Generating a random sparse hermitian matrix in Python
I'd like to find a way to generate random sparse hermitian matrices in Python, but don't really know how to do so efficiently. How would I go about doing this?
Obviously, there are slow, ugly ways to do this, but since I'm going to be doing this a lot, I'd like if there was a faster way to do it.
Is there an easy way to calculate the density of the matrix? It's the parameter that I'd be using to compare two factorisation algorithms. It's defined as
$$ d = frac{mathrm{nnz}}{n^2} $$
where $mathrm{nnz}$ is defined as the number of nonzero entries in the matrix and $n$ is its number of rows or columns (hence $n^2$ is the number of elements in the matrix).
EDIT
Calculating the density should be easy:
density = np.count_nonzero(A)/n**2
should do the trick.
matrices numerical-linear-algebra random python sparse-matrices
asked Nov 30 at 8:27
Peiffap
367
add a comment |
I'd like to find a way to generate random sparse hermitian matrices in Python, but don't really know how to do so efficiently. How would I go about doing this?
Obviously, there are slow, ugly ways to do this, but since I'm going to be doing this a lot, I'd like if there was a faster way to do it.
Is there an easy way to calculate the density of the matrix? It's the parameter that I'd be using to compare two factorisation algorithms. It's defined as
$$ d = frac{mathrm{nnz}}{n^2} $$
where $mathrm{nnz}$ is defined as the number of nonzero entries in the matrix and $n$ is its number of rows or columns (hence $n^2$ is the number of elements in the matrix).
EDIT
Calculating the density should be easy:
density = np.count_nonzero(A)/n**2
should do the trick.
matrices numerical-linear-algebra random python sparse-matrices
asked Nov 30 at 8:27
Peiffap
367
add a comment |
I'd like to find a way to generate random sparse hermitian matrices in Python, but don't really know how to do so efficiently. How would I go about doing this?
Obviously, there are slow, ugly ways to do this, but since I'm going to be doing this a lot, I'd like if there was a faster way to do it.
Is there an easy way to calculate the density of the matrix? It's the parameter that I'd be using to compare two factorisation algorithms. It's defined as
$$ d = frac{mathrm{nnz}}{n^2} $$
where $mathrm{nnz}$ is defined as the number of nonzero entries in the matrix and $n$ is its number of rows or columns (hence $n^2$ is the number of elements in the matrix).
EDIT
Calculating the density should be easy:
density = np.count_nonzero(A)/n**2
should do the trick.
matrices numerical-linear-algebra random python sparse-matrices
asked Nov 30 at 8:27
Peiffap
367
I'd like to find a way to generate random sparse hermitian matrices in Python, but don't really know how to do so efficiently. How would I go about doing this?
Obviously, there are slow, ugly ways to do this, but since I'm going to be doing this a lot, I'd like if there was a faster way to do it.
Is there an easy way to calculate the density of the matrix? It's the parameter that I'd be using to compare two factorisation algorithms. It's defined as
$$ d = frac{mathrm{nnz}}{n^2} $$
where $mathrm{nnz}$ is defined as the number of nonzero entries in the matrix and $n$ is its number of rows or columns (hence $n^2$ is the number of elements in the matrix).
EDIT
Calculating the density should be easy:
density = np.count_nonzero(A)/n**2
should do the trick.
matrices numerical-linear-algebra random python sparse-matrices
matrices numerical-linear-algebra random python sparse-matrices
asked Nov 30 at 8:27
Peiffap
367
asked Nov 30 at 8:27
Peiffap
367
edited Nov 30 at 8:33
asked Nov 30 at 8:27
Peiffap
367
asked Nov 30 at 8:27
Peiffap
367
asked Nov 30 at 8:27
Peiffap
367
367
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
This generates a random mask with of a given size n and density dens, you just need to apply it to a dense matrix of your choice
import numpy as np
np.random.seed(0)
n = 300
dens = 0.2
mask = np.array([np.random.choice([True, False], n, p = [dens, 1 - dens]) for i in range(n)])
print(np.count_nonzero(mask) / n**2)
The result of this is
>>> 0.20224444444444445
To force the result to be Hermitian just use
$$
H = frac{1}{2}(A + A^*)
$$
answered Nov 30 at 9:58
caverac
13k21028
Alright, I see how this works but how do I apply the mask to a matrix?
