List of mathematical and logical operators that can be employed in the logic/algebraic expression.
Precedence | Operator | Description | Symbol | Usage Example |
---|---|---|---|---|
1 | Conditional | Execute the second or third term of the equation conditionally to the first | if then else | if not isNull(i1) and isNull(i2) then i3 else if isNull(i1) then i1 – i1 / i2 else (i1 / i2) ? (i1 – i2) |
2 | Boolean Or | or || | not isNull(i1) or isNull(i2) not isNull(i1) || isNull(i2) |
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Boolean And | and && | not isNull(i1) and isNull(i2) not isNull(i1) && isNull(i2) |
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3 | Equal | = == | i1 = 2 i1 == 2 |
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Not Equal | != /= <> | i1 != 2 i1 /= 2 i1 <> 2 |
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4 | Greater Than | > | i1 > 2 | |
Greater Than Or Equal | >= | i1 >= 2 | ||
Less Than | < | i1 < i2 | ||
Less Than Or Equal | <= | i1 <= i2 | ||
5 | Add | + | i1 + i2 | |
Subtract | – | i1 – i1 / i2 | ||
6 | Times | * | i1 * i2 | |
Divide | / | i1 / i2 | ||
Mod | % | i1 % 100 | ||
7 | Power | ^ | i1 ^ 3 | |
8 | Catch Error | Catch an algebraic error and replace it with the result of another expression | ? | (i1 / i2) ? (i1 – i2) |
9 | Boolean Not | ! not | not isNull(i1) ! isNull(i1) |
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Negate | – | – ceil(i1 + i2) |
Operator | Description | Symbol | Usage Example |
---|---|---|---|
Value | 2 + i1 / -3.5e-2 | ||
Random | Generate a random value using the uniform probability distribution | rand | if rand > 0.5 then 1 else i2 |
Squared Root | sqrt() | sqrt(i1 / i4) | |
Sin | Sin (input in radians) | sin() | sin(i1 / i4) |
Cos | Cos (input in radians) | cos() | cos(i1 + i2) |
Tan | Tan (input in radians) | tan() | tan(i1 * i5 + 6) |
Acos | Acos (output in radians) | acos() | acos(i1 + i2) |
Asin | Asin (output in radians) | asin() | asin(i1 + i2) |
Atan | Atan (output in radians) | atan() | atan(i1 + i2) |
Ceil | ceil() | ceil(i1 + i2) | |
Exp | exp() | exp(i1[i1 + i2]) | |
Floor | floor() | floor(i1 + i2) | |
Round | round() | round(i1 / i4) | |
Abs | abs() | abs(i1 + i2) | |
Ln | ln() | ln(i1 / i4) | |
Log | log() | log(i1 / i4) | |
Max | max() | max(i1, i2) | |
Min | min() | min(i1, i4) | |
Signal | Return +1, if the expression is positive, -1, if it is negative, and 0, otherwise. | signal() | signal(i1 - 4) |
Abort | Abort the model execution | abort | if i1 > 0 then i1 * i2 + 4 else abort |
Operator | Description | Symbol | Usage Example |
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Get Variable Value | Return the variable value | vX where X is an integer value from 1 to 100 | v1 + t1[v2 + 4] |
Operator | Description | Symbol | Usage Example |
---|---|---|---|
Get Image Value | Return the image value at the current cell | iX where X is an integer value from 1 to 100 | i2 |
Get Image Value At Location | Return the image value on the specified cell coordinate | iX[ , ] where X is an integer value from 1 to 100 | i1[line – 1, column – 2] |
Get Image Null Value | Return the null value of the current image | null null(iX) | if i1 > 2 then i1 else null if null(i2) > 2 then 1 else null |
Is Null | isNull(iX) where X is an integer value from 1 to 100 | if not isNull(i1) then i1 else i2 | |
Get Line Number | Return the line number of the current cell | line | line + 1 |
Get Column Number | Return the column number of the current cell | column | if column / 2 > 50 then 1 else null |
Table operators return the value corresponding to a given key according to a rule-operator.
