Difference between revisions of "INF, NAN, and Null"

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[[Category:Doc Status C]] <!-- For Lumina use, do not change -->
 
[[Category:Doc Status C]] <!-- For Lumina use, do not change -->
 
   
 
   
These are special values that Analytica returns in particular conditions. You can also use them in expressions:
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'''Inf''', '''NAN''', and '''Null'''  are special values, which can be very useful. Analytica returns them under conditions when it can't return a number. You can also type them directly into an expression or Edit table. 
  
'''Inf''' means infinity -- e.g.,  
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'''Inf''' means infinity, and is the result of dividing a positive number by zero -- e.g.,
:1/0  &rarr; Inf
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:<code>1/0  &rarr; Inf</code>
or a number larger than 1.796E308 (the largest number that your computer can represent explicitly) -- e.g.
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:1E307 * 100 &rarr; Inf
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'''-Inf''' means negative infinity (or a number less than 1.796E308) -- e.g.
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:-1/0  &rarr; -Inf
+
  
'''NAN''' means "Not A Number" -- i.e. not a well-defined number nor infinity -- e.g.
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or computing a number larger than 1.796E308 (the largest number that your computer can represent in 64 bits) -- e.g.  
:0/0 &rarr; NAN
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:<code>1E307 * 100 &rarr; Inf</code>
:Sqrt(-1) &rarr; NAN
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(If you enable [[Complex Numbers]], Sqrt(-1) returns the valid imaginary number, 1j.)
+
  
'''Null''' means that there is no such value. For example, [[Slice]] and [[Subscript]] return Null if you try to get the ''n''th slice over an Index with less than ''n'' values. For example:
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'''-Inf''' means negative infinity, the result of dividing a negative number by zero (or a number less than -1.796E308) -- e.g.
 +
:<code>-1/0  &rarr; -Inf</code>
  
:Index Year := [2015, 2016, 2017]
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'''NAN''' means "Not A Number". It is the result of a calculation that is not a well-defined number nor infinity -- e.g.
:Slice(Year, 4)  &rarr; NULL
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:<code>0/0 &rarr; NAN</code>
:Variable X := Array(Year, [20, 23, 28])
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:<code>Sqrt(-1) &rarr; NAN</code>
:X[Year = 2018] &rarr; NULL
+
 
 +
(If you enable [[Complex Numbers]], <code>Sqrt(-1)</code> returns the valid imaginary number, ''1j''.)
 +
 
 +
'''Null''' means that there is no such value. For example,  [[Subscript]] returns <code>Null</code> if the indexing value doesn't match a value of the Index:
 +
 
 +
:<code>Index Year := [2015, 2016, 2017]</code>
 +
:<code>Slice(Year, 4)  &rarr; NULL</code>
 +
:<code>Variable X := Array(Year, [20, 23, 28])</code>
 +
:<code>X[Year = 2018] &rarr; NULL</code>
 +
You can also specify a different default result for an index value that doesn't match the index:
 +
 
 +
<code>X[Year = 2018, defValue: 0] &rarr; 0</code>
  
 
=== More on INF and NAN ===
 
=== More on INF and NAN ===
  
Calculations using INF and NAN follow ANSI (Association of National Standards Institutes) standards, which follow the laws of mathematics as far as possible:
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Calculations using <code>INF</code> and <code>NAN</code> follow ANSI (Association of National Standards Institutes) recommendations, which follow the laws of mathematics as far as possible:
:1/Inf &rarr; 0
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:<code>1/Inf &rarr; 0</code>
:1/(-Inf) &rarr; 0
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:<code>1/(-Inf) &rarr; 0</code>
:Inf + Inf &rarr; Inf
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:<code>Inf + Inf &rarr; Inf</code>
:Inf - Inf &rarr; NAN
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:<code>Inf - Inf &rarr; NAN</code>
  
Expressions taking NAN as an operand or parameter give NAN as their result unless the expression has a well-defined logical or numerical value for any value of NAN:
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Expressions taking <code>NAN</code> as an operand or parameter give <code>NAN</code> as their result unless the expression has a well-defined logical or numerical value for any value of <code>NAN</code>:
  
:True OR NAN &rarr; True
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:<code>True OR NAN &rarr; True</code>
:NaN AND False &rarr; False
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:<code>NaN AND False &rarr; False</code>
:IF True THEN 5 ELSE NAN &rarr; 5
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:<code>IF True THEN 5 ELSE NAN &rarr; 5</code>
  
 
=== More on NULL ===
 
=== More on NULL ===
  
When NULL appears in scalar operations, it generally produces a warning and evaluates to NULL, for example:
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When <code>Null</code> appears in scalar operations, it generally produces a warning and evaluates to <code>Null</code>, for example:
:10 + NULL &rarr; NULL
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:<code>10 + NULL &rarr; NULL</code>
:NULL - 10 &rarr; NULL
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:<code>NULL - 10 &rarr; NULL</code>
:1 AND NULL &rarr; NULL
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:<code>1 AND NULL &rarr; NULL</code>
  
