Question

This format tries to compress the sparse matrix further compared to COO format. Suppose you have the following coordinate representation of a sparse matrix where you sort by row index:

```    rows   = [0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6]
cols   = [1, 2, 4, 0, 2, 3, 0, 1, 3, 4, 1, 2, 5, 6, 0, 2, 5, 3, 4, 6, 3, 5]
values = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
```

If there are nnz nonzeroes, then this representation requires 3*nnz units of storage since it needs three arrays, each of length nnz.

Observe that when we sort by row index, values are repeated wherever there is more than one nonzero in a row. The idea behind CSR is to exploit this redundancy. From the sorted COO representation, we keep the column indices and values as-is. Then, instead of storing every row index, we just store the starting offset of each row in those two lists, which we'll refer to as the row pointers, stored as the list rowptr, below:

```    cols   = [1, 2, 4, 0, 2, 3, 0, 1, 3, 4, 1, 2, 5, 6, 0, 2, 5, 3, 4, 6, 3, 5]
values = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
rowptr = [0,       3,       6,         10,         14,      17,      20,   22]
```

If the sparse matrix has n rows, then the rowptr list has n+1 elements, where the last element (rowptr[-1] == rowptr[n]) is nnz. (Why might you need this last element?)

Exercise 8 (3 points). Complete the function, coo2csr(coo_rows, coo_cols, coo_vals), below. The inputs are three Python lists corresponding to a sparse matrix in COO format, like the example illustrated above. Your function should return a triple, (csr_ptrs, csr_inds, csr_vals), corresponding to the same matrix but stored in CSR format, again, like what is shown above, where csr_ptrs would be the row pointers (rowptr), csr_inds would be the column indices (colind), and csr_vals would be the values (values).

To help you out, we show how to calculate csr_inds and csr_vals. You need to figure out how to compute csr_ptrs. The function is set up to return these three lists.

Although the test cell does not check it, in principle, your implementation should also work correctly if a row has an empty row. In such cases, what should the CSR data structure look like?

Write code here

def coo2csr(coo_rows, coo_cols, coo_vals):

from operator import itemgetter

C = sorted(zip(coo_rows, coo_cols, coo_vals), key=itemgetter(0))

nnz = len(C)

assert nnz >= 1

csr_inds = [j for _, j, _ in C]

csr_vals = [a_ij for _, _, a_ij in C]

###

Testing codes

# Test cell 0: `create_csr_test` (1 point)

csr_ptrs, csr_inds, csr_vals = coo2csr(coo_rows, coo_cols, coo_vals)

assert type(csr_ptrs) is list, "`csr_ptrs` is not a list."

assert type(csr_inds) is list, "`csr_inds` is not a list."

assert type(csr_vals) is list, "`csr_vals` is not a list."

assert len(csr_ptrs) == (num_verts + 1), "`csr_ptrs` has {} values instead of {}".format(len(csr_ptrs), num_verts+1)

assert len(csr_inds) == num_edges, "`csr_inds` has {} values instead of {}".format(len(csr_inds), num_edges)

assert len(csr_vals) == num_edges, "`csr_vals` has {} values instead of {}".format(len(csr_vals), num_edges)

assert csr_ptrs[num_verts] == num_edges, "`csr_ptrs[{}]` == {} instead of {}".format(num_verts, csr_ptrs[num_verts], num_edges)

# Check some random entries

for i in sample(range(num_verts), 10000):

assert i in G

a, b = csr_ptrs[i], csr_ptrs[i+1]

msg_prefix = "Row {} should have these nonzeros: {}".format(i, G[i])

assert (b-a) == len(G[i]), "{}, which is {} nonzeros; instead, it has just {}.".format(msg_prefix, len(G[i]), b-a)

assert all([(j in G[i]) for j in csr_inds[a:b]]), "{}. However, it may have missing or incorrect column indices: csr_inds[{}:{}] == {}".format(msg_prefix, a, b, csr_inds[a:b])

assert all([(j in csr_inds[a:b] for j in G[i].keys())]), "{}. However, it may have missing or incorrect column indices: csr_inds[{}:{}] == {}".format(msg_prefix, a, b, csr_inds[a:b])

print ("n(Passed.)")

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