LPED
C
IF(X.GT.XL)X=X-XL
C
FIL00320
P~~~~~~FIL00
FII00350O
C
C
TO COMPUTF
~~~~~~~~~C
C
C
C
~~~FIL00310
USED
FIL550
TRACK
FL00560
FILOOS70
FILO0580
FILOOS90
FIL00600
~~~~~~~
B-9
1
CVE
VERTICAL
C
C
FrILO0630
TO 6
IF(X.LT.X1})O
TO 2
IF(X.GF.X2)GO
XT=x-x 1
Y=O.000o2En*XT
50 TO 1
CONTINUE
CURVF
~VEPTICAL
CURtVE 2?
VER'TICAL
C
C: C
FIL00740
FIL00750
CONTINUE
PLATEAU
IF(X.GE.X4)
GO TO 4
FIL00820
FIL00830
GO TO 1
CONTINUE
VERqTItL
FIL00840
CURVF 3
FIL00870
FIL00680
Dy=-O.O-O?*XT
FIL00 99 00
FILO0 10
CINTINUE
C
C
VERTICAL
IF(X.GE.X6)GCO
CUtJ:VF 4
TO 6
XT=X-X6
rY=0o.0002EO*XT
HORIZ3NTAL TRACK
FIL00920
rIL00930
FIL009 40
-IL009 50
FIL00960
FIL1l000
PILO1010
FIL01020
FIL01030
rIL010O40
CONTINUE
G=GN*DY
FILO1050
FIL01050
FIL01070
FIL01080
SLOPE=OY
RE TURN
FIL01.090
FILOI 100
COMPUTE GRAVITY COM'ONENT
C
C
FILOl 110
END
SUBROUTINE 'MULD(AH.CL9MN)
FIL01120
DO 1 I=1*L
DO 1 J=1N
C( I ,J)=0.00
DOn2 K=1M
C(IqJ)=C(I.J)+A(I,K)*R(KJ)
FILOI 140
FILOl150
FIL01160
rIL01170
FILOI 190
CONTINUE
CONTINUE
FILO1 00
RFAL A(LM) .3(.N)
2
1
FIL00890
FIL00970
FIL00980
FIL00 9 90
1
GO T
CONTINUE
DY=O.OEO
I
C
FIL00850
FIL00860
IF(X.GF.X9) GO TO 5
XT=X-X4
GO TO 1
6
C
C
C
FIL00760
FIL00770
FIL00780
FIL00790
FIL00800
FIL00o810
DY=0.OEO
C
C
C
¢IL00 7 10
FIL00 7 30
XT=X-X3
~Y=-0.0002EO*XT
60 TO 1
3
C
C
C
FIL00640
FIL00650
FIL00660
FIL00 6 70
rIL00680
FIL00690
FIL0o 7 00
FIL00 7 20
TO 3
IF(X.GF.X3)5O
FIL00610
rIL00620
RFTURN
,C(!-N)
FIL01 130
FILOl190
2
FILO1210
B-10
END
SUSPOUTINE
jF4L A (P.A)
iO 1 I=1,M
DO 1 J
FIL01220
F1L01230
FILO1Ž40
FILO1250
ADOrD(A,R,C,MN)
R (,')
*C M.N)
N
FILO1260
C(I-j)=A(I.J)+R(IqJ)
1
CO(NTI NLE
RETUkN
FIL01270
*FIL0120BO
FIL01290
FIL01300
E-NID
SUBROUTINE SJR0 (A.RvCqMN)
RFAL A('¾N)9,("*N),C(MN)
FIL01310
FIL01320
DO 1 I=19M
OD 1 J19N
FIL01330
F1L01340
C(I,J)=A(I,J)-R(IJ)
CONTINUE
FIL01350
FIL01360
RF TUkN
FIL01370
END
SUBROUTINE POFLL(VCOMM, MAX.JAX.DT*AAVCAX.IFLIMD)
rl
PPOFLE:
C
C
C
C
TO MAXIMUM
JMX
OT
IFL
-
JFR
FIL01 4 70
FIL014qO
(FT/SEC**3)
CITERIA
-
INTErPATlN
-
FLAG
~~~r ~1
0
-
-
FIL01490
INTERVAL
VELOCITY
NW
RETAIN
FIL0150n
COA44AND -
RESEN
T A'l OE
SELECT
FIL3SlO0
FILO1520
NEW MODF
FILO153O
IIMD - FLAG
C
C
FIL01430
FIL01440
FIL
FILO1 4 50
*FIL01460
VCOM4- FXTERNAl CMMANnED VELDCITY (FT/SEC)
AMAX - 4CCELCRATION CITFEPIA (/SEC**2)
C
C
FIL0140n
--D cAt<
VELOCITY
COMMAND
SUBJECT
CITE?IA
a-RK Ew~r
ION h>Jr)
J
JCIEI
-4
IJPUkT
C
C
C
r~~~~~~FIL
FIL01420
CREATFS A POFI
ACCELE-:RATION A
C
IL0380
FIL01390
~~~~~~~~~C
C
1 - STANOARD PROFILE
MOD T. I E D
A AX PF ILE
3 RO ACCELERATION ROFILE (PFD
FIL01540
FILOi5O
FIL01560
;?