It uses the following syntax:
tX[N ]
where:
X is a table identifier;
N is the rule-operator.
Operator | Description | Symbol | Usage Example |
---|---|---|---|
Get Table Value | Return the table value in the X key position of the table | tX[ ] where X is an integer value from 1 to 100 | t2[i1 + 2] |
Get Table Equal Lower Bound Value | Return the table value in the greater key less than or equal to the X key position of the table. | tX[<= ] tX{ } where X is an integer value from 1 to 100 | 2[<= 14] t2{14} |
Get Table Lower Bound Value | Return the table value in the greater key less than the X key position of the table. | tX[< ] where X is an integer value from 1 to 100 | t2[< i1 + 2] |
Get Table Equal Upper Bound Value | Return the table value in the lesser key greater than or equal to the X key position of the table. | tX[>= ] where X is an integer value from 1 to 100 | t2[>= i1 + i3]= |
Get Table Upper Bound Value | Return the table value in the lesser key greater than the X key position of the table. | tX[> ] where X is an integer value from 1 to 100 | t2[> i7] |
Get Table Closest Value | Return the table value in the key closest to the X key position of the table. | tX[>< ] where X is an integer value from 1 to 100 | t2[>< 3 + i7] |
Get Table Interpoled Value | Return a linear interpoled value drawn through the neighbor keys of the X key position of the table. | tX[/ ] where X is an integer value from 1 to 100 | t2[/ i2] |
Test Table Key | Return 1, if expression corresponds to a key stored in the table, and 0, otherwise. | tX[? ] tX[=? ] tX[==? ] where X is an integer value from 1 to 100 | t2[? i2] t2[=? i2] |
Neighborhood operators return the value of an operation within a defined neighborhood window.
It uses the following syntax:
nbN(iX, h, w, y, x)
where:
N is the operator name;
X is an image identifier;
h is the number of window lines;
w is the number of window columns;
y is the line where the window center is anchored at the image;
x is the column where the window center is anchored at the image.
The calculation usually includes the center of the window.
Even-sided windows have the center displaced toward the top left corner.
The window anchor (y and x) can be omitted when the window center is anchored at the current line and column. The shortened syntax is:
nbN(iX, h, w)
Operator | Description | Symbol | Usage Example |
---|---|---|---|
Min | Returns the minimum value of the neighbor non-null cells. | nbMin() | nbMin(i4, 2, 3, line-1, column) |
Max | Returns the maximum value of the neighbor non-null cells. | nbMax() | nbMax(i1, 4, 4) - 1 |
Sum | Returns the sum of the neighbor non-null cells. | nbSum() | nbSum(i3, 5, 5) + 7 |
Product | Returns the product of the neighbor non-null cells. | nbProd() | if not isNull(i1) then nbProd(i1, 2, 2, 0, column) else 0 |
Count | Returns the number of neighbor non-null cells. | nbCount() | nbCount(i2, 3, 3) + nbCount(i1, 3, 3, line, column+3) |
Average | Returns the arithmetic mean of the neighbor non-null cells. | nbAverage() | round(nbAverage(i1, 7, 7)) |
Median | Returns the median value of the neighbor non-null cells. For an even number of values, the greater of the two median values is returned. | nbMedian() | nbMedian(i1, 5, 5) |
Mode | Returns the mode of the neighbor non-null cells. If a mode does not exist, null is returned. If there is more than one, the lesser one is returned. | nbMode() | nbMode(i1, 5, 5) |
Variance | Returns the variance of the values of the neighbor non-null cells according to the expression: ![]() where x1, x2, …, xi are the neighbor cells; X is the mean of the neighbor cells. | nbVar() | nbVar(i4, 7, 7) / 25 |
Standard Deviation | Returns the standard deviation of the neighbor non-null cells according to the expression: ![]() where x1, x2, …, xi are the neighbor cells; X is the mean of the neighbor cells. | nbStdDev() | nbStdDev(i2, 3, 3, line-1, column) + nbStdDev(i2, 3, 3) + nbStdDev(i2, 3, 3, line+1, column) |