The IML file is our user readable import or input file to the IMPL modeling and solving platform. IMPL is an acronym for Industrial Modeling and Programming Language provided by Industrial Algorithms LLC. The IML file allows the user to configure the necessary data to model and solve large-scale and complex industrial optimization problems (IOP's) such as planning, scheduling, control and data reconciliation and regression in either off or on-line environments.
Please see our IML “(Basic) Reference Manual for Quantities” for a complete introduction on the basics of IML. This manual describes the configuration data necessary to model and solve IOP’s with quality variables and constraints i.e., densities, components, properties, conditions and coefficients.
The symbol "&" denotes an address, index, pointer or key, the "@" denotes an attribute, property, characteristic or value and the prefix "s" stands for string of which there are two other prefixes "r" and "i" for reals (double precision) and integers respectively. String addresses and attributes are case sensitive and do not require any quotes where essentially any character is allowed including spaces except for ",". Each address string field may have no more than 64 characters for it to be considered as unique and each attribute string field may have no more than 512 characters.
1.
i
M
P
l
Industrial
Modeling
Language
(IML)
"(Advanced)
Reference
Manual
for
Qualities"
i
n
d
u
s
t
r
I
A
L
g
o
r
i
t
h
m
s
LLC.
www.industrialgorithms.com
Version
1.0
April
2014
IAL-‐IMPL-‐IML-‐RMQQ-‐1-‐0.docx
Copyright
and
Property
of
Industrial
Algorithms
LLC.
2. Introduction
The
IML
file
is
our
user
readable
import
or
input
file
to
the
IMPL
modeling
and
solving
platform.
IMPL
is
an
acronym
for
Industrial
Modeling
and
Programming
Language
provided
by
Industrial
Algorithms
LLC.
The
IML
file
allows
the
user
to
configure
the
necessary
data
to
model
and
solve
large-‐scale
and
complex
industrial
optimization
problems
(IOP's)
such
as
planning,
scheduling,
control
and
data
reconciliation
and
regression
in
either
off
or
on-‐line
environments.
Please
see
our
IML
“(Basic)
Reference
Manual
for
Quantities”
for
a
complete
introduction
on
the
basics
of
IML.
This
manual
describes
the
configuration
data
necessary
to
model
and
solve
IOP’s
with
quality
variables
and
constraints
i.e.,
densities,
components,
properties,
conditions
and
coefficients.
The
symbol
"&"
denotes
an
address,
index,
pointer
or
key,
the
"@"
denotes
an
attribute,
property,
characteristic
or
value
and
the
prefix
"s"
stands
for
string
of
which
there
are
two
other
prefixes
"r"
and
"i"
for
reals
(double
precision)
and
integers
respectively.
String
addresses
and
attributes
are
case
sensitive
and
do
not
require
any
quotes
where
essentially
any
character
is
allowed
including
spaces
except
for
",".
Each
address
string
field
may
have
no
more
than
64
characters
for
it
to
be
considered
as
unique
and
each
attribute
string
field
may
have
no
more
than
512
characters.
Constituent
Data
IMPL
allows
for
the
configuration
of
several
global
sets
to
create
user-‐defined
intensive
quality
variables
assigned,
associated
or
attached
to
any
unit-‐operation-‐port-‐state
where
conditions
and
coefficients
can
only
be
assigned
to
unit-‐operations
of
subtype
blackbox.
Factors
do
not
propagate
across
the
flowsheet
or
superstructure
like
the
other
intensive
qualities
enumerated
below
and
are
essentially
constant.
&sFactor
FACTOR
&sFactor
3. Densities
allow
any
mass
to
volume,
volume
to
mole,
energy
to
mass,
etc.
type
of
mass,
mole,
volume,
energy,
etc.
basis
conversions.
&sDensity
DENSITY
&sDensity
Components
are
similar
to
pure-‐components,
pseudo-‐components,
hypotheticals,
used
in
process
engineering
simulators.
&sComponent
COMPONENT
&sComponent
Properties
are
any
non-‐density
and
non-‐component
such
as
research
and
motor
octane,
sulfur,
melting
point,
etc.
&sProperty
PROPERTY
&sProperty
Conditions
are
essentially
non-‐densities,
non-‐components
and
non-‐properties
such
as
temperature,
pressure,
severity,
conversion,
etc.
that
can
be
used
to
model
the
ad
hoc
behavior
of
blackbox
unit-‐
operation
subtypes.