C
ET
I=12)
FILOI1OO
FIL01570
FIL01450
c
OUTPUT
QAA
VC AX
C
COMMANnFD
C
T
RAL*4(A-HgO-Z)
FIL01650
FILO1650
REALJAXJmX
TEST
FOR
ODE
FL01670
FIOlISO
rIL01690
SELECT
'FL01700
=VCOT(M-VC
-
IF(IFL.FT).) IM=3
TO 10
IF(IFL.NE-.)GD
TO n
VI=AMAX**2/(2.E0*JMAX)
FIL01730
FL01740
FIL0750
IF(AS(A4).GE.l.E-,)ImD=3
IF(AbS(AA).5E.1.E-6)G
T
IF(AdS(nV).E.?.FO*VI)I)1
IF(A3S(OV).GE.?.E*VI)GO
IMD0=c
CONTINUE
~~~~~~~C
FILO 7 1O
FILO1720
IF(IFL.FO.2)GO
10
FL01600
FIL01610
F IL01620
FIL01 6 30
1L00FIL01640
~~~~~~~~~~~C
IMPLICIT
PEAL*8
C
C
C
FIL01590
FIL0160
ACCELERATION
COMMANDED VELOCITY
COMMANDED POSITION
FTL760
10
TO 10
FIL01770
FIL07B
FILO1790
FILO11 AOOFIL110
FIL1 8 20
B-11
C
MODE SELECT LOCATION
FIL01830
FIL01840
TF(IiH).FU.!)GO
IF(I;qD.ED.?)G0
FIL01850
FIL01860
T
100
TO 200
IF(IMD.Eu(.)GO TO 300
IF(ImDL).FQ.)GO T 400
C
C
rILO1890
MODE 1 - STAND4ARD VELOCITY PROFILE
C
10
Il0
CONTINUE
IF(IFL.NE.n)5O TO 110
TCOU T=0o.On0DO
AA=O.EO
TI=A,4AX/JMAX
FIL01 9 20
rIL01930
FIL01940
FIL01950
FIL01960
T2=(AaSg()V)-Tl*AqAX)/aMAX
FIL01970
IT1=T1/OT+l
-rTI=FLOAT(IT)
nT
IT2=T:?/)T+]
T?=FLOAT(IT2)*r)T
JtX=ABS(DV) / (Tl**2+Tl*T2)
FILO1980
FTL01990
FIL02000
FILO0lO
FIL02020
A X=JMX*T 1
FILO2030
JMX=JMX*SGi(DV)
FILO0240
AMX=AX*SG\O(DV)
FIL2O?050
T?=T2+T1
13=T1+T?
FILO2060
rIL02070
IFL=l
FIL020O80
CONTINUE
ICOtJNT=TCOJNT+OT
I(TCOUNJT.E..EO.AND.TCJUNT.LF.T1)A4=A+JMX*DOT
I ( TCOUNT. T .TI . AJD.TC OU\T.LT.T2)
=M4X
FILO?090
FILO2100
FiL02110
FILO?120
IF(TCOUNT.Er.TP.AN.TO!J4T.LT.T3)AA=AA-JMX*DT
Ir(TCOUNT.SE.T3)AA=0.FO
FIL02130
FIL02140
210
FIL02150
AX=AA+VC*OT
FIL02160
FILt2170
RFTUktRN
rIL02180
MODE 2 - MDIFIED
VELOCITY PROFILE
C
200
FILO1900
FILO1910
IF(AdS(AA).GT.AMAX)AA=AMX
VC=VC+AA*Dr
C
C
rILOl170
FIL0138O
rILO190
FIL02200
FILO?210
CONTINUE
IF(IFL.NE.1)GO TO 210
FILO220
FILO?230
TCOUNT=O.OO0000
FILO?240
DnV=ABS(DV)/2.EO
AAkAA=SOQRT(2.EO*DDV*JMAX)
TI=AAMAX/JMAX
IT=TI/DT+l.
