1 /*
2  * Copyright (C) 2016 The Android Open Source Project
3  *
4  * Licensed under the Apache License, Version 2.0 (the "License");
5  * you may not use this file except in compliance with the License.
6  * You may obtain a copy of the License at
7  *
8  *      http://www.apache.org/licenses/LICENSE-2.0
9  *
10  * Unless required by applicable law or agreed to in writing, software
11  * distributed under the License is distributed on an "AS IS" BASIS,
12  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13  * See the License for the specific language governing permissions and
14  * limitations under the License.
15  */
16 /////////////////////////////////////////////////////////////////////////
17 /*
18  * This module contains matrix math utilities for the following datatypes:
19  * -) Mat33 structures for 3x3 dimensional matrices
20  * -) Mat44 structures for 4x4 dimensional matrices
21  * -) floating point arrays for NxM dimensional matrices.
22  *
23  * Note that the Mat33 and Mat44 utilities were ported from the Android
24  * repository and maintain dependencies in that separate codebase. As a
25  * result, the function signatures were left untouched for compatibility with
26  * this legacy code, despite certain style violations. In particular, for this
27  * module the function argument ordering is outputs before inputs. This style
28  * violation will be addressed once the full set of dependencies in Android
29  * have been brought into this repository.
30  */
31 #ifndef LOCATION_LBS_CONTEXTHUB_NANOAPPS_COMMON_MATH_MAT_H_
32 #define LOCATION_LBS_CONTEXTHUB_NANOAPPS_COMMON_MATH_MAT_H_
33 
34 #include <stdbool.h>
35 #include <stddef.h>
36 #include <stdint.h>
37 
38 #include "common/math/vec.h"
39 
40 #ifdef __cplusplus
41 extern "C" {
42 #endif
43 
44 struct Mat33 {
45   float elem[3][3];
46 };
47 
48 struct Size3 {
49   uint32_t elem[3];
50 };
51 
52 struct Mat44 {
53   float elem[4][4];
54 };
55 
56 struct Size4 {
57   uint32_t elem[4];
58 };
59 
60 // 3x3 MATRIX MATH /////////////////////////////////////////////////////////////
61 void initZeroMatrix(struct Mat33 *A);
62 
63 // Updates A with the value x on the main diagonal and 0 on the off diagonals,
64 // i.e.:
65 // A = [x 0 0
66 //      0 x 0
67 //      0 0 x]
68 void initDiagonalMatrix(struct Mat33 *A, float x);
69 
70 // Updates A such that the columns are given by the provided vectors, i.e.:
71 // A = [v1 v2 v3].
72 void initMatrixColumns(struct Mat33 *A, const struct Vec3 *v1,
73                        const struct Vec3 *v2, const struct Vec3 *v3);
74 
75 // Updates out with the multiplication of A with v, i.e.:
76 // out = A v.
77 void mat33Apply(struct Vec3 *out, const struct Mat33 *A, const struct Vec3 *v);
78 
79 // Updates out with the multiplication of A with B, i.e.:
80 // out =  A B.
81 void mat33Multiply(struct Mat33 *out, const struct Mat33 *A,
82                    const struct Mat33 *B);
83 
84 // Updates A by scaling all entries by the provided scalar c, i.e.:
85 // A = A c.
86 void mat33ScalarMul(struct Mat33 *A, float c);
87 
88 // Updates out by adding A to out, i.e.:
89 // out = out + A.
90 void mat33Add(struct Mat33 *out, const struct Mat33 *A);
91 
92 // Updates out by subtracting A from out, i.e.:
93 // out = out - A.
94 void mat33Sub(struct Mat33 *out, const struct Mat33 *A);
95 
96 // Returns 1 if the minimum eigenvalue of the matrix A is greater than the
97 // given tolerance. Note that the tolerance is assumed to be greater than 0.
98 // I.e., returns: 1[min(eig(A)) > tolerance].
99 // NOTE: this function currently only checks matrix symmetry and positivity
100 // of the diagonals which is insufficient for testing positive semidefinite.
101 int mat33IsPositiveSemidefinite(const struct Mat33 *A, float tolerance);
102 
103 // Updates out with the inverse of the matrix A, i.e.:
104 // out = A^(-1)
105 void mat33Invert(struct Mat33 *out, const struct Mat33 *A);
106 
107 // Updates out with the multiplication of A's transpose with B, i.e.:
108 // out = A^T B
109 void mat33MultiplyTransposed(struct Mat33 *out, const struct Mat33 *A,
110                              const struct Mat33 *B);
111 
112 // Updates out with the multiplication of A with B's transpose, i.e.:
113 // out = A B^T
114 void mat33MultiplyTransposed2(struct Mat33 *out, const struct Mat33 *A,
115                               const struct Mat33 *B);
116 
117 // Updates out with the transpose of A, i.e.:
118 // out = A^T
119 void mat33Transpose(struct Mat33 *out, const struct Mat33 *A);
120 
121 // Returns the eigenvalues and corresponding eigenvectors of the symmetric
122 // matrix S.
123 // The i-th eigenvalue corresponds to the eigenvector in the i-th row of
124 // the matrix eigenvecs.
