1050_Circuit_Analysis_on_the_Recomp_II_Jan61 1050 Circuit Analysis On The Recomp II Jan61

1050_Circuit_Analysis_on_the_Recomp_II_Jan61 1050_Circuit_Analysis_on_the_Recomp_II_Jan61

User Manual: 1050_Circuit_Analysis_on_the_Recomp_II_Jan61

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RECOMP

II

USERS'

PROGRAM

NO.

1050

PROGRAM

TITLE:

OPERATING

INSTRUCTIONS

FOR

MOMENT

METHOD

CIRCUIT

ANALYSIS

ON

THE

RECOMP

II

PROGRAM

CLASSIFICATION:

General

AUTHORS:

A.

Lechler, M.

Durry,

J.

E.

Drennan

Battelle

Memorial

Institute

PURPOSE:

To

present

detailed

operating

instructions

for

the

circuit

subroutine

generator

(com-

piler)

and

the

moment

method computer

pro-

grams which have

recently

been developed

and checked

out

on

the

RECOMP.

DATE:

19

January

1961

Published

by

RECOMP

Users I

Library

at

AUTONETICS

INDUSTRIAL

PRODUCTS

A DIVISION

OF

NORTH

AMERICAN

AVIATION,

INC.

3400

E. 70th

St.,

Long

Beach

5,

Calif.

TABLE

OF

CONTENTS

SECTION

I - CmCUIT

SUBROUTINE

GENERATION

(COMPILATION)

LIMITATIONS

ROUND

OFF

ERROR

SECTION

II

-

MOMENT

METHOD

CmCUIT

ANALYSIS

CALCUIATION

OF

PARTIAL

DERIVITIES,

AND

VARIANCES

OF

OUTPUT

PARAMETERS

APPENDIX

-

(SAMPLE

PROBLEM)

TABLE

1

TABLE

2

Page 1 - 2

Page 2 -

10

Page

11

-

15

Page 1 -

15

Page

2-

Page

3-

OPERATING

INSTRUCTIONS

FOR

MOMENT

METHOD

CIRCUIT

ANALYSIS

ON

THE

RECOMP

II

The

purpose

is

to

present

detailed

operating

instructions

for

the

cir-

cuit

subroutine

g;en;erator

(compiler)

and

the

moment

method computer

programs

which have

recently

been

developed

and

checked

out

on

the

RECOMP.

The programs

are

logically

divided

into

two

sections:

I

Circuit

subroutine

generation

(compilation),

and

II

Moment

method

circuit

analysis.

Division

I

is

essentially

performed

by

loading

one

tape

and

typing

one

set

of

input.

The

results

are

one

tape

punched from

the

computer.

The

operating

instructions

are

described

in

Section

I.

Division

II

consists

of

two

phases.

Phase

1

is

the

calculation

of

par-

tial

derivitives

and

is

performed

by

loading

two

tapes,

typing

one

set

of

input

and

waiting

for

the

typeout

of

the

partials.

Phase

2

consists

of

loading

a

third

tape,

typing

one more

set

of

input

and

waiting

for

the

typeout

of

the

output

parameter

variances.

The

operating

instruc-

tions

are

described

in

Section

II.

Limitations

Throughout

the

programming

of

this

problem,

an

effort

was

made

to

con-

serve

space

so

that

as

large

a

circuit

as

possible

could

be

used

in

this

analysis.

Even

so,

the

memory

size

of

the

RECOMP

makes

certain

limita-

tions

necessary,

the

most

important

of

which

are

given

below:

(1)

The number

of

input

parameters

must

be

not

greater

than

30.

(2)

The number

of

output

parameters

must

be

not

greater

than

25.

(4)

The

size

ot

the

matrix

of

coefficients

must

be

not

greater

than

12 x

120

The number

of

constants

appearing

in

the

matrix

equation

other

than

the

constant

lJ)

must

be

not

greater

than

490

If

the

same

constant

appcmrs more

than

once

it

is

counted

for

each

appea.ra.nceo

(E;<TOr

stop

0002.,0)

(5)

'l!le number or

orders

generated

by

the

comp1l.er

must

be

not

greater

than

8960

(Error

stop

00041)0)

(

6)

The

number

ot

pairs

of

parenthesis

in

any

one

expression

(1ceo,

matrix

element,

failure

test"

or

stress

:lmction)

must

be

not

greater

tban

l.00

(Error

stop

OOOl()O)

(7)

During

com,pUe.t1cm. a

table

called

the

A

table

is

generated~

The

table

contai...'ls

tor

ectcil

input

parameter:

'A)

One

word

of

identification

B)

One

word

for

ea.ch

t~ppearan.ce

of

that

particular

input

parameter

in

any

matrix

element"

This

table

must

contain

not

more

than

1.50

W'ordso

(Error

stop

0003.0)

Round

off

error

During

the

calcula:tion

ot

pa.r-~a.l.s

the

method

used

to

solve

the

matriX

eq'UEltion

is

a.

convergence

techniqueo

As

the

program

1s

now

wr1

tten

each

solution

must

8.gree

with

the

value

of

the

same

8t~lutlon

from

the

previOUS 1

tera-tioD

to

a

tolerance

of

0)00010

This

means

that

each

matrix

sol.ution

lIbose

absolute

va.lue

is

not

less

than

1,

is

accurate

to

5

significant

f1gureso

A

glance

at

the

formula used.

to

calculate

the

partial

derlv1t1ves

(Ret

\)

1 above)

will

reveal., however" 1hs:t. when an

input

param.eter

has

vet::!