TI=FLOAT(IT)*DT
aMAX=2-.EO*DDV/T1
J!X=A4AMAX/Tl
AMX=ABS(AAAAX)*SGN(DV)
JAX=ABS(JMx)*SGN(DV)
T2=2.EO*T1
FILO?250
FIL02250
rILO?270
FILO?280
FILO'290
FIL02300
FIL02310
FIL023 20
FILO?330
FIL02340
4AA=OEO
FIL02350
IFL=I
CONTINUE
TCOU4T=TCOJNT+OT
IF(TCOUNT.SE.O.EO.ANO.TCDUNT.LF.T1)A=AA+J4X*DT
IF(TCOUtJNT.3T.T!.AtJNO.TCOUJT.LE.T2)AA=4A-JMX*DT
IF(TCOUJNT.$T.T2)AA=0.FO
VC=VC+AA*DT
Ax=4X+VC*DT
FIL02350
FIL02370
FIL02380
FILO?390
FILO?400
FILO?410
FIL2O?420
rILO?430
B-12
PFTUt-(N
FILO?
C
C
C
300
K)DE
3 -
PEPARE
CONTINJUE
IF(IFL.EQ.?)GO
POFTLE
F
MOQES
1 O
2
TO 330
IF(IFL.NE.O)GO
TCOUJT=O.DO
TO 310
T1=A3S(AA/JMAX)
310
IFL=I
COi.TINUE
FIL02570
FIL0?550
P-TJUtN
F IL02640
CNJTINUE
FIL02650
AA=O.EO
AX=Ax+VC*DT
TcOlJ'T=TCOJ4T+nT
IPL=O
FILO?650
FIL02670
FILO2680
FILO?690
QWTIijRt
CONTINUE
FIL02700
FILO?710
AA=DV/DT
A.JIT=A
A-AA
A.!T= AJT/JT
I (AiS(AJT).GT.JAX)AA:AA4+JMAX*SGN(AJT)*DT
I (A'S ( A).GT . !AX)A =A=AX*SGN(AA)
V = VC+A -0T
a =A+VC,.JT
R;TURN
FILO?720
FIL02730
FIL02740
FIL02750
FILO?760
FIL02770
FILO? 7 80
FILO?790
FIL0?800
qllJNlP(A,Mh)
DIAENSIN
I I0A(N)
FORMAT(' ,
FTIL0850
FILO?870
WUITE (6, 100)
1
10
FIL02810
FIL02820
FFIL0280
I L0 ?8 3+0
FrILO?50
oT
,n IUE
o
QRTUN
END
SUPPOUTINE
100
FIL02600
FIL02610
FIL?02620
FIL02630
C¢~~~~~~~~~~~~~~~
AODE 4 - UJSPECIFIED
4
FILO?540
FIL02590
TO 320
AA=AA-JMA*DT
VC=VC+AA*OT
AX=AA+vc*Dr
C
C
FIL02490
FILO?500
FIL2O?510
FIL02520
FILO?530
FIL02550
FILO?560
IF(TCOIJ"T.3T.TI)GO0
n0
40
TTi=T1/Ot.l
Ti=FLOAT(ITl)*DT
J'AX=AA/T1
J'X=-S6N (A')*AS(JMX)
TCOUWJT=TCOJJT+DT
320
4
RIL02450
FTLO2?4 60
FIL02 4 70
FIL0480
FILO?850
)
FIL02890
gO 1 I=1lM
rIL0?900
P;?IIT1OI.
(A (I K) K=1,N)
CONTINUE
FCGAT (I2,1X,10(E9.3,1X))
FILO2910
FIL02920
FIL02930
PF
rTURN
FIL02940
END
FIL02950
B-13
:DOE4fn
-?T;RAN4
ILE2
S:IDOUTINE
Al DISCA
,/2?/7S
17:40
ILTE (NX'ES,Y!4ESIFLAGXINI
,TTTEND9,TOLYUUFPS1)
FIL0020
FILOn030
CnlO,'N/T/9 FT,:TDFT. EDFTrjOET,FDET IP,IO IS,IJ,FPS,BP
0I*E10,SIO;ADET(6,6),FnET (6,2),CDET(2?,b),DDET(6,2)
,X.E(6) ,YMFS(?) ,XINI (6)
r)TMF'NION -DT(?.2)
DINENSION PS1l(2),V(4),A)1l(,1),AD2(5,1)
FILOOO40
,I(5) ~f(3}
,.U()
~E;(?)
FILOOO
FILOOO9O
FIL00100
T=Tt'jD-T
3
fr
2
FILoo00110
FIL00120
1 xFS(I)=X.INI(I)
FIL00130
I=,ID
FIL001O0
FpS(I)=O.
