egttools.analytical.sed_analytical.lil_matrix¶

class lil_matrix(arg1, shape=None, dtype=None, copy=False)[source]¶

Bases: spmatrix, IndexMixin

Row-based list of lists sparse matrix

This is a structure for constructing sparse matrices incrementally. Note that inserting a single item can take linear time in the worst case; to construct a matrix efficiently, make sure the items are pre-sorted by index, per row.

This can be instantiated in several ways:

lil_matrix(D): with a dense matrix or rank-2 ndarray D
lil_matrix(S): with another sparse matrix S (equivalent to S.tolil())
lil_matrix((M, N), [dtype]): to construct an empty matrix with shape (M, N) dtype is optional, defaulting to dtype=’d’.

dtype¶

Data type of the matrix

Type: dtype

shape¶

Shape of the matrix

Type: 2-tuple

ndim¶

Number of dimensions (this is always 2)

Type: int

nnz¶: Number of stored values, including explicit zeros

data¶: LIL format data array of the matrix

rows¶: LIL format row index array of the matrix

Notes

Sparse matrices can be used in arithmetic operations: they support addition, subtraction, multiplication, division, and matrix power.

Advantages of the LIL format

supports flexible slicing
changes to the matrix sparsity structure are efficient

Disadvantages of the LIL format

arithmetic operations LIL + LIL are slow (consider CSR or CSC)
slow column slicing (consider CSC)
slow matrix vector products (consider CSR or CSC)

Intended Usage

LIL is a convenient format for constructing sparse matrices
once a matrix has been constructed, convert to CSR or CSC format for fast arithmetic and matrix vector operations
consider using the COO format when constructing large matrices

Data Structure

An array (self.rows) of rows, each of which is a sorted list of column indices of non-zero elements.
The corresponding nonzero values are stored in similar fashion in self.data.

Methods

`asformat`	Return this matrix in the passed format.
`asfptype`	Upcast matrix to a floating point format (if necessary)
`astype`	Cast the matrix elements to a specified type.
`conj`	Element-wise complex conjugation.
`conjugate`	Element-wise complex conjugation.
`copy`	Returns a copy of this matrix.
`count_nonzero`	Number of non-zero entries, equivalent to
`diagonal`	Returns the kth diagonal of the matrix.
`dot`	Ordinary dot product
`getH`	Return the Hermitian transpose of this matrix.
`get_shape`	Get shape of a matrix.
`getcol`	Returns a copy of column j of the matrix, as an (m x 1) sparse matrix (column vector).
`getformat`	Format of a matrix representation as a string.
`getmaxprint`	Maximum number of elements to display when printed.
`getnnz`	Number of stored values, including explicit zeros.
`getrow`	Returns a copy of the 'i'th row.
`getrowview`	Returns a view of the 'i'th row (without copying).
`maximum`	Element-wise maximum between this and another matrix.
`mean`	Compute the arithmetic mean along the specified axis.
`minimum`	Element-wise minimum between this and another matrix.
`multiply`	Point-wise multiplication by another matrix
`nonzero`	nonzero indices
`power`	Element-wise power.
`reshape`	Gives a new shape to a sparse matrix without changing its data.
`resize`	Resize the matrix in-place to dimensions given by `shape`
`set_shape`	See `reshape`.
`setdiag`	Set diagonal or off-diagonal elements of the array.
`sum`	Sum the matrix elements over a given axis.
`toarray`	Return a dense ndarray representation of this matrix.
`tobsr`	Convert this matrix to Block Sparse Row format.
`tocoo`	Convert this matrix to COOrdinate format.
`tocsc`	Convert this matrix to Compressed Sparse Column format.
`tocsr`	Convert this matrix to Compressed Sparse Row format.
`todense`	Return a dense matrix representation of this matrix.
`todia`	Convert this matrix to sparse DIAgonal format.
`todok`	Convert this matrix to Dictionary Of Keys format.
`tolil`	Convert this matrix to List of Lists format.
`trace`	Returns the sum along diagonals of the sparse matrix.
`transpose`	Reverses the dimensions of the sparse matrix.

Attributes

`format`
`ndim`
`nnz`	Number of stored values, including explicit zeros.
`shape`	Get shape of a matrix.