– Peiffap
Nov 30 at 10:08
@Peiffap Define the matrixMand then runA = M[mask]
– caverac
Nov 30 at 10:09
M[mask], no? Thanks!
– Peiffap
Nov 30 at 10:11
add a comment |
When I apply the $M[$mask$]$, I only get the values of $M$ where True is defined in mask. How do I get the sparse matrix $M$ (where false$=0$, True=real value).
(I think we are following the same course ;))
edited Dec 8 at 0:11
dantopa
6,41132042
answered Dec 5 at 21:08
emanuelPaul
1
I found it ! M[mask]=0 if you swap the True with probability = 1-dens and False with probability = dens.
– emanuelPaul
Dec 5 at 21:25
If you have an easier way please feel free to contact me! And if you are from UCL, and you got ideas about LUcsr... contact me as well please!
– emanuelPaul
Dec 5 at 21:26
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
This generates a random mask with of a given size n and density dens, you just need to apply it to a dense matrix of your choice
import numpy as np
np.random.seed(0)
n = 300
dens = 0.2
mask = np.array([np.random.choice([True, False], n, p = [dens, 1 - dens]) for i in range(n)])
print(np.count_nonzero(mask) / n**2)
The result of this is
>>> 0.20224444444444445
To force the result to be Hermitian just use
$$
H = frac{1}{2}(A + A^*)
$$
answered Nov 30 at 9:58
caverac
13k21028
Alright, I see how this works but how do I apply the mask to a matrix?
– Peiffap
Nov 30 at 10:08
@Peiffap Define the matrixMand then runA = M[mask]
– caverac
Nov 30 at 10:09
M[mask], no? Thanks!
– Peiffap
Nov 30 at 10:11
add a comment |
This generates a random mask with of a given size n and density dens, you just need to apply it to a dense matrix of your choice
import numpy as np
np.random.seed(0)
n = 300
dens = 0.2
mask = np.array([np.random.choice([True, False], n, p = [dens, 1 - dens]) for i in range(n)])
print(np.count_nonzero(mask) / n**2)
The result of this is
>>> 0.20224444444444445
To force the result to be Hermitian just use
$$
H = frac{1}{2}(A + A^*)
$$
answered Nov 30 at 9:58
caverac
13k21028
Alright, I see how this works but how do I apply the mask to a matrix?
– Peiffap
Nov 30 at 10:08
@Peiffap Define the matrixMand then runA = M[mask]
– caverac
Nov 30 at 10:09
M[mask], no? Thanks!
– Peiffap
Nov 30 at 10:11
add a comment |
This generates a random mask with of a given size n and density dens, you just need to apply it to a dense matrix of your choice
import numpy as np
np.random.seed(0)
n = 300
dens = 0.2
mask = np.array([np.random.choice([True, False], n, p = [dens, 1 - dens]) for i in range(n)])
print(np.count_nonzero(mask) / n**2)
The result of this is
>>> 0.20224444444444445
To force the result to be Hermitian just use
$$
H = frac{1}{2}(A + A^*)
$$
answered Nov 30 at 9:58
caverac
13k21028
This generates a random mask with of a given size n and density dens, you just need to apply it to a dense matrix of your choice
import numpy as np
np.random.seed(0)
n = 300
dens = 0.2
mask = np.array([np.random.choice([True, False], n, p = [dens, 1 - dens]) for i in range(n)])
print(np.count_nonzero(mask) / n**2)
The result of this is
>>> 0.20224444444444445
To force the result to be Hermitian just use
$$
H = frac{1}{2}(A + A^*)
$$
answered Nov 30 at 9:58
caverac
13k21028
answered Nov 30 at 9:58
caverac
13k21028
answered Nov 30 at 9:58
caverac
13k21028
answered Nov 30 at 9:58
caverac
13k21028
13k21028
Alright, I see how this works but how do I apply the mask to a matrix?
– Peiffap
Nov 30 at 10:08
@Peiffap Define the matrixMand then runA = M[mask]
– caverac
Nov 30 at 10:09
M[mask], no? Thanks!
– Peiffap
Nov 30 at 10:11
add a comment |
Alright, I see how this works but how do I apply the mask to a matrix?
– Peiffap
Nov 30 at 10:08
@Peiffap Define the matrixMand then runA = M[mask]
– caverac
Nov 30 at 10:09
M[mask], no? Thanks!
