Compressed Sparse Array

The csarray class represents a Compressed Sparse Array object which is essentially a 2d matrix or 1d vector with few nonzero elements. The underlying implementation uses the Eigen sparse matrix code. A csarray is initially specified using a size, data type (int, float etc.) and storage type (row or column major format).

As an example, a csarray of shape (5, 5) can be created in the following manner:

>>> import numpy
>>> from sppy import csarray
>>> #Create a new column major dynamic array of float type
>>> B = csarray((5, 5), storagetype="col", dtype=numpy.float)
>>> B[3, 3] = -0.2
>>> B[0, 4] = -1.23

Alternatively, one can create a csarray using a numpy array, a scipy sparse matrix, or a csarray:

>>> A = numpy.random.rand(5, 7)
>>> B = csarray(A, storagetype="col")
>>> C = csarray(B, storagetype="row")

In addition, one can generate arrays using a predefined structure, for example diagonal matrices or randomly generated. See the documentation below for details and also for information on the operations on these objects.

Generating Arrays

sppy.diag(a, storagetype='col')

Takes a 1d numpy array and creates a csarray with the corresponding diagonal elements.

Parameters:

• a (numpy.ndarray) – A 1d numpy array
• storagetype (str) – The storage type of the csarray (“row” or “col”)

sppy.eye(n, dtype=<type 'float'>)

Create the identity matrix of size n by n.

Parameters:

• n (int) – The size of the output array
• dtype – The data type of the output array (e.g. numpy.int)

sppy.ones(shape, dtype=<type 'float'>, storageType='col')

Create a ones matrix of the given shape and dtype. Generally a bad idea for large matrices.

Parameters:

• shape – The shape of the output array
• dtype – The data type of the output array (e.g. numpy.int)
• storagetype (str) – The storage type of the csarray (“row” or “col”)

sppy.zeros(shape, dtype=<type 'float'>, storageType='col')

Create a zeros matrix of the given shape and dtype.

Parameters:

• shape – The shape of the output array
• dtype – The data type of the output array (e.g. numpy.int)
• storagetype (str) – The storage type of the csarray (“row” or “col”)

sppy.rand(shape, density, dtype=<type 'float'>, storagetype='col')

Generate a random sparse matrix with m rows and n cols with given density and dtype.

Parameters:

• shape – The shape of the output array (m, n)
• density – The proportion of non zero elements to create
• dtype – The data type of the output array (only supports floats at the moment)
• storagetype (str) – The storage type of the csarray (“row” or “col”)

Methods

class sppy.csarray(self, S, dtype=numpy.float, storagetype='col')

T

csarray.transpose(self)

Swap the rows and columns of this matrix, i.e. perform a transpose operation.

ceil(self)

Take the ceil of the nonzero elements of this array, and return a new array.

clip(self, minVal, maxVal)

Given an interval, values outside the interval are clipped to the interval edges. For example, if an interval of [0, 1] is specified, values smaller than 0 become 0, and values larger than 1 become 1.

Parameters:

• minVal – The minimum value to allow
• maxVal – The maximum value to allow

compress(self)

Turn this matrix into compressed sparse format by freeing extra memory space in the buffer.

copy(self)

Return a copy of this array.

cos(self)

Take the cosine of the nonzero elements of this array, and return a new array.

diag(self)

Return a numpy array containing the diagonal entries of this matrix. If the matrix is non-square then the diagonal array is the same size as the smallest dimension.

dot(self, A)

Compute the dot product between this and either a csarray or numpy array A.

Parameters:A – The input numpy array or csarray.

dtype

csarray.__getDType(self)

floor(self)

Take the floor of the nonzero elements of this array, and return a new array.

getnnz(self)

Return the number of non-zero elements in the array

hadamard(self, A)

Compute the hadamard (element-wise) product between this array and A.

Parameters:A – The input numpy array or csarray.

max(self)

Find the maximum element of this array.

mean(self, axis=None)

Find the mean value of this array.

Parameters:axis – The axis of the array to compute the mean.

min(self)

Find the minimum element of this array.

nonzero(self)

Return a tuple of arrays corresponding to nonzero elements.

nonzeroRowsList(self)

Return a list such that the ith element is an array of nonzero elements in the ith row of this matrix.

nonzeroRowsPtr(self)

Returns two arrays indPtr, colInds, such that colInds[indPtr[i]:indPtr[i+1]] is the set of nonzero elements in the ith row of this matrix.

pdot(self, A)

Compute the dot product between this and either a csarray or numpy array using multithreading.

Parameters:A – The input numpy array or csarray.

power(self, n)

Returns a new array in which all nonzero elements in the array are raised to the nth power.

Parameters:n – The exponent of the power.

prune(self, double eps=1e-10, double precision=1e-20)

Suppresses all nonzeros which are much smaller in magnitude than eps under the tolerence precision.

put(self, data, rowInds, colInds, init=False)

Put some values into this matrix into the corresponding rowInds and colInds. We have A[rowInds[i], colInds[i]] = data[i]/data. Notice that this is faster if init=True but this setting is to be used only if the matrix has just been created.

Parameters:

• vals – A scalar or numpy array with the same dimension as rowsInds and colInds
• rowInds – A 1d numpy array of row indices.
• colInds – A 1d numpy array of column indices.

reserve(self, int n)

Reserve n nonzero entries and turns the matrix into uncompressed mode.

Parameters:n (int) – The number of elements of space to reserve.

rowInds(self, int i)

Returns the non zero indices for the ith row.

Parameters:i (int) – The index of the row of the array.

sign(self)

Take the sign of the nonzero elements of this array, and return a new array.

sin(self)

Take the sine of the nonzero elements of this array, and return a new array.

std(self)

Return the standard deviation of the array elements.

submatrix(self, startRow, startCol, blockRows, blockCols)

Return a submatrix of the matrix given by A[startRow:startRows+blockRows, startCol:startCol+blockCols] in an efficient manner.

Parameters:

• startRow (int) – The starting row index
• startCol (int) – The starting column index
• blockRows (int) – The number of rows to take.
• blockCols (int) – The number of columns to take.

sum(self, axis=None)

Sum all of the elements in this array. If one specifies an axis then we sum along the axis.

Parameters:axis – The axis to sum along.

toScipyCsc(self)

Convert this matrix to a scipy sparse matrix. Returns a copy of the data in csc_matrix form.

toScipyCsr(self)

Convert this matrix to a scipy sparse matrix. Returns a copy of the data in csr_matrix form.

toarray(self)

Convert this sparse array into a numpy array.

trace(self)

Returns the trace of the array which is simply the sum of the diagonal entries.

transpose(self)

Swap the rows and columns of this matrix, i.e. perform a transpose operation.

values(self)

Return the values of this object according to the elements returned using nonzero.

var(self)

Return the variance of the elements of this array.