&sCondition
CONDITION
&sCondition
Coefficients
are
similar
to
conditions
and
may
either
be
of
the
“static”
or
“dynamic”
type
where
static
coefficients
have
no
implied
temporal
dimension
and
represent
parameters
that
can
be
fitted
or
estimated
to
past/present
data
in
data
reconciliation
and
regression
problems
for
example.
Dynamic
coefficients
may
be
used
to
allow
function
calls
to
third-‐party
DLL’s
or
SO’s
to
compute
physical
properties
such
as
enthalpy,
entropy
or
equilibrium
values
and
these
quality
variables
are
indexed
by
time-‐periods
as
their
type
suggests.
4. The
attributes
after
type
are
only
valid
for
dynamic
coefficients
where
the
path,
library
and
function
names
determine
how
to
locate
and
call
the
third-‐party
function.
The
number
of
conditions
states
the
number
of
condition
arguments
to
the
third-‐party
function,
the
perturb
size
is
the
size
of
the
perturbation
to
compute
first-‐order
derivatives
(10-‐6
)
with
respect
to
the
conditions
and
the
list
of
condition
names
separated
by
commas
are
the
condition
argument
names
also
known
in
the
global
condition
set.
&sCoefficient,@sType,@sPath_Name,@sLibrary_Name,@sFunction_Name,
@iNumber_Conditions,@rPerturb_Size,@sCondition_Names
COEFFICIENT,TYPE,PATH,LIBRARY,FUNCTION,NCONDITIONS,PERTURBSIZE,CONDITIONS
&sCoefficient,@sType,@sPath_Name,@sLibrary_Name,@sFunction_Name,
@iNumber_Conditions,@rPerturb_Size,@sCondition_Names
Chains
are
reactions
found
inside
unit-‐operations
of
type
process
and
of
subtype
reactor.
Chains
are
used
to
configure
stoichiometry-‐data
i.e.,
reaction
coefficients
per
chain
or
reaction.
&sChain
CHAIN
&sChain
Cuts
are
sub-‐
or
meta-‐components
found
inside
unit-‐operations
of
type
process
and
of
subtype
fractionator.
Cuts
are
used
to
configure
assay-‐data
in
terms
of
how
a
component
is
distributed
or
distilled
over
for
example
its
temperature
boiling-‐point
range
where
each
cut
has
a
starting
or
initial
boiling-‐point
and
an
ending
or
final
boiling-‐point.
&sCut,@rInitialPoint_Value,@rFinalPoint_Value
CUT,IVALUE,FVALUE
&sCut,@rInitialPoint_Value,@rFinalPoint_Value
Component-‐density’s
and
property-‐density’s
are
used
to
model
heterogeneous
components
and
properties
in
the
sense
that
a
mass-‐based
quality
such
as
sulfur
can
be
calculated
or
predicted
using
a
volume-‐based
quantity
or
flow.
&sComponent,@sDensity
COMPONENT,DENSITY
&sComponent,@sDensity
&sProperty,@sDensity
PROPERTY,DENSITY
&sProperty,@sDensity
5.
Property-‐property’s
and
condition-‐condition’s
are
ranking,
volatility
or
ordering
inequality
constraints
to
ensure
that
the
first
quality
variable
result
is
greater
than
the
second
quality
variable
result.
Ranking
constraints
are
useful
when
solving
with
linear
and
spline
interpolations
in
order
to
maintain
the
monotonicity
of
the
x-‐axis
or
abscissa.
&sProperty,@sProperty
PROPERTY,PROPERTY2
&sProperty,@sProperty
&sCondition,@sCondition
CONDITION,CONDITION2
&sCondition,@sCondition
Property-‐transforms
are
nonlinear
expressions
or
formulas
that
can
be
applied
to
a
single
property
to
transform
it
before
and
after
the
solving
to
some
other
number
and
is
essentially
useful
for
blending
and
mixing
unit-‐operations.
An
example
of
a
property-‐transform
or
blending-‐index
is
converting
SG
to
API
i.e,
API=141.5/SG-131.5.