Array-reducing functions ignore NULL. These examples demonstrate (assume A is indexed by I as indicated).
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[[Sum]], [[Min]], [[Max]], [[ArgMax]], [[JoinText]],  [[Npv]], and other [[Array-reducing functions]] ignore <code>Null. For example:</code>
 +
 
 +
:<code>Variable A :=</code>
 
:{| class="wikitable"
 
:{| class="wikitable"
! I: !!  1  !!  2  !!  3  !!  4  !!  5
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! colspan="5" style="text-align: left;" ! | I &#9654;
 
|-
 
|-
! A: || 8 || NULL || 4 || NULL || 0
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!|1
 +
!|2
 +
!|3
 +
!|4
 +
!|5
 +
|-
 +
|8
 +
|NULL
 +
|4
 +
|NULL
 +
|0
 
|}
 
|}
  
:[[Sum]](A, I) &rarr; 12
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:<code>Sum(A, I) &rarr; 12</code>
:[[Average]](A, I) &rarr; 4  
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:<code>Average(A, I) &rarr; 4</code>
:[[JoinText]](A, I, ', ') &rarr; "8, 4, 0"
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:<code>JoinText(A, I, ', ') &rarr; "8, 4, 0"</code>
 +
 
 +
Graphs also ignore (do not show) any point whose value is <code>Null</code>.
  
Graphs will simply ignore (not show) any point whose value is NULL.
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Some  [[Array-reducing functions]], notably [[Sum]], [[Min]] and [[Max]] also accept an optional parameter «IgnoreNaN» to ignore <code>NaN</code> values (which otherwise propagate, i.e. return <code>NaN</code>).
  
Array-reducing functions include [[Sum]], [[Min]], [[Max]], [[ArgMin]], [[ArgMax]], [[Product]], [[Average]], [[JoinText]], [[Irr]], [[Npv]]. 
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[[Regression]] also ignores any data points which have <code>Y = Null</code>, which is useful for missing data.
Array functions [[Sum]], [[Min]] and [[Max]] also accept an optional parameter ''IgnoreNaN'' to ignore NaN values (which otherwise propagate, i.e. return NaN).
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[[Regression]] also ignores any data points which have Y=Null, which is useful for missing data.
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==See Also==
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* [[INF, NAN, and NULL - Exception values]]
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* [[Undefined]]
 +
* [[IsNaN]]
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* [[IsNull]]
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* [[Data_Type_Functions#Comparison_to_Null|Comparison to Null]]

Latest revision as of 19:25, 22 February 2019


Inf, NAN, and Null are special values, which can be very useful. Analytica returns them under conditions when it can't return a number. You can also type them directly into an expression or Edit table.

Inf means infinity, and is the result of dividing a positive number by zero -- e.g.,

1/0 → Inf

or computing a number larger than 1.796E308 (the largest number that your computer can represent in 64 bits) -- e.g.

1E307 * 100 → Inf

-Inf means negative infinity, the result of dividing a negative number by zero (or a number less than -1.796E308) -- e.g.

-1/0 → -Inf

NAN means "Not A Number". It is the result of a calculation that is not a well-defined number nor infinity -- e.g.

0/0 → NAN
Sqrt(-1) → NAN

(If you enable Complex Numbers, Sqrt(-1) returns the valid imaginary number, 1j.)

Null means that there is no such value. For example, Subscript returns Null if the indexing value doesn't match a value of the Index:

Index Year := [2015, 2016, 2017]
Slice(Year, 4) → NULL
Variable X := Array(Year, [20, 23, 28])
X[Year = 2018] → NULL

You can also specify a different default result for an index value that doesn't match the index:

X[Year = 2018, defValue: 0] → 0

More on INF and NAN

Calculations using INF and NAN follow ANSI (Association of National Standards Institutes) recommendations, which follow the laws of mathematics as far as possible:

1/Inf → 0
1/(-Inf) → 0
Inf + Inf → Inf
Inf - Inf → NAN

Expressions taking NAN as an operand or parameter give NAN as their result unless the expression has a well-defined logical or numerical value for any value of NAN:

True OR NAN → True
NaN AND False → False
IF True THEN 5 ELSE NAN → 5

More on NULL

When Null appears in scalar operations, it generally produces a warning and evaluates to Null, for example:

10 + NULL → NULL
NULL - 10 → NULL
1 AND NULL → NULL

Sum, Min, Max, ArgMax, JoinText, Npv, and other Array-reducing functions ignore Null. For example:

Variable A :=
I ▶
1 2 3 4 5
8 NULL 4 NULL 0
Sum(A, I) → 12
Average(A, I) → 4
JoinText(A, I, ', ') → "8, 4, 0"

Graphs also ignore (do not show) any point whose value is Null.

Some Array-reducing functions, notably Sum, Min and Max also accept an optional parameter «IgnoreNaN» to ignore NaN values (which otherwise propagate, i.e. return NaN).

Regression also ignores any data points which have Y = Null, which is useful for missing data.

See Also

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