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visual3d:documentation:pipeline:expressions:mathematical_operators [2024/06/19 12:49] – sgrangervisual3d:documentation:pipeline:expressions:mathematical_operators [2024/11/04 20:30] (current) – wikisysop
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-{{{{===== contents =====+====== Mathematical Operators  ======
  
 +The [[visual3d:documentation:pipeline:expressions:expressions_overview|Evaluate_Expression]] command can be used to evaluate arbitrary mathematical expressions. Use the following characters for your mathematical operators. 
  
 +**Arithmetic Operators** 
 +  * [[#Plus|Plus ]]
 +  * [[#Minus|Minus]]
 +  * [[#Multiply|Multiply]]
 +  * [[#Divide|Divide]]
 +  * [[#Power|Power]]
  
-  * [[#plus|1 plus]] +**Boolean Operators**  
-  * [[#minus|2 minus]] +  * [[#Logical_Or|Logical OR]] 
-  * [[#multiply|3 multiply]] +  * [[#Logical_And|Logical AND]] 
-  * [[#divide|4 divide]] +  * [[#Using_the_Adjective_NOT|The Adjective NOT]]
-  * [[#power|5 power]] +
-  * [[#logical_or|6 logical_or]] +
-  * [[#logical_and|7 logical_and]] +
-  * [[#equals|8 equals]] +
-  * [[#not_equals|9 not_equals]] +
-  * [[#using_the_adjective_not|10 using the adjective not]] +
-  * [[#less_than|11 less_than]] +
-  * [[#less_than_or_equals|12 less_than_or_equals]] +
-  * [[#greater_than|13 greater_than]] +
-  * [[#greater_than_or_equals|14 greater_than_or_equals]]+
  
 +**Comparison Operators**
 +  * [[#Equals|Equals]]
 +  * [[#Not_Equals|Not Equals]]
 +  * [[#Less_Than|Less Than]]
 +  * [[#Less_Than_Or_Equals|Less Than Or Equals]]
 +  * [[#Greater_Than|Greater Than]]
 +  * [[#Greater_Than_Or_Equals|Greater Than Or Equals]]
  
-===== plus =====+Note: Visual3D parses the mathematical operators before it parses the signal names. If you have a signal name that contains a mathematical operator (e.g. R-Foot1), Visual3D will probably not be able to parse the equation expression properly.
  
-note: pipeline command parameters use + as delimiter+===== Arithmetic Operators =====
  
-if the user wants to use an expression containing a + in a command parameter that allows multiple signals, visual3d will likely interpret this plus sign incorrectly.+Arithmetic operations can generally be performed using syntax that is similar to that found in a variety of programming and scripting languages.
  
-the workaround is to use a mathematical function add() to express the addition.+==== Plus ====
  
-**add(a,b)** -- adds two expressions. +Addition is accomplished using the + character. An alternative syntax is **add(a,b)** where a and b are expressions that evaluate to numbers. 
-===== minus =====+
  
-===== multiply =====+NOTE: Pipeline command parameters use the + character as a delimiter. If the user wants to use an expression containing a + in a command parameter that allows multiple signals, then Visual3D will likely interpret this plus sign incorrectly. In this case the **add(a,b)** syntax should be used.
  
-===== divide =====+<code> 
 +2 + 3 = 5 
 +add(2,3) = 5 
 +</code>
  
-===== power =====+==== Minus ====
  
-===== logical_or =====+Subtraction is accomplished using the - character.
  
-logical or +<code> 
-===== logical_and =====+3 - 2 = 1 
 +</code>
  
-logical and +==== Multiply ====
-===== equals =====+
  
-**= or ==** - boolean operator //equals// +Multiplication is accomplished using the * character.
-example: comparing a model metric with a string+
  
-consider a model metric that is defined as a string. +<code> 
-**set_model_metric** +3 * 2 = 6 
-! /calibration_file= +</code>
-/metric_name=test +
-/metric_value="ttt" +
-**;** +
-now compare it to the text string "ttt" +
-**evaluate_expression** +
-/expression=model::metric::test="ttt" +
-/result_name=scott +
-/result_type=metric +
-! /result_folder=processed +
-**;** +
-the text strings should be equal so the resulting signal contains a 1 +
-===== not_equals =====+
  
-**<> or ><** - boolean operator "not equals" +==== Divide ====
-===== using the adjective not =====+
  
-not can be used with the logical and and logical or+Division is accomplished using the / character.
  
