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.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/matrix.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_matrix.py: Matrix multiplication and Kronecker product. ============================================ .. GENERATED FROM PYTHON SOURCE LINES 5-176 .. raw:: html

.. code-block:: Python from __future__ import annotations from egglog import * egraph = EGraph() class Dim(Expr): """ A dimension of a matix. >>> Dim(3) * Dim.named("n") Dim(3) * Dim.named("n") """ @method(egg_fn="Lit") def __init__(self, value: i64Like) -> None: ... @method(egg_fn="NamedDim") @classmethod def named(cls, name: StringLike) -> Dim: # type: ignore[empty-body] ... @method(egg_fn="Times") def __mul__(self, other: Dim) -> Dim: # type: ignore[empty-body] ... a, b, c, n = vars_("a b c n", Dim) i, j = vars_("i j", i64) egraph.register( rewrite(a * (b * c)).to((a * b) * c), rewrite((a * b) * c).to(a * (b * c)), rewrite(Dim(i) * Dim(j)).to(Dim(i * j)), rewrite(a * b).to(b * a), ) class Matrix(Expr, egg_sort="MExpr"): @method(egg_fn="Id") @classmethod def identity(cls, dim: Dim) -> Matrix: # type: ignore[empty-body] """ Create an identity matrix of the given dimension. """ @method(egg_fn="NamedMat") @classmethod def named(cls, name: StringLike) -> Matrix: # type: ignore[empty-body] """ Create a named matrix. """ @method(egg_fn="MMul") def __matmul__(self, other: Matrix) -> Matrix: # type: ignore[empty-body] """ Matrix multiplication. """ @method(egg_fn="nrows") def nrows(self) -> Dim: # type: ignore[empty-body] """ Number of rows in the matrix. """ @method(egg_fn="ncols") def ncols(self) -> Dim: # type: ignore[empty-body] """ Number of columns in the matrix. """ @function(egg_fn="Kron") def kron(a: Matrix, b: Matrix) -> Matrix: # type: ignore[empty-body] """ Kronecker product of two matrices. https://en.wikipedia.org/wiki/Kronecker_product#Definition """ A, B, C, D = vars_("A B C D", Matrix) egraph.register( # The dimensions of a kronecker product are the product of the dimensions rewrite(kron(A, B).nrows()).to(A.nrows() * B.nrows()), rewrite(kron(A, B).ncols()).to(A.ncols() * B.ncols()), # The dimensions of a matrix multiplication are the number of rows of the first # matrix and the number of columns of the second matrix. rewrite((A @ B).nrows()).to(A.nrows()), rewrite((A @ B).ncols()).to(B.ncols()), # The dimensions of an identity matrix are the input dimension rewrite(Matrix.identity(n).nrows()).to(n), rewrite(Matrix.identity(n).ncols()).to(n), ) egraph.register( # Multiplication by an identity matrix is the same as the other matrix rewrite(Matrix.identity(n) @ A).to(A), rewrite(A @ Matrix.identity(n)).to(A), # Matrix multiplication is associative rewrite(A @ (B @ C)).to((A @ B) @ C), rewrite((A @ B) @ C).to(A @ (B @ C)), # Kronecker product is associative rewrite(kron(A, kron(B, C))).to(kron(kron(A, B), C)), rewrite(kron(kron(A, B), C)).to(kron(A, kron(B, C))), # Kronecker product distributes over matrix multiplication rewrite(kron(A @ C, B @ D)).to(kron(A, B) @ kron(C, D)), rewrite(kron(A, B) @ kron(C, D)).to( kron(A @ C, B @ D), # Only when the dimensions match eq(A.ncols()).to(C.nrows()), eq(B.ncols()).to(D.nrows()), ), ) egraph.register( # demand rows and columns when we multiply matrices rule(eq(C).to(A @ B)).then( A.ncols(), A.nrows(), B.ncols(), B.nrows(), ), # demand rows and columns when we take the kronecker product rule(eq(C).to(kron(A, B))).then( A.ncols(), A.nrows(), B.ncols(), B.nrows(), ), ) # Define a number of dimensions n = egraph.let("n", Dim.named("n")) m = egraph.let("m", Dim.named("m")) p = egraph.let("p", Dim.named("p")) # Define a number of matrices A = egraph.let("A", Matrix.named("A")) B = egraph.let("B", Matrix.named("B")) C = egraph.let("C", Matrix.named("C")) # Set each to be a square matrix of the given dimension egraph.register( union(A.nrows()).with_(n), union(A.ncols()).with_(n), union(B.nrows()).with_(m), union(B.ncols()).with_(m), union(C.nrows()).with_(p), union(C.ncols()).with_(p), ) # Create an example which should equal the kronecker product of A and B ex1 = egraph.let("ex1", kron(Matrix.identity(n), B) @ kron(A, Matrix.identity(m))) rows = egraph.let("rows", ex1.nrows()) cols = egraph.let("cols", ex1.ncols()) egraph.run(20) egraph.check(eq(B.nrows()).to(m)) egraph.check(eq(kron(Matrix.identity(n), B).nrows()).to(n * m)) # Verify it matches the expected result simple_ex1 = egraph.let("simple_ex1", kron(A, B)) egraph.check(eq(ex1).to(simple_ex1)) ex2 = egraph.let("ex2", kron(Matrix.identity(p), C) @ kron(A, Matrix.identity(m))) egraph.run(10) # Verify it is not simplified egraph.check_fail(eq(ex2).to(kron(A, C))) egraph .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.081 seconds) .. _sphx_glr_download_auto_examples_matrix.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: matrix.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: matrix.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_