LSST Applications 27.0.0,g0265f82a02+469cd937ee,g02d81e74bb+21ad69e7e1,g1470d8bcf6+cbe83ee85a,g2079a07aa2+e67c6346a6,g212a7c68fe+04a9158687,g2305ad1205+94392ce272,g295015adf3+81dd352a9d,g2bbee38e9b+469cd937ee,g337abbeb29+469cd937ee,g3939d97d7f+72a9f7b576,g487adcacf7+71499e7cba,g50ff169b8f+5929b3527e,g52b1c1532d+a6fc98d2e7,g591dd9f2cf+df404f777f,g5a732f18d5+be83d3ecdb,g64a986408d+21ad69e7e1,g858d7b2824+21ad69e7e1,g8a8a8dda67+a6fc98d2e7,g99cad8db69+f62e5b0af5,g9ddcbc5298+d4bad12328,ga1e77700b3+9c366c4306,ga8c6da7877+71e4819109,gb0e22166c9+25ba2f69a1,gb6a65358fc+469cd937ee,gbb8dafda3b+69d3c0e320,gc07e1c2157+a98bf949bb,gc120e1dc64+615ec43309,gc28159a63d+469cd937ee,gcf0d15dbbd+72a9f7b576,gdaeeff99f8+a38ce5ea23,ge6526c86ff+3a7c1ac5f1,ge79ae78c31+469cd937ee,gee10cc3b42+a6fc98d2e7,gf1cff7945b+21ad69e7e1,gfbcc870c63+9a11dc8c8f
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Matrix3d.h
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1/*
2 * This file is part of sphgeom.
3 *
4 * Developed for the LSST Data Management System.
5 * This product includes software developed by the LSST Project
6 * (http://www.lsst.org).
7 * See the COPYRIGHT file at the top-level directory of this distribution
8 * for details of code ownership.
9 *
10 * This software is dual licensed under the GNU General Public License and also
11 * under a 3-clause BSD license. Recipients may choose which of these licenses
12 * to use; please see the files gpl-3.0.txt and/or bsd_license.txt,
13 * respectively. If you choose the GPL option then the following text applies
14 * (but note that there is still no warranty even if you opt for BSD instead):
15 *
16 * This program is free software: you can redistribute it and/or modify
17 * it under the terms of the GNU General Public License as published by
18 * the Free Software Foundation, either version 3 of the License, or
19 * (at your option) any later version.
20 *
21 * This program is distributed in the hope that it will be useful,
22 * but WITHOUT ANY WARRANTY; without even the implied warranty of
23 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
24 * GNU General Public License for more details.
25 *
26 * You should have received a copy of the GNU General Public License
27 * along with this program. If not, see <http://www.gnu.org/licenses/>.
28 */
29
30#ifndef LSST_SPHGEOM_MATRIX3D_H_
31#define LSST_SPHGEOM_MATRIX3D_H_
32
35
36#include <iosfwd>
37
38#include "Vector3d.h"
39
40
41namespace lsst {
42namespace sphgeom {
43
45class Matrix3d {
46public:
49
52 Matrix3d(double m00, double m01, double m02,
53 double m10, double m11, double m12,
54 double m20, double m21, double m22)
55 {
56 _c[0] = Vector3d(m00, m10, m20);
57 _c[1] = Vector3d(m01, m11, m21);
58 _c[2] = Vector3d(m02, m12, m22);
59 }
60
63 explicit Matrix3d(Vector3d const & v) {
64 _c[0] = Vector3d(v.x(), 0.0, 0.0);
65 _c[1] = Vector3d(0.0, v.y(), 0.0);
66 _c[2] = Vector3d(0.0, 0.0, v.z());
67 }
68
70 explicit Matrix3d(double s) {
71 _c[0] = Vector3d(s, 0.0, 0.0);
72 _c[1] = Vector3d(0.0, s, 0.0);
73 _c[2] = Vector3d(0.0, 0.0, s);
74 }
75
76 bool operator==(Matrix3d const & m) const {
77 return _c[0] == m._c[0] &&
78 _c[1] == m._c[1] &&
79 _c[2] == m._c[2];
80 }
81
82 bool operator!=(Matrix3d const & m) const {
83 return _c[0] != m._c[0] ||
84 _c[1] != m._c[1] ||
85 _c[2] != m._c[2];
86 }
87
89 Vector3d getRow(int r) const {
90 return Vector3d(getColumn(0)(r), getColumn(1)(r), getColumn(2)(r));
91 }
92
94 Vector3d const & getColumn(int c) const { return _c[c]; }
95
98 double operator()(int r, int c) const { return getColumn(c)(r); }
99
101 double inner(Matrix3d const & m) const {
103 Vector3d sum = p._c[0] + p._c[1] + p._c[2];
104 return sum(0) + sum(1) + sum(2);
105 }
106
109 double getSquaredNorm() const { return inner(*this); }
110
112 double getNorm() const { return std::sqrt(getSquaredNorm()); }
113
116 Vector3d operator*(Vector3d const & v) const {
117 return Vector3d(_c[0] * v(0) + _c[1] * v(1) + _c[2] * v(2));
118 }
119
122 Matrix3d operator*(Matrix3d const & m) const {
123 Matrix3d r;
124 for (int i = 0; i < 3; ++i) { r._c[i] = this->operator*(m._c[i]); }
125 return r;
126 }
127
129 Matrix3d operator+(Matrix3d const & m) const {
130 Matrix3d r;
131 for (int i = 0; i < 3; ++i) { r._c[i] = _c[i] + m._c[i]; }
132 return r;
133 }
134
136 Matrix3d operator-(Matrix3d const & m) const {
137 Matrix3d r;
138 for (int i = 0; i < 3; ++i) { r._c[i] = _c[i] - m._c[i]; }
139 return r;
140 }
141
144 Matrix3d r;
145 for (int i = 0; i < 3; ++i) { r._c[i] = _c[i].cwiseProduct(m._c[i]); }
146 return r;
147 }
148
151 Matrix3d t;
152 t._c[0] = Vector3d(_c[0].x(), _c[1].x(), _c[2].x());
153 t._c[1] = Vector3d(_c[0].y(), _c[1].y(), _c[2].y());
154 t._c[2] = Vector3d(_c[0].z(), _c[1].z(), _c[2].z());
155 return t;
156 }
157
160 Matrix3d inv;
161 Matrix3d const & m = *this;
162 // Find the first column of Adj(m), the adjugate matrix of m.
