Lines Matching refs:matrix
24 * matrix functions.
33 * - \ref matrixbase_cos "MatrixBase::cos()", for computing the matrix cosine
34 * - \ref matrixbase_cosh "MatrixBase::cosh()", for computing the matrix hyperbolic cosine
35 * - \ref matrixbase_exp "MatrixBase::exp()", for computing the matrix exponential
36 * - \ref matrixbase_log "MatrixBase::log()", for computing the matrix logarithm
37 * - \ref matrixbase_pow "MatrixBase::pow()", for computing the matrix power
38 …* - \ref matrixbase_matrixfunction "MatrixBase::matrixFunction()", for computing general matrix f…
39 * - \ref matrixbase_sin "MatrixBase::sin()", for computing the matrix sine
40 * - \ref matrixbase_sinh "MatrixBase::sinh()", for computing the matrix hyperbolic sine
41 * - \ref matrixbase_sqrt "MatrixBase::sqrt()", for computing the matrix square root
50 * converges to \f$ f(x) \f$. In this case, we can define the matrix
76 Compute the matrix cosine.
82 \param[in] M a square matrix.
85 This function computes the matrix cosine. Use ArrayBase::cos() for computing the entry-wise cosine.
95 Compute the matrix hyberbolic cosine.
101 \param[in] M a square matrix.
112 Compute the matrix exponential.
118 \param[in] M matrix whose exponential is to be computed.
119 \returns expression representing the matrix exponential of \p M.
121 The matrix exponential of \f$ M \f$ is defined by
123 The matrix exponential can be used to solve linear ordinary
128 The matrix exponential is different from applying the exp function to all the entries in the matrix.
133 norm of the matrix.
135 The matrix exponential is computed using the scaling-and-squaring
136 method combined with Padé approximation. The matrix is first
137 rescaled, then the exponential of the reduced matrix is computed
144 scaling and squaring method for the matrix exponential revisited,"
164 \note \p M has to be a matrix of \c float, \c double, \c long double
170 Compute the matrix logarithm.
176 \param[in] M invertible matrix whose logarithm is to be computed.
177 \returns expression representing the matrix logarithm root of \p M.
179 The matrix logarithm of \f$ M \f$ is a matrix \f$ X \f$ such that
180 \f$ \exp(X) = M \f$ where exp denotes the matrix exponential. As for
182 multiple solutions; this function returns a matrix whose eigenvalues
185 The matrix logarithm is different from applying the log function to all the entries in the matrix.
188 In the real case, the matrix \f$ M \f$ should be invertible and
193 This function computes the matrix logarithm using the Schur-Parlett
222 \note \p M has to be a matrix of \c float, \c double, <tt>long
232 Compute the matrix raised to arbitrary real power.
238 \param[in] M base of the matrix power, should be a square matrix.
239 \param[in] p exponent of the matrix power.
241 The matrix power \f$ M^p \f$ is defined as \f$ \exp(p \log(M)) \f$,
242 where exp denotes the matrix exponential, and log denotes the matrix
243 logarithm. This is different from raising all the entries in the matrix
248 Therefore, the matrix \f$ M \f$ should meet the conditions to be an
249 argument of matrix logarithm.
252 this function computes the matrix power using the Schur-Padé
274 \warning Fractional power of a matrix with a non-semisimple zero
301 matrix," <em>SIAM J. %Matrix Anal. Applic.</em>,
323 better for computing various powers for the same matrix.
329 \note \p M has to be a matrix of \c float, \c double, <tt>long
338 Compute a matrix function.
344 \param[in] M argument of matrix function, should be a square matrix.
349 Suppose that \p M is a matrix whose entries have type \c Scalar.
361 "A Schur-Parlett algorithm for computing matrix functions",
384 \c x, even though the matrix \c A is over the reals. Instead of
394 Compute the matrix sine.
400 \param[in] M a square matrix.
403 This function computes the matrix sine. Use ArrayBase::sin() for computing the entry-wise sine.
414 Compute the matrix hyperbolic sine.
420 \param[in] M a square matrix.
431 Compute the matrix square root.
437 \param[in] M invertible matrix whose square root is to be computed.
438 \returns expression representing the matrix square root of \p M.
440 The matrix square root of \f$ M \f$ is the matrix \f$ M^{1/2} \f$
441 whose square is the original matrix; so if \f$ S = M^{1/2} \f$ then
443 the entries in the matrix; use ArrayBase::sqrt() if you want to do the
446 In the <b>real case</b>, the matrix \f$ M \f$ should be invertible and
448 complex conjugate eigenvalues are allowed). In that case, the matrix
452 The matrix square root is computed by first reducing the matrix to
454 root of the quasi-triangular matrix can then be computed directly. The
461 "Computing real square roots of a real matrix", <em>Linear Algebra
464 If the matrix is <b>positive-definite symmetric</b>, then the square
468 In the <b>complex case</b>, the matrix \f$ M \f$ should be invertible;
475 complex Schur decomposition is used to reduce the matrix to a
476 triangular matrix. The theoretical cost is the same. Details are in:
478 square root of a matrix", <em>Linear Algebra Appl.</em>,