Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 sage: len(B.nonzero_positions()) 17550 # 32-bit 125449 # 64-bit # long time We must pass in a list of indices: sage: A=random_matrix(ZZ,100,density=.02,sparse=True) sage: A.matrix_from_rows_and_columns(1,[2,3]) Traceback (most recent call last): ... TypeError: rows must be a list of integers sage: A.matrix_from_rows_and_columns([1,2],3) Traceback (most recent call last): ... TypeError: columns must be a list of integers AUTHORS: •Jaap Spies (2006-02-18) •Didier Deshommes: some Pyrex speedups implemented •Jason Grout: sparse matrix optimizations stack(bottom, subdivide=False) Stack self on top of bottom. [ self ] [ bottom ] EXAMPLES: sage: M = Matrix(QQ, 2, 3, range(6), sparse=True) sage: N = Matrix(QQ, 1, 3, [10,11,12], sparse=True) sage: M.stack(N) [ 0 1 2] [ 3 4 5] [10 11 12] A vector may be stacked below a matrix. sage: A = matrix(QQ, 2, 5, range(10), sparse=True) sage: v = vector(QQ, 5, range(5), sparse=True) sage: A.stack(v) [0 1 2 3 4] [5 6 7 8 9] [0 1 2 3 4] The subdivide option will add a natural subdivision between self and other. For more details about how subdivisions are managed when stacking, see sage.matrix.matrix1.Matrix.stack(). sage: A = matrix(ZZ, 3, 4, range(12), sparse=True) sage: B = matrix(ZZ, 2, 4, range(8), sparse=True) sage: A.stack(B, subdivide=True) [ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11] [-----------] [ 0 1 2 3] [ 4 5 6 7] transpose() Returns the transpose of self, without changing self. 286 Chapter 11. Base class for sparse matrices
Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 EXAMPLES: We create a matrix, compute its transpose, and note that the original matrix is not changed. sage: M = MatrixSpace(QQ, sage: A = M([1,2,3,4]) sage: B = A.transpose() sage: print B [1 3] [2 4] sage: print A [1 2] [3 4] 2, sparse=True) .T is a convenient shortcut for the transpose: sage: A.T [1 3] [2 4] 287
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Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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