mikera/core.matrix.complex

Complex numerical arrays in Clojure, as an extension to core.matrix

core.matrix.complex

A core.matrix imlementation for complex valued matrices.

Structure

Matrices are implemented as a real/imaginary matrix pairs, and by default operations are outsourced to the underlying matrices. This implies that users can use whatever core.matrix implementations they wish for the underlying matrices.

For example, matrix multiplication can be treated as:

(A + Bi) * (C + Di) = (AC - BD) + (AD + BC)i

Addition is even simpler:

(A + Bi) + (C + Di) = (A + C) + (B + D)i

This demonstrates that in many computational instances, we can benefit from performance characteristics of the underlying matrix implementations. More tailored algorithms and routines can of course be added as needed, as well as functions which would only pertain to complex valued matrices.

core.matrix.complex's Issues

Comparing 0.0 and -0.0 during tests

While writing some tests for the PMatrixOps protocol, I've realized that 0.0 != -0.0 for Java doubles (see this stackoverflow question). Since complex numbers in Clojure ultimately just Java doubles, some tests that I've written which should pass, are reported as having failed.

;; from complex.core
(defn complex-number
  "..."
  ([^double a] (Complex. a))
  ([^double a ^double b] (Complex. a b)))

To get around this, I just add 0.0 but it seems ugly. Can anyone suggest a better way to do this? Is there a comparison function I can use which will map -0.0 to 0.0?

Here is an example of -0.0 showing up where 0.0 makes more sense.

(m/pm 
   (m/inverse 
      (cm/complex-array (m/identity-matrix 3))))
;;=>[[(1.0, -0.0) (0.0, -0.0) (0.0, -0.0)]
;;   [(0.0, -0.0) (1.0, -0.0) (0.0, -0.0)]
;;   [(0.0, -0.0) (0.0, -0.0) (1.0, -0.0)]]

Here is my part of test for the Hermitian Transpose function where I add 0.0 to each matrix element to coerce -0.0 to 0.0:

(deftest herm-transpose
  (is (m/e= (m/add (cm/hermitian-transpose
                     (cm/complex-array (m/identity-matrix 2))) (c/complex-number 0 0))
            (cm/complex-array (m/identity-matrix 2))))
;;...
)

This test returns passes, but I wonder if there is a better (more straightforward) way to do this.

Fix mmul for complex matrices

Current mmul is broken with core.matrix 0.50.0. Needs a fix to ensure that this works with complex numbers.

In the meantime, inner-product works as a replacement