Dense Matrices¶
Matrix Class Reference¶
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class
diofant.matrices.dense.
DenseMatrix
[source]¶ -
__getitem__
(key)[source]¶ Return portion of self defined by key. If the key involves a slice then a list will be returned (if key is a single slice) or a matrix (if key was a tuple involving a slice).
Examples
>>> m = Matrix([ ... [1, 2 + I], ... [3, 4 ]])
If the key is a tuple that doesn’t involve a slice then that element is returned:
>>> m[1, 0] 3
When a tuple key involves a slice, a matrix is returned. Here, the first column is selected (all rows, column 0):
>>> m[:, 0] Matrix([ [1], [3]])
If the slice is not a tuple then it selects from the underlying list of elements that are arranged in row order and a list is returned if a slice is involved:
>>> m[0] 1 >>> m[::2] [1, 3]
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applyfunc
(f)[source]¶ Apply a function to each element of the matrix.
Examples
>>> m = Matrix(2, 2, lambda i, j: i*2+j) >>> m Matrix([ [0, 1], [2, 3]]) >>> m.applyfunc(lambda i: 2*i) Matrix([ [0, 2], [4, 6]])
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as_mutable
()[source]¶ Returns a mutable version of this matrix
Examples
>>> X = ImmutableMatrix([[1, 2], [3, 4]]) >>> Y = X.as_mutable() >>> Y[1, 1] = 5 # Can set values in Y >>> Y Matrix([ [1, 2], [3, 5]])
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equals
(other, failing_expression=False)[source]¶ Applies
equals
to corresponding elements of the matrices, trying to prove that the elements are equivalent, returning True if they are, False if any pair is not, and None (or the first failing expression if failing_expression is True) if it cannot be decided if the expressions are equivalent or not. This is, in general, an expensive operation.Examples
>>> A = Matrix([x*(x - 1), 0]) >>> B = Matrix([x**2 - x, 0]) >>> A == B False >>> A.simplify() == B.simplify() True >>> A.equals(B) True >>> A.equals(2) False
See also
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reshape
(rows, cols)[source]¶ Reshape the matrix. Total number of elements must remain the same.
Examples
>>> m = Matrix(2, 3, lambda i, j: 1) >>> m Matrix([ [1, 1, 1], [1, 1, 1]]) >>> m.reshape(1, 6) Matrix([[1, 1, 1, 1, 1, 1]]) >>> m.reshape(3, 2) Matrix([ [1, 1], [1, 1], [1, 1]])
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tolist
()[source]¶ Return the Matrix as a nested Python list.
Examples
>>> m = Matrix(3, 3, range(9)) >>> m Matrix([ [0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> m.tolist() [[0, 1, 2], [3, 4, 5], [6, 7, 8]] >>> ones(3, 0).tolist() [[], [], []]
When there are no rows then it will not be possible to tell how many columns were in the original matrix:
>>> ones(0, 3).tolist() []
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class
diofant.matrices.dense.
MutableDenseMatrix
[source]¶ -
col_op
(j, f)[source]¶ In-place operation on col j using two-arg functor whose args are interpreted as (self[i, j], i).
Examples
>>> M = eye(3) >>> M.col_op(1, lambda v, i: v + 2*M[i, 0]); M Matrix([ [1, 2, 0], [0, 1, 0], [0, 0, 1]])
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col_swap
(i, j)[source]¶ Swap the two given columns of the matrix in-place.
Examples
>>> M = Matrix([[1, 0], [1, 0]]) >>> M Matrix([ [1, 0], [1, 0]]) >>> M.col_swap(0, 1) >>> M Matrix([ [0, 1], [0, 1]])
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copyin_list
(key, value)[source]¶ Copy in elements from a list.
Parameters: - key (slice) – The section of this matrix to replace.
- value (iterable) – The iterable to copy values from.
Examples
>>> I = eye(3) >>> I[:2, 0] = [1, 2] # col >>> I Matrix([ [1, 0, 0], [2, 1, 0], [0, 0, 1]]) >>> I[1, :2] = [[3, 4]] >>> I Matrix([ [1, 0, 0], [3, 4, 0], [0, 0, 1]])
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copyin_matrix
(key, value)[source]¶ Copy in values from a matrix into the given bounds.
Parameters: - key (slice) – The section of this matrix to replace.
- value (Matrix) – The matrix to copy values from.
Examples
>>> M = Matrix([[0, 1], [2, 3], [4, 5]]) >>> I = eye(3) >>> I[:3, :2] = M >>> I Matrix([ [0, 1, 0], [2, 3, 0], [4, 5, 1]]) >>> I[0, 1] = M >>> I Matrix([ [0, 0, 1], [2, 2, 3], [4, 4, 5]])
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row_op
(i, f)[source]¶ In-place operation on row
i
using two-arg functor whose args are interpreted as(self[i, j], j)
.Examples
>>> M = eye(3) >>> M.row_op(1, lambda v, j: v + 2*M[0, j]); M Matrix([ [1, 0, 0], [2, 1, 0], [0, 0, 1]])
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row_swap
(i, j)[source]¶ Swap the two given rows of the matrix in-place.
Examples
>>> M = Matrix([[0, 1], [1, 0]]) >>> M Matrix([ [0, 1], [1, 0]]) >>> M.row_swap(0, 1) >>> M Matrix([ [1, 0], [0, 1]])
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class
diofant.matrices.dense.
MutableMatrix
¶ alias of
MutableDenseMatrix
ImmutableMatrix Class Reference¶
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class
diofant.matrices.immutable.
ImmutableMatrix
[source] Create an immutable version of a matrix.
Examples
>>> ImmutableMatrix(eye(3)) Matrix([ [1, 0, 0], [0, 1, 0], [0, 0, 1]]) >>> _[0, 0] = 42 Traceback (most recent call last): ... TypeError: Cannot set values of ImmutableDenseMatrix
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C
By-element conjugation.
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adjoint
() Conjugate transpose or Hermitian conjugation.
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as_mutable
() Returns a mutable version of this matrix
Examples
>>> X = ImmutableMatrix([[1, 2], [3, 4]]) >>> Y = X.as_mutable() >>> Y[1, 1] = 5 # Can set values in Y >>> Y Matrix([ [1, 2], [3, 5]])
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conjugate
() By-element conjugation.
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equals
(other, failing_expression=False) Applies
equals
to corresponding elements of the matrices, trying to prove that the elements are equivalent, returning True if they are, False if any pair is not, and None (or the first failing expression if failing_expression is True) if it cannot be decided if the expressions are equivalent or not. This is, in general, an expensive operation.Examples
>>> A = Matrix([x*(x - 1), 0]) >>> B = Matrix([x**2 - x, 0]) >>> A == B False >>> A.simplify() == B.simplify() True >>> A.equals(B) True >>> A.equals(2) False
See also
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is_zero
Checks if a matrix is a zero matrix.
A matrix is zero if every element is zero. A matrix need not be square to be considered zero. The empty matrix is zero by the principle of vacuous truth. For a matrix that may or may not be zero (e.g. contains a symbol), this will be None
Examples
>>> a = Matrix([[0, 0], [0, 0]]) >>> b = zeros(3, 4) >>> c = Matrix([[0, 1], [0, 0]]) >>> d = Matrix([]) >>> e = Matrix([[x, 0], [0, 0]]) >>> a.is_zero True >>> b.is_zero True >>> c.is_zero False >>> d.is_zero True >>> e.is_zero
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