PropertyTransform-&sProperty,@sType,@rValue,@sValue
PROPERTY,TYPE,RVALUE,SVALUE
PropertyTransform-&sProperty,@sType,@rValue,@sValue
Properties-‐property
are
nonlinear
expressions
or
formulas
that
can
be
used
to
model
derived
or
secondary
properties
and
are
useful
to
model
one
dependent
property
as
a
function
of
any
other
independent
or
dependent
property
i.e.,
ROAD=(RON+MON)/2.
PropertiesProperty-&sProperty,@sType,@rValue,@sValue
PROPERTY,TYPE,RVALUE,SVALUE
PropertiesProperty-&sProperty,@sType,@rValue,@sValue
Condition
Data
(For
Unit-‐Operation
Blackboxes
Only)
For
unit-‐operations
of
type
process
and
subtype
blackbox
we
can
assign,
associate
or
attach
condition
variables
from
the
global
set
of
conditions
and
global
set
of
coefficients.
Then,
these
unit-‐operation-‐
conditions
can
be
used
in
nonlinear
expressions
or
formula
to
model
any
nonlinear
relationship
that
may
be
required
to
accurately
and
precisely
represent
its
behavior
over
time.
6.
In
most
situations,
condition
variables
are
dependent
on
upstream
and/or
downstream
unit-‐operation
and/or
unit-‐operation-‐port-‐state
quantity
and
quality
variables
and
these
can
be
configured
using
the
following
linear
and
simple
connection
,
transfer
or
linking
types
of
equations.
UOHoldupUOCondition-&sUnit,&sOperation,&sUnit,&sOperation,&sCondition
UNIT,OPERATION,UNIT2,OPERATION2,CONDITION
UOHoldupUOCondition-&sUnit,&sOperation,&sUnit,&sOperation,&sCondition
UOPSFlowUOCondition-&sUnit,&sOperation,&sPort,&sState,&sUnit,&sOperation,&sCondition
UNIT,OPERATION,PORT,STATE,UNIT2,OPERATION2,CONDITION
UOPSFlowUOCondition-&sUnit,&sOperation,&sPort,&sState,&sUnit,&sOperation,&sCondition
UOPSYieldUOCondition-&sUnit,&sOperation,&sPort,&sState,&sUnit,&sOperation,&sCondition
UNIT,OPERATION,PORT,STATE,UNIT2,OPERATION2,CONDITION
UOPSYieldUOCondition-&sUnit,&sOperation,&sPort,&sState,&sUnit,&sOperation,&sCondition
UOPSDensityUOCondition-&sUnit,&sOperation,&sPort,&sState,&sDensity,
&sUnit,&sOperation,&sCondition
UNIT,OPERATION,PORT,STATE,DENSITY,UNIT2,OPERATION2,CONDITION
UOPSDensityUOCondition-&sUnit,&sOperation,&sPort,&sState,&sDensity,
&sUnit,&sOperation,&sCondition
UOPSComponentUOCondition-&sUnit,&sOperation,&sPort,&sState,&sDensity,
&sUnit,&sOperation,&sCondition
UNIT,OPERATION,PORT,STATE,COMPONENT,UNIT2,OPERATION2,CONDITION
UOPSComponentUOCondition-&sUnit,&sOperation,&sPort,&sState,&sDensity,
&sUnit,&sOperation,&sCondition
UOPSPropertyUOCondition-&sUnit,&sOperation,&sPort,&sState,&sDensity,
&sUnit,&sOperation,&sCondition
UNIT,OPERATION,PORT,STATE,PROPERTY,UNIT2,OPERATION2,CONDITION
UOPSPropertyUOCondition-&sUnit,&sOperation,&sPort,&sState,&sDensity,
&sUnit,&sOperation,&sCondition
After
any
dependent
conditions
have
been
configured
on
the
unit-‐operation
blackbox,
then
nonlinear
formulas
of
how
to
relate
a
condition
expression
to
another
condition
on
the
same
unit-‐operation
as
well
as
relating
to
other
quantity
and
quality
variables
on
the
unit-‐operation-‐port-‐states
can
also
be
configured
as
follows.