FILL0150
E1'S(I)=2.
COT INUE
IF L.AG=IFLAS+l 1
NW=Nvl+ 1
FILOO150
FIL00170
FILOOlBO180
FILOOI90
i1(1)
=UU(2)
FIL0O200
JU(2) =1.
FILO210
V(l)=UU(2)
FIL00220
C
FIL00230
C
C)tJLO'A FICrTION COMPONENT
C
-IL00280
V(4) EPS(2)
TIKr=1
CALL FItDI-(ADET,6,p.4,xmESVTINT,),DiAD2)
C
CALL DVERK(,9TC,T,CMT
ESTENDINDC,NW,9l,tFR)
C** C'APUTATIOt ')F YESE,.PS
4
FIL00240
FIL00250
FILO0O26O
FIL0o0270
V(2) =1.
V(2)=O.
V (3) =EPS (l1)
C
FIL00290
FIL00300
FIL003 10
FTLO0320
FIL00330
nn 4 1=1,ID
IU)F(I)=0.
FIL00340
FIL00350
r)n 4 J=1N
FIL00360
FIL00370
FILOO380
BAIF(I)=-UJF(I)+CD-ET(I,J)*KMES(J)
Or, 5 I=lIq
y4c S(I)=O.
n
5 J=lI9)
FiL00340
FIL0O400
%
YMES
( !) =Y;AS() +EOET(IJ)*U(J)
FIL00410
A
r)o A !=1ID
yvES.(
) = Y,'- S ( I
Onr)7 L=lI-J
FIL00420
FIL00430
FIL00440
7
C
Cp
C
FIL0070
T
qr 1 I=1iN
C?
I
FILOO50
FIL00060
nTMENSIOKJ Dt6.4),Y(3)
I'(IFLAG.N4F.O) GO TO
?
FIL000O10
FYTFk'; L O-TEC
PEFtL*8 TINT
FPS(i
',.BUF ( I)
=Y(I)-YMES(I)
C .
I,I)
EPS1(I)=EPc(I)
EPS1 (1)=EP(1)+I1OO..*FPS(2)
ESl1(2)=373.*EP5
(2)
ml (2)=31n.83FDS?(2)
RFTU<N
FIL00470
FILOQ48O
FIL00490
FIL00500
FIL00510
Hfl
FIL00520
SUPPOUTINE DETFC(NTY5ESXESP)
COM4~ON/rFT/OF T,
qiDT ,C
T,09FT,ErT, P, IQZISUEPS,BP
0IMENSIONt-DET(6,6) RraET(6,2) ,CDET(2,b) rDOT(6,2)
)TME"'JSTIN
T(2)
()
P
)
F (b) J
(6)
DTMENSION X"ES(5),tXMFSP(5),aP(6,4)
C** CDULTES
FIL00450
FIL00460
E P=4aDET*X-ES+RDtT*U+DDET*E;)S
00 1 I=1,N
P'IF1 (I)=0.
FIL00530
FIL00540
FIL00 5 50
FIL0560
FTLO0570
FIL00580
FIL00590
FIL00600
B-14
00 1 J=1iN
1
rILOOS10
P:RFl(I)=bU-I(I).ADET(TJ))X' ES(J)
0O~~~~~
2?~~~~
00
J1
R9,~~~~~~itl~F?
~(B=0.
9 I0
B'.JF2(I)=
lJ3UF2(
I)+3DET
2
3
n
(,
I-~1=~I
=19,N
FIL00680
FlL00690
AESP(I)=xRSP(I)+nFT(T*,J)*EpS(J)
'
X'ES;(I)=XmESP(I)+URFI
4
FIL00700
lIN
4
FIL00710
(I)+fiUF2(I)
FIL00720
OrTI!RjH
JND
q'JfPCO)JTIrE
OGFrL(AM4V,A'iVST,A2,A3, A4.AK1 ,Aq2.,AK3tAK4)
C CnmPijTrFSAr)ET,
C
CET,)r)TETEDOET,qP
Ct0"4"ON/r)ET/trET
qF)FTCO T ,ODETFDFT.
Ia,
IQ*
nT"EN-JCTON:DET(?,)
r)TlMnNSIOtN
*(5,4) ,Ij(?) ,EfS(2)
To=p
I
.
C
FL00 9 70
FIL00950
FIL00 9 90
pN
FILOI000
FIL01010
FOET(IJ)=0.
FIL01020
FILO1030
/
FIL100
QrET(6,1)=1.
