Storing the maximum values of diagonals in the matrix
Let's say I have a matrix A that represents the height values:
A = matrix(c(100,105,106,109,101,101,106,104,107,106,101,102,105,106,108,102,102,104,110,104), nrow=5, ncol=4)
I would like to create a new matrix that generated a diagonal analysis of matrix A. Starting with. in the top left corner I want to analyze each diagonal and store the maximum values step by step. The expected results should be as follows:
B = matrix(c(100,105,106,109,101,101,106,105,107,109,101,102,106,106,108,102,102,102,110,106), nrow=5, ncol=4)
Can anyone help me?
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If I understand you correctly, you need the cumulative maximum for each diagonal. With cummax
and two for-loops, you can get what you want:
A[row(A)==col(A)] <- cummax(A[row(A)==col(A)])
for(i in 1:(nrow(A)-1)) {
A[row(A)==col(A)-i] <- cummax(A[row(A)==col(A)-i])
}
for(i in 1:(ncol(A)-1)) {
A[row(A)-i==col(A)] <- cummax(A[row(A)-i==col(A)])
}
The matrix now A
looks like this:
> A
[,1] [,2] [,3] [,4]
[1,] 100 101 101 102
[2,] 105 106 102 102
[3,] 106 105 106 104
[4,] 109 107 106 110
[5,] 101 109 108 106
You can also wrap this in a function if you need this routine more often:
diagcummax <- function(m) {
m[row(m)==col(m)] <- cummax(m[row(m)==col(m)])
for(i in 1:(nrow(m)-1)) {
m[row(m)==col(m)-i] <- cummax(m[row(m)==col(m)-i])
}
for(i in 1:(ncol(m)-1)) {
m[row(m)-i==col(m)] <- cummax(m[row(m)-i==col(m)])
}
m
}
Then you just need to do:
diagcummax(A)
to get the desired result.
If you want to go from the top-right corner and then down-left, you need to enable rev
at some points the functions:
diagcummax.upright <- function(m) {
m[row(m)==rev(col(m))] <- rev(cummax(rev(m[row(m)==rev(col(m))])))
for(i in 1:(nrow(m)-1)) {
m[row(m)==rev(col(m))-i] <- rev(cummax(rev(m[row(m)==rev(col(m))-i])))
}
for(i in 1:(ncol(m)-1)) {
m[row(m)-i==rev(col(m))] <- rev(cummax(rev(m[row(m)-i==rev(col(m))])))
}
m
}
Now using
diagcummax.upright(A)
the following matrix is returned:
[,1] [,2] [,3] [,4]
[1,] 100 101 101 102
[2,] 105 106 102 102
[3,] 106 104 105 104
[4,] 109 107 106 110
[5,] 107 106 110 104
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