__abs__()¶

__add__(other)¶

__bool__()¶

__div__(other)¶

__eq__(other)¶: Return self==value.

__ge__(other)¶: Return self>=value.

__getattr__(attr)¶

__getitem__(key)[source]¶

__gt__(other)¶: Return self>value.

__iadd__(other)[source]¶

__idiv__(other)¶

__imul__(other)[source]¶

__init__(arg1, shape=None, dtype=None, copy=False)[source]¶

__isub__(other)[source]¶

__iter__()¶

__itruediv__(other)[source]¶

__le__(other)¶: Return self<=value.

__len__()¶

__lt__(other)¶: Return self<value.

__matmul__(other)¶

__mul__(other)¶

__ne__(other)¶: Return self!=value.

__neg__()¶

__nonzero__()¶

__pow__(other)¶

__radd__(other)¶

__rdiv__(other)¶

__repr__()¶: Return repr(self).

__rmatmul__(other)¶

__rmul__(other)¶

__round__(ndigits=0)¶

__rsub__(other)¶

__rtruediv__(other)¶

__setitem__(key, x)[source]¶

__str__()[source]¶: Return str(self).

__sub__(other)¶

__truediv__(other)[source]¶

asformat(format, copy=False)¶

Return this matrix in the passed format.

Parameters

format ({str, None}) – The desired matrix format (“csr”, “csc”, “lil”, “dok”, “array”, …) or None for no conversion.
copy (bool, optional) – If True, the result is guaranteed to not share data with self.

Returns

A

Return type

This matrix in the passed format.

asfptype()¶: Upcast matrix to a floating point format (if necessary)

astype(dtype, casting='unsafe', copy=True)¶

Cast the matrix elements to a specified type.

Parameters

dtype (string or numpy dtype) – Typecode or data-type to which to cast the data.
casting ({'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional) – Controls what kind of data casting may occur. Defaults to ‘unsafe’ for backwards compatibility. ‘no’ means the data types should not be cast at all. ‘equiv’ means only byte-order changes are allowed. ‘safe’ means only casts which can preserve values are allowed. ‘same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed. ‘unsafe’ means any data conversions may be done.
copy (bool, optional) – If copy is False, the result might share some memory with this matrix. If copy is True, it is guaranteed that the result and this matrix do not share any memory.

conj(copy=True)¶

Element-wise complex conjugation.

If the matrix is of non-complex data type and copy is False, this method does nothing and the data is not copied.

Parameters: copy (bool, optional) – If True, the result is guaranteed to not share data with self.
Returns: A
Return type: The element-wise complex conjugate.

conjugate(copy=True)¶

Element-wise complex conjugation.

If the matrix is of non-complex data type and copy is False, this method does nothing and the data is not copied.

Parameters: copy (bool, optional) – If True, the result is guaranteed to not share data with self.
Returns: A
Return type: The element-wise complex conjugate.

copy()[source]¶

Returns a copy of this matrix.

No data/indices will be shared between the returned value and current matrix.

count_nonzero()[source]¶

Number of non-zero entries, equivalent to

np.count_nonzero(a.toarray())

Unlike getnnz() and the nnz property, which return the number of stored entries (the length of the data attribute), this method counts the actual number of non-zero entries in data.

diagonal(k=0)¶

Returns the kth diagonal of the matrix.

Parameters

k (int, optional) –

Which diagonal to get, corresponding to elements a[i, i+k]. Default: 0 (the main diagonal).

New in version 1.0.

See also

numpy.diagonal: Equivalent numpy function.

Examples

>>> from scipy.sparse import csr_matrix
>>> A = csr_matrix([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
>>> A.diagonal()
array([1, 0, 5])
>>> A.diagonal(k=1)
array([2, 3])

dot(other)¶

Ordinary dot product

Examples

>>> import numpy as np
>>> from scipy.sparse import csr_matrix
>>> A = csr_matrix([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
>>> v = np.array([1, 0, -1])
>>> A.dot(v)
array([ 1, -3, -1], dtype=int64)

getH()¶

Return the Hermitian transpose of this matrix.

See also

numpy.matrix.getH: NumPy’s implementation of getH for matrices

get_shape()¶: Get shape of a matrix.

getcol(j)¶: Returns a copy of column j of the matrix, as an (m x 1) sparse matrix (column vector).

getformat()¶: Format of a matrix representation as a string.

getmaxprint()¶: Maximum number of elements to display when printed.

getnnz(axis=None)[source]¶

Number of stored values, including explicit zeros.