-example: given a workspace containing 3 trials (*trial1.c3d, *trial2.c3d, and *trial3.c3d)+<code> 
 +6 / 3 = 2 
 +</code>
  
-all trials are assigned a tag labeled walk+==== Power ====
  
-  * trial1.c3d is also assigned a tag labeled bad+Exponentiation is accomplished using the ^ character.
  
-[[visual3d:documentation:pipeline:file_commands:select_active_file|select_active_file]] +<code> 
-/file_name=walk +2^3 = 8 
-/query=bad +</code>
-**;** +
-this command results in *trial1.c3d being active+
  
-[[visual3d:documentation:pipeline:file_commands:select_active_file|select_active_file]] +===== Boolean Operators =====
-/file_name=walk +
-/query=not(bad) +
-**;** +
-this command results in *trial2.c3d and *trial3.c3d being active.+
  
-===== less_than =====+Boolean operators deal with boolean values, such as TRUE and FALSE. These are represented numerically as 1 (TRUE) and 0 (FALSE).
  
-**<** boolean operator //less than//+==== Logical OR ====
  
-**example**+The Logical OR operator is signified by the | character. It takes two boolean values as input and returns TRUE if either of the input values is TRUE.
  
-given two signals +<code> 
-target::original::rft1 +FALSE | FALSE = FALSE 
-target::original::lft1 +FALSE | TRUE = TRUE 
-use the boolean operator < to identify when the z component of rft1 is less than the z component of lft1 +TRUE | FALSE = TRUE 
-**evaluate_expression** +TRUE | TRUE = FALSE 
-/expression= target::original::rft1::z < target::original::lft1::z +</code> 
-/result_name=rft1_greater + 
-/result_type=derived +==== Logical AND ==== 
-/result_folder=processed + 
-**;** +The Logical AND operator is signified by the & character. It takes two boolean values as input and returns TRUE when both input values are TRUE. 
-the output signal will be 1 when rft1::z is less than lft1::z and 0 otherwise + 
-**example - foot clearance**+<code> 
 +FALSE | FALSE = FALSE 
 +FALSE | TRUE = FALSE 
 +TRUE | FALSE = FALSE 
 +TRUE | TRUE = FALSE 
 +</code> 
 + 
 +==== The Adjective NOT ==== 
 + 
 +The logical adjective NOT can be used with both the logical AND and logical OR operators. It takes one boolean value as input and negates that boolean value. 
 + 
 +<code> 
 +NOT(FALSE) = TRUE 
 +NOT(TRUE) = FALSE 
 +</code> 
 + 
 +===Example=== 
 + 
 +Given a workspace containing 3 trials (*trial1.c3d, *trial2.c3d, and *trial3.c3d). 
 +  * All trials are assigned a TAG labeled WALK 
 +  * trial1.c3d is also assigned a TAG labeled BAD 
 + 
 +<code> 
 +Select_Active_File 
 +/FILE_NAME=WALK 
 +/QUERY=BAD 
 +; 
 +</code> 
 + 
 +This command results in *trial1.c3d being active 
 + 
 +<code> 
 +Select_Active_File 
 +/FILE_NAME=WALK 
 +/QUERY=NOT(BAD) 
 +; 
 +</code> 
 + 
 +This command results in *trial2.c3d and *trial3.c3d being active. 
 + 
 +===== Comparison Operators ===== 
 + 
 +Comparison operators take two inputs of the same type and return a boolean value. 
 + 
 +==== Equals ==== 
 + 
 +Equality is tested using either = or ==. It returns TRUE if the two inputs have the same value and FALSE if they do not. 
 + 
 +===Example=== 
 + 
 +Consider a model metric that is defined as a string and compare it to an explicitly defined string. 
 + 
 +<code> 
 +Set_Model_Metric 
 +! /CALIBRATION_FILE= 
 +/METRIC_NAME=TEST 
 +/METRIC_VALUE="TTT" 
 +; 
 + 
 +Evaluate_Expression** 
 +/EXPRESSION=MODEL::METRIC::TEST="TTT" 
 +/RESULT_NAME=SCOTT 
 +/RESULT_TYPE=METRIC 
 +! /RESULT_FOLDER=PROCESSED 
 +; 
 +</code> 
 + 
 +The text strings are equal, so the resulting signal contains a 1 (indicating TRUE). 
 + 
 +==== Not Equals ==== 
 + 
 +Non-equality is tested using either <> or ><. Its behaviour is opposite that of equality. 
 + 
 +If (a==b) is TRUE then (a<>b) is FALSE. Similarly, if (a==b) is FALSE, then (a<>b) is TRUE. 
 + 
 +==== Less Than ==== 
 + 
 +We can test is one value is less than another using the < character. 
 + 
 +===Example=== 
 + 
 +Given two signals TARGET::ORIGINAL::RFT1 and TARGET::ORIGINAL::LFT1, use the Boolean operator < to identify when the Z component of RFT1 is less than the Z component of LFT1. 
 + 
 +<code> 
 +Evaluate_Expression 
 +/EXPRESSION= TARGET::ORIGINAL::RFT1::Z < TARGET::ORIGINAL::LFT1::Z 
 +/RESULT_NAME=RFT1_GREATER 
 +/RESULT_TYPE=DERIVED 
 +/RESULT_FOLDER=PROCESSED 
 +; 
 +</code> 
 + 
 +The output signal will be 1 when RFT1::Z is less than LFT1::Z and 0 otherwise 
 + 
 +===Example - Foot Clearance=== 
 + 
 +Heel and toe clearance are defined by two paths. It is possible to model "foot clearance" as the lower value of the heel and toe clearance values at each frame. 
 +{{:heel_toe_clearance.jpg}} 
 + 
 +Here is a simplified test of this. First, make the Global Workspace Active. Then, create 2 toy signals and calculate a third signal containing the lower value of the two toy signals. 
 + 
 +<code> 
 +Evaluate_Expression 
 +/EXPRESSION=LIST(1,2,3,4,5) 
 +! /SIGNAL_TYPES= 
 +! /SIGNAL_FOLDER=ORIGINAL 
 +! /SIGNAL_NAMES= 
 +! /SIGNAL_COMPONENTS= 
 +/RESULT_TYPES=DERIVED 
 +/RESULT_FOLDERS=PROCESSED 
 +/RESULT_NAME=SIGNAL1 
 +! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE 
 +; 
 + 
 +Evaluate_Expression 
 +/EXPRESSION=LIST(5,4,3,2,1) 
 +! /SIGNAL_TYPES= 
 +! /SIGNAL_FOLDER=ORIGINAL 
 +! /SIGNAL_NAMES= 
 +! /SIGNAL_COMPONENTS= 
 +/RESULT_TYPES=DERIVED 
 +/RESULT_FOLDERS=PROCESSED 
 +/RESULT_NAME=SIGNAL2 
 +! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE 
 +;
  
