Please refer to my question at the following link:
https://ask.sagemath.org/question/63305/writing-a-matrix-as-a-sum-of-matrices/
There John Palmieri has written a very good code. As the output is huge and hence time-taking(No output even for 4th order matrices with 4 summands even after many days), so I tried to split the code in parts according to the logic given in the following link:
https://ask.sagemath.org/question/45606/divide-combinationsnk-into-multiple-parts-n-1110/
and hence have this code:
def sum_list(length, total):
"""
INPUT:
- length -- how many terms
- total -- desired total
Return list of lists, each of which has ``length`` entries chosen
from {0, 1, -1} and adds up to ``total``.
"""
C = IntegerListsLex(length=length, n=length+total, min_part=0, max_part=2)
return [[a-1 for a in L] for L in C]
def mat_list_NEW(mat, length):
"""
INPUT:
- mat -- matrix, assumed to have entries in {1, -1}
- length -- how many terms
Return list of lists, each of which has ``length`` entries and
adds up to ``mat``, and each entry is either a `(0, 1)` or a `(0,
-1)` matrix.
"""
sum_plus = sum_list(length, 1)
sum_minus = sum_list(length, -1)
old_attempts = []
for x in mat.list():
if x == 1:
sums = sum_plus
elif x == -1:
sums = sum_minus
else:
raise ValueError('each entry of matrix should be 1 or -1')
if not old_attempts: # initial step
new_attempts = set(tuple([(s,) for s in S]) for S in sums)
else:
new_attempts = set()
for mats in old_attempts:
NEW = set()
for S in sums:
new_M = tuple(sorted(M + (s,) for (M, s) in zip(mats, S)))
# keep only entries that correspond to (0,1) or (0,-1) matrices
if all(max(entries) - min(entries) < 2 for entries in new_M):
NEW.add(new_M)
new_attempts.update(NEW)
old_attempts = new_attempts
LOA=list(old_attempts)
P=len(LOA)
N=floor(P/5)
R = range(0,P , N)
c0 = LOA[R[0]:R[0]+N]
#c1 = LOA[R[1]:R[1]+N]
#c2 = LOA[R[2]:R[2]+N]
#c3 = LOA[R[3]:R[3]+N]
#c4 = LOA[R[4]:R[4]+N]
#c5 = LOA[R[5]:R[5]+N]
matrices = [[matrix(mat.base_ring(), mat.nrows(), mat.ncols(), entries) for entries in L] for L in c0]
return (matrices)
mat=matrix(3,3, [1, 1, 1, -1, 1, 1, -1, -1, 1])#Enter your matrix
mat_list_NEW(mat,4)#Specify in how many matrices you want to break it up
In the above link it mentions storing of c0,c1,c2,….in csv file because of memory limitations. I have no idea of csv files. So thought of writing each of ci’s individually (as I have written above in the code) and run codes separately. Kindly guide me how to use csv files to further help in running this code.
Note that in the above code for 3rd order matrix with 4 summands P is 73261 and for 5 summands P is 11740316. And we need for higher order matrices(upto say 30) and summands(upto say10) for which P will be very very huge. Somebody told me that if code is written in parallel, then it will run faster.
Also, I will be using supercomputing facility with the following details:
OS: CentOS 7 Hardware Specifications
Type I: Total no. of compute nodes: 420
CPU only nodes: 259
CPU Architecture : Haswell
2x Intel Xeon E5-2680 v3/12-Core(24 cores each)
RAM: 64 GB
-----------------------------------
GPU accelerated nodes: 161
(CPU config same as above + GPU cards)
GPU Architecture : 2x NVIDIA K40 (each)
(12GB, 2880 CUDA cores)
-----------------------------------
High Memory Nodes : 512 GB RAM
12 CPU, 8 GPU nodes
TYPE II:Total no. of compute nodes: 184
CPU only nodes: 144
CPU Architecture : Skylake
2x Intel Xeon G-6148/20 cores(40 cores per node)
RAM: 96 GB
--------------------------------------------
GPU accelerated nodes: 40 (CPU config same )
GPU Architecture : NVIDIA V100
(32GB,5120 CUDA cores)
1 Nvidia V100 card each GPU node: 17
2 Nvidia V100 cards each GPU node:23
High Memory Nodes : 192 GB RAM
8 CPU, 40 GPU nodes
Requesting for resources will be clear with following examples:
1.Request for 2 chunks with 20 cpus, 2 gpu cards for 2 hrs by mentioning as follows:
" -lselect=2: ncpus=20: ngpus=2 : -lwalltime=02:00:00"
2. Request for 2 chunks i.e. full skylake nodes, 1gpu card for 3 hours by mentioning as follows:
" -lselect=2: ncpus=40: ngpus=1: centos=skylake: -l walltime=03:00:00"
Kindly guide me how to choose the resources viz. lselect, ncpus, ngpus for my code.
So kindly guide with respect to the above mentioned points. Thanks.