163 Vector3d a0(m(1, 1) * m(2, 2) - m(2, 1) * m(1, 2),
164 m(1, 2) * m(2, 0) - m(2, 2) * m(1, 0),
165 m(1, 0) * m(2, 1) - m(2, 0) * m(1, 1));
166 // Find 1.0/det(m), where the determinant of m is the dot product of
167 // the first row of m with the first column of Adj(m).
168 double rdet = 1.0 / (a0(0) * m(0,0) + a0(1) * m(0,1) + a0(2) * m(0,2));
169 // The inverse of m is Adj(m)/det(m); compute it column by column.
170 inv._c[0] = a0 * rdet;
171 inv._c[1] = Vector3d((m(0, 2) * m(2, 1) - m(2, 2) * m(0, 1)) * rdet,
172 (m(0, 0) * m(2, 2) - m(2, 0) * m(0, 2)) * rdet,
173 (m(0, 1) * m(2, 0) - m(2, 1) * m(0, 0)) * rdet);
174 inv._c[2] = Vector3d((m(0, 1) * m(1, 2) - m(1, 1) * m(0, 2)) * rdet,
175 (m(0, 2) * m(1, 0) - m(1, 2) * m(0, 0)) * rdet,
176 (m(0, 0) * m(1, 1) - m(1, 0) * m(0, 1)) * rdet);
177 return inv;
178 }
179
180private:
181 Vector3d _c[3];
182};
183
184std::ostream & operator<<(std::ostream &, Matrix3d const &);
185
186}} // namespace lsst::sphgeom
187
188#endif // LSST_SPHGEOM_MATRIX3D_H_
double z
Definition Match.cc:44
int y
Definition SpanSet.cc:48
int m
Definition SpanSet.cc:48
This file declares a class for representing vectors in ℝ³.
A 3x3 matrix with real entries stored in double precision.
Definition Matrix3d.h:45
Vector3d getRow(int r) const
getRow returns the r-th matrix row. Bounds are not checked.
Definition Matrix3d.h:89
Matrix3d inverse() const
inverse returns the inverse of this matrix.
Definition Matrix3d.h:159
bool operator!=(Matrix3d const &m) const
Definition Matrix3d.h:82
Matrix3d operator+(Matrix3d const &m) const
The addition operator returns the sum of this matrix and m.
Definition Matrix3d.h:129
Vector3d const & getColumn(int c) const
getColumn returns the c-th matrix column. Bounds are not checked.
Definition Matrix3d.h:94
Matrix3d(Vector3d const &v)
This constructor creates a diagonal matrix with diagonal components set to the components of v.
Definition Matrix3d.h:63
bool operator==(Matrix3d const &m) const
Definition Matrix3d.h:76
Matrix3d()
This constructor creates a zero matrix.
Definition Matrix3d.h:48
Matrix3d(double s)
This constructor returns the identity matrix scaled by s.
Definition Matrix3d.h:70
double operator()(int r, int c) const
The function call operator returns the scalar at row r and column c.
Definition Matrix3d.h:98
double getNorm() const
getNorm returns the L2 (Frobenius) norm of this matrix.
Definition Matrix3d.h:112
double inner(Matrix3d const &m) const
inner returns the Frobenius inner product of this matrix with m.
Definition Matrix3d.h:101
Matrix3d(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)
This constructor creates a matrix from its components, where mij specifies the component for row i an...
Definition Matrix3d.h:52
Vector3d operator*(Vector3d const &v) const
The multiplication operator returns the product of this matrix with vector v.
Definition Matrix3d.h:116
Matrix3d transpose() const
transpose returns the transpose of this matrix.
Definition Matrix3d.h:150
Matrix3d cwiseProduct(Matrix3d const &m) const
cwiseProduct returns the component-wise product of this matrix and m.
Definition Matrix3d.h:143
Matrix3d operator-(Matrix3d const &m) const
The subtraction operator returns the difference between this matrix and m.
Definition Matrix3d.h:136
double getSquaredNorm() const
getSquaredNorm returns the Frobenius inner product of this matrix with itself.
Definition Matrix3d.h:109
Matrix3d operator*(Matrix3d const &m) const
The multiplication operator returns the product of this matrix with matrix m.
Definition Matrix3d.h:122
Vector3d is a vector in ℝ³ with components stored in double precision.
Definition Vector3d.h:51
Vector3d cwiseProduct(Vector3d const &v) const
cwiseProduct returns the component-wise product of this vector and v.
Definition Vector3d.h:157
double x() const
Definition Vector3d.h:73
double y() const
Definition Vector3d.h:75
double z() const
Definition Vector3d.h:77
std::ostream & operator<<(std::ostream &, Angle const &)
Definition Angle.cc:41
T sqrt(T... args)