– Peiffap
Nov 30 at 10:11
Alright, I see how this works but how do I apply the mask to a matrix?
– Peiffap
Nov 30 at 10:08
Alright, I see how this works but how do I apply the mask to a matrix?
– Peiffap
Nov 30 at 10:08
@Peiffap Define the matrix
M and then run A = M[mask]– caverac
Nov 30 at 10:09
@Peiffap Define the matrix
M and then run A = M[mask]– caverac
Nov 30 at 10:09
M[mask], no? Thanks!
– Peiffap
Nov 30 at 10:11
M[mask], no? Thanks!
– Peiffap
Nov 30 at 10:11
add a comment |
When I apply the $M[$mask$]$, I only get the values of $M$ where True is defined in mask. How do I get the sparse matrix $M$ (where false$=0$, True=real value).
(I think we are following the same course ;))
edited Dec 8 at 0:11
dantopa
6,41132042
answered Dec 5 at 21:08
emanuelPaul
1
I found it ! M[mask]=0 if you swap the True with probability = 1-dens and False with probability = dens.
– emanuelPaul
Dec 5 at 21:25
If you have an easier way please feel free to contact me! And if you are from UCL, and you got ideas about LUcsr... contact me as well please!
– emanuelPaul
Dec 5 at 21:26
add a comment |
When I apply the $M[$mask$]$, I only get the values of $M$ where True is defined in mask. How do I get the sparse matrix $M$ (where false$=0$, True=real value).
(I think we are following the same course ;))
edited Dec 8 at 0:11
dantopa
6,41132042
answered Dec 5 at 21:08
emanuelPaul
1
I found it ! M[mask]=0 if you swap the True with probability = 1-dens and False with probability = dens.
– emanuelPaul
Dec 5 at 21:25
If you have an easier way please feel free to contact me! And if you are from UCL, and you got ideas about LUcsr... contact me as well please!
– emanuelPaul
Dec 5 at 21:26
add a comment |
When I apply the $M[$mask$]$, I only get the values of $M$ where True is defined in mask. How do I get the sparse matrix $M$ (where false$=0$, True=real value).
(I think we are following the same course ;))
edited Dec 8 at 0:11
dantopa
6,41132042
answered Dec 5 at 21:08
emanuelPaul
1
When I apply the $M[$mask$]$, I only get the values of $M$ where True is defined in mask. How do I get the sparse matrix $M$ (where false$=0$, True=real value).
(I think we are following the same course ;))
edited Dec 8 at 0:11
dantopa
6,41132042
answered Dec 5 at 21:08
emanuelPaul
1
edited Dec 8 at 0:11
dantopa
6,41132042
edited Dec 8 at 0:11
dantopa
6,41132042
edited Dec 8 at 0:11
dantopa
6,41132042
6,41132042
answered Dec 5 at 21:08
emanuelPaul
1
answered Dec 5 at 21:08
emanuelPaul
1
answered Dec 5 at 21:08
emanuelPaul
1
1
I found it ! M[mask]=0 if you swap the True with probability = 1-dens and False with probability = dens.
– emanuelPaul
Dec 5 at 21:25
If you have an easier way please feel free to contact me! And if you are from UCL, and you got ideas about LUcsr... contact me as well please!
– emanuelPaul
Dec 5 at 21:26
add a comment |
I found it ! M[mask]=0 if you swap the True with probability = 1-dens and False with probability = dens.
– emanuelPaul
Dec 5 at 21:25
If you have an easier way please feel free to contact me! And if you are from UCL, and you got ideas about LUcsr... contact me as well please!
– emanuelPaul
Dec 5 at 21:26
I found it ! M[mask]=0 if you swap the True with probability = 1-dens and False with probability = dens.
– emanuelPaul
Dec 5 at 21:25
I found it ! M[mask]=0 if you swap the True with probability = 1-dens and False with probability = dens.
– emanuelPaul
Dec 5 at 21:25
If you have an easier way please feel free to contact me! And if you are from UCL, and you got ideas about LUcsr... contact me as well please!
– emanuelPaul
Dec 5 at 21:26
If you have an easier way please feel free to contact me! And if you are from UCL, and you got ideas about LUcsr... contact me as well please!
– emanuelPaul
Dec 5 at 21:26
add a comment |
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