Is there a MATLAB function to generate this matrix?:
[1 2 3 4 5 6 7 ... n;
2 3 4 5 6 7 8 ... n+1;
3 4 5 6 7 8 9 ... n+2;
...;
n n+1 n+2 ... 2*n-1];
Is there a name for it?
Thanks.
Yes indeed there's a name for that matrix. It's known as the Hankel matrix.
Use the hankel function in MATLAB:
out = hankel(1:n,n:2*n-1);
Example with n=10:
out =
1 2 3 4 5 6 7 8 9 10
2 3 4 5 6 7 8 9 10 11
3 4 5 6 7 8 9 10 11 12
4 5 6 7 8 9 10 11 12 13
5 6 7 8 9 10 11 12 13 14
6 7 8 9 10 11 12 13 14 15
7 8 9 10 11 12 13 14 15 16
8 9 10 11 12 13 14 15 16 17
9 10 11 12 13 14 15 16 17 18
10 11 12 13 14 15 16 17 18 19
Alternatively, you may be inclined to want a bsxfun based approach. That is certainly possible:
out = bsxfun(#plus, (1:n), (0:n-1).');
The reason why I wanted to show you this approach is because in your answer, you used repmat to generate the two matrices to add together to create the right result. You can replace the two repmat calls with bsxfun as it does the replication under the hood.
The above solution is for older MATLAB versions that did not have implicit broadcasting. For recent versions of MATLAB, you can simply do the above by:
out = (1:n) + (0:n-1).';
My standard approach is
repmat(1:n,n,1)+repmat((1:n)',1,n)-1
Related
given list of lists, how to merge them into a single list taking up to k items at a time from each of the lists until all items are merged?
for example, the following input and output is expected:
q)alternate[1] ("abc";"de";"fghi")
"adfbegchi"
for k~1 items at a time, the solution is:
q)mesh:{raze[y]rank x} / https://code.kx.com/phrases/sort/#mesh
q)alternate:{mesh[raze where each 1&{0|x-1}\[count each x];x]}
q)alternate ("abc";"de";"fghi")
"adfbegchi"
the above works because:
q)mesh[0 1 2 0 1 2 0 2 2;] ("abc";"de";"fghi")
"adfbegchi"
How to elegantly generalize alternate for any k<=max count each x ? python solution is here
the below should achieve this
q)f:{raze[y]iasc raze(x-1)|til'[count'[y]]};
q)f[1;("abc";"de";"fghi")]
"adfbegchi"
q)f[2;("abc";"de";"fghi")]
"abdefgchi"
Not sure if this is any faster or cleaner but a different approach:
q)alt:{(raze/)value each(s;::;)each til max count each s:x cut'y};
q)alt[1;("abc";"de";"fghi")]
"adfbegchi"
q)alt[2;("abc";"de";"fghi")]
"abdefgchi"
q)alt[2;(1 2 3 4;5 6 7;8 9 10 11;12 13 14 15)]
1 2 5 6 8 9 12 13 3 4 7 10 11 14 15
q)alt[3;(1 2 3 4;5 6 7;8 9 10 11;12 13 14 15)]
1 2 3 5 6 7 8 9 10 12 13 14 4 11 15
I was hoping to use case but unfortunately case doesn't like lists of different count (that aren't atomic values)
not sure if this is the fastest solution, substituting x for the hardcoded 1 in the alternate function above, and thus making it dyadic:
q)alternate:{mesh[raze where each x&{0|y-x}[x]\[count each y];y]}
q)alternate[2] ("abc";"de";"fghi")
"abdefgchi"
q)alternate[2] (1 2 3 4;5 6 7;8 9 10 11;12 13 14 15)
1 2 5 6 8 9 12 13 3 4 7 10 11 14 15
q)alternate[3] (1 2 3 4;5 6 7;8 9 10 11;12 13 14 15)
1 2 3 5 6 7 8 9 10 12 13 14 4 11 15
edit:
naïve benchmark comparison with #terrylynch 's alt and #Matthew Madill's f :
q)\t:10000 f[2] ("abc";"de";"fghi")
49
q)\t:10000 alternate[2] ("abc";"de";"fghi")
56
q)\t:10000 alt[2] ("abc";"de";"fghi")
87
q)\t:10000 f[3] (1 2 3 4;5 6 7;8 9 10 11;12 13 14 15)
55
q)\t:10000 alternate[3] (1 2 3 4;5 6 7;8 9 10 11;12 13 14 15)
61
q)\t:10000 alt[3] (1 2 3 4;5 6 7;8 9 10 11;12 13 14 15)
103
I would like to explore a better way to apply binary function which iterate via each element of the two argument. Let make the question simpler by using below function as an example:
func:{x+y}
a:til 10
q)a
0 1 2 3 4 5 6 7 8 9
b:a
q)b:a
q)b
0 1 2 3 4 5 6 7 8 9
What I what to get is the cross production such that each element of the argument will cross each other and apply the function. My expected result is
0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 11 3 4 5 6 7 8 9 10 11 12 4 5 6 7 8 9 10 11 12 13 5 6 7 8 9 10 11 12 13 14 6 7 8 9 10 11 12 13 14 15 7 8 9 10 11 12 13 14 15 16 8 9 10 11 12 13 14 15 16 17 9 10 11 12 13 14 15 16 17 18
My current solution is crossing the the list of argument first:
(func/) each (a cross b)
I wonder is there a better way to doing that? simply using func'[a;b] will just get a pairwise result which not what I want.
The following should be what you are looking for:
a +/:\: b
The same can apply for other defined functions too, for example:
a {x mod y}/:\: b
You do not need cross for this just each-right or each-left. Because '+' is a vector function you can just iterate over one list and use other list as full vector.
q) a+/:b
I have an array A, I want to arrange each row in descending order to get a new array B. How could I do this ?
E.g.
Array A (original array):
11 9 13 10
12 4 1 6
13 5 12 11
Array B (rearranged array):
13 11 10 9
12 6 4 1
13 12 11 5
>> A=[11 9 13 10;12 4 1 6;13 5 12 11]
A =
11 9 13 10
12 4 1 6
13 5 12 11
>> sort(A,2,'descend')
ans =
13 11 10 9
12 6 4 1
13 12 11 5
For details type: help sort at Matlab command window
I need a function that splits a vector in smaller frames with an overlap, like buffer, but instead of column-wise, it should be done row-wise.
This is how buffer works:
x = 1:20
x = buffer(x, 10, 5);
x = 0 1 6 11
0 2 7 12
0 3 8 13
0 4 9 14
0 5 10 15
1 6 11 16
2 7 12 17
3 8 13 18
4 9 14 19
5 10 15 20
What I want would be this though:
x = 0 0 1 2
1 2 3 4
3 4 5 6
5 6 7 8
7 8 9 10
9 10 11 12
11 12 13 14
13 14 15 16
15 16 17 18
17 18 19 20
Is there any function or way to achieve that? Maybe combination of buffer + some rearranging?
First figure out the answer in columns, then transpose the resulting matrix:
buffer(x, 4, 2).'
How to export a matrix with the first row telling names of columns
like
A=
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
export to matrix.txt
x1 x2 x3 x4
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
I was checking
dlmwrite('matrix.txt',A,'delimiter',',');
But how to modify it?
Use the '-append' option:
dlmwrite('matrix.txt', {'a','b','c'});
dlmwrite('matrix.txt', [1,2,3;4,5,6], '-append');