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CODESYS Math Libraries

Introduction

CODESYS Math Libraries includes the Matrix library and the internal FloatingPointUtils library. The Matrix library supports matrices of arbitrary dimensions and basic mathematical operations on them. The following operations are supported: addition, multiplication, solving linear equations, inversion, and calculation of the determinant.

Product Description

The Matrix library provides a data type to define matrices of arbitrary dimension and functions to perform basic operations on matrices.

Data Types and Functions

Matrices are defined through the mtx.Matrix data type. The mtx.Matrix data type saves a matrix as ARRAY of LREAL. The array is in row-major form.

Basic mathematical operations are provided as functions which have 3 matrices as a VAR_IN_OUT argument: result, source, target. For example, the function for matrix addition has the following interface:

(* Adds two matrices : C := A + B. 
* A, B, and C must have identical dimensions.
* Note: A, B, and C may all be the same matrix. *)
FUNCTION AddM : ResultCode
VAR_IN_OUT
   C : Matrix ; (* The result *)
   A : Matrix ; (* The first summand *)
   B : Matrix ; (* The second summand *)
END_VAR

The library offers following mathematical operations:

  • Addition of matrices (element-wise): AddM

  • Subtraction of matrices (element-wise): SubM

  • Multiplication of matrices (element-wise): TimesM

  • Division of matrices (element-wise): RDivideM

  • Scalar multiplication of a matrix: MultMS

  • Multiplication of matrices: MultM

  • Transposition of a matrix: TransposeM

There are also some auxiliary functions for initializing matrices, copying, and accessing elements:

  • Initialize a matrix with an ARRAY of values: InitMatrix

  • Copy ARRAY elements to matrix: CopyElems

  • Copy matrices with same dimension: CopyMatrix

  • Initialize as identity matrix: IdentityMatrix

  • Initialize as zero matrix: ZeroMatrix

  • Read and write elements: Elem, SetElem

More complex operations are also provided:

  • Solve a linear equation A * X = B: SolveLU

  • Invert a quadratic matrix: InvertLU

  • Calculate the determinant of a quadratic matrix: DeterminantLU

  • Determine an LU decomposition (this decomposition serves as the basis for the above three functions): DecomposeLU

Memory Management

The user is responsible for memory management. Matrices will be initialized with a pointer to the memory (via the InitMatrix function). In some cases, it is possible for the user to provide a suitable memory. Furthermore, the auxiliary function blocks MatrixS, ColVectorS, and RowVectorS can be used to initialize matrices with arrays of constant size. They implement the IMatrixAllocator interface which is also available to the user.

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