solve

R2026b

Class: FunctionApproximation.Problem
Namespace: FunctionApproximation

Solve for optimized solution to function approximation problem

Syntax

solution = solve(problem)


Description

solution = solve(problem) solves the optimization problem defined by the FunctionApproximation.Problem object, problem, and returns the optimized result, solution, as a FunctionApproximation.LUTSolution object.

Input Arguments

problem — Optimization problem

FunctionApproximation.Problem

Optimization problem specified as a FunctionApproximation.Problem object defining the functions or Math Function blocks to approximate, or the Lookup Table blocks to optimize, and other parameters and constraints to use during the optimization process.

Output Arguments

solution — Approximation solution

FunctionApproximation.LUTSolution object

Approximation solution, returned as a FunctionApproximation.LUTSolution object.

Examples

Approximate a Math Function

Create a FunctionApproximation.Problem object, specifying a math function to approximate.

problem = FunctionApproximation.Problem('log')

problem = 
  1×1 FunctionApproximation.Problem with properties:

    FunctionToApproximate: @(x)log(x)
           NumberOfInputs: 1
          NumberOfOutputs: 1
               InputTypes: "numerictype(1,16,10)"
         InputLowerBounds: 0.6250
         InputUpperBounds: 15.6250
               OutputType: "numerictype(1,16,13)"
                  Options: [1×1 FunctionApproximation.Options]

Use the solve method to generate an approximation of the function

solution = solve(problem)

Searching for fixed-point solutions.

|  ID |  Memory (bits) | Feasible | Table Size | Breakpoints WLs | TableData WL | BreakpointSpecification |             Error(Max,Current) | 
|   0 |             64 |        0 |          2 |              16 |           16 |             EvenSpacing |     7.812500e-03, 1.020687e+00 |
|   1 |            912 |        0 |         55 |              16 |           16 |             EvenSpacing |     7.812500e-03, 1.687575e-02 |
|   2 |            896 |        0 |         54 |              16 |           16 |             EvenSpacing |     7.812500e-03, 1.737290e-02 |
|   3 |           1776 |        1 |        109 |              16 |           16 |             EvenSpacing |     7.812500e-03, 5.131055e-03 |
|   4 |           1760 |        1 |        108 |              16 |           16 |             EvenSpacing |     7.812500e-03, 5.169212e-03 |
|   5 |           1328 |        1 |         81 |              16 |           16 |             EvenSpacing |     7.812500e-03, 7.723356e-03 |
|   6 |           1120 |        1 |         68 |              16 |           16 |             EvenSpacing |     7.812500e-03, 7.723356e-03 |
|   7 |           1008 |        1 |         61 |              16 |           16 |             EvenSpacing |     7.812500e-03, 7.723356e-03 |
|   8 |            960 |        1 |         58 |              16 |           16 |             EvenSpacing |     7.812500e-03, 7.798586e-03 |
|   9 |            928 |        0 |         56 |              16 |           16 |             EvenSpacing |     7.812500e-03, 1.635354e-02 |
|  10 |            944 |        0 |         57 |              16 |           16 |             EvenSpacing |     7.812500e-03, 1.586526e-02 |
|  11 |            704 |        0 |         42 |              16 |           16 |             EvenSpacing |     7.812500e-03, 2.639592e-02 |
|  12 |            688 |        0 |         41 |              16 |           16 |             EvenSpacing |     7.812500e-03, 2.755002e-02 |
|  13 |            832 |        0 |         50 |              16 |           16 |             EvenSpacing |     7.812500e-03, 1.981209e-02 |
|  14 |            480 |        0 |         28 |              16 |           16 |             EvenSpacing |     7.812500e-03, 5.018443e-02 |
|  15 |            464 |        0 |         27 |              16 |           16 |             EvenSpacing |     7.812500e-03, 5.303877e-02 |
|  16 |            720 |        0 |         43 |              16 |           16 |             EvenSpacing |     7.812500e-03, 2.538244e-02 |
|  17 |            512 |        0 |         30 |              16 |           16 |             EvenSpacing |     7.812500e-03, 4.514940e-02 |
|  18 |            736 |        0 |         44 |              16 |           16 |             EvenSpacing |     7.812500e-03, 2.452795e-02 |
|  19 |            848 |        0 |         51 |              16 |           16 |             EvenSpacing |     7.812500e-03, 1.915421e-02 |
|  20 |             64 |        0 |          2 |              16 |           16 |         EvenPow2Spacing |     7.812500e-03, 7.831517e-01 |
|  21 |            528 |        0 |         31 |              16 |           16 |         EvenPow2Spacing |     7.812500e-03, 4.300416e-02 |
|  22 |            352 |        1 |         11 |              16 |           16 |          ExplicitValues |     7.812500e-03, 7.102135e-03 |
|  23 |            352 |        0 |         11 |              16 |           16 |          ExplicitValues |     7.812500e-03, 1.184082e-02 |
|  24 |            352 |        0 |         11 |              16 |           16 |          ExplicitValues |     7.812500e-03, 1.079952e-02 |
|  25 |            416 |        1 |         13 |              16 |           16 |          ExplicitValues |     7.812500e-03, 7.725618e-03 |
|  26 |           1008 |        1 |         61 |              16 |           16 |         EvenPow2Spacing |     7.812500e-03, 7.723356e-03 |