ConditionsUOCondition-&sUnit,&sOperation,&sCondition,@sType,@rValue,@sValue
UNIT,OPERATION,CONDITION,TYPE,RVALUE,SVALUE
ConditionsUOCondition-&sUnit,&sOperation,&sCondition,@sType,@rValue,@sValue
ConditionsUOPSFlow-&sUnit,&sOperation,&sPort,&sState,@sType,@rValue,@sValue
7. UNIT,OPERATION,PORT,STATE,TYPE,RVALUE,SVALUE
ConditionsUOPSFlow-&sUnit,&sOperation,&sPort,&sState,@sType,@rValue,@sValue
ConditionsUOPSRate-&sUnit,&sOperation,&sPort,&sState,@sType,@rValue,@sValue
UNIT,OPERATION,PORT,STATE,TYPE,RVALUE,SVALUE
ConditionsUOPSRate-&sUnit,&sOperation,&sPort,&sState,@sType,@rValue,@sValue
ConditionsUOPSYield-&sUnit,&sOperation,&sPort,&sState,@sType,@rValue,@sValue
UNIT,OPERATION,PORT,STATE,TYPE,RVALUE,SVALUE
ConditionsUOPSYield-&sUnit,&sOperation,&sPort,&sState,@sType,@rValue,@sValue
ConditionsUOPSDensity-&sUnit,&sOperation,&sPort,&sState,&sDensity,
@sType,@rValue,@sValue
UNIT,OPERATION,PORT,STATE,DENSITY,TYPE,RVALUE,SVALUE
ConditionsUOPSDensity-&sUnit,&sOperation,&sPort,&sState,&sDensity,
@sType,@rValue,@sValue
ConditionsUOPSComponent-&sUnit,&sOperation,&sPort,&sState,&sComponent,
@sType,@rValue,@sValue
UNIT,OPERATION,PORT,STATE,COMPONENT,TYPE,RVALUE,SVALUE
ConditionsUOPSComponent-&sUnit,&sOperation,&sPort,&sState,&sComponent,
@sType,@rValue,@sValue
ConditionsUOPSProperty-&sUnit,&sOperation,&sPort,&sState,&sProperty,
@sType,@rValue,@sValue
UNIT,OPERATION,PORT,STATE,PROPERTY,TYPE,RVALUE,SVALUE
ConditionsUOPSProperty-&sUnit,&sOperation,&sPort,&sState,&sProperty,
@sType,@rValue,@sValue
Constituent
Capacity
Data
IMPL
allows
Constituent
Capacity
Data
to
be
configured
or
specified
to
each
unit-‐operation-‐port-‐state
in
the
superstructure.
If
a
quality
in
a
global
quality
set
is
not
assigned,
associated
or
attached
to
a
particular
unit-‐operation-‐port-‐state
internal
stream
then
the
quality
variable
will
not
be
created
or
generated
in
the
model.
A
quality
variable
must
have
a
lower
and
upper
(hard)
bound
but
it
may
or
may
not
have
a
target
(soft)
bound.
If
its
target
is
left
blank
or
it
is
specified
as
RNNON
then
a
target
is
ignored.
If
the
target
field
is
populated
but
its
corresponding
performance-‐weight
is
zero
(0)
then
the
target
will
be
used
as
an
initial-‐
value,
starting-‐point
or
default-‐result.
&sUnit,&sOperation,&sPort,&sState,&sFactor,@rFactor_Value
UNIT,OPERATION,PORT,STATE,FACTOR,F
VALUE
&sUnit,&sOperation,&sPort,&sState,&sFactor,@rFactor_Value
9. For
each
chain
and
for
each
unit-‐operation,
configure
its
lower
and
upper
extent
of
reaction
or
rate.
A
chain
or
reaction
can
be
likened
to
a
sub
batch
or
charge-‐size.
&sChain,&sUnit,&sOperation,@rRate_Lower,@rRate_Upper
CHAIN,
UNIT,OPERATION,LRATE,URATE
&sChain,&sUnit,&sOperation,@rRate_Lower,@rRate_Upper
The
component-‐cut-‐yields
(assay-‐data)
are
valid
for
unit-‐operations
of
type
process
and
subtype
fractionator
and
specify
for
each
component
and
for
each
cut
its
yield
value.
&sComponent,&sCut,@rYield_Value
COMPONENT,
CUT,YVALUE
&sComponent,&sCut,@rYield_Value
Component-‐cut-‐densities,
components
and
properties
provide
the
necessary
assay-‐data
to
calculate
or
predict
for
each
component
the
quality
of
each
cut
i.e.,
how
each
quality
is
distributed
or
profiled
over
the
temperature
boiling-‐point
range
of
the
component
discretized
by
the
cuts.
