Dataframe

Minimalist Panda-like library in C++ which allows you to create and manage series and dataframes. It also provides math functions to play with Series.

Compared to Panda, we have some differences since our main consern is linear algebra.

Requirements

• C++23
• cmake

Main functionalities are:

• Compared to Panda, each item of a Serie is either a scalar (i.e., a number) or an array of scalars... and that's it!. This is it because our main concern is linear algebra. Tensors are stored as packed array, hense the notion of itemSize.

  • A first example is given by a itemSize=6 with dimension=3 which represents a symmetric matrix of dimension 3 (6 coefficients)
  • A second exmaple is given by a itemSize=3 with dimension=3 which represents a vector of dimension 3 (3 coefficients)
  • However, the same last example but with itemSize=2 represents a matrix of dimension 2 (still 3 coefficients).
  • When itemSize=9 and dimension=3, we have a non-symmetric matrix of dimension 3 (9 coefficients)

• Serie of scalar items or n-dim items

• Mathematical functions on Serie

• Decomposition of a Serie into a new Serie (virtual Serie) using the Manager and some Decomposers

• Functional programming (no mutating, less bugs, very simple to use)

• Very simple API for both Serie and Dataframe

• Can be easily extended for mathematical functions such as eigenValues or eigenVectors on a Serie

Not yet tested under Windows, but will have to add export for shared library.

Organization of this lib

• Main files are Dataframe and Serie
• Folders:
  • attributes provides a way of decomposing any Serie into other Serie. For example, a Serie with itemType=6 might represent symmetric matrices 3x3. Therefore, attributes (i.e., possible decomposed Series) can be :
    • Components of the matrices
    • Eigen vectors
    • Eigen values
    • ...
  • operations provides some examples of what is possible to do with Serie in term of linear algebra, statistics etc... (see also the dataframe in TypeScript). It also provides some examples of functions to create Series from geometry, geophysics and so on...

Compilation

Create a build directory, go inside and type

cmake .. && make -j12

Running unit tests

NOTE: The internal cmake test is used to perform unit testing.

In the same directory as for the compilation (i.e., the build directory), only type

ctest

or

make test

API

Example 1

df::Serie a(3, {1,2,5,  3,4,9}) ; // first param is the item size of the Serie: 3
df::Serie b(3, {4,3,3,  2,1,0}) ;

df::Serie dot = df::dot(a, b) ;
dot.dump();

Example 2

Performs a weighted sum of Series ;-)

Constraints:

• All Serie must have the same count()
• All Serie must have the same itemSize()
• Size of weights must be equal to the size of array of the provided Series

df::Serie a(2, {1,2,  3,4}) ;
df::Serie b(2, {4,3,  2,1}) ;
df::Serie c(2, {2,2,  1,1}) ;

// Performs s = 2*a + 3*b + 4*c
auto s = df::weigthedSum({a, b, c}, {2, 3, 4}) ;

Example 3

Eigen

df::Serie s(6, {....}) ; // symmetric 3x3 matrices => 6 coefs
auto vectors = df::eigenVectors(s) ; // and that's it!

// Display
vectors.forEach([](const Array& v, uint32_t index) {
    std::cout << "eigen vector at index " 
              << std::to_string(index)
              << " is: " << v  << std::endl ;
});

Example 4: Chaining...

df::Serie a(2, {1,2,  3,4}) ;
df::Serie b(2, {4,3,  2,1}) ;
df::Serie c(2, {2,2,  1,1}) ;

auto s = df::weigthedSum({a, b, c}, {2, 3, 4})
    .map([](const Array& arr, uint32_t) {
        return std::sqrt( pow(arr[0],2) + pow(arr[1],2) + pow(arr[2],2) );
    })
    .forEachScalar([](double v, uinit32_t index) {
        std::cout << index << ": " << v << std::endl ;
    }) ;

Example 5: Attributes

df::Dataframe dataframe;
dataframe.add("positions", Serie(3, {...})); // geometry
dataframe.add("indices", Serie(3, {...})); // topology (triangles)
dataframe.add("S", Serie(6, {...})); // Stresses (sym 3x3 matrices)

df::Manager mng(dataframe, {
    Coordinates(),
    Components(),
    EigenValues(),
    EigenVectors(),
    Normals("n")
])

// Gather all possible scalar serie names
console.log( mng.names(1) )
// Will display: Sxx, Sxy, Sxz, Syy, Syz, Szz, S1, S2, S3, x, y, z, nx, ny, nz

// Gather all possible vector serie names
console.log( mng.names(3) )
// Will display: S1, S2, S3, n

// Gather all possible symmetric matrix serie names
console.log( mng.names(6) )
// Will display: S

Serie scalarS1 = mng.serie(1, 'S1') // eigen value S1 for all items
Serie vectorS1 = mng.serie(3, 'S1') // eigen vector S1 for all items

Licence

MIT

Contact

fmaerten@gmail.com