Parameters: axis (None, 0, or 1) – Select between the number of values across the whole matrix, in each column, or in each row.

See also

count_nonzero: Number of non-zero entries

getrow(i)[source]¶: Returns a copy of the ‘i’th row.

getrowview(i)[source]¶: Returns a view of the ‘i’th row (without copying).

maximum(other)¶: Element-wise maximum between this and another matrix.

mean(axis=None, dtype=None, out=None)¶

Compute the arithmetic mean along the specified axis.

Returns the average of the matrix elements. The average is taken over all elements in the matrix by default, otherwise over the specified axis. float64 intermediate and return values are used for integer inputs.

Parameters

axis ({-2, -1, 0, 1, None} optional) – Axis along which the mean is computed. The default is to compute the mean of all elements in the matrix (i.e., axis = None).
dtype (data-type, optional) –
Type to use in computing the mean. For integer inputs, the default is float64; for floating point inputs, it is the same as the input dtype.

New in version 0.18.0.
out (np.matrix, optional) –
Alternative output matrix in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary.

New in version 0.18.0.

Returns

m

Return type

np.matrix

See also

numpy.matrix.mean: NumPy’s implementation of ‘mean’ for matrices

minimum(other)¶: Element-wise minimum between this and another matrix.

multiply(other)¶: Point-wise multiplication by another matrix

nonzero()¶

nonzero indices

Returns a tuple of arrays (row,col) containing the indices of the non-zero elements of the matrix.

Examples

>>> from scipy.sparse import csr_matrix
>>> A = csr_matrix([[1,2,0],[0,0,3],[4,0,5]])
>>> A.nonzero()
(array([0, 0, 1, 2, 2]), array([0, 1, 2, 0, 2]))

power(n, dtype=None)¶: Element-wise power.

reshape(self, shape, order='C', copy=False)[source]¶

Gives a new shape to a sparse matrix without changing its data.

Parameters

shape (length-2 tuple of ints) – The new shape should be compatible with the original shape.
order ({'C', 'F'}, optional) – Read the elements using this index order. ‘C’ means to read and write the elements using C-like index order; e.g., read entire first row, then second row, etc. ‘F’ means to read and write the elements using Fortran-like index order; e.g., read entire first column, then second column, etc.
copy (bool, optional) – Indicates whether or not attributes of self should be copied whenever possible. The degree to which attributes are copied varies depending on the type of sparse matrix being used.

Returns

reshaped_matrix – A sparse matrix with the given shape, not necessarily of the same format as the current object.

Return type

sparse matrix

See also

numpy.matrix.reshape: NumPy’s implementation of ‘reshape’ for matrices

resize(*shape)[source]¶

Resize the matrix in-place to dimensions given by shape

Any elements that lie within the new shape will remain at the same indices, while non-zero elements lying outside the new shape are removed.

Parameters: shape ((int, int)) – number of rows and columns in the new matrix

Notes

The semantics are not identical to numpy.ndarray.resize or numpy.resize. Here, the same data will be maintained at each index before and after reshape, if that index is within the new bounds. In numpy, resizing maintains contiguity of the array, moving elements around in the logical matrix but not within a flattened representation.

We give no guarantees about whether the underlying data attributes (arrays, etc.) will be modified in place or replaced with new objects.

set_shape(shape)¶: See reshape.

setdiag(values, k=0)¶

Set diagonal or off-diagonal elements of the array.

Parameters

values (array_like) –
New values of the diagonal elements.

Values may have any length. If the diagonal is longer than values, then the remaining diagonal entries will not be set. If values are longer than the diagonal, then the remaining values are ignored.

If a scalar value is given, all of the diagonal is set to it.
k (int, optional) – Which off-diagonal to set, corresponding to elements a[i,i+k]. Default: 0 (the main diagonal).

sum(axis=None, dtype=None, out=None)¶

Sum the matrix elements over a given axis.

Parameters

axis ({-2, -1, 0, 1, None} optional) – Axis along which the sum is computed. The default is to compute the sum of all the matrix elements, returning a scalar (i.e., axis = None).
dtype (dtype, optional) –
The type of the returned matrix and of the accumulator in which the elements are summed. The dtype of a is used by default unless a has an integer dtype of less precision than the default platform integer. In that case, if a is signed then the platform integer is used while if a is unsigned then an unsigned integer of the same precision as the platform integer is used.

