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A complete list of symbolic utility function can be found here.

Evaluate Mathematica Expression

The original Ben’s toolbox has only one function math for communicating between Matlab and Mathematica. The function, however, does not handle errors during the evaluation and requires to write the complete Mathematica expression in the original format. So I wrote two wrapper functions eval_math and eval_math_fun in FROST to extend this function.

eval_math

This function has the exact same functionality and syntax as the original math function, except it stops if an error is detected during the Mathematica evaluation. This function has three different operating modes:

  • Send Mathematica commands directly, and print out the results. In this case, only one input argument is required. For example:
>> eval_math('N[EulerGamma]') % the input must be a string of valid Mathematica expression

ans =

0.5772156649015329
  • Assign Mathematica numerical results to a Matlab variable. It requires two input arguments: the first one is the string of Mathematica expression, and the second argument is the specific flag: math2matlab. For example:
>> hilbert=eval_math('Inverse[hilbert]', 'math2matlab')

hilbert =

    9.0000  -36.0000   30.0000
  -36.0000  192.0000 -180.0000
   30.0000 -180.0000  180.0000
  • Assign Matlab numerical data to a Mathematica symbolic variable. Three input arguments are required: the first argument is the name of the symbolic variable (in Mathematica), the second one must be the flag matlab2math, and the last argument is the numerical data to given. For example:
>> eval_math('hilbert','matlab2math', hilb(3))

ans =

hilbert

>> eval_math('hilbert')

ans =

{{1., 0.5, 0.333333}, {0.5, 0.333333, 0.25}, {0.333333, 0.25, 0.2}}

Specifically, to quit the Mathematica kernal, run:

>> eval_math('quit')
Mathematica Kernel quitting per your request...

eval_math_fun

This function can be used to call a specific Mathematica function block with input arguments and options. Unlike eval_math, you do not need to write down the whole Mathematica expression and the input argument can be native Matlab data types (numerical, char/string, struct, cell, etc.) The return value is a SymExpression object that stores the evaluated Mathematica expression. The basic syntax of this function is:

eval_math_fun('SomeMathFunc',{input1,input2,..,inputN},options);

where options is a Matlab struct data specifies the options of the Mathematica function that has specific options pattern.

For example:

>> eval_math_fun('RandomReal',{10}) % == eval_math('RandomReal[10]')

ans =
5.703973525491923

>> eval_math_fun('Plus',{2,2})      % == eval_math('2+2')

ans =

4

Data Conversion

These functions convert a specific Matlab variable to a character string represents a valid Mathematica expression.

str2mathstr

It converts a matlab character vector into a character vector of valid Mathematica expression. For example:

>> str2mathstr('hello world')

ans =

"hello world"

If you want to preserve the original form, call the function with ConvertString option being false. For example:

>> str2mathstr('hello world','ConvertString',false)

ans =

hello world

num2mathstr

It converts a numerical scalar number into a character vector of valid numerical number in Mathematica. This function is particularly designed to address inf and integer numbers.

For example:

>> num2mathstr(inf)

ans =

Infinity

>> num2mathstr(23)

ans =

23

>> num2mathstr(23.023)

ans =

23.023000

mat2math

It converts a 2-D numerical matrix into a valid representation of Mathematica matrix.

For example:

>> mat2math(hilb(3))

ans =

{{1, 0.500000, 0.333333},{0.500000, 0.333333, 0.250000},{0.333333, 0.250000, 0.200000}}

cell2tensor

It converts a cell array to valid representation of tensor array in Mathematica.

For example:

>> cell2tensor({'hello',hilb(3),inf})

ans =

{"hello", {{1, 0.500000, 0.333333},{0.500000, 0.333333, 0.250000},{0.333333, 0.250000, 0.200000}}, Infinity}

struct2assoc

It converts a Matlab struct data to a association data representation in Mathematica.

>> b
b = 

  struct with fields:

      text: 'hello world'
    matrix: [3×3 double]
       num: -Inf

>> struct2assoc(b)

ans =


<| "text"->"hello world", "matrix"->{{1, 0.500000, 0.333333},{0.500000, 0.333333, 0.250000},{0.333333, 0.250000, 0.200000}}, "num"->Infinity |>

general2math

This function is a wrapper for the other conversion functions. It detects the data type of the input arguments, and call the appropriate conversion function.

For example:

>> general2math(b)

ans =


<| "text"->"hello world", "matrix"->{{1, 0.500000, 0.333333},{0.500000, 0.333333, 0.250000},{0.333333, 0.250000, 0.200000}}, "num"->Infinity |>


>> general2math({'hello',hilb(3),inf})

ans =

{"hello", {{1, 0.500000, 0.333333},{0.500000, 0.333333, 0.250000},{0.333333, 0.250000, 0.200000}}, Infinity}
Tags: symbolic