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Compute

Category

Transformation

Function

Evaluates an expression on each data point in a specified field or value list.

Syntax


output = Compute(expression, input, ...);

Inputs
Name Type Default Description
expression string none expression to be computed
input field or value list no default input value
... ... ... more input values

Outputs
Name Type Description
output field, value, or value list output values

Functional Details

This module applies an expression to every data value in a field.

expression

is the mathematical expression to be applied to input. Table 1 lists the operators.

input

is the field or value list to which expression is to be applied. If there are more than one, the input fields must be isomorphic (i.e., their hierarchies must match exactly).

A single Compute module can operate on a maximum of 21 input values. In the user interface, the default number of enabled input tabs is two. The default number of enabled input tabs is two. (Tabs can be added to the module icon and removed with the appropriate ...Input Tab options in the Edit pull-down menu of the VPE.)

In the user interface, variables have names and expression does not require quotation marks. If the vector variable is "sample," the vector elements are "sample.x," "sample.y," ... or "sample.0," "sample.1," ....

In the scripting language, the parameters of an expression are indicated by $n, where n is the index of the parameter, and counting begins at 0. The first three components of a vector can be expressed by ".x," ".y," and ".z," or by ".0," ".1," and ".2." The syntax for creating a vector from multiple inputs is [$0, $1, $2, ... ], where the commas separators are required.

Thus, in the user interface the expression used to add the value 3 to every data value of the input field would be "a + 3.," while in the scripting language it would be "$0 + 3."

Multiple expressions can be entered if they are separated by semicolons; the final expression is used as the output. For example, "temp=a.x; sin(temp)" is equivalent to "sin(a.x)".

Compute uses C-language-style order of precedence for mathematical operations.

Operations applied to invalid elements of fields typically result in invalid elements. (For more information, see "Invalid Positions and Invalid Connections Components" in the IBM Visualization Data Explorer User's Guide.) For example, if at a particular element field "a" and "c" are valid, but field "b" is not, "a+b" is invalid, and "a? b: c" is valid only if "a" is 0; otherwise, it is invalid. An exception is the "invalid" function, which returns the integer 1 if the entry is invalid and 0 otherwise.

Operations such as multiplying a vector by a scalar have the expected effect: each element of the vector is multiplied by the scalar. Likewise, the addition of two equal-length vectors or equal-size matrices results in an element-by-element sum. The Compute module defines the multiplication (*) of two equal-length vectors as an element-by-element multiplication (as opposed to the dot product). Other operations, such as the sine of a vector, are defined similarly.

Constants may be specified as double precision by using scientific notation with "d" indicating the exponent (e.g., 1d0 is double-precision 1).

Note that you can convert a "ref" type invalid component (see "Invalid Positions and Invalid Connections Components" in IBM Visualization Data Explorer User's Guide) using the expression "byte (invalid (a))". Then use Replace to substitute this new array into the original field as the "invalid positions" or "invalid connections" component.


Table 1. Operators for the Compute Module
Functions Types of Operands
Trigonometric Functions (argument in radians)
     sin(a), cos(a), tan(a), asin(a), acos(a), atan(a), atan2(a, b)   float, double

 

Hyperbolic Functions
     sinh(a), cosh(a), tanh(a)   float, double

 

Logarithmic Functions
     log(a), In(a) (natural logarithm), log10(a)     
     (log base 10--see Note 1), exp(a)

 

 float, double  
IEEE inquiry functions
     isnan(a), finite(a)   float, double

 

Unary Functions
     +a, -a (negation)   any type

 

Binary Functions
     a+b, a-b, a*b, a/b, a%b (modulus--see Note 1),     
     a^b or a**b (exponentiation--see Note 4)

 

 any type  
Vector Functions (see Note 1)
     a dot b or dot(a, b)   float vector  
     a cross b or cross(a,b)   float 3-vector  
     mag(a)   double, float vector  
     norm(a)   float vector

 

Miscellaneous Functions
     sqrt(a)   float, double, complex  
     pow(a, b) (see Note 4)   float, double, complex  
     abs(a) (see Note 2)   double, float, integer, complex  
     arg(a)   complex only  
     sign(a)   all real types  
     min(a, b, ...), max(a, b, ...)   scalar  
     invalid(a) (see Note 5)   any type  
     random(a,seed) (see note 8)   produces random values in the range 0<=r<1 for each item in a.

 

Type Manipulation Functions
     int(a), float(a), byte(a), char(a), double(a), short(a),   float, integer, byte,  
      sbyte, ubyte, ushort, uint (see Note 6)    short, double  
     trunc(a), floor(a), ceil(a), rint(a)   float, double  
     complex(a,b) or complex(a),   float, integer, byte, short,   double  
     real(a)   complex only  
     imag(a)   complex only

 

Vector Construction
     [a, b, ...]   any type

 

Vector Selection Functions
     a.x or a.0, a.y or a.1, and so on   vector  
     select(a,b) (selects bth element of a,     
      where element is of rank r-1)   a is a vector, b is an integer

 

Conditional Functions
     a?b:c
if a != 0, then b, else c. (b and c must be of the same type.) Expressions b and c are always evaluated, and the output value depends on the value of a.

