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calculate_map [2011/07/25 00:01]
hermann [General Operators]
calculate_map [2022/08/19 23:49] (current)
admin [Notes]
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 ===== Inputs ===== ===== Inputs =====
  
-^ Name       ​^ Type                                         ​^ Description ​                                                      ​+^ Name  ^ Type  ^ Description ​ 
-| Expression | [[Image Expression Type | Image Expression]] | Algebraic or logical expression used to calculate the output map. |+| Expression ​ | [[Image Expression Type]] ​ | Algebraic or logical expression used to calculate the output map.  |
  
 ===== Optional Inputs ===== ===== Optional Inputs =====
  
-^ Name             ​^ Type                           ​^ Description ​                                                                                                                                                                          ​^ Default Value         ​+^ Name  ^ Type  ^ Description ​ ^ Default Value  
-| Cell Type        | [[Cell Type Type | Cell Type]] | Data cell type                                                                                                                                                                        | Signed 32 Bit Integer | +| Cell Type  | [[Cell Type Type]] ​ | Data cell type  | Signed 32 Bit Integer ​ 
-| Null Value       ​| [[Int Type | Int]]             ​| Null value                                                                                                                                                                            -2147483648 ​          +| Null Value  | [[Null Value Type]] ​ | Null value  Default((Based on the value of the Cell Type input.))  ​
-| Result Is Sparse | [[Bool Type | Bool]]           ​| If true, the resulting map is created as a sparse image. Sparse images have the advantage of storing only the cells containing non-null values, but they have diminished access time. | False                 ​|+| Result Is Sparse ​ | [[Boolean Value Type]] ​ | If true, the resulting map is created as a sparse image. Sparse images have the advantage of storing only the cells containing non-null values, but they have diminished access time.  | False  | 
 +| Result Format ​ | [[Map Type]] ​ | Map representing the output format. Any category information presents in the given map is not used as part of the map format. ​ | None  ​|
  
 ===== Outputs ===== ===== Outputs =====
  
-^ Name   ​^ Type               ​^ Description ^ +^ Name  ^ Type  ^ Description ​ 
-| Result | [[Map Type | Map]] | Output map. |+| Result ​ | [[Map Type]] ​ | Output map.  |
  
 ===== Group ===== ===== Group =====
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 The expression result is calculated as a real value and converted to the data cell type of the output map. The expression result is calculated as a real value and converted to the data cell type of the output map.
  
-If the calculation of the expression diverges ​or if the data cell type is not large enough, the corresponding cell is filled with the null value.+If the calculation of the expression diverges, the corresponding cell is filled with the null value. In practice, it means that every time a null value is found in a expression calculation,​ the calculation results in null value, unless the occurrence of the null value is isolated from the rest of the expression by a special operator like ''​[[image_expression_type#​image_operators_and_functions|isNull()]]''​ or ''​[[image_expression_type#​general_operators|?​]]''​.
  
-List of mathematical and logical operators, in order of precedence that can be employed in the logic/​algebraic expression. Operators separated by blank lines have the same precedence.+The examples below illustrates:​
  
-==== General Operators ====+^ Example ​ ^ Analysis ​ ^ 
 +| <code cpp>i1 / 0</​code> ​ | The expression always results in null value (division by zero). ​ | 
 +| <code cpp>i1 + i2 / i3 ^ 3</​code> ​ | If the current cell of any of the images involved in the calculation is null value, the expression results in null value .  | 
 +| <code cpp>if isNull(i1) then 
 +    1 
 +else 
 +    2 
 +</​code> ​ | The expression never results in null value. ​ | 
 +| <code cpp>if isNull(i1) then 
 +    i2 
 +else 
 +    i3 
 +</​code> ​ | The expression might result in null value depending on the the value of i2 and i3.  | 
 +| <code cpp>(100 / i2) ? 0</​code> ​ | The expression never results in null value. ​ | 
 +| <code cpp>(100 / i2) ? i1</​code> ​ | The expression might result in null value depending on the the value of i1.  |
  
-^ Operator ^ Description ^ Symbol ^ Usage Example ^ +If the data cell type is not large enough, the corresponding cell is also filled with the null value.
-| Boolean Or | | or \\ <​nowiki>​||</​nowiki>​ | not isNull(i1) or isNull(i2) \\ not isNull(i1) <​nowiki>​||</​nowiki>​ isNull(i2) | +
-| Boolean And | | and \\ && | not isNull(i1) and isNull(i2) \\ not isNull(i1) && isNull(i2) | +
-| Equal | | = \\ == | i1 = 2 \\ i1 == 2 | +
-| Not Equal | | != \\ /= \\ <> | i1 != 2 \\ i1 /= 2 \\ i1 <> 2 | +
-| Greater Than | | > | i1 > 2 | +
-| Greater Than Or Equal | | >= | i1 >= 2 | +
-| Less Than | | < | i1 < i2 | +
-| Less Than Or Equal | | <​nowiki><​=</​nowiki>​ | i1 <​nowiki><​=</​nowiki>​ i2 | +
-| Add | | + | i1 + i2 | +
-| Subtract | | – | i1 – i1 / i2 | +
-| Times | | * | i1 * i2 | +
-| Divide | | / | i1 / i2 | +
-| Mod | | % | i1 % 100 | +
-| Power | | <​nowiki>​^</​nowiki>​ | i1 <​nowiki>​^</​nowiki>​ 3 | +
-| Catch Error | Catch an algebraic error and replace it with the result of another expression | ? | (i1 / i2) ? (i1 – i2) | +
-| Boolean Not | | ! \\ not | not isNull(i1) \\ ! isNull(i1) |  +
-| 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 |  +
-| Negate | | – | – ceil(i1 + 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(i1i2) | +
-| 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 | +
-| 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) |+
  
-==== Value Operators ====+The list of mathematical and logical operators that can be employed in the logic/​algebraic expression can be found in the [[Image Expression Type | image expression reference]].
  
-^ Operator ^ Description ^ Symbol ^ Usage Example ^ +The maps used by the "​Calculate Map" must be provided by a corresponding ​[[Number Map]], the tables must be provided by a corresponding [[Number Table]] and the values must be provided by a corresponding [[Number Value]].
-| Get Variable Value | Return ​the variable value | vX \\ where X is an integer value from 1 to 100 | v1 + t1[v2 + 4|+
  
-==== Image Operators ==== +For additional information about how the null values are handled during ​image and value calculationsee [[Image ​Expression ​Null Value Handling|this reference]].
- +
-^ 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 ==== +
- +
-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[<​nowiki><​=</​nowiki>​ ] \\ tX{ } \\ where X is an integer value from 1 to 100 | 2[<​nowiki><​=</​nowiki>​ 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] |  +
- +
-==== Image Neighborhood Operators ==== +
- +
-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: \\ <m 10>​sigma^2 ​ = {1/​{n-1}}sum{i=1}{n}{(x_i-X)^2}</​m>​ \\ where x<​sub>​1</​sub>,​ x<​sub>​2</​sub>,​ ..., x<​sub>​i</​sub>​ 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: \\ <m 8>sigma = sqrt{{1/​{n-1}}sum{i=1}{n}{(x_i-X)^2}}</​m>​ \\ where x<​sub>​1</​sub>,​ x<​sub>​2</​sub>,​ ..., x<​sub>​i</​sub>​ 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) | +
- +
 ===== Internal Name ===== ===== Internal Name =====
  
 CalculateMap CalculateMap
-