11

ttl-e

a.ffect

on

an

output

pe.rameter,(i.eo

l

the

partial.

Is

very

small)

numbers which

are

very

nearly

equal

are

subtracted.

When

this

occurs,

significant

figures

are

l.ost

on occas101l0

In

the

flight

control

flip

:f1op

(i.eojt

the

test

case),

dur1Dg

the

caJ.culation

of

partials

eJ.l

:five

significant

figures

were

losto

This

meana

that

some

of

the

part1a1s

were

not

accurate.e even

in

the

first

significant

f'igureo

At

f1rs·t

thought

this

seems

cr1tice.1o

However

we

anticipa.te

that

those

partials

which

are

inaccurate

will

contribute

very

little

to

the

output

variances

any

way.

So

the

output

variances

should

be

accurate

to

at

least

2

or

3

s1gn1t1caut

figures.

It,

hovever,

the

situation

1s

still

considered

cr1tlcal.,

the

tolerance

on

the

matrix

sol.utions

may

be

tightened

by

modifying

the

tl.oat1Dg

point

number

in

locatiaJ

1506

and

1507

on

Tape

No.1,

the

caJ.culat1on

of

partials

tapeo

This

increase

in

accuracy

will

only

be

achieved

at

the

expense

of'

computer

time.

The

sample

problem

used

to

check

out

these

programs

was

the

flight

control

tlip

tl.opo The

matrix,

stress

functions,

tailu:re

test,

and

computer

in-

put

and

output

are

included

·in

Appendix A

of

this

lUI".

"'3<ID

10

Circuit

Subroutine

Generation

(Co!pilat1on)

In

order

to

generate

the

c1rcu.1t

subroutine

tape"

the

following

steps

should

be

performed

in

sequence

o

(1)

Load

tape

#3

(compiler

tepe)

0

(2)

Verify

tape

#30

(3)

Push

"start"

buttono

*

(

4)

Short.ly

thereafter

the

computer

w111

type

tlMATRIX

ORDER"

and

stop,

va!

t:tng

tor

the

size

ot

the

matrix

ot

coeffici-

ents

(::12)

to

be

typedo

Type

this

vaJ..ue

and

hit

"carriage

return"

0

(5)

Immt!d1ately

thereafter

tbe

computer

will

type

"COEFFICIENTS";

do

a

carriage

return;

anCL

stop"

waiting

for

the

non-zero

matrix

elements

to

be

entered

o

(

6),

For

each

non-zero

matrix

element

two

lines

ot

information

must

'be

typedo

They

are:

80 The

locat.ion

ot

the

matriX

element

in

the

following

form:

rotf,

comma.,

column,

carriage

return~

eogo,

for

the

second

elemenit

in

the

third

row

type

"3"

n,1I

"2"

"ca.rria.ge

returr:~

'"

0

For

the

third

element

ot

the

dependent,

col.umn

vector

of

8

10

x

10

matr1x"

type

tf

3"

..

P

~t

"ll

It

"ee.rr1age

return"

0

b..."

The a.lgebra.1c

re=presentation

of

the

matrix

elem.e!nt

in

the

following

format,

which

is

intu.:!.

ti

vely

ori~nt~d:

1)

The

entire

expression

must

be

en

o

closed

in

parentheses~

Other

sets

of

parentheses

are

used,

as

needed,

to

avoid

amb.iguity

in

the

algebraic

ex

..

pressionc

2)

This

expression

must

be

a

tunctlon

of

A

9 S and

c:~onsta.nts

only

tOt

The A

(J

S

are

the

1dent1f'!cation

of

the

input.

parameters;·

these

should

be

assigned

prio,.'"

to

compilationo

The

sub-

scripts

of

the

A~s

are

not

enclosed

in

parantheEieso

Immediately

preceding

each

A

"letter

shif'c"

must

be

typed

end

immedi-

ately

:rollowing

each

A

1tfigure

s:Mft'"

must

...

The

location

counter

sho'uld

be

set

a't

0100.

O~

This

should

be

ilone

at

the

end

ot

the

tape;

if

not

a

ne..¥

tape

shoul6t

be

mll.deo

be

type(lo The

only

two

times

these

two

keys

are

hit

1s

in

typi:ng

the

letters

A

JJ

V,

GE;,

GD

L,

LEg

or

L

or

in

typing

the

word

STeP

(each

of

these

1etters

will

be

describe;d

8.8

they

appear)"

The

constants

are

typed

in

the

following

format:

XX_a-XoXX-_-X

1 C)

eo,

the

value

of

the

constant

(~500

000 000

000)

without

!ASing

an

exponent

and

1ncJ..ud1ng a

dec1mal

pointo

eogo,

60,

60

0,

605,

05,

0050

3)

Four

operations

are

pe:rm1ttedo

+ add

-

subt.m.ct

&

multiply'

I

divide

Mul

t1pU

cations

and

d1

visions

are

performed

first

(f'rom

lett

to

right)

and

then

e.ddi-=

tiona

an.d

subtractionso

eogo,

(Al

+A2./A3)

is

eompUed

as:

d.1

vide

A2

by

A3

and

then

add

Al

to

the

quotiento

(120+2

0

/30)