-given the following situation. heel and toe clearance are defined by two paths. 
-one might consider foot clearance to be the lower value of the heel and toe clearance values at each frame. 
-heel_toe_clearance.jpg 
-here is a simplified test of this 
-make the global workspace active. 
-create 2 signals as follows 
-**evaluate_expression** 
-/expression=list(1,2,3,4,5) 
-! /signal_types= 
-! /signal_folder=original 
-! /signal_names= 
-! /signal_components= 
-/result_types=derived 
-/result_folders=processed 
-/result_name=signal1 
-! /apply_as_suffix_to_signal_name=false 
-**;** 
-**evaluate_expression** 
-/expression=list(5,4,3,2,1) 
-! /signal_types= 
-! /signal_folder=original 
-! /signal_names= 
-! /signal_components= 
-/result_types=derived 
-/result_folders=processed 
-/result_name=signal2 
-! /apply_as_suffix_to_signal_name=false 
-**;** 
 !create a new signal that is the lower value of the two signals !create a new signal that is the lower value of the two signals
 +Evaluate_Expression
 +/EXPRESSION=(DERIVED::PROCESSED::SIGNAL1<=DERIVED::PROCESSED::SIGNAL2)*DERIVED::PROCESSED::SIGNAL1
 ++(DERIVED::PROCESSED::SIGNAL2<DERIVED::PROCESSED::SIGNAL1)*DERIVED::PROCESSED::SIGNAL2
 +! /SIGNAL_TYPES=
 +! /SIGNAL_FOLDER=ORIGINAL
 +! /SIGNAL_NAMES=
 +! /SIGNAL_COMPONENTS=
 +/RESULT_TYPES=DERIVED
 +/RESULT_FOLDERS=PROCESSED
 +/RESULT_NAME=SIGNAL_LOWER
 +! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
 +;
 +</code>
 +
 +{{:heel_toe_clearance2.jpg}}
 +
 +==== Less Than Or Equals ====
 +
 +This boolean operator uses one of the following syntaxes: <= or =<.
 +
 +The expression (a <= b) is equivalent logically to ((a < b) | (a == b)).
 +
 +===Example===
 +
 +Given two signals TARGET::ORIGINAL::RFT1 and TARGET::ORIGINAL::LFT1, use the Boolean operator <= or the boolean operative =< to identify when the Z component of RFT1 is less than or equal to the Z component of LFT1.
 +
 +<code>
 +Evaluate_Expression
 +/EXPRESSION= TARGET::ORIGINAL::RFT1::Z <= TARGET::ORIGINAL::LFT1::Z
 +/RESULT_NAME=RFT1_GREATER
 +/RESULT_TYPE=DERIVED
 +/RESULT_FOLDER=PROCESSED
 +;
 +</code>
 +
 +The output signal will be 1 (indicating TRUE) when RFT1::Z is less than or equal to LFT1::Z and 0 (indicating FALSE) otherwise.
 +
 +==== Greater Than ====
 +
 +We can test is one value is less than another using the > character.
  
