OM Tools

Introduction

omtools (i.e. OpenMDAO Tools) provides an interface to OpenMDAO framework, making it easier for the user to define Group subclasses by alowing the user to write expressions without the need to define a new Component subclass or provide analytic derivatives. The result is that omtools Group subclasses are easier to read and write, with assurance that analytic derivatives for their models are correct.

Benefits

• OpenMDAO Group subclass definitions are easier to read and write.

• Provides stock Component subclasses with pre-defined analytic partial derivatives.

• Prevents unnecessary feedback that can result from manually adding subsystems out of order.

In addition to the above benefits, omtools has a stable API, so any improvements in efficiency for the models that omtools generates are performance improvements for all user defined models. This means that users can update omtools and expect performance improvements to their models without making any changes to their models.

How it Works

omtools stores a graph of nodes and edges representing variables and their dependencies, analyzing the graph, and directing OpenMDAO to construct corresponding Component objects and issuing the necessary connections.

The source code is hosted on GitHub.

Documentation

• Getting Started
  • Basic User Guide
    • Simple Explicit Expressions
    • Simple Explicit Expressions with Subsystems
  • Additional Examples
    • Array Indexing
    • Implicit Relationships
    • Implicit Relationships with Subsystems
    • Expressing Cyclic Relationships with Explicit Outputs
    • Omtools and OpenMDAO Group Examples
      • An Omtools Group within an Omtools Group
      • An Omtools Group within an OpenMDAO Group
      • An OpenMDAO Group within an Omtools Group
• OM Tools Group
• OM Tools Library of Operations
  • Unary Expressions
    • Trigonometric Functions
    • Logarithmic and Exponential Functions
  • Array Operations
    • Minimum
      • Minimum Returning a Scalar
      • Elementwise Minimum
      • Axiswise Minimum
    • Maximum
      • Maximum Returning a Scalar
      • Elementwise Maximum
      • Axiswise Maximum
    • Average
      • Average of a Single Vector
      • Average of a Single Matrix
      • Average of a Single Tensor
      • Average of Multiple Vectors
      • Average of Multiple Matrices
      • Average of Multiple Tensors
      • Average of a Single Matrix along Columns
      • Average of a Single Matrix along Rows
      • Average of Multiple Matrices along Columns
      • Average of Multiple Matrices along Rows
    • Sum
      • Sum of a Single Vector
      • Sum of a Single Matrix
      • Sum of a Single Tensor
      • Sum of Multiple Vectors
      • Sum of Multiple Matrices
      • Sum of Multiple Tensors
      • Sum of a Single Matrix along Columns
      • Sum of a Single Matrix along Rows
      • Sum of Multiple Matrices along Columns
      • Sum of Multiple Matrices along Rows
    • Array Expansion and Contraction
      • Scalar Expansion
      • Array Expansion
    • Reshape
      • Reshape a Tensor to a Vector
      • Reshape a Vector to a Tensor
    • Reorder
      • Reordering a Matrix
      • Reordering a Tensor
  • Vector Algebra
    • Dot
      • Dot Product between Two Vectors
      • Dot Product between Two Tensors Across the First Axis
      • Dot Product between Two Tensors Across the Last Axis
    • Cross
      • Cross Product between Two Vectors
      • Cross Product between Two Tensors
    • Rotation Matrix
      • X-Axis Rotation Matrix
      • Y-Axis Rotation Matrix
      • X-Axis Rotation Tensor For Different Angles in a Tensor
  • Linear Algebra
    • Pnorm
      • Axis Free Pnorm Computation
      • Axiswise Pnorm Computation
    • Transpose
      • Matrix Transpose
      • Tensor Transpose
    • Inner
      • Inner Product between Two Vectors
      • Inner Product between a Tensor and a Vector
      • Inner Product between Two Tensors
    • Outer
      • Outer Product between Two Vectors
      • Outer Product between a Tensor and a Vector
      • Outer Product between Two Tensors
    • Matrix-Vector Multiplication
    • Matrix-Matrix Multiplication
    • Einstein Summation Numpy API
      • Vector-Vector Inner Product using Einsum
      • Vector-Vector Inner Product using Einsum with Sparse Partials
      • Tensor-Vector Inner Product using Einsum
      • Tensor-Vector Inner Product using Einsum with Sparse Partials
      • Vector-Vector Outer Product using Einsum
      • Vector-Vector Outer Product using Einsum with Sparse Partials
      • Tensor-Vector Outer Product using Einsum
      • Tensor-Vector Outer Product using Einsum with Sparse Partials
      • Reordering a Matrix using Einsum
      • Reordering a Matrix using Einsum with Sparse Partials
      • Reordering a Tensor using Einsum
      • Reordering a Tensor using Einsum with Sparse Partials
      • Single Vector Summation using Einsum
      • Single Vector Summation using Einsum with Sparse Partials
      • Single Tensor Summation using Einsum
      • Single Tensor Summation using Einsum with Sparse Partials
      • Multiple Vector Summation using Einsum
      • Multiple Vector Summation using Einsum with Sparse Partials
    • Einstein Summation New API
      • Vector-Vector Inner Product using Einsum
      • Vector-Vector Inner Product using Einsum with Sparse Partials
      • Tensor-Vector Inner Product using Einsum
      • Tensor-Vector Inner Product using Einsum with Sparse Partials
      • Vector-Vector Outer Product using Einsum
      • Vector-Vector Outer Product using Einsum with Sparse Partials
      • Tensor-Vector Outer Product using Einsum
      • Tensor-Vector Outer Product using Einsum with Sparse Partials
      • Reordering a Matrix using Einsum
      • Reordering a Matrix using Einsum with Sparse Partials
      • Reordering a Tensor using Einsum
      • Reordering a Tensor using Einsum with Sparse Partials
      • Single Vector Summation using Einsum
      • Single Vector Summation using Einsum with Sparse Partials
      • Single Tensor Summation using Einsum
      • Single Tensor Summation using Einsum with Sparse Partials
      • Multiple Vector Summation using Einsum
      • Multiple Vector Summation using Einsum with Sparse Partials
• OM Tools Developer API