::

12066

«(Al+A2)/A3)

1s

compiled

as:

add

Al

to

A2.

and

then

divide

the

sum

by'

A3e

«(120 +

2~

)/30)

=

4066

(Al

&

A2

&

A3)

1s

compUecl

as:

mul

tipJ,.y

A.l

by

A2

aud

then

multiply

this

product

by

A30

{120

&

20

&

30}

=

240

&

30

a

720

(A1

Be

(A2 &

A3»

is

compUed

as:

inult1ply

A2

by

A3

arid

then

inult1ply'

this

product

by

Alo

(120

&

(20

~

30»

~

120

& 60 :

720

(.ut

A2

to

A3)

1s

compiled

as:

,11

v1~

Al

by

A2

and

then

mul

t1ply

this

quotient

by

A30

(120/20

&

3~)

:

180

(;U/

(12

Be

A3»

is

compiled

as

~

111

vide

AJ.

by

the

product

of

A2

end

A30

(12.~1(2o.

"

3.»

= 20

(7)

After

the

COll'.q)uter

types

"COEFFICIENTS"

and

the

carr:t.age

returns

then»

for

ea.ch

noncazero

matrix element,

type:

e.

o

"row

numbertt~

"~omma",

"col.umn number",

"ca:rr1age retur.il." 0

bo

When

the

cOIJg;)uter

stops

type:

"left

parenthesIs""

"a.lgebraic

representation

of

the

matrix

e1ement",

"right

paren-

thesis",

ficarr1'~e

retum"

\)

eogo,

It

Al

.

__

A4

were

in

row

3,

A2+A3

column

3.,

one would tY,pe:

3

i

3

carriage

return

(

letter

shift

A

figure

shift

1

{

letter

shift

A

:figure

shift

2

+

letttu-

shIft

A

figure

shift

3

)

letter

shift

A

figure

shift

'"

)

ca.rr1ag,::

return

(8)

For

each

non-zero

matrix

element

the

generated

instructions

for

evaluating

each

matrix

element

are

punched

out

and

the

computer

halts

when

It

is

ready

to

receive

the

next

matrix

element

0 Repeat

Step

(7)0

When'

all

non-zero

matriX e1ements

have been

entered

and tJla computer

is

ready

to

accept

another

element

t:f.pe:

.tletter

shift's,

"STOP"

I)

tt1

car

riage

retum-

0

(9)

~e

computer

v1U

1mmed1a.tely

-q,pe

"FUNCTIONS";

the

carriage

will

return;

and

the

cauputer

will

stop,

waiting

for

the.

first

stl.~ss

function

to

be

typedl.l Wi

th

wo

except:1ona

tJlese

are

entered

exa.etl:1

the

same

as

the

coeffic1entao

ao

There

1s

no

ide:nt1t1cation

Une

typed

1oeol

Nothing

11lte

"1

09

3

carriage

retum"

1s

typed

bQ

These funct:lO!lS

~

depend

em

not

only

the

A

1/

s

(the

:lnput

pa"t'al'aetel-t;) and

con/lQ

st.ants

but

on

the

Vila

(the

n'.v.tr:tx

solu

cal

t1oo8)

as

weLLe>

The

first

element

in

the

matrlx

solut1<m

vectC:)l:O

is

Vl.

tbe

second

V~1J

etco

eog

o Suppose )t1

~

Al

+-

'13

were

a.

stress

605

fUnction"

One

woul.d

we:

(

letter

shift,

V

f:t~

shir-t

1

&

lette:r-

sh:l.ft

A

tigu.re

shift

1

(,

o

5

+

:letter

shift

V

figure

shift

3

)

carriage

return

(10)

For

ea.ch

stress

fUnct1oI\

the

generated

instructions

for

evaluating

it

are

punc:hE:d

out

and.

the

c~uter

stops

when

1 t

1s

ready

-00

rece1

ve

t:be

next

stress

f'unct1ono

Repeat

step

(9)

it

When

all

stre:ss

:fUnctions

ha.ve been

entered

and

the

computer

is

ready

tc'

receive

another"

type

"letter

shift",

"STapH

~

fOcarrie.ge

return"

0

(ll)

The computer

will

1mmed19,teJ..y

type

"FAILURE

TESTS";

the

carriage

will

return;

a.n,i

the

computer

will

stop,

va.!.

ting

for

the

first

failure

test

to

be

typedo

Each

failure

test

consists

of

two

algebra1~

expressions,

each

ot

which

is

completely

enclosed

in

p:9.l"entheses"

and

the

wo

are

separated

by

one

of

the

f'oll.ow'ing

tour

expressionso

8.0

GE

bo G

Co

I.E

do L

co7t:!J

In

order

for

t.be

ciraui

t

to

fail:

-

8.0

If

GE

is

used£>

the

expression

on

the

lett

must

be

greate:r

than

01'

equal.

to

the

eltliil

pression

on

th£~

r:lght~

bo

If'

G

is

used,

'!'me

expression

on

the

le:rt

must

be

greater

than

the

expression

on

the

righto

Co

If

LE

is

used£j

the

expression

on

the

left

must

be

less

than

or

equal

to

the

ex

.....

pression

on

the

righto

do

If

L

is

used,

"~e

expression

on

the

lett

must

'be

less

then

the

expression

on

the

rigbtQ

Wi

thin

each

of

the

two

~upressic,ns

(referred

to

above

a.8

'lithe

expression

on

the

:Left"

and

"the

expression

on

the

right")

typing

is

exact.:ty

the

same

e.a.

for

the

stress

e

ogo

II

Suppose

a

circu:t

t

lI.~ll

fail

when

V1

~=--yg

~

V2

2

functions

G

(.

