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<tt class="label">1770</tt></td>
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<tt class="label">Field_Math</tt></td>
<td nowrap width="150"><tt class="label">02/03/94</tt></td>
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<tr><td align="left" colspan="3"><p>The module does some field mathematics -- I am intended to talk about it at the AVS94. The module interprets a short (up to 60 lines) program written in AVSFOL (A Very Simple Field Operation Language). AVSSPL admits two types of variables -simple variables with values being single float numbers; field variables with values being float arrays of dimensions determined by the output field.</p></td></tr>
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<tr valign="top"><td><b>Author:</b></td><td>Krzysztof (Chris) S. Nowinski, Institute of Applied Mathematics and Mechanics, Warsaw University</td></tr>
<tr><td><b>Version:</b></td><td>1.000</td></tr>
<tr><td><b>Language:</b></td><td>C</td></tr>
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<td><b>Path:</b></td><td>source/filters/Field_Math/</td></tr>
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<title> Field Math - an interpreter of AVSFOL programming language
for creation or modification of float fields
</title>
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<body bgcolor=#FFFFCC>
<h2> Field Math - an interpreter of AVSFOL programming language
for creation or modification of float fields
</h2>
<h3>Name</h3>
<blockquote>
<pre>
Field Math - an interpreter of AVSFOL programming language
for creation or modification of float fields
</pre>
</blockquote>
<h3>Description</h3>
<blockquote>
<pre>
The module interprets a short (up to 60 lines) program written in
AVSFOL (A Very Simple Field Operation Language) conforming to the
following syntax:
<program> := <declaration lines><instruction_lines>
<declaration lines> := !dimensions <dim0> <dim1> ...
!veclen=<veclen>
!nspace=<nspace>
<instruction_line> := <comment line>|<substitution line>|
<structural instruction line>|
<output statement line>
<comment line> := #<any text>
<substitution line> := <left_hand_side>=<expression>
<left_hand_side> := <output_var>|<temporary_var>
</pre>
</blockquote>
<h3>Output</h3>
<blockquote>
<pre>
var> := w0 | w1 ... (output field components)
y0 | y1 ... (output field coordinates)
<temporary_var> := any valid C variable name (up to 20 chars)
<expression> := any valid algebraic expression formed form:
<input_vars>,<temporary_vars>,<parameters>,
<functions>,<scalars>,
<algebraic_operators>,<delimiters>
</pre>
</blockquote>
<h3>Input</h3>
<blockquote>
<pre>
var> := [a0 | a1 ... (input field 1 components)]
..............
[f0 | f1 ... (input field 2 components)]
[x0 | x1 ... (input field coordinates)]
i0 | i1 ... (output field indexes)
</pre>
</blockquote>
<h3>Parameter</h3>
<blockquote>
<pre>
:= p0 | p1 | p2 | p3 | p4 | p5
<function> := <unary field function>|<binary field function>
<folding function>|<convolution function>
<unary function> := sin | cos | tan | exp | ln | log | sqr | sqrt | abs
<binary function> := min | max
<folding function> := fmin | fmax | avg
<convolution function> := cnv
<scalar> := any C float
<algebraic_operator> := + | - | * | / | ^
<delimiter> := ( | )
<structural instruction line> :=while <expression>|end while
<output statement line> := flush
AVSSPL admits two types of variables:
simple variables with values being single float numbers;
field variables with values being float arrays of dimensions
determined by the output field.
Unary function can have arguments of arbitrary type, result has the type
of the argument.
sin(3.14159) is scalar 1,
sqrt(a0) is the array of square roots of elements of first component
of infield.
Binary operations and binary functions pmin (pointwise minimum)
and pmax (pointwise maximum) allow for any combination of argument types
with result being simple if both arguments were simple, and result
of array type otherwise.
3^3 is scalar 27,
a0*5 is the arrray of values of infield multiplied by 5.
Folding functions return always scalars being maximum, minimum and average
taken over all matrix - respectively.
avg(a0^3) is average of cubes of first component of infield.
Convolution functions take two field variables as arguments and return
convolution or local (masked) minima or maxima.
cnv(a0,f0) is convolution.
The parameters p0,...,p5 can be used both as inputs (e.g. w0=p0*a0+(1-p0)*b0
will evaluate a weighted average of two fields) and as outputs (e.g.
p0=sqrt(avg((a0-avg(a0))^2) will output standard deviation of infield).
while <expr>/ end while pair encloses a series of statements that will be
executed as long as the value of (scalar) expr is non-0.
while 1 will loop forever
.......
end while
t0=10
while t0
t0=t0-1
........
end while will loop 10 times.
flush statement causes output of <outfield> when all of its components
and co-ordinates are defined.
</pre>
</blockquote>
<h3>Examples</h3>
<blockquote>
<pre>
p0=avg(a0)
p1=sqrt(avg(sqr(a0-p0)))
evaluates (numerical) laplacian of the field
!dimensions 50 50
!min_ext -5 -5
!max_ext 5 5
!veclen=2
w0=0
p2=0
while 1
p2=p2+p0
u0=p1*cos(p2)
u1=p1*sin(p2)
w1=1/(0.3+sqr(y0-u0)+sqr(y1-u1))
w0=cnv(w0,f0)+w1
flush
end while
with f0= [[0 0.25 0][0.25 0 0.25][0 0.25 0]]
starts a continuous simulation of temperature distribution in
a square plate heatened by a source rotating at a radius p1
with rotation speed p0.
Programs can be edited with a primitive line editor, saved and loaded.
New fields can be created. The module waits for dimensions
parameter to create outfield.
INPUTS
infield - field float
................
infield6 - field float
PARAMETERS
Output dimensions (typein)
requires input of the form dim0 dim1 dim2 ...
(a list of <ndim> integers separated by blanks);
together with Output ndim determine dimensionality
of outfield
Output veclen (islider)
determines veclen of the output field
Make points (toggle)
if on, outfield will be irregular with user-defined
point coordinates; otherwise, coordinates of infield
will be copied to outfield or, if Create field is on,
an uniform outfield is created
Output space dimension (islider)
active when Make points is on
variables (textblock)
output only -- shows the list of all predefined variables
(input field components and coordinates - when present,
indexes and output field components and coordinates - to be
determined
functions (textblock)
output only -- shows the list of all available functions
input line (typein)
currently edited program line
program (choice_browser)
displays current program
execute (boolean)
starts/stops parsing and execution of the program
clear (oneshot)
clears all program (does not clear temporary variables
and outputs)
reset (oneshot)
clear temporary variables and outputs
edit (choice_browser)
Append -- add current input line after the highlighted line
Insert -- add current input line before the highlighted line
Edit -- the highlighted line
Delete -- the highlighted line
Formula file (browser)
Read formula (oneshot)
Write formula (oneshot)
control writing/reading of the program to/from disk file;
program files use .fmla extension and are easily editable
OUTPUTS
outfield - field float
the module outputs only after all outfield components and
coordinates are evaluated
</pre>
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<td width="100%"> Last Updated:
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