#include <libDC.h>


Public Member Functions | |
| ldmat (const mat &L, const vec &D) | |
| Construct by copy of L and D. | |
| ldmat (const mat &V) | |
| Construct by decomposition of full matrix V. | |
| ldmat (vec D0) | |
| Construct diagonal matrix with diagonal D0. | |
| ldmat () | |
| Default constructor. | |
| ldmat (const int dim0) | |
| Default initialization with proper size. | |
| virtual | ~ldmat () |
| Destructor for future use;. | |
| void | opupdt (const vec &v, double w) |
| mat | to_mat () |
| Conversion to full matrix. | |
| void | mult_sym (const mat &C) |
| Inplace symmetric multiplication by a SQUARE matrix $C$, i.e. $V = C*V*C'$. | |
| void | mult_sym_t (const mat &C) |
| Inplace symmetric multiplication by a SQUARE transpose of matrix $C$, i.e. $V = C'*V*C$. | |
| void | add (const ldmat &ld2, double w=1.0) |
| Add another matrix in LD form with weight w. | |
| double | logdet () const |
| Logarithm of a determinant. | |
| double | qform (const vec &v) const |
| Evaluates quadratic form $x= v'*V*v$;. | |
| void | clear () |
| Clearing matrix so that it corresponds to zeros. | |
| int | cols () const |
| access function | |
| int | rows () const |
| access function | |
| vec | sqrt_mult (const vec &v) const |
| Multiplies square root of $V$ by vector $x$. | |
| virtual void | inv (ldmat &Inv) const |
| Matrix inversion preserving the chosen form. | |
| void | mult_sym (const mat &C, ldmat &U) const |
| Symmetric multiplication of $U$ by a general matrix $C$, result of which is stored in the current class. | |
| void | mult_sym_t (const mat &C, ldmat &U) const |
| Symmetric multiplication of $U$ by a transpose of a general matrix $C$, result of which is stored in the current class. | |
| void | ldform (const mat &A, const vec &D0) |
| Transforms general $A'D0 A$ into pure $L'DL$. | |
| void | setD (const vec &nD) |
| Access functions. | |
| void | setD (const vec &nD, int i) |
| Access functions. | |
| void | setL (const vec &nL) |
| Access functions. | |
| ldmat & | operator+= (const ldmat &ldA) |
| add another ldmat matrix | |
| ldmat & | operator-= (const ldmat &ldA) |
| subtract another ldmat matrix | |
| ldmat & | operator *= (double x) |
| multiply by a scalar | |
Protected Attributes | |
| vec | D |
| Positive vector $D$. | |
| mat | L |
| Lower-triangular matrix $L$. | |
Friends | |
| std::ostream & | operator<< (std::ostream &os, const ldmat &sq) |
print both L and D | |
Matrix is decomposed as follows:
where only $L$ and $D$ matrices are stored. All inplace operations modifies only these and the need to compose and decompose the matrix is avoided.
| void ldmat::opupdt | ( | const vec & | v, | |
| double | w | |||
| ) | [virtual] |
Perfroms a rank-1 update by outer product of vectors: $V = V + w v v'$.
| v | Vector forming the outer product to be added | |
| w | weight of updating; can be negative |
Implements sqmat.
| void ldmat::mult_sym | ( | const mat & | C | ) | [virtual] |
Inplace symmetric multiplication by a SQUARE matrix $C$, i.e. $V = C*V*C'$.
| C | multiplying matrix, |
Implements sqmat.
| void ldmat::mult_sym_t | ( | const mat & | C | ) | [virtual] |
Inplace symmetric multiplication by a SQUARE transpose of matrix $C$, i.e. $V = C'*V*C$.
| C | multiplying matrix, |
Implements sqmat.
| vec ldmat::sqrt_mult | ( | const vec & | v | ) | const [virtual] |
Multiplies square root of $V$ by vector $x$.
Used e.g. in generating normal samples.
Implements sqmat.
| void ldmat::inv | ( | ldmat & | Inv | ) | const [virtual] |
Matrix inversion preserving the chosen form.
| Inv | a space where the inverse is stored. |
| void ldmat::mult_sym | ( | const mat & | C, | |
| ldmat & | U | |||
| ) | const |
Symmetric multiplication of $U$ by a general matrix $C$, result of which is stored in the current class.
| C | matrix to multiply with | |
| U | a space where the inverse is stored. |
| void ldmat::mult_sym_t | ( | const mat & | C, | |
| ldmat & | U | |||
| ) | const |
Symmetric multiplication of $U$ by a transpose of a general matrix $C$, result of which is stored in the current class.
| C | matrix to multiply with | |
| U | a space where the inverse is stored. |
| void ldmat::ldform | ( | const mat & | A, | |
| const vec & | D0 | |||
| ) |
Transforms general $A'D0 A$ into pure $L'DL$.
The new decomposition fullfills: $A'*diag(D)*A = self.L'*diag(self.D)*self.L$
| A | general matrix | |
| D0 | general vector |
add another ldmat matrix
Operations: mapping of add operation to operators
subtract another ldmat matrix
mapping of negative add operation to operators
1.5.3