)

(J

Al

.....

V2

\.

One

would

type:

(

:Letter

shirt

V

figure

shift

1

&

letter

shift

V

figure

shift

2

/

(

letter

shift

A

figure

shift

1

+

~etter

shift

V

t1sure

shift

2

)

)

letter

shift

L

E

:f'1gu."1:'e

shift

(

lett

or

shift

V

f:1gu::oe

shift

2

&

letter

shift

V

figure

shift

2

)

ce.rr1e.ge

return

(12)

For

each

fail.ure

"test

the

generated

1nstruct~ons

for

detemirti.ng

the

success

or

fail.ure

of

the

circu1

1:.

are

punched

out

and

the

computer

stops

when

it

1..8

ready

to

receive

the

next

failure

testa

Repeat

step

(ll)

")

When

all

fail.ure

tests

ha.ve

been

entered

and

the

com,pute;r

is

reeiJ:y

to

accept

another

failure

(13)

test

type

"l.etter

shift"t

a

"STOpY-

i "ea.rr1a.ge

return""

The computer

will

punch

out

the

memory

of

the

comp11era

the

A

tabl.e,

and

stop

a't

0006000

This

is

the

end

of

the

program

0 Advance

the

~~pe

and

tear

1

t:

off

0

This

is

the

complete com.PUed

portir,m

of

the

circuit

subroutine"

ready

to

be

read

into

the

mac:hine

for

Phase

II

(ca.lculat1on

of

partials

and va.r1ances)?

(lia.) There

are

error

halts

PMgrammed

into

the

com.p11er 0 These

can

be

distinguished

it'D

stops

where

the

comguter

is

wa.1

tins

for

typed

infor:118.

t10n

bY

the

alpha

light

on

the

console

0

This

llght

w1.U

be

on if" ·the cOllrputer

1s

val

ting

for

information

from

th~

t;ypewr1terQ The

error

halts

are

ldent1f1~d

by

the

:location

ligbts

on

the

consoleo

0001

00 ..

There

are

too

mtm.Y

parentheses

in

a

statement

0

Each

of

the

coefficients

end

stress

tunctions

end

each

half

ot

the

fail.ure

test'tfJlq

have

up

to

ten

sets

of

parentheseso

0002~O

-There

are

too

many

cons"'o.iSllts

in

the

compiled

:progr&mo The

Xlum.ber

of

conaD

stant&,

counting

each

repeated

occurrence

separa:tely

but

not

counting

the

constant

100,

must

be

1.ess

than

fittyo

00030<0

en The A

table

is

too

b1go The number

of

input

l"arame'ters

(the

A {j

8)

pl.us

the

num'bel"

of

DOnq;aZero

matrix

el.ements

each

ot

tt'.em

appears

in

must

not

00

greater

than

one

hundred

and

fifty

0

000400

....

There

are

too

many

ordera

in

the

canon

pUed

p~'T8mo

The

number

of

orders

must

not

exceed

eight

huntlred

and

ninety

SUo

000500

lID

The number

of

lett

parentheses

1s

not

equal

to

the

number

of

right

paren~

thesesQ

Push

the

appropriate

numbered

start

sw11iCh

as

deser!. bed bel.ow y

000600 to

This

is

the

end

of

the

programo

1220

00

....

Something

bas

been

typed

wrong;

eogO$

a

figure

e~h1ft

when 1 t was

not

needed

or

WO

le'tter

shifts

before

an

A

or

V 0

Push

the

'tstart"

button

(not

one

of

the

numbeled

start

buttons)o

The

tape

will

auto!!'atlcall.y

be

reset

and

the

com-

puter

wilJ,

soon

stop,

ready

for

the

statement

to

be

typed

in

aga1no

.

In

the

case

of

tl.e

coetf'lc1ents

the

identification,

"row"»

"CC\lIIDlS." I "columnn,

«carriage

return"a

must

be

rE;aentered

alsoo

There

are

three

numberec-:'

start

sn

tches

at

the

right

hand

side

of

the

consoleo

These

ere

to,

be

used

in

conjunctian

with

error

step

0005

00

and

&r'Y'

other

time

when

an

error

in

the

~cjg

in

has

been made

and

reCognized

before

the

carriage

return

1s

hit

which

sends

the

com.I;uter- on

to

compUing

and

punching

out

an

algebraic

sta:temento Simply

press

the

error

reset

button

and the!?

the

appropriate:

start

buttono

SW

#1

..