&sComponent,&sCut,&sDensity,@rDensity_Value
COMPONENT,
CUT,DENSITY,DVALUE
&sComponent,&sCut,&sDensity,@rDensity_Value
&sComponent,&sCut,&sComponent,@rComponent_Value
COMPONENT,
CUT,COMPONENT,CVALUE
&sComponent,&sCut,&sComponent,@rComponent_Value
&sComponent,&sCut,&sProperty,@rProperty_Value
COMPONENT,
CUT,PROPERTY,PVALUE
&sComponent,&sCut,&sProperty,@rProperty_Value
For
each
unit-‐operation-‐port-‐state
and
each
cut
,
these
values
provide
the
lower
and
upper
yield
bounds.
These
values
essentially
stipulate
how
each
cut
on
a
unit-‐operation-‐port-‐state
is
distributed
where
the
values
should
lie
between
zero
(0)
and
one
(1).
&sUnit,&sOperation,&sPort,&sState,&sCut,@rYield_Lower,@rYield_Upper
UNIT,OPERATION,PORT,STATE,
CUT,
LYIELD,UYIELD
&sUnit,&sOperation,&sPort,&sState,&sCut,@rYield_Lower,@rYield_Upper
Constituent
Cost
Data
10. The
Cost
Data
for
qualities
is
straightforward
where
again
we
have
a
profit-‐weight,
performance1-‐
weight
(1-‐norm
deviations
from
target),
performance2-‐weight
(2-‐norm)
and
penalty-‐weight
for
each
unit-‐operation-‐port-‐state-‐density,
component
and
property
as
well
as
unit-‐operation-‐condition
and
coefficient
sets
of
objective
function
weights.
&sUnit,&sOperation,&sPort,&sState,&sDensity,@rDensityPro_Weight,
@rDensityPer1_Weight,@rDensityPer2_Weight,@rDensityPen_Weight
UNIT,OPERATION,PORT,STATE,DENSITY,WDPRO,WDPER1,WDPER2,WDPEN
&sUnit,&sOperation,&sPort,&sState,&sDensity,@rDensityPro_Weight,
@rDensityPer1_Weight,@rDensityPer2_Weight,@rDensityPen_Weight
&sUnit,&sOperation,&sPort,&sState,&sComponent,@rComponentPro_Weight,
@rComponentPer1_Weight,@rComponentPer2_Weight,@rComponentPen_Weight
UNIT,OPERATION,PORT,STATE,COMPONENT,WCPRO,WCPER1,WCPER2,WCPEN
&sUnit,&sOperation,&sPort,&sState,&sComponent,@rComponentPro_Weight,
@rComponentPer1_Weight,@rComponentPer2_Weight,@rComponentPen_Weight
&sUnit,&sOperation,&sPort,&sState,&sProperty,@rPropertyPro_Weight,
@rPropertyPer1_Weight,@rPropertyPer2_Weight,@rPropertyPen_Weight
UNIT,OPERATION,PORT,STATE,PROPERTY,WPPRO,WPPER1,WPPER2,WPPEN
&sUnit,&sOperation,&sPort,&sState,&sProperty,@rPropertyPro_Weight,
@rPropertyPer1_Weight,@rPropertyPer2_Weight,@rPropertyPen_Weight
&sUnit,&sOperation,&sCondition,@rConditionPro_Weight,
@rConditionPer1_Weight,@rConditionPer2_Weight,@rConditionPen_Weight
UNIT,OPERATION,CONDITION,WCPRO,WCPER1,WCPER2,WCPEN
&sUnit,&sOperation,&sCondition,@rConditionPro_Weight,
@rConditionPer1_Weight,@rConditionPer2_Weight,@rConditionPen_Weight
&sUnit,&sOperation,&sCoefficient,@rCoefficientPro_Weight,
@rCoefficientPer1_Weight,@rCoefficientPer2_Weight,@rCoefficientPen_Weight
UNIT,OPERATION,COEFFICIENT,WCPRO,WCPER1,WCPER2,WCPEN
&sUnit,&sOperation,&sCoefficient,@rCoefficientPro_Weight,
@rCoefficientPer1_Weight,@rCoefficientPer2_Weight,@rCoefficientPen_Weight
Constituent
Content
(Current)
Data
The
Constituent
Content
or
Current
Data
configures
the
opening
qualities
of
density,
component
and
property
for
the
physical
units
of
type
pool
in
the
past/present
time-‐horizon.