FIL01050
.FIL0100
Ct0HLOMK FRICTION PPAtATERS
FIL01070
FIL01080
PrFT (1*2)=-100./AAv
FIL01090
BDFT(5.2)=41*AK4*100./AV
't),
n0
3 I=191D
3 J=1,N
cnFT(IJ)=n.
COET(1,5)=.
COFT(2,1) =1.4
DO 4 I=1ID
nn 4 J='Io
4
EET(IIJ)=0.
EDET(11)=AMVEST
00 5 I=1N
n
5 J=19I
FIL00850
FIL00940
FIL00950
FIL0090
J=1,Io
BDET(5$1)=-I
C
FIL00840
FL00920
=-AK1*MA4/AV
Rr)FT(4 ,.1) =A<3*AVFST
C
FIL00830
FL00930
A£ET(5,6) =A2
?
FIL00800
FIL00900
FIL0O910
AVET(5,1) =AK2*AK4
nn?
80
FF~~~~~~~~~~~~~~~~~IL00890
L00890
t5
rT(4,3)=A3
AMET(4,4)=A2
,fET (45) =4K3
00 2 I=1
7
FTILOo790
FIL00870
FIL00830
AnET(4,2)=A4
ArET (52)
FILO0750
FILO0760
FIL00770
FIL00810
FILOO820
'111=6~~~~~
~FILO086O0
i
A"FT (1?) = ./AMV
AfFT(2,3)=l.
A)ET (3,4)=
FIL00730
FIL00O740
FIL00
ISIIEPSBP
nT"'FES10i4 ADE-T(b.6).B0ET(b6,2),CDET(2,b),DDET(6,2)
0
1 =19N
DO I J=1,N
aEtVT(I.J)=n.
FIL00640
FIL0065O
FIL00660
cIL00670
J) *U(J)
XMESP(I)=O.
DO 3 J=1I'
r
FIL00620
FL00630
FIL01100
.
IL01 110
FILOll2O
FIL01130
FILI140
FIL
150
rIL110O
FIL01170
FIL01180
FIL01190
FIL1200
FTLO1210
B-15
C;
PP (T J)=)D-T(
.J)
FILO1220
FIL012 30
DO 6 I=1*N
J=lI.'
J=J+ I Q
RQ (I,
JJ) D E T (1 .J)
DO
A
WITE (.
1 00)
FO.)P'-~T
(6 ( X
FILO12O40
'CO,c
,.)1
)
FILO1250
l'RDFT'
FI . J:ItN)
)
( (OET (,.I)
I=1
104
104
tO?1
FlPYAT(l+(1X9
wPFITE(6,10l)
'CnKT=,
((£OrTt EIO.4))
I.
J=lt),I=l[
F,~'4AT(4(1x
n.
'w2ITE
lOP)
F(AT (6.
(6(1
x
WP IE (6,1 ) ((F.'T(,J)
'w~ITE(5,10q)
)
)
J=IIS)*I=IIP)
P(PI ,J),J=l ,4) ,1=1,6)
P='
E ] O.
4))
104 Fr)R~AT(4+( 1 X ,
!O0t FnP~-aT ((1 ~ 'FDET=',E]O.4))
SURJPOUTINE
C
SOLLUT(N)
FIL01 4 00
RFADS DDET
C
CO.'uurOk/DET/ADETq
TDET.
DrTf,ODET.EDET.I~,IO[S*lJEPSBP
nT*IN(SION aDET(6,6). nET(62),CDET(P7b) 0D-T(6,2)
Dn4FNSIONJ -DET(2,2).P(64),U(1),FPS(,)
lO=--
!0O
V'i
ITTE (6,100)
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C-1
APPENDIX C
A PROBLEM MET IN THE FILTER DESIGN
The reference model for the filter is the following one:
Initially, K4 nominal value was selected to be 1.
of states was Vind,
the input is a c .
T, T, T, Te, Vc
The outputs
We have the equations
I
V.
K4T
m
nd
m
(T) = T
(T) = T
3
(T) = a4T +
-aT+
= a4T
e
a
2
,T+K
3
+ a3 T + a 2 T + K 3 Te +
K3 ma
vcc
Kl(Vc-Vd) ++ K2
2 (VcVind)
Vind)
= K1 a
Vc = a
c
- K1K4 T + K2 Vc - K2 ind
The first choice
are Tc and Vind '
C-2
Furthermore
= T
T
t
+ mva
Vind = Vind
In matrix form
V.r
0
0
0
",
1~
O-Cr
k
~
Kr
C)0
0
'4f
0
C)
O
-
OC)
3
2
3
C
C
C
~V
At,_
C)
C
3
C
-)
C)
C:;'.