This

svltck\

is

to

be

used

during

the

"coeffici-

ents"

pha.8€

of

the

compU1llgo

It

can

be

used

e:ny

time

before

the

car.d.age

return

following

the

e.lgegn1c

stateuent

baa

been

hito

Thus

it

can be usee,

if

an

error

1n

the

identification

is

d1scover-ed wh11e

one

is

'tl'P1Ds

in

the

correspond:t.ng

algebraic

statemen.to

In

all

cases

the

1dentlf'1cat10D1

"row",

"comma", "column",

"carr1age

%'eturn" I must

be

typed

ega1n,

as

veU

as

the

algebraic

sta.temento

SA

//2

-

This

SWltcJl

is

to

be

used

during

the

"stress

functions"

phase

of

the

campll.1Dgo The

alge-

braic

statement

must

be

reoentered

tram

the

typewriter

II

sw

#3

..

This

swltcl\

is

used

during

the

"ta.:llure

tests"

phaHe

..

rt

the

com.p1.l.:tngo

Tile

algebraic

f:tatements

must

be

retypedo

It

1s

hoped

that

these

e~rror

halts

wUl

catch

1llOst

of

the

errors

ot

the

typist

buii

no

attempt

was made

to

catch

all

errors

0

It

there

is

an

errors

noticed

later

by

the

typist»

but

not

noticed

by

the

IJaCh1ne

at

the

time

ot

compilD.:t1on

of

tbat

statementj1

there

is

only

one

easy

thing

to

do

CD

start

overo

*

~'T

METHOD

OPERATING

INSTRUCTIONS

=

IIo

,Palculat1on

of

Pe.rt1a.l.

Derlv1t1ves,

and

Ve.r1ances

of

Ou5!ut

parameter.!

Upon

comp~et1on

of

the

c1rcu.1t

subroutine

compller,

calculation

ot

the

pa.rt1a.l

dert

vi

t1

vas

and

va..risnces

of

output

parameters

"tfJf!q

beS1no

~e

following

steps

should

be

performed

in

aequenceo

(1)

Loa.d

tape

#1

(ceJ.culat1on

of

partials

tape)

(2)

Verify

tape

/13.0

(3)

Loa.d

the

oomplled

circuit

subroutine

tape,

loeo,

the

tape

that

was

punched

dur.Lng

the

compilation

phaseo

( 4)

Verity

the

circu1

t

subroutine

tapeo

( 6) The computer

.v1ll

1noed1ately

type

"N

IS",

and

atop

wa.1

tins

tor

the

number

ot

different

input

pa:rameters,

1oeo$

the

number

ot

different

A':so

T.Y:pe

the

value

of

N,

and

hit

carr:tage

return

o

(7)

The

computer

will

1noed1ately

type

"ITS

IS",

and

atop

wa1

t1ng

tor

the

number

of

different

out,put pa.rameters.9

(1'1e08 number

of

matriX

sol.utions

+

the

number

of

tuncttons)

~

Type

the

value

0'1

ITS,

and

hit

carr1age

retumo

(8)

The

computer

will

immed1ately

type

~S",

do

a

carriage

ret\...rll and

stop

val

t1ng

tor

the

means

of

each

input

parameter

to

be

typed

ine

Type:

80

The mean

~

of

input

parameter

Ai

in

the

format ±xxxxx

•••

xoxxx---x

i.e

..

,

~'ype

the

value

of' Ai

without

using

an

exponent

and

be

sure

to

include

the

dec1ma.l

pointo

b.

Hi

t

the

carriage

return.

Co

Do

.Ca)

and

(b)

tor

1 • 1,2,3,4.DoNo

After

each

carriage

return

be

au:.re

to

vat

t

tor

the

computer t.o

stop

before

typing

the

next

mean

value.

(9)

'!he

Recomp

will

then

solve

the

matrix

equation

with

all

parameters

at

their

mean

value..

It

any'

of

the

failure

teats

1nd1ca.te

failure,

the

RecompvUl

stop

with

(5060.1)

in

the

l.ooatton

countero

This

stop

prababl.y

means

that

It

any

mean

or

correlation

coefficient

18

neptive

type

ft_ft"

it

the,-

are

.

positive,

however,

do

not

type a 81§!lo

something

is

wrong

wi

th

-~e

equ1

valent

c1rcu1

to

PuShing

the

start

button

will

C&-;18e

the

mean

matrix

solutions

to

be

typed

out

in

dec1m!u.

floating

point"

five

words

per

Une

o

If

the

c1rcu1'~

passes

all

the

faUure

tests

the

mean

matrix

801ttt1onr:3

will

automatical.ly

be

typed

out

1n

dec1ma.l

f'loat1IJg

}1Q1nt,

five

vorda

per

linea

(10)

In

either

case

after

the

type-out

ot

the

mean

matrlx

so1utl0nB,

the

computer

will

proceed

automatics]]

y

to

the

calcula.tions

ot

partial.s

0

This

operation

will

run

interrupted

tor

a

fairly

long

period

of

t1meo

For

a 6 x 6

matrix,

21

input

parameters

and

2

fUnctions

the

time

rea:!

qu1red

is

one

hour

and

23

m1nuteso

As

the

partials

are

calculated

they

are

typed

out

(dec1mal. floa:t1ng

potnt,t

f1

ve

words

per

Une)

in

groups

ot

ITSo The

first

group

wiU

be:

the

secand

and

so

on,

until

the

last

group,

which

will

be

The o.ppro:d.ma.to

time

required

tor

the

calculation

ot

partiaJ.s

can

be

deteriid.ned

by

noting

the

time

e1a.psed between

the

t)'pe-

out

of

the

mean.

matrix

solutions

and

the

typecuout

of

the

first

set

of

part1el.s

and

DlUltipl3ing

by

No

(11)

After

e.ll

the

partials

are

calculated,

the

Recomp

wUl

stop

with

(0003)

in

the

location

counter~

(l2)

The

next

thing

to

do

1s

load

TapejJ2

(cal.culQ,t1on

ot

Variance

Tape) 0 Be

sure

not

to

use

a

memory

zero

routineo

-

-13-

(13)

Verity

Tape

i20

(14)

Push

the

start

buttono

...

