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- from sympy.matrices.expressions.matexpr import MatrixExpr
- from sympy.core.basic import Basic
- from sympy.core.containers import Tuple
- from sympy.functions.elementary.integers import floor
- def normalize(i, parentsize):
- if isinstance(i, slice):
- i = (i.start, i.stop, i.step)
- if not isinstance(i, (tuple, list, Tuple)):
- if (i < 0) == True:
- i += parentsize
- i = (i, i+1, 1)
- i = list(i)
- if len(i) == 2:
- i.append(1)
- start, stop, step = i
- start = start or 0
- if stop is None:
- stop = parentsize
- if (start < 0) == True:
- start += parentsize
- if (stop < 0) == True:
- stop += parentsize
- step = step or 1
- if ((stop - start) * step < 1) == True:
- raise IndexError()
- return (start, stop, step)
- class MatrixSlice(MatrixExpr):
- """ A MatrixSlice of a Matrix Expression
- Examples
- ========
- >>> from sympy import MatrixSlice, ImmutableMatrix
- >>> M = ImmutableMatrix(4, 4, range(16))
- >>> M
- Matrix([
- [ 0, 1, 2, 3],
- [ 4, 5, 6, 7],
- [ 8, 9, 10, 11],
- [12, 13, 14, 15]])
- >>> B = MatrixSlice(M, (0, 2), (2, 4))
- >>> ImmutableMatrix(B)
- Matrix([
- [2, 3],
- [6, 7]])
- """
- parent = property(lambda self: self.args[0])
- rowslice = property(lambda self: self.args[1])
- colslice = property(lambda self: self.args[2])
- def __new__(cls, parent, rowslice, colslice):
- rowslice = normalize(rowslice, parent.shape[0])
- colslice = normalize(colslice, parent.shape[1])
- if not (len(rowslice) == len(colslice) == 3):
- raise IndexError()
- if ((0 > rowslice[0]) == True or
- (parent.shape[0] < rowslice[1]) == True or
- (0 > colslice[0]) == True or
- (parent.shape[1] < colslice[1]) == True):
- raise IndexError()
- if isinstance(parent, MatrixSlice):
- return mat_slice_of_slice(parent, rowslice, colslice)
- return Basic.__new__(cls, parent, Tuple(*rowslice), Tuple(*colslice))
- @property
- def shape(self):
- rows = self.rowslice[1] - self.rowslice[0]
- rows = rows if self.rowslice[2] == 1 else floor(rows/self.rowslice[2])
- cols = self.colslice[1] - self.colslice[0]
- cols = cols if self.colslice[2] == 1 else floor(cols/self.colslice[2])
- return rows, cols
- def _entry(self, i, j, **kwargs):
- return self.parent._entry(i*self.rowslice[2] + self.rowslice[0],
- j*self.colslice[2] + self.colslice[0],
- **kwargs)
- @property
- def on_diag(self):
- return self.rowslice == self.colslice
- def slice_of_slice(s, t):
- start1, stop1, step1 = s
- start2, stop2, step2 = t
- start = start1 + start2*step1
- step = step1 * step2
- stop = start1 + step1*stop2
- if stop > stop1:
- raise IndexError()
- return start, stop, step
- def mat_slice_of_slice(parent, rowslice, colslice):
- """ Collapse nested matrix slices
- >>> from sympy import MatrixSymbol
- >>> X = MatrixSymbol('X', 10, 10)
- >>> X[:, 1:5][5:8, :]
- X[5:8, 1:5]
- >>> X[1:9:2, 2:6][1:3, 2]
- X[3:7:2, 4:5]
- """
- row = slice_of_slice(parent.rowslice, rowslice)
- col = slice_of_slice(parent.colslice, colslice)
- return MatrixSlice(parent.parent, row, col)
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