# Ticket #8046: trac_8046-ref.patch

File trac_8046-ref.patch, 3.9 KB (added by John Palmieri, 11 years ago)
• ## sage/matrix/matrix_double_dense.pyx

# HG changeset patch
# User J. H. Palmieri <palmieri@math.washington.edu>
# Date 1326350430 28800
# Node ID 5d72b52fa3c5d8817483402f209cbb2891d1f46b
diff --git a/sage/matrix/matrix_double_dense.pyx b/sage/matrix/matrix_double_dense.pyx
 a cdef class Matrix_double_dense(matrix_de INPUT: - p - default: 'frob' - controls which norm is used to compute the condition number, allowable values are 'frob' (for the Frobenius norm), integers -2, -1, 1, 2, positive and negative infinity. See output discussion for specifics. to compute the condition number, allowable values are 'frob' (for the Frobenius norm), integers -2, -1, 1, 2, positive and negative infinity. See output discussion for specifics. OUTPUT: cdef class Matrix_double_dense(matrix_de INPUT: - self -- an invertible matrix - b -- a vector - self -- an invertible matrix - b -- a vector .. NOTE:: cdef class Matrix_double_dense(matrix_de INPUT: A -- a matrix - A -- a matrix OUTPUT: U, S, V -- immutable matrices such that $A = U*S*V.conj().transpose()$ where U and V are orthogonal and S is zero off of the diagonal. - U, S, V -- immutable matrices such that $A = U*S*V.conj().transpose()$ where U and V are orthogonal and S is zero off of the diagonal. Note that if self is m-by-n, then the dimensions of the matrices that this returns are (m,m), (m,n), and (n, n). cdef class Matrix_double_dense(matrix_de INPUT: self -- a real matrix A - self -- a real matrix A OUTPUT: Q, R -- immutable matrices such that A = Q*R such that the columns of Q are orthogonal (i.e., $Q^t Q = I$), and R is upper triangular. - Q, R -- immutable matrices such that A = Q*R such that the columns of Q are orthogonal (i.e., $Q^t Q = I$), and R is upper triangular. EXAMPLES:: cdef class Matrix_double_dense(matrix_de AUTHOR: - Rob Beezer (2011-03-30) - Rob Beezer (2011-03-30) """ import sage.rings.complex_double global numpy cdef class Matrix_double_dense(matrix_de AUTHOR: - Rob Beezer (2011-03-31) - Rob Beezer (2011-03-31) """ global scipy from sage.rings.real_double import RDF cdef class Matrix_double_dense(matrix_de r""" Calculate the exponential of this matrix X, which is the matrix e^X = sum_{k=0}^{infty} frac{X^k}{k!}. .. math:: e^X = \sum_{k=0}^{\infty} \frac{X^k}{k!}. INPUT: - algorithm -- 'pade', 'eig', or 'taylor'; the algorithm used to compute the exponential. - order -- for Pade or Taylor series algorithms, order is the order of the Pade approximation or the order of the Taylor series used.  The current defaults (from scipy) are 7 for 'pade' and 20 for 'taylor'. - algorithm -- 'pade', 'eig', or 'taylor'; the algorithm used to compute the exponential. - order -- for Pade or Taylor series algorithms, order is the order of the Pade approximation or the order of the Taylor series used.  The current defaults (from scipy) are 7 for 'pade' and 20 for 'taylor'. EXAMPLES::