(15)

The

Reccm,p

wUl

1lmnedin:tely

type

"Va.r1e.nces",

do

a

carr1age

return

end

stop

wai't1ng

tor

the

variance

of

each

1l;lput

parameter

to

be

typed.

Type

~

(A)

The var:l.a.nce

ot

input

parameter

Ai

in

the

format

JCCC---xoxxx---x

ioe.,

type

the

value

ot

a-

2

Ai

wi

tbout

using

en

exponent

and

be

sure

to

include

the

decimal. po1ntD

(B)

Bit

the

carriage

return

o

(C) Do

(A)

end

(B)

for

18

1,2,3

000

No

After

each

carr1age

return

be

sure

to

'1&1 t

tor

the

computer

':;0

stop

before

typing

the

next

vs.r1ance

')

(16)

After

the

vari.a.nces

~

read

in,

the

computer

1s

ready

to

accept

the

correlation

coetticiE'..nts

for

all

input

parameters

ot

multi-parameter

pa.r-~o

For

each

such

part

it

1s

necessary

to

type

in

the

foll.ow1ng

1nf'ormat1on:

(A)

Part

I.D

o

(a:n::'

2-dig1

t

identification

tor

the

part)

this

nULlber

w1ll

appear

in

the

output

as

en

idenUf'1ca

a

;;lon

ot

the

parto

(B

) NaP,

the

number

of

parameters

in

the

part.

(e)

For

evefLpoSSlbl.e

ccmb1naUon

ot

parameters

in

the r

nUt1ed

part a

correlation

coeffici-

ent

must

be

typed

in,

even

it

it

1s

zeroo

AJ.ong

vi

th

this

correlation

coetficient

the

input

parameter

numbers

of

the

two

parameters

being

corre18"~

are

~edQ

The above

information

~,:.s

typed

as

:rollcus:

(17) The com.puter

will

type

"MULTI

PARA

PARTS",

do

a ca:rr1e.ge

return,

type

"PART

ID"

II end

stop

wa1

ting

tor

a

mu1ti-parmueter

part

1dentification.

~1.'ype

any

two-digit

number

you

choose.

1)0

not

hit

the

carriagO

returno

The

computer·

w1ll

1mmed1ate.1.y

type

"NOP",

ana

stop

va!

t1ng

tor

the

number

ot

parameters

in

this

mul.t1-para.meter

port

to

be

typedo

Type

the

value

0'1

NOP,

and

hit

carriage

returno

(18)

Tbe

canputer

wUl

1DIDediately

-tn»e

"CORR

COElPP",

do

a

carriage

return

end

stop

wa1

ting

tor

the

correlatiol.\

coef't1-

cients

tor

this

part

to

be

typed

in.

For

ever:!

pos81bl.e

pair

ot

input

pa.nmeters·

in

this

multi-parameter

part

type:

.·The l.ocaUon

counter

should

be

set

to

0100.0,

it it

1s

not,the

ll.OCat1on

counter

wUl

have

to

be

set

:tram

the

k.e7'bOardo

It

tis

18

the

case,

a

118W'

tape

:IJ2

should

be

punched

1nclui

J1n

g

the

setting

0'1

the

location

counter

to01QO.O.

(A) The

correlation

coefficient

in

the

format

*

±GXXXX---X,

ioeo,

type

the

number

wIth-

out

using

an

exponent,

end

be

sure

to

in-

clude

the

decimal.

point.

(:8)

Hit

the

'!Pa.ce

bar,

and

vd

t

for

the

Recamp

to

stop.

(C) Type

the

input

parameter

number

of

one

of

the

two

parameters

being

correlated

o

(D)

Hit

the

space

barJ

and

wait

tor

the

computer

to

stop.

(E) Type

the

input

parameter

number

ot

the

second

of

the

two

parameters

being

correlated

0

(F)

Hi

t

the

carrtage

return.

(0)

Perform

stapa

(A)

through

(F)

tor

all

posslb].e

combinations

ot

the

parameters

in

this

part

(10

eo,

it

there

are

n

input

parameters

in

this

part,

~2-11

lines

ot

correlation

coeffi-

cients

must

be

~ed).

(19)

When

the

input

tor

on(~

mul

t1-parameter

part

1s

compl.eted

the

com

..

puter

types

"PART

ID"

again,

expecting

input

tor

another

mul

tl-

parameter

parto

If

there

are

moremul:t1-parameter

parts,

repeat

steps

17

end

18,

when

there

are

no more mul

t1-param.eter

parts,

type

letter

shift,

ENDo

(20)

The

input

18

now

complete.

The computer

automatically

starts

to

calculate

the

output

parameter

variances.

For

each

of

the

r.t'S

output

parameters

the

tollOW'ing

information

1s

typed

out.