For
projectional
unit-‐
operations
of
type
process
and
subtype
blackbox
we
also
can
configure
their
opening
conditions.
&sUnit,&sDensity,@rDensity_Value,@rStart_Time
UNIT,DENSITY,DVALUE,START
&sUnit,&sDensity,@rDensity_Value,@rStart_Time
&sUnit,&sComponent,@rComponent_Value,@rStart_Time
11. UNIT,COMPONENT,CVALUE,START
&sUnit,&sComponent,@rComponent_Value,@rStart_Time
&sUnit,&sProperty,@rProperty_Value,@rStart_Time
UNIT,PROPERTY,PVALUE,START
&sUnit,&sProperty,@rProperty_Value,@rStart_Time
&sUnit,&sOperation,&sCondition,@rCondition_Value,@rStart_Time
UNIT,OPERATION,CONDITION,CVALUE,START
&sUnit,&sOperation,&sCondition,@rCondition_Value,@rStart_Time
Constituent
Command
(Control)
Data
The
Constituent
Command
or
Control
Data
configures
the
order,
transaction
or
proviso
details
of
how
the
lower,
upper
(hard)
and
target
(soft)
bounds
can
vary
over
time
for
unit-‐operation-‐port-‐state-‐
densities,
components
and
properties
and
unit-‐operation-‐conditions.
&sUnit,&sOperation,&sPort,&sState,&sDensity,
@rDensity_Lower,@rDensity_Upper,@rDensity_Target,@rBegin_Time,@rEnd_Time
UNIT,OPERATION,PORT,STATE,DENSITY
,DLOWER,DUPPER,DTARGET,BEGIN,END
&sUnit,&sOperation,&sPort,&sState,&sDensity,
@rDensity_Lower,@rDensity_Upper,@rDensity_Target,@rBegin_Time,@rEnd_Time
&sUnit,&sOperation,&sPort,&sState,&sComponent,
@rComponent_Lower,@rComponent_Upper,@rComponent_Target,@rBegin_Time,@rEnd_Time
UNIT,OPERATION,PORT,STATE,COMPONENT
,CLOWER,CUPPER,CTARGET,BEGIN,END
&sUnit,&sOperation,&sPort,&sState,&sComponent,
@rComponent_Lower,@rComponent_Upper,@rComponent_Target,@rBegin_Time,@rEnd_Time
&sUnit,&sOperation,&sPort,&sState,&sProperty,
@rProperty_Lower,@rProperty_Upper,@rProperty_Target,@rBegin_Time,@rEnd_Time
UNIT,OPERATION,PORT,STATE,PROPERTY,PLOWER,PUPPER,PTARGET,BEGIN,END
&sUnit,&sOperation,&sPort,&sState,&sProperty,
@rProperty_Lower,@rProperty_Upper,@rProperty_Target,@rBegin_Time,@rEnd_Time
&sUnit,&sOperation,&sCondition,
@rCondition_Lower,@rCondition_Upper,@rCondition_Target,@rBegin_Time,@rEnd_Time
UNIT,OPERATION,CONDITION,CLOWER,CUPPER,CTARGET,BEGIN,END
&sUnit,&sOperation,&sCondition,
@rCondition_Lower,@rCondition_Upper,@rCondition_Target,@rBegin_Time,@rEnd_Time
Configuration
Demo
(Pooling
Optimization
Problem)
12. The
Configuration
Demo
provided
below
is
a
small
pooling
optimization
problem
with
one
(1)
pool,
three
(3)
component
materials
(A,
B
and
C),
two
(2)
product
materials
(P1
and
P2),
one
(1)
property
sulfur
(S)
and
one
(1)
time-‐period
as
shown
in
Figure
1.0.
This
is
the
well-‐known
Haverly
pooling
problem
and
has
been
studied
extensively
in
the
chemical
engineering
literature
on
global
optimization
because
it
exhibits
three
(3)
local
optimum
of
$0,
$100
and
$400.
Figure
1.0
Flowsheet
of
Pooling
Optimization
Problem.
i M P l (c)
Copyright and Property of i n d u s t r I A L g o r i t h m s LLC.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Calculation Data (Parameters)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
&sCalc,@sValue
START,-1.0
BEGIN,0.0
END,1.0
PERIOD,1.0
&sCalc,@sValue
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Chronological Data (Periods)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!