Matlab expression:
dA.*(A*N - N.*sum(A,2))
where
dA: real number
A: 10 x 10 matrix
N: 10 X 1 matrix
A*N: matrix multiplication
sum(A,2): sum of rows in A (10x1 matrix)
N.*sum(A,2): element by element multiplication (10 x 1 matrix)
Let's set up the following example in R:
A = matrix(data = 1:100,nrow = 10)
N = matrix(data = 1:10)
dA = 0.1
> A
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 1 11 21 31 41 51 61 71 81 91
[2,] 2 12 22 32 42 52 62 72 82 92
[3,] 3 13 23 33 43 53 63 73 83 93
[4,] 4 14 24 34 44 54 74 84 94
[5,] 5 15 25 35 45 55 65 75 85 95
[6,] 6 16 26 36 46 56 66 76 86 96
[7,] 7 17 27 37 47 57 67 77 87 97
[8,] 8 18 28 38 48 58 68 78 88 98
[9,] 9 19 29 39 49 59 69 79 99
[10,] 10 20 30 40 50 60 70 80 90 100
> N
[,1]
[1,] 1
[2,] 2
[3,] 3
[4,] 4
[5,] 5
[6,] 6
[7,] 7
[8,] 8
[9,] 9
[10,] 10
The first term is:
z1 = A %*% N
And the second term:
srow = rowSums(A)
z2 = srow * N
Which leads to the final result:
result = dA * (z1-z2)
Final equation
result = dA * (A %*% N - rowSums(A)*N)
This should give you the same answer as Matlab's dA.*(A*N - N.*sum(A,2))