Best Solution
|  ID |  Memory (bits) | Feasible | Table Size | Breakpoints WLs | TableData WL | BreakpointSpecification |             Error(Max,Current) |
|  22 |            352 |        1 |         11 |              16 |           16 |          ExplicitValues |     7.812500e-03, 7.102135e-03 |

solution = 
  1×1 FunctionApproximation.LUTSolution with properties:

          ID: 22
    Feasible: "true"

You can then use the approximate method to generate a subsystem containing the lookup table approximation.

Approximate Multiple Math Functions

Create a FunctionApproximation.Problem object to optimize two math functions.

funcs = {@(x) sin(x), @(x) exp(-x)};
multiFunctionProblem = FunctionApproximation.Problem(funcs)

multiFunctionProblem = 
  1×1 FunctionApproximation.Problem with properties:

    FunctionToApproximate: {[@(x)sin(x)]  [@(x)exp(-x)]}
           NumberOfInputs: 1
          NumberOfOutputs: 2
               InputTypes: "numerictype(0,16,13)"
         InputLowerBounds: 0
         InputUpperBounds: 6.2832
               OutputType: ["numerictype(1,16,14)"    "numerictype(1,16,14)"]
                  Options: [1×1 FunctionApproximation.Options]

Use the solve method to generate an approximation of the functions.

multiFunctionSolution = solve(multiFunctionProblem)

Searching for fixed-point solutions.

|  ID | Total Memory (bits) | Feasible | Table Size | Breakpoints WLs | TableData WL | BreakpointSpecification | Normalized error (%) | 
|   0 |                  96 |        0 |          2 |              16 |      [16 16] |             EvenSpacing |          12800.0000% |
|   1 |                1536 |        1 |         47 |              16 |      [16 16] |             EvenSpacing |             68.9781% |
|   2 |                1504 |        1 |         46 |              16 |      [16 16] |             EvenSpacing |             58.0406% |
|   3 |                1184 |        1 |         36 |              16 |      [16 16] |             EvenSpacing |             52.3490% |
|   4 |                1152 |        1 |         35 |              16 |      [16 16] |             EvenSpacing |             54.6875% |
|   5 |                 800 |        1 |         24 |              16 |      [16 16] |             EvenSpacing |             79.3817% |
|   6 |                 768 |        1 |         23 |              16 |      [16 16] |             EvenSpacing |             89.0738% |
|   7 |                 416 |        0 |         12 |              16 |      [16 16] |             EvenSpacing |            513.7166% |
|   8 |                 576 |        0 |         17 |              16 |      [16 16] |             EvenSpacing |            241.5638% |
|   9 |                 672 |        1 |         20 |              16 |      [16 16] |             EvenSpacing |             99.9395% |
|  10 |                 608 |        0 |         18 |              16 |      [16 16] |             EvenSpacing |            217.0469% |
|  11 |                 640 |        1 |         19 |              16 |      [16 16] |             EvenSpacing |             99.9688% |
|  12 |                  96 |        0 |          2 |              16 |      [16 16] |         EvenPow2Spacing |          16834.1217% |

Best Solution
|  ID | Total Memory (bits) | Feasible | Table Size | Breakpoints WLs | TableData WL | BreakpointSpecification | Normalized error (%) |
|  11 |                 640 |        1 |         19 |              16 |      [16 16] |             EvenSpacing |             99.9688% |
ans = 
  1×1 FunctionApproximation.LUTSolution with properties:

          ID: 11
    Feasible: "true"

The solve method returns a FunctionApproximation.LUTSolution object that contains the lookup table approximations of both functions.

Version History

Introduced in R2018a