Operate: subtraction (applicable to blocks).

• minus

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

With the exception that subtraction is not commutative the applicable cases are basically the same as those described for the plus operator. Thus,

Note that in (minus A B) is equal to A “−” B where A is the minuend and B is the subtrahend.

Case 1: scalar s is the minuend or the subtrahend

Case 2: between row r and column c

Case 3: between row r and matrix A

Case 4: between column c and matrix A

Case 5: blocks of same order

Case 6: between different ordered block-row and block-column

Case 6.1; mother of block-column is a column matrix (vector)

Case 6.2; mother of block-column is a matrix

Case 7: between different ordered block-matrix and block-row

Case 8: between different ordered block-matrix and block-column

Examples

Scalar as minuend or subtrahend

Scalar subtracted from scalar

=> (minus 3 2)
 1

Scalar subtracted from row matrix

=> (def r1 [[1 2 3 4]])
=> (def r2 [[4 3 2 1]])
=> (view r1)
 [1 2 3 4]
Order -> 1 x 4
=> (view (minus r1 2))
 [-1 0 1 2]
Order -> 1 x 4

Subtraction is not commutative.

=> (view (minus 2 r1))
 [1 0 -1 -2]
Order -> 1 x 4

Scalar subtracted from column matrix

=> (def c1 [[1][2][3][4]])
=> (def c2 [[4][3][2][1]])
=> (view c1)
 [1]
 [2]
 [3]
 [4]
Order -> 4 x 1
=> (view (minus c1 2))
 [-1]
 [0]
 [1]
 [2]
Order-> 4 x 1

Subtraction is not commutative.

=> (view (minus 2 c1))
 [1]
 [0]
 [-1]
 [-2]
Order -> 4 x 1

Scalar subtracted from matrix

=> (def M1 [[1 2] [3 4]])
=> (def M2 [[4 3] [2 1]])
=> (view M1)
 [1 2]
 [3 4]
Order -> 2 x 2
=> (view (minus M1 2))
 [-1 0]
 [1 2]
Order -> 2 x 2

Subtraction is not commutative.

=> (view (minus 2 M1))
 [1 0]
 [-1 -2]
Order -> 2 x 2

Scalar subtracted from block matrix

(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]])
=> (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 (minus B1 2))
 [[{:A11 [[-1 0 1 2 3]
          [-1 0 1 2 3]
          [-1 0 1 2 3]
          [-1 0 1 2 3]
          [-1 0 1 2 3]],
    :A12 [[4 5 6 7 8]
          [4 5 6 7 8]
          [4 5 6 7 8]
          [4 5 6 7 8]
          [4 5 6 7 8]]}]
  [{:A22 [[4 5 6 7 8]
          [4 5 6 7 8]],
    :A21 [[-1 0 1 2 3]
          [-1 0 1 2 3]]}]]

Subtraction is not commutative.

=> (pprint (minus 2 B1))
 [[{:A11 [[1 0 -1 -2 -3]
          [1 0 -1 -2 -3]
          [1 0 -1 -2 -3]
          [1 0 -1 -2 -3]
          [1 0 -1 -2 -3]],
    :A12 [[-4 -5 -6 -7 -8]
          [-4 -5 -6 -7 -8]
          [-4 -5 -6 -7 -8]
          [-4 -5 -6 -7 -8]
          [-4 -5 -6 -7 -8]]}]
  [{:A22 [[-4 -5 -6 -7 -8]
          [-4 -5 -6 -7 -8]],
    :A21 [[1 0 -1 -2 -3]
          [1 0 -1 -2 -3]]}]]

Subtrahend is not a scalar

Row matrix subtracted from row matrix

=> (view r1)
 [1 2 3 4]
Order -> 1 x 4
=> (view r2)
 [4 3 2 1]
Order -> 1 x 4
=> (view (minus r1 r2))
 [-3 -1 1 3]
Order -> 1 x 4
=> (view (minus r2 r1))
 [3 1 -1 -3]
Order -> 1 x 4

Row subtracted from matrix or vice versa

=> (view M1)
 [1 2]
 [3 4]
Order -> 2 x 2
=> (view (minus M1 [[1 2]]))
 [0 0]
 [2 2]
Order -> 2 x 2
=> (view (minus [[1 2]] M1))
 [0 0]
 [-2 -2]
Order -> 2 x 2

Column matrix subtracted from column matrix

=> (view c1)
 [1]
 [2]
 [3]
 [4]
Order -> 4 x 1
=> (view c2)
 [4]
 [3]
 [2]
 [1]
Order -> 4 x 1
=> (view (minus c1 c2))
 [-3]
 [-1]
 [1]
 [3]
Order -> 4 x 1
=> (view (minus c2 c1))
 [3]
 [1]
 [-1]
 [-3]
Order -> 4 x 1

Column subtracted from matrix or vice versa

=> (view M2)
 [4 3]
 [2 1]
Order -> 2 x 2
=> (view (minus M2 [[1][2]]))
 [3 2]
 [0 -1]
Order -> 2 x 2
=> (view (minus [[1][2]] M2))
 [-3 -2]
 [0 1]
Order -> 2 x 2

Column matrix subtracted from row matrix or vice versa

=> (view (minus r1 c1))
 [0 1 2 3]
 [-1 0 1 2]
 [-2 -1 0 1]
 [-3 -2 -1 0]
Order -> 4 x 4
=> (view (minus c1 r1))
 [0 -1 -2 -3]
 [1 0 -1 -2]
 [2 1 0 -1]
 [3 2 1 0]
Order -> 4 x 4

Matrix subtracted from Matrix

=> (view M1)
 [1 2]
 [3 4]
Order -> 2 x 2
=> (view M2)
 [4 3]
 [2 1]
Order -> 2 x 2
=> (view (minus M1 M2))
 [-3 -1]
 [1 3]
Order -> 2 x 2
=> (view (minus M2 M1))
 [3 1]
 [-1 -3]
Order -> 2 x 2

Block subtracted from block

=> (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]],
   :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]]}]
 [{:A21 [[10 9 8 7 6]
         [10 9 8 7 6]],
   :A22 [[5 4 3 2 1]
         [5 4 3 2 1]]}]]
=> (pprint (minus B1 B2))
[[{:A11 [[-9 -7 -5 -3 -1]
         [-9 -7 -5 -3 -1]
         [-9 -7 -5 -3 -1]
         [-9 -7 -5 -3 -1]
         [-9 -7 -5 -3 -1]],
   :A12 [[1 3 5 7 9]
         [1 3 5 7 9]
         [1 3 5 7 9]
         [1 3 5 7 9]
         [1 3 5 7 9]]}]
 [{:A21 [[-9 -7 -5 -3 -1]
         [-9 -7 -5 -3 -1]],
   :A22 [[1 3 5 7 9]
         [1 3 5 7 9]]}]]
=> (pprint (minus B2 B1))
[[{:A11 [[9 7 5 3 1]
         [9 7 5 3 1]
         [9 7 5 3 1]
         [9 7 5 3 1]
         [9 7 5 3 1]],
   :A12 [[-1 -3 -5 -7 -9]
         [-1 -3 -5 -7 -9]
         [-1 -3 -5 -7 -9]
         [-1 -3 -5 -7 -9]
         [-1 -3 -5 -7 -9]]}]
 [{:A21 [[9 7 5 3 1]
         [9 7 5 3 1]],
   :A22 [[-1 -3 -5 -7 -9]
         [-1 -3 -5 -7 -9]]}]]