(21) The cOlDputertY,pes

"VAR

ot

1tt

(1

1s

the

number

ot

the

output

pe.remeter

being

eval.ue:ted),

does

a

carriage

return

and

types

out

the

total

variance

of

output

parameter

1

in

dec1mal

float-

11lg

pointo

It

then

does

a

carriage

return,

types

"ST

DV

IS",

does

a ca.rr1age

return

and

types

the

standard

dev1aticm.

of

output

parameter

1

in

dec1mal

floating

point.

(22)

The

Recomp.

next

types

"PERCENT

OF

VAB

DUE

TO

EACH

PARA",

and

does

a

carri86e

return.

(23)

It

w1ll

then

type

out

NUnes

of

1ntomaUono

Each

line

w1ll

contain

two numberao The

f'irst

1s

in

dec1mel.

floating

point

and

represents

the

percent

of

the

total

variance

of

output

para-

meter

1

that

1s

attributable

to

the

input

parameter

whose

Identi.

fication

is

the

second number on

the

same

line.

*

If

ezr:y

_an

or

correlation

coefficient

18

negetive

type

".tt,

it

the7

are

positive,

however,

do

not

type

a

sipo

-15-

(24)

N~.xt

the

computer

types

"PERCENT

Olt'

VAR

DUE

rro

EACH

PART" b and

does a

carriage

return"

(25)

One

line

of

output

1s

then

typed

tor

each

mul

ti-pa.rameter

part

:for

which

input

data

has

been

typed

ino

Each

Une

contains

two

numbers 0

The

first

1s

in

dec1mal.

floating

point

end

is

the

percent

of'

the

total

variance

ot

output

parameter

i

that

is

attr1buta'bl.e

to

the

multi-parameter

part

whose

identification

is

the

second number on

the

same

line

0

(26)

Steps

(2l)

through

(26)

are

performed

for

each

output

parameter

(iceo,

for

i~l,

2,

3

---

ITS)

(27)

The

program

1s

finished

and

stops

with

(0002)

in

the

location

cOlmtero

For

a.

c1rcu1

t

with

2l.

input

parameters,

8

output

parameters,

and 3 mult1"parameter

partso

The

variance

section

required

29

minutes

including

typing

in

the

data

o

J:£,v

J 0

Eo

Drennan

Battelle

Memorial

Institute

Appendix

A (S3:mple

Problem)

As

mentioned

above,

the

sazn;p:i.e

problem

used

to

check

O'llt

these

progrv.riW

is

the

f'light

control

flip

fiopo

This

circuit

and

the

same

set

of

(lata

~th8;t

t-tas

used

on

the

Recamp

were

run

throt.\gh

the

Moment Method

Pl"gram

on

the

m·i

709

0

The

outgut

is

labeled~:

00

6380

..

53

(004) 1.00

27

J DUFFY

3CJ~3-054

06/03/

20

If'

this

out-,1;lut

is

not

availahl.e

at

NoA.A

o1

it

can

be

obtained

from

Ao

Lecbler

at

Battelle

Memorial

!nat!

tllte

o

Vo

-

5.

1 _

V,,"

R

fsr

Ro

k'l)

-IEO'+

R1+R;

-

~/.-}f

V6~

Sa...

---

~~

~£

-("~

I-~

'~_

qu

If,

-fI,

.,.;r;

+I,o

.,.1£0

SJ

-1<.0

R~

.5

1

~

I

,

-

I((J

I

.:=

-,,f~+Rc,..-:;

:-

... ,

..

, ,

....

~~=

..

"

Kd

R?

rlf":5

o

o

CON

STAN

T.5

;f(!~

'I

f!

/ X

10'

o/'hJ$

Ita

, ,

6--

Va

If..J

...

Vk.t' ,

14d'

valls

....

,fcl

~

3o)(

I~'

ol."'».s

TABLE

1

The

Flight

Control

Flip

Matrix

as

Provided

by

the

Designer

or

the

Circuit

A;nalystQ

I

-/(0

I

--,;;

o

o

I

--

Rev

•

..1-

..

I

"J

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.,..~£

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TONCTIONS

o

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1?7

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MATRIX

ORDER

6

COEFFICIENTS

1,1

Clo/(All+A14)+10/A21+o00000003333+10/Al5+1o/CA6+lOOOOOOo»

1,2

(-10/A21)

1,3

(-10/(A6+1OOoooo.»

1.,4

(-000000003333=1./(A11+A14»

1,'1

((A3-A19)/AlS-0026/A21-A17+oS/(All+A14))

2,1

(-10/A21)

2,2

(lo/AS+lo/A21+1o/A4)

2,,3

(-l./AS)

2,6

(-lo/AIt.)

2,7

(0026/121-A2O/15)

3,7

(12O/A5-A19/19)

4,1

(-000000003333-10/(A11+114»

4,4

(lo/A2+o00000006661+1o/AlO+lo/(A~i+A14»

49'

(-000000003333)

4~6

(-10/A2)

4,.,

(-A19/Alo-.5/(Al1+Al4)+Al6+1l?)

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(-l./AS)

',4

(-000000003333)

S,'

(10/'7+10/A12+000000003333+10/1IJ)

',1

(118/1'7-'16)

6,2

(-l.Iv.)