C
t
(C
rl"
%-
C'I
c7
rc 0
Z"
(/
V
A
-- -
C
C.
C)
e_?
&
Event associated with K4:
-
C
L4
-
r- 4
em
/%
I
19 It
/i
Ca.
C-3
C
C
Event associated with K:
4
V
<--:b -j :-
C
C
I
&
Event associated with K2 :
(bl
=
b2 )
':
(A
A
- 12v
--
{/
0
Event associated with K3 :
0w
But Cb 3 = 0.
3
we compute A
We compute Ab 3 , C A bt = 0=
0,3we
3,
CA 2 b 3 =0.
We compute
kr
3
-2
3 -2
l
K
4 C~~
1<1
ito
It appears that failures in K1 and K2 are detection equivalent,
which can be accepted.
However, with this choice of states, failures
in K3 and failures in K4 are not output separable (in fact
b3 and
4 are detection equivalent).
3e
This cannot be tolerated.
R4 ,
C-4
As C is of rank 2, the easiest way to distinguish between 3
kinds of failures is to have 2 of them generate a unidirectional
output, and the 3rd one generate a planar output.
To do this, a
set of states was selected such that one failure was a sensor
failure.
The new set selected was Xv, T, T, T, Tel Vc.
We have
the equations
Tc = Te + mvac
T
Te
4
=Klac
-K1K4 m- + K2Vc - K2K4Xv
e
(Xv) = T/m
(T)
T
/
. =
(T) = T
(T) =K 3 Te + K3 mvac + a2 T + a3 T + a 4T
Vc = ac
In matrix form
C)
o
Iv
QJ
r"
C>
0
-
o
(a.3) T
a
C
-(
3
C f,,~
rT
oo0 ' o
o
4
XV
O
0
0
/
V
dc
3
2
(2
0
0
1-<2
l
0
Q
4>a
0)
v
rO
4
C)
Q
(C.
4-
V7111
O
o
C
0
o
o
C,
o
. .(
'
I7V
C-5
o
C.
Event associated with K1:
0
I
:
1
0
0
,0
I)
Event associated with K2 :
CI
0
I¥ /
o1
Event associated with K3
()I
Cb 3 = 0
we compute
Ab 3, CAb 3 = 0, A2b3, CA b3 = 0
.-
-
C -
43
? 3/
3
4
It,-
+ ,
z
Event associated with K4 :
:/
. 4 6
6-
A,
=
j
J•
k1
C-6
0
As the vector e6l =
0
is such that
C e61 //
-/
and Ae6 1
//
e61 and bL.
bl1
The events associated with a failure in K4 are
As Ce 6 1 and Cbl are linearly independent, a failure in
K4 generates an output constrained to a plane.
With K4 = 1 , a detection filter was designed for the events
1l and A 3b 3 .
Its numerical value was
A-of
(a~~~~~~
0 --5
_
{-1
o
I
a. 1.
C 4
~0
C
GOto
c
2
'1 f
I
Running the simulation with this filter, it was discovered that
a failure in K4 generated a unidirectional output along
physical reason is obvious:
only in two places-the
the A matrices in (A-l) and A-3) differ
Furthermore, the C matrices in
(A-4) differ only in one place:
equations
A-2) and
C 21 has a different value, the
ratio between the two different values being K 4 .
numerically equal.
The
terms A 12 and A51 are different in each
case, by a factor of K 4 .
to 1, the matrix
2'
in (A-l),
If K 4 is equal
(A-3) and in (A-2),
(A-4) are
A detection filter designed for tl and A 3 b3
will have the same numerical value in the two cases.
In other
words, more intuitively, if K4 = 1, an outside observer would not
C-7
know in looking only at the numerical equations whether the states
,
.
..
Vind, T, T, T, Te, V c or the states X v , T, T, T,TeVc
ted.
are selec-
It does then make sense that a failure in K4 generates uni-
directional output along
2
because in the first case (to which it
is numerically equal), this is what happens.
The solution is obvious:
1.
to give to K4 a value different from
It was first attempted to perform this without changing the
physical value of the tachometer gain, but just the system model.
The new reference model was:
a
If K 5 K 4 = 1, nothing
is changed
in the real system.
This could be done physically by multiplying the real output
Vind by K
before the comparison of the system output # 2 and the
reference output # 2.
If this multiplication is digitally made
by a computer, it could be considered exact.
