Operate: matrix multiplication (applicable to blocks).

• mtimes

(require '[kigubkur.op [mtimes :refer [mtimes]]])

The definition and properties for the matrix multiplication operator mtimes is described here.

Examples

Example 1

=> (def A [[2 4]
           [3 2]])
=> (def B [[1 3]
           [-2 5]])
=> (view (mtimes A B))
 [-6 26]
 [-1 19]
Order -> 2 x 2
=> (view (mtimes B A))
 [11 10]
 [11 2]
Order -> 2 x 2

Example 2

=> (def A [[2 3 4]
           [3 4 5]
           [4 5 6]])
=> (def B [[1 -3 5]
           [0 2 4]
           [3 0 5]])
=> (view (mtimes A B))
 [14 0 42]
 [18 -1 56]
 [22 -2 70]
Order -> 3 x 3

Example 3

=> (def A [[1 -2]
           [2 3]])
=> (def B [[1 2 3]
           [2 3 1]])
=> (view (mtimes A B))
 [-3 -4 1]
 [8 13 9]
Order -> 2 x 3

Example 4

=> (def A [[3 -1 3]
           [-1 0 2]])
=> (def B [[2 -3]
           [1 0]
           [3 1]])
=> (view (mtimes A B))
 [14 -6]
 [4 5]
Order -> 2 x 2

Example 5

=> (def A [[2 1]
           [3 2]
           [-1 1]])
=> (def B [[1 0 3]
           [-1 2 1]])
=> (view (mtimes A B))
 [1 2 7]
 [1 4 11]
 [-2 2 -2]
Order -> 3 x 3

Example 6

=> (def r [[7 3 5]])
=> (def c [[-8] [4] [2]])
=> (mtimes r c)
 [[-34]]

Note that mtimes is the matrix multiplication operator therefore it returns a matrix. So although mtimes can produce the dot-product it is returned as a single-element matrix. But if the multiplication order is changed such that the column is the multiplier we see

=> (view (mtimes c r))
 [-56 -24 -40]
 [28 12 20]
 [14 6 10]
Order -> 3 x 3

Block

(require '[kigubkur.construct [blocking :refer [block]]])

=> (def L1 [[1 2 3 4 5 6 7 8 9 10]
            [1 2 3 4 5 6 7 8 9 10]
            [1 2 3 4 5 6 7 8 9 10]
            [1 2 3 4 5 6 7 8 9 10]
            [1 2 3 4 5 6 7 8 9 10]
            [1 2 3 4 5 6 7 8 9 10]
            [1 2 3 4 5 6 7 8 9 10]])
=> (def B1 (block L1 5))
=> (def L2 [[10 9 8 7 6 5 4 3 2 1]
            [10 9 8 7 6 5 4 3 2 1]
            [10 9 8 7 6 5 4 3 2 1]
            [10 9 8 7 6 5 4 3 2 1]
            [10 9 8 7 6 5 4 3 2 1]
            [10 9 8 7 6 5 4 3 2 1]
            [10 9 8 7 6 5 4 3 2 1]
            [10 9 8 7 6 5 4 3 2 1]
            [10 9 8 7 6 5 4 3 2 1]
            [10 9 8 7 6 5 4 3 2 1]])
=> (def B2 (block L2 5))
=> (pprint B1)
 [[{:A11 [[1 2 3 4 5]
          [1 2 3 4 5]
          [1 2 3 4 5]
          [1 2 3 4 5]
          [1 2 3 4 5]],
    :A12 [[6 7 8 9 10]
          [6 7 8 9 10]
          [6 7 8 9 10]
          [6 7 8 9 10]
          [6 7 8 9 10]]}]
  [{:A22 [[6 7 8 9 10]
          [6 7 8 9 10]],
    :A21 [[1 2 3 4 5]
          [1 2 3 4 5]]}]]
=> (pprint B2)
 [[{:A11 [[10 9 8 7 6]
          [10 9 8 7 6]
          [10 9 8 7 6]
          [10 9 8 7 6]
          [10 9 8 7 6]],
    :A12 [[5 4 3 2 1]
          [5 4 3 2 1]
          [5 4 3 2 1]
          [5 4 3 2 1]
          [5 4 3 2 1]]}]
  [{:A22 [[5 4 3 2 1]
          [5 4 3 2 1]
          [5 4 3 2 1]
          [5 4 3 2 1]
          [5 4 3 2 1]],
    :A21 [[10 9 8 7 6]
          [10 9 8 7 6]
          [10 9 8 7 6]
          [10 9 8 7 6]
          [10 9 8 7 6]]}]]
=> (pprint (mtimes B1 B2))
 [[{:A11 [[550 495 440 385 330]
          [550 495 440 385 330]
          [550 495 440 385 330]
          [550 495 440 385 330]
          [550 495 440 385 330]],
    :A12 [[275 220 165 110 55]
          [275 220 165 110 55]
          [275 220 165 110 55]
          [275 220 165 110 55]
          [275 220 165 110 55]]}]
  [{:A21 [[550 495 440 385 330]
          [550 495 440 385 330]],
    :A22 [[275 220 165 110 55]
          [275 220 165 110 55]]}]]