604

(-1./12)

6.6

{1

0/11+1./12+10/113+1

0/&4)

6,7

(A18/Al)

SlOP

FUIC'lIOIS I

«(V3-Vl)/CA6+lOOOOOOo»)i«(V3-V1)!(A6+lOOODOOo»)lA6)

( (Al8-V')&(AlS-Y5)/A'1)

Sl'OP

FAILURE

TESTS

(V6)U(-16.,

STOP

I IS21

ITS

ISS

MEAlS

3300.

9100.

602

100

3SO.

10000.

33000

91000

33000.

33000.

lOOOOo

~.

1000.

2'.

100

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250

2'0

oS

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=18420641

...

02

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+02

93108267

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<=18110236

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<=3849569'

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-=4041

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-38784192

...oJ.

c:m521,2S4,8

=04

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=04

~3099568

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66142211

-m

11198094

c:{f!

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2Ol27708

..q;

-61049262

c::()4

290~274

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99265952

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8438.4964

-16

-2'16366W

-11

98592984

~

98'23291 +00

94SYl997I

+00

8S~1~16

+00 16953383 +00

97243294 +00

=11680098

-08 -16120276

c=()2

-3Cf131671

-03

-.41188452

-03

-400<)4622

-03

136670)0 ·-01 -71138584

...Q4

30210886

-01

-104!S4S31

-12

6"1~'

-06

ClD30136S33

-05

=31656186

cO,

2'3S6278 -02 -26203241

-os

45458624 =03

-31243333

-0,

7312)80' -10

-43224141

-0;

-USSl914

-11

S404996S

-13

4826,,al

-4>9

=33122929

-12

863S106tl

<=10

-41161129

-12

139.W.S2

-16

a82143818

-12'

-24424649

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-25645439

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-04

-25029393

-0,

-23664007

-02

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-05

-24982488

-11

22501134

-Q4

-2464'268

-0,

-251!mZ12

-0,

-90009022

-04

-2l242919

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50210207

-03

-2"397"

=0,

-25216560 -11 -4W42826

-0,

69498662 -c'1 72972590 -m 2'380703

-0,

61933305

-m

4550216, -06

72023186

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71105425

-13

-43266719

-os

4456~~39

=C1

4"10172

=t11

43904352

-ffI

21763166 ..Q4 90537589

-os

686'3807

-en

-19044711

-16

-86087739

-10

47041S09

-os

38892686 -08

37024643

-08 -UWtTI61

=04

-15013521

...09

-12396186

=a7

-28852937

-16

14299800 czll

63139966

-06

66295163

-c6

23052388

-04

64703244

-4l6

61173648

-03

6"'2240

-06

64~2038

-12

-58167513

-0,

-17610990 -03 -1849J221

-03

-1"1'142f111

-03

-238S8720

-03

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-04

-36117362 -03 -38016213

-13

302S8104 -a6

4l1W162

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329S9393

-08 29780146 -08 -14980217 -04 -2Z1W999

-09

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-33ll3081

-16

17713491

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33178173 ..01

33154'120

-01

318l3602

-01

287n422

-01

,.,050944

-02

32723980

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-10

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684218,6

+01

69810822

+01

o,347031:~

+02

41743268

+04

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+04

1140,814 +02

-1"1372468

=05

1560114:2 +02

~13018878

+01

=10153207

+01

-10228920 +01 41675120

+04

40946450 =01

344'43802+01 80291626

....

08

-3889726,

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34605053

-02

36334686

002

2172S431

001

4,186292

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49827199

+00

65758240

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52610802

-09

=4731864J

-02

-98641546

+00

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+00

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+00

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+00

=17146213

+00

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c-..{)9

16303631

....

02

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95806706

+00

=99004238

003 17176184 +00

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27629228

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=16332129

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=46930908

=03

33189554

-01

31835809

-01

14791321

·01

57083150

-02

32143181

-01

93052571

~09

-.54278082

=04

VARIANCE

500

0

35000'

oOl

So

10000

0

45000

500

0.

3500

0

,000000.

,000000

4.500

0

10000

450

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0

100

000000000001

000000000004

003

003

00015

002

r.fULTI

PARA

PARTS

PART

1D

10

NOP

2

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COEFF

00 3

15

PART

ID

11

NOP

4

CORR

COEFF

001 4 5

00

4

20

001 4

21

00 5

20

001 5

21

00 20 21

PART

ID

12

NOP

2

CORR

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001 16

17

PART

ID

END

VAR

UF

01

49926392

11";)01

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22344214

+00

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OF

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02

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03

25294937

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04

18190993

.;..03

05

19086337

a,16

06

59144302

wo,

07

425199.32

=04

08

48371852

P.OO,5

09

19890154

-05

10

19945495

....

09

11

79850660

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12

27954381

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13

16997084

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14

220h8282

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15

68225965

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12350289

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06

17

11956505

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41518095

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16.377106

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01

312,4162 -08 02

19460618

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03

28007956

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04

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05

26356165

-19

06

65927889

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07

46987669

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13646688

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19404094

-03

18

58449024

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20

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21

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TO

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79034909

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12

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03

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18533282 ..

04

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17

12615211 -01

18

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20

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21

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OF

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16979507

+02

10

58541600

+02

11

185830,0

...

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12

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33150124

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31890034

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16247227+01

12

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05

15131386..01

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12300910

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11

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43069228

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21

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VAR

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1.39S1608

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21

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63014b15

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5.3144000

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12