-**evaluate_expression** +===Example===
-/expression=(derived::processed::signal1<=derived::processed::signal2)*derived::processed::signal1 +
-+(derived::processed::signal2<derived::processed::signal1)*derived::processed::signal2 +
-! /signal_types= +
-! /signal_folder=original +
-! /signal_names= +
-! /signal_components= +
-/result_types=derived +
-/result_folders=processed +
-/result_name=signal_lower +
-! /apply_as_suffix_to_signal_name=false +
-**;** +
-heel_toe_clearance2.jpg +
-===== less_than_or_equals =====+
  
-! style="text-align:left;" |      **<=** or **=<** boolean operator //less than or equal to//+Given two signals TARGET::ORIGINAL::RFT1 and TARGET::ORIGINAL::LFT1, use the Boolean operator > to identify when the Y component of RFT1 is greater than the Y component of LFT1.
  
-example:+<code> 
 +Evaluate_Expression 
 +/EXPRESSION= TARGET::ORIGINAL::RFT1::Y > TARGET::ORIGINAL::LFT1::Y 
 +/RESULT_NAME=RFT1_GREATER 
 +/RESULT_TYPE=DERIVED 
 +/RESULT_FOLDER=PROCESSED 
 +; 
 +</code>
  
-given two signals +The output signal will be 1 (indicating TRUE) when RFT1::Y is greater than LFT1::Y and 0 (indicating FALSE) otherwise.
-target::original::rft1 +
-target::original::lft1 +
-use the boolean operator <= or the boolean operative =< to identify when the z component of rft1 is less than or equal to the z component of lft1 +
-**evaluate_expression** +
-/expression= target::original::rft1::z <= target::original::lft1::z +
-/result_name=rft1_greater +
-/result_type=derived +
-/result_folder=processed +
-**;** +
-the output signal will be 1 when rft1::z is less than or equal tolft1::z and 0 otherwise +
-===== greater_than =====+
  
-**>** boolean operator //greater than//+==== Greater Than Or Equals ====
  
-example:+This boolean operator uses one of the following syntaxes: >= or =>.
  
-given two signals +The expression (a >= b) is equivalent logically to ((a > b) | (a == b)).
-target::original::rft1 +
-target::original::lft1 +
-use the boolean operator > to identify when the y component of rft1 is greater than the y component of lft1 +
-**evaluate_expression** +
-/expression= target::original::rft1::y > target::original::lft1::y +
-/result_name=rft1_greater +
-/result_type=derived +
-/result_folder=processed +
-**;** +
-the output signal will be 1 when rft1::y is greater than lft1::y and 0 otherwise +
-===== greater_than_or_equals =====+
  
-**>=** boolean operator //greater than or equals// 
  
  
-}}}} 
visual3d/documentation/pipeline/expressions/mathematical_operators.1718801397.txt.gz · Last modified: 2024/06/19 12:49 by sgranger