125 void mat33GetEigenbasis(struct Mat33 *S, struct Vec3 *eigenvals,
126                         struct Mat33 *eigenvecs);
127 
128 // Computes the determinant of a 3 by 3 matrix.
129 float mat33Determinant(const struct Mat33 *A);
130 
131 // 4x4 MATRIX MATH /////////////////////////////////////////////////////////////
132 // Updates out with the multiplication of A and v, i.e.:
133 // out = Av.
134 void mat44Apply(struct Vec4 *out, const struct Mat44 *A, const struct Vec4 *v);
135 
136 // Decomposes the given matrix LU inplace, such that:
137 // LU = P' * L * U.
138 // where L is a lower-diagonal matrix, U is an upper-diagonal matrix, and P is a
139 // permutation matrix.
140 //
141 // L and U are stored compactly in the returned LU matrix such that:
142 // -) the superdiagonal elements make up "U" (with a diagonal of 1.0s),
143 // -) the subdiagonal and diagonal elements make up "L".
144 // e.g. if the returned LU matrix is:
145 //      LU = [A11 A12 A13 A14
146 //            A21 A22 A23 A24
147 //            A31 A32 A33 A34
148 //            A41 A42 A43 A44], then:
149 //       L = [A11  0   0   0      and   U = [ 1  A12 A13 A14
150 //            A21 A22  0   0                  0   1  A23 A24
151 //            A31 A32 A33  0                  0   0   1  A34
152 //            A41 A42 A43 A44]                0   0   0   1 ]
153 //
154 // The permutation matrix P can be reproduced from returned pivot vector as:
155 // matrix P(N);
156 // P.identity();
157 // for (size_t i = 0; i < N; ++i) {
158 //    P.swapRows(i, pivot[i]);
159 // }
160 void mat44DecomposeLup(struct Mat44 *LU, struct Size4 *pivot);
161 
162 // Solves the linear system A x = b for x, where A is a compact LU decomposition
163 // (i.e. the LU matrix from mat44DecomposeLup) and pivot is the corresponding
164 // row pivots for the permutation matrix (also from mat44DecomposeLup).
165 void mat44Solve(const struct Mat44 *A, struct Vec4 *x, const struct Vec4 *b,
166                 const struct Size4 *pivot);
167 
168 // MXN MATRIX MATH /////////////////////////////////////////////////////////////
169 /*
170  * The following functions define basic math functionality for matrices of
171  * arbitrary dimension.
172  *
173  * All matrices used in these functions are assumed to be row major, i.e. if:
174  * A = [1 2 3
175  *      4 5 6
176  *      7 8 9]
177  * then when A is passed into one of the functions below, the order of
178  * elements is assumed to be [1 2 3 4 5 6 7 8 9].
179  */
180 
181 // Returns the maximum diagonal element of the given matrix.
182 // The matrix is assumed to be square, of size n x n.
183 float matMaxDiagonalElement(const float *square_mat, size_t n);
184 
185 // Adds a constant value to the diagonal of the given square n x n matrix and
186 // returns the updated matrix in place:
187 // A = A + uI
188 void matAddConstantDiagonal(float *square_mat, float u, size_t n);
189 
190 // Updates out with the result of A's transpose multiplied with A (i.e. A^T A).
191 // A is a matrix with dimensions nrows x ncols.
192 // out is a matrix with dimensions ncols x ncols.
193 void matTransposeMultiplyMat(float *out, const float *A,
194                              size_t nrows, size_t ncols);
195 
196 // Updates out with the result of A's transpose multiplied with v (i.e. A^T v).
197 // A is a matrix with dimensions nrows x ncols.
198 // v is a vector of dimension nrows.
199 // out is a vector of dimension ncols.
200 void matTransposeMultiplyVec(float* out, const float *A, const float *v,
201                              size_t nrows, size_t ncols);
202 
203 // Updates out with the result of A multiplied with v (i.e. out = Av).
204 // A is a matrix with dimensions nrows x ncols.
205 // v is a vector of dimension ncols.
206 // out is a vector of dimension nrows.
207 void matMultiplyVec(float *out, const float *A, const float *v,
208                     size_t nrows, size_t ncols);
209 
210 // Solves the linear system L L^T x = b for x, where L is a lower diagonal,
211 // symmetric matrix, i.e. the Cholesky factor of a matrix A = L L^T.
212 // L is a lower-diagonal matrix of dimension n x n.
213 // b is a vector of dimension n.
214 // x is a vector of dimension n.
215 // Returns true if the solver succeeds.
216 bool matLinearSolveCholesky(float *x, const float *L, const float *b,
217                             size_t n);
218 
219 // Performs the Cholesky decomposition on the given matrix A such that:
220 // A = L L^T, where L, the Cholesky factor, is a lower diagonal matrix.
221 // Updates the provided L matrix with the Cholesky factor.
222 // This decomposition is only successful for symmetric, positive definite
223 // matrices A.
224 // Returns true if the solver succeeds (will fail if the matrix is not
225 // symmetric, positive definite).
226 bool matCholeskyDecomposition(float *L, const float *A, size_t n);
227 
228 #ifdef __cplusplus
229 }
230 #endif
231 
232 #endif  // LOCATION_LBS_CONTEXTHUB_NANOAPPS_COMMON_MATH_MAT_H_
233