New in version 0.18.0.
out (np.matrix, optional) –
Alternative output matrix in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary.

New in version 0.18.0.

Returns

sum_along_axis – A matrix with the same shape as self, with the specified axis removed.

Return type

np.matrix

See also

numpy.matrix.sum: NumPy’s implementation of ‘sum’ for matrices

toarray(order=None, out=None)[source]¶

Return a dense ndarray representation of this matrix.

Parameters

order ({'C', 'F'}, optional) – Whether to store multidimensional data in C (row-major) or Fortran (column-major) order in memory. The default is ‘None’, which provides no ordering guarantees. Cannot be specified in conjunction with the out argument.
out (ndarray, 2-D, optional) – If specified, uses this array as the output buffer instead of allocating a new array to return. The provided array must have the same shape and dtype as the sparse matrix on which you are calling the method. For most sparse types, out is required to be memory contiguous (either C or Fortran ordered).

Returns

arr – An array with the same shape and containing the same data represented by the sparse matrix, with the requested memory order. If out was passed, the same object is returned after being modified in-place to contain the appropriate values.

Return type

ndarray, 2-D

tobsr(blocksize=None, copy=False)¶

Convert this matrix to Block Sparse Row format.

With copy=False, the data/indices may be shared between this matrix and the resultant bsr_matrix.

When blocksize=(R, C) is provided, it will be used for construction of the bsr_matrix.

tocoo(copy=False)¶

Convert this matrix to COOrdinate format.

With copy=False, the data/indices may be shared between this matrix and the resultant coo_matrix.

tocsc(copy=False)¶

Convert this matrix to Compressed Sparse Column format.

With copy=False, the data/indices may be shared between this matrix and the resultant csc_matrix.

tocsr(copy=False)[source]¶

Convert this matrix to Compressed Sparse Row format.

With copy=False, the data/indices may be shared between this matrix and the resultant csr_matrix.

todense(order=None, out=None)¶

Return a dense matrix representation of this matrix.

Parameters

order ({'C', 'F'}, optional) – Whether to store multi-dimensional data in C (row-major) or Fortran (column-major) order in memory. The default is ‘None’, which provides no ordering guarantees. Cannot be specified in conjunction with the out argument.
out (ndarray, 2-D, optional) – If specified, uses this array (or numpy.matrix) as the output buffer instead of allocating a new array to return. The provided array must have the same shape and dtype as the sparse matrix on which you are calling the method.

Returns

arr – A NumPy matrix object with the same shape and containing the same data represented by the sparse matrix, with the requested memory order. If out was passed and was an array (rather than a numpy.matrix), it will be filled with the appropriate values and returned wrapped in a numpy.matrix object that shares the same memory.

Return type

numpy.matrix, 2-D

todia(copy=False)¶

Convert this matrix to sparse DIAgonal format.

With copy=False, the data/indices may be shared between this matrix and the resultant dia_matrix.

todok(copy=False)¶

Convert this matrix to Dictionary Of Keys format.

With copy=False, the data/indices may be shared between this matrix and the resultant dok_matrix.

tolil(copy=False)[source]¶

Convert this matrix to List of Lists format.

With copy=False, the data/indices may be shared between this matrix and the resultant lil_matrix.

trace(offset=0)¶

Returns the sum along diagonals of the sparse matrix.

Parameters: offset (int, optional) – Which diagonal to get, corresponding to elements a[i, i+offset]. Default: 0 (the main diagonal).

transpose(axes=None, copy=False)[source]¶

Reverses the dimensions of the sparse matrix.

Parameters

axes (None, optional) – This argument is in the signature solely for NumPy compatibility reasons. Do not pass in anything except for the default value.
copy (bool, optional) – Indicates whether or not attributes of self should be copied whenever possible. The degree to which attributes are copied varies depending on the type of sparse matrix being used.

Returns

p

Return type

self with the dimensions reversed.

See also

numpy.matrix.transpose: NumPy’s implementation of ‘transpose’ for matrices

__array_priority__ = 10.1¶

__hash__ = None¶

format = 'lil'¶

ndim = 2¶

property nnz¶

Number of stored values, including explicit zeros.

See also

count_nonzero: Number of non-zero entries

property shape¶: Get shape of a matrix.