 

 a is an integer  
Logical Operations
     binary: <, >, <=, >= (true = 1; false = 0)   any scalar type  
     binary: ==, !=   any type  
     Unary: ! (not), binary: && (and), || (or)   integer

 

Bitwise Operations
     and(a,b), xor(a,b), or(a,b), not(a) (one's complement)   byte, int

 

String functions (see Note 7)
     strcmp(a,b)
compares strings a and b and returns 0 if a==b, a negative integer if a<b, and a positive integer if a>b
stricmp is identical to strcmp except that it ignores case  
 strings  
     strlen(a)
returns the length of string a  
 string  
     strstr(a,b)
finds substring b in string a and returns 1-based offset of b in a. Thus strstr('artist','art') = 1 strstr('artist','picasso') = 0 strstr('monet','one') = 2
stristr(a,b) is identical to strstr except that it ignores case  
 strings

 

Notes:

  1. The vector functions, modulus function, and log10() function do not accept complex numbers as arguments.

  2. Given an integer or floating-point value, the abs() function yields the absolute value. Given a complex number, the abs() function yields a real absolute value.

  3. If a string is passed as a parameter to Compute, it is treated as an array of bytes, with its values being the ASCII values of the string elements.

  4. This function returns a floating-point value if inputs are floating point or integer. It returns a complex if the first input is complex.

  5. Returns integer 1 if entity is marked invalid, and 0 otherwise.

  6. Byte and char are same as ubyte.

  7. Strings can be passed into Compute as the data component or directly from String and StringList interactors. Strings can also be specified in the Compute expression directly by enclosing them in single quotes. A single quote character is represented by a pair of single quotes. Thus if a is the string "can't", then strcmp(a,'can''t') = 0.

  8. The random number generator will be seeded by the integer seed. If a corresponds to a group then each member of a will be seeded by seed+n, where n corresponds to the member's enumerated location in a. This results in repeatable behavior even when a composite field is being processed in parallel on an SMP machine. To generate different random results, use a different seed.

To operate on a component other than "data," use the Mark and Unmark modules together with Compute.

A single Compute module can operate on a maximum of 21 ...Input values. The default number of enabled input tabs is two. (Tabs can be added to the module icon and removed with the appropriate ...Input Tab options in the Edit pull-down menu of the VPE.)
Note:Other than a divide by zero, Compute operations are unchecked.

Components

Modifies the "data" and "invalid positions" or "invalid connections" components. All other components are propagated to the output.

Script Language Examples

  1. The Compute module converts all the temperature data to Fahrenheit.
    tempf = Compute("$0*(9.0/5.0) + 32", tempc);
    ·
    

  2. The input field is a vector field of dimension 9. The output field is scalar, consisting of the sixth component of the input field.
    new_field = Compute("$0.5",field);
    

  3. The input field is a vector field, and the output field is also a vector field, with the x component multiplied by 2.
    new_field = Compute("[2*$0.x, $0.y, $0.z]", field);
    
    or
    new_field = Compute("[2, 1, 1]*$0", field);
    

  4. Here field1 is a vector field and field2 and field3 are scalar. Therefore, the output field will have a data component equal (on a point-by-point basis) to the magnitude of field1 added to the quantity field2 divided by 4.5 times field3.
    new_field = Compute("mag($0) + $1/($2*4.5)", field1, field2, field3);
    

  5. The Mark module to place the "positions" component of the 2-dimensional object slice in the "data" component, allowing Compute to operate on the positions. The formula string is assigned to function to simplify the call to Compute and is equivalent to the following formula for converting slice positions to 2-dimensional vectors: [ x, y, z ] = [ sin ( 2 π × ((x + 1) / 3.9) ) , y , - cos ( 2 π × ((x + 1) / 3.9) )]. When the computation is done, the Unmark module replaces the original "data" component for use in warped. The resulting positions are warped onto the shape of a cylinder.
    ·
    slice = Slice(electrondensity, "z", 5);
        // Mark the positions so that they can be computed on
        // The original x positions go from -1 to 2.9
        // The original y positions go from -3 to 2.9
    markedslice = Mark(slice,"positions");
        // Warp the positions onto the shape of a cylinder
    pi = 3.14159;
    exp = "[sin(2*$1*($0.x+1)/3.9), $0.y, -cos(2*$1*($0.x+1)/3.9)]";
    warped = Compute(exp, markedslice, pi);
        // Unmark the warped positions, returning them to the positions
        // component
    warped = Unmark(warped, "positions");
    ·
    

  6. This example differs from the previous one in that the exp) function warps the positions onto a double cone shape, by implementing the following formula: [ x, y, z ] = [ y × sin( 2 π × ((x + 1) / 3.9) ) , y , -y × cos ( 2 π × ((x + 1) / 3.9) ) ]
    ·
        // Now warp the positions onto the shape of a doubled cone
        // by multiplying the x and z positions by the original
        // y value, which goes from -3 to 2.9
    exp = "[$0.y*sin(2*$1*($0.x+1)/3.9),$0.y, -$0.y*cos(2*$1*($0.x+1)/3.9)]";
    warped = Compute(exp, markedslice, pi);
        // Unmark the warped positions, returning them to the positions
        // component
    warped = Unmark(warped, "positions");
    ·
    

Example Visual Programs

Many of the example visual programs use Compute, including:

ComputeOnData.net
DataDrivenInteractors.net
PlotTwoLines.net
WarpingPositions.net

See Also

 Mark,  Unmark


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