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--- image_expression_null_value_handling [2022/08/20 19:28]
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-====== Image Expression Null Value Handling ======
-===== Expressions =====
-  * The entire expression is one single expression resulting in one single value.
-  * Everything  is an expression and produces one single value. So, even an ''if then else'' is just one expression resulting in one single value. Therefore,  you can sum the results of two separate ''if then else''s like ''(if the  else) + (if then else)''.  Since even the test clause of an ''if then else'' is an expression, you can also replace that with another ''if then else''. Example: ''if (if i1 > 0 then 1 else i2) then i2 else 1 + i3''
-  * The ''if then else'' test assumes that 0 is false and any non-zero value is true.
-===== Null Evaluation =====
-  * Every time the expression being evaluated results in null, the entire  expression becomes null. So, ''i1 + null'' will always be null since  something ''+'' null is always null.
-  * The only operators that can contain the //destructive power// of a null value are ''isnull(  expression )'' or ''expression1 ? expression2'':
-    - ''isnull( expression )'' evaluates the expression and results 1 if the ''expression'' evaluates to null, and 0 otherwise.
-    - ''expression1  ? expression2'' evaluates the ''expression1'' and, if the result is  non-null, returns that value. Otherwise, it evaluates ''expression2'' and returns the resulting value as its own result.
-  * Null can come from an image, but it can also be produced by some other  events, such as dividing by zero, failing to find a key in a lookup  table etc.
-  * If the ''if then else'' test evaluates to null, the entire ''if then else'' evaluates to null. Example:
-     * ''(if (i1/3 > 9) then i2 else 1 + i3) + 10'':
-        - If ''i1'' is null, ''i1/3'' is also null, and ''i1/3 > 9'' also becomes null. Therefore, the ''if then else'' test is null and the entire ''if then else'' is null.
-        - Now, null is being added to 10, and that also becomes null.
-     * ''( (if (i1/3 > 9) then i2 else 1 + i3) + 10 ) ? 20'' -- Note that we are using the operator ''?'' now:
-        - If ''i1'' is null, ''i1/3'' is also null, and ''i1/3 > 9'' also becomes null. Therefore, the ''if then else'' test is null and the entire ''if then else'' is null.
-        - Then, null is being added to 10, and that also becomes null.
-        - Now, null is being caught by the expression ''null ? 20'', since the ''if then else + 10'' is null, and the result is 20.
-The  null evaluation mechanism allows us to write short expressions like ''i1 + 10'' to add 10 to every //valid cell// of the ''i1'' map, or ''i1 * i2'' to  multiply two maps. If one of the map cells is null, the result is null, so in the last example, we are basically just multiplying the corresponding cells where the  two values are valid: **everything else will be null**.
-If we  want to treat all null values as values 1s, in the previous expression, we can write ''(i1 ? 1) * (i2 ? 1)''. We can also use the more complicated form using the ''if then else'' to achieve the same result:
-  (if isnull(i1) then 1 else i1) * (if isnull(i2) then 1 else i2),
-or
-  if isnull(i1) and isnull(i2) then 1
-  else if not isnull(i1) and not isnull(i2) then i1*i2
-  else if not isnull(i1) and isnull(i2) then i1
-  else i2
-If you need to retrieve the number corresponding to a image null value, you can use the ''null( iX )'' expression. For instance, ''null(i1)'' returns the number corresponding to the null value of image ''i1''. So if, so some reason, you need to retrieve the image value or its corresponding numeric null value, you can use ''i1 ? null(i1)'' or ''if isnull(i1) then null(i1) then i1''. Note that ''null(i1)'' is very different from expression ''null'', since ''null(i1)'' always returns a valid numeric value and ''null'' returns a special construct that, if not contained, invalidates the expression evaluation producing null as a result.