With this reference model, the equations are
C-8
Tc = Te + mva c
Te
=K
e
T
- K1 K5Kj m
+ K 2 Vc - K2 K5K
Kc
Xv
(Xv) = T/m
(T) = T
4
I
(T) = T
(T) = K 3 Te + K3 mvac + a2 T + a3T + a4T
In matrix form
4
c
v
C)
(
0
C )
I4
67:~~~~~~~~~~
?
0
a
C
e
V
--
0
C
-
-'(
c
Iw
3
t
ca-
(/W
I
1
0
C)
0 (~~~~~)
-0
X
)
C)
c
0
2
C)
0
0
(a
C)
c
1<2
C1
0-
f
Cs
I
C
v
t-
c
4c
C-9
oa
-
Event associated with K:
°
.4~~
(
)
Event associated with K2 :
U
0
Event associated with K3:
~3 =
00
= 0, as CA2 b
such that CA3 b
A3 b
3
-3 is
-33
-3
3
0, the event associated
with K3 will be A3 b
3 -3
3
+
3
2.
| + 4-ky 4 s
0
Events associated with K
a - variation
in A along bl =
V0
(o
K4
C-10
b-variation
in C along
-
4s Fr-
/1
is suchthat
V
cF (
and
A f//
1
The events associated with K
are
and
.
A detection filter was designed for failures in K1 and K 3, with
the same eigenvalues as those selected for (A-5). Numerically, it
was found, with K 5 = 2, K
= .5.
-._3
0
- ~ 6 6 2 , 7S_
C)
Y=
( 2
c
o
C
C o
0
j?_?
2 9. - 443 29s 67. 6
40'
,Io
1
O,
o-1
0
9 ' -6 7/
t
,
2 2 .26
6?7
It appears that, except for numerical roundoff, the products
DC of the matrices given in (A-5) and in (A-7) are equal.
havior of the error
J=(A_DC) 1
&, whose
differential equation is
+ bini(t) will be the same.
D in (A-7) cannot distinguish
The be-
This explains why the filter
between a failure
in K 4 and a
failure in K3 , as was discovered in running a test.
It was then decided to give to K4 a value of 1.20, a failure
in K 4 then generated outputs along both channels
value 1.20 is, of course, arbitrary.
1 and
2
The
An actual velocity indicator
would have a scale factor relating input velocity to output signal
C-ll
which is determined by the instrument.
certainly
not be 1.0.
steady state, X
However,
Its value would almost
if K 4 is not equal
to 1, in
will not be equal to Vc, but to V/K
4,
with
the actual system configuration, when the integrator of ac has
a gain 1.
In other words, physically, to reach a desired velocity
V, the velocity command must be equal to K4 V.
This can be done
by inserting a gain K4 at the output of the profiler, just before
the beginning of the velocity control loop.
It must be emphasized that these filters were not designed
to detect velocity sensor failures; therefore they do not prescribe by design the behavior of the errors in response to a
velocity sensor failure.
These filters were designed only to
constrain the error due to controller failures to
error due to propulsion failures to
E2 .
1 and the
The error response to
a velocity sensor failure is then a matter of chance, and it just
happens that with K4 = 1.0 the error is contained along
2'
ID-
APPENDIX
D
ORTHOGONAL REDUCTION PROCEDURE
Orthogonal reduction is a procedure which determines the null
space of a matrix V; i.e., all independent solutions of Vw = 0.
Suppose V is n
n
*
7
A
V =
The orthogonal reduction procedure is
'
an iterative process which generates an
,Y
n
L
n symmetric positive semi-definite
matrix whose range space coincides with the null space of V.
each iteration,
a row of V is tested
if it is orthogonal
to determine
If not, the range space
to the range space of the symmetric matrix.
of the matrix is reduced so that this is the case.
begins with any symmetric positive definite n
auxiliary n-vector is defined by Wl = _()
will be nonzero, since JQ
T
v 1 will be nonzero.
(1)
In
*
v1
The procedure
n matrix JL ( l).
If
is positive definite.
An
1
is nonzero
Furthermore
A new symmetric positive semi-definite
matrix is defined by
T
_7(2) = Jz(l)
-1
E1
w Tv
This matrix has the property that JQL(2 ) Yl = 0.
The procedure continues according to the following general
iteration
(1) with Jl
(i )
vector wi -= 13-(i)vi
-1
from the previous iteration, form the auxiliary
D-2
W.
(2) if wi $ 0
set
j/i+l)
=
_(i)
W.
W
-
W
-1
(i
if w i = 0 set 3
l )=
T
J7-(i) and return
V.
-1
to (1).
The algorithm has the following important properties:
L (i) is positive
(1) If J-
w. = 0.
