# coding: utf-8

# # Building and Using Sparse Matrices

# In[2]:


import numpy as np
import matplotlib.pyplot as pt

import scipy.sparse as sps


# ## Building a sparse matrix

# **COO**rdinate format is typically convenient for building ("assembling") a sparse matrix:

# In[3]:


data = [5, 6, 7]
rows = [1, 1, 2]
columns = [2, 4, 6]

A = sps.coo_matrix(
        (data, (rows, columns)),
        shape=(10, 10), dtype=np.float64)
A


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A.todense()


# In[5]:


A.nnz


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pt.spy(A)


# For a COO matrix, the juicy attributes are `data`, `row`, and `col`.

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print("row:", A.row)
print("col:", A.col)
print("data:", A.data)


# **COO**rdinate format is not the only format. 
# 
# There is also [**C**ompressed **S**parse **R**ow](https://en.wikipedia.org/wiki/Sparse_matrix#Compressed_sparse_row_.28CSR.2C_CRS_or_Yale_format.29):

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Acsr = A.tocsr()
Acsr


# For Compressed Sparse Row, look in `data`, `indptr`, and `indices`.

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print("indptr:", Acsr.indptr)
print("indices:", Acsr.indices)
print("data:", Acsr.data)


# ## Performance of the Matrix-Vector Product

# The following code randomly generates a sparse matrix that has a given `fill_percent` percentage of nonzero entries:

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fill_percent = 5

size = 1000
nentries = size**2 * fill_percent // 100

data = np.random.randn(nentries)
rows = (np.random.rand(nentries)*size).astype(np.int32)
columns = (np.random.rand(nentries)*size).astype(np.int32)

B_coo = sps.coo_matrix(
        (data, (rows, columns)),
        shape=(size, size), dtype=np.float64)

B_csr = sps.csr_matrix(B_coo)

B_dense = B_coo.todense()


# Next, we time matrix-vector multiplication for different versions of `B`:

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vec = np.random.randn(size)

from time import time
start = time()

for i in range(2000):
    B_dense.dot(vec)
    
print("time: %g" % (time() - start))