-1-1
wiT vi = 0 if and only if
semidefinite,
This follows from the definition of w.
(2) If JL(i)
is positive
obviously true if w
so is J'(i+l).
semidefinite
0.
Assume wi
= 0.
This is
For any arbitrary
n-vector z and any scalar d
J.T(i) (z -
(z - vv
> 0
v)
(A-8)
In particular this must be true for
0}'= W.T
-i T -z
A
w.
v.
-1 -1
Substituting this value of
- ov.)J2v T_(iz (z _
(z(z
-
<
= zT_(i)z-
Vi) = T
2~
iTz +
in (AS) and expanding it, we get
Mz
iz +
(i)z - 22 viT
Tz-z+-
2v TJi-v
(i)v.
2 wTv
T
= zTji)z
-=
T
_ (-)
WiTv.
Vi
w.
-1 -1
--
(i+l)
z
z~
O
(A-9)
By induction, this shows that allJ2(i)
are positive semidefinite
if the starting matrix Q(1) is at least positive semidefinite.
(3) If w i t
0 then rk)iL'+ 1 ) = rkQ
and the null space of -Qi+l)
(i )
- 1
is the subspace formed by vi and the
D-3
null space of
(i).
j
In equation
(A.9) equality
and only if (z -
(and thus J2
holds
vi ) Iies in the null space of
(i+l )
z = 0) if
(i). But this
implies z must be in the subspace formed by vi and the null space
(i).
of
(4) At any point in the process the range space of
of all vectors orthogonal to
is positive definite only.
Vl
vi_1
...
(i) is made up
(if the starting matrix
In step 5b and 5c of the detection
filter design algorithm, the range space of _(i)' contains all
vectors orthogonal to
as well).
If
3 2
jVl,...,vi 1>
but may have additional ones
(i) is positive definite, when all the rows of V
have been processed, the final matrix
J.(
which coincides with the null space of V.
made is equal
'+1)
has a range space
The number of reductions
to the rank of V.
(5) If _Q(1) is positive definite and w i = 0, then vi is linearly
vl
1 ...
dependent on the preceding vectors
property (4), the vectors ivl,...,vi
2 (i)
Since w
.
vil
By virtue of
1) span the null space of
= 0 implies vi is in the null space of j2i)
it
must be expressible as a linear combination of the vectors
' .. 0,
Vi-l
In step 5c of the detection filter design algorithm, a matrix
i was found where columns span the space Ri.
In step 5d the
orthogonal reduction procedure is applied to
enA
starting with
As, by definition, Ri CQ(C)
end on a zero matrix.
.
(for i = 1,...,r)
this orthogonal reduction will
The detection generator
i
of Ri is a
D-4
multiple of the last nonzero auxiliary vector before termination,
if rk (Ri )
1.
Wi =
(i)(c
A
)
$ 0
By construction wi lies in the null space of M and satisfies
w.
= 0
and
CA
-a1
0
These are all the requirements for a detection generator, except
for the magnitude.
If rk
wi is a multiple of the detection generator
(Ri) = 1, rk(R i)
otherwise, use Ab.
etc).
-1
= 0 as
Then J.
1
=
i
Ri
(if Cbi
i
0,
= 0, and there is no nonzero
auxiliary vector before termination in the orthogonal reduction of
M.
It is trivial in this case to find the detection generator:
it is bi.
Intermediate turning points
In step 5b of the detection filter design algorithm, orthogonal
reduction is applied to a matrix
CS
S
I
MD
=
Ir
~*ii1
IfC ( - S1-Jj
starting with a positive definite matrix (on option).
MD
correspond to the -i T defined earlier.
manner in which the rows of MD
to process all the rows.
The rows of
Because of the cyclic
are generated it is not necessary
A row can be skipped if it is known that
D-5
it is linearly dependent on preceding rows, because the auxiliary
vector in that case will be zero.
When a particular auxiliary vec-
tor is found to be zero, for example wi = Ji(i)(Cj(A-DC))T
where
C. is the jth row of C
3
, it is then known that C (A-D C)
S
J
is linearly dependent on the preceding rows in MD.
so, then all the remaining rows of MD
C(A-DC)k k
= 0,
But if this is
generated by C
(i.e.,
) will also be dependent on preceding rows of MD
The auxiliary vectors associated with these rows will all be zero,
so there is no need to consider them in the reduction procedure.
The appearance of the first zero auxiliary vector will be referred
to as the intermediate turning point for Cj.
(Note: this intermediate turning point notion is not valid when
the starting matrix is not positive definite.
In that case an
auxiliary vector could be zero even if the row processed were not
linearly dependent on the preceding rows.)