Skip to content
Snippets Groups Projects
Commit 80506448 authored by Alexander Rose's avatar Alexander Rose
Browse files

mat3 symmetricEigenvalues and eigenvectors

parent 347c1986
No related branches found
No related tags found
No related merge requests found
Hide whitespace changes
Inline Side-by-side
src/mol-math/linear-algebra/3d/mat3.ts
+ 190
− 2
View file @ 80506448
/**
* Copyright (c) 2017-2018 mol* contributors, licensed under MIT, See LICENSE file for more info.
* Copyright (c) 2017-2019 mol* contributors, licensed under MIT, See LICENSE file for more info.
*
* @author David Sehnal <david.sehnal@gmail.com>
* @author Alexander Rose <alexander.rose@weirdbyte.de>
......@@ -17,10 +17,11 @@
* furnished to do so, subject to the following conditions:
*/
import { Mat4 } from '../3d'
import { Mat4, Vec3 } from '../3d'
import { NumberArray } from '../../../mol-util/type-helpers';
interface Mat3 extends Array<number> { [d: number]: number, '@type': 'mat3', length: 9 }
interface ReadonlyMat3 extends Array<number> { readonly [d: number]: number, '@type': 'mat3', length: 9 }
function Mat3() {
return Mat3.zero();
......@@ -102,6 +103,20 @@ namespace Mat3 {
return out;
}
export function create(a00: number, a01: number, a02: number, a10: number, a11: number, a12: number, a20: number, a21: number, a22: number): Mat3 {
const out = zero();
out[0] = a00
out[1] = a01
out[2] = a02
out[3] = a10
out[4] = a11
out[5] = a12
out[6] = a20
out[7] = a21
out[8] = a22
return out;
}
export function hasNaN(m: Mat3) {
for (let i = 0; i < 9; i++) if (isNaN(m[i])) return true
return false
......@@ -114,6 +129,13 @@ namespace Mat3 {
return Mat3.copy(Mat3.zero(), a);
}
export function areEqual(a: Mat3, b: Mat3, eps: number) {
for (let i = 0; i < 9; i++) {
if (Math.abs(a[i] - b[i]) > eps) return false;
}
return true;
}
export function setValue(a: Mat3, i: number, j: number, value: number) {
a[3 * j + i] = value;
}
......@@ -210,6 +232,172 @@ namespace Mat3 {
// Calculate the determinant
return a00 * b01 + a01 * b11 + a02 * b21;
}
export function trace(a: Mat3) {
return a[0] + a[4] + a[8]
}
export function sub(out: Mat3, a: Mat3, b: Mat3) {
out[0] = a[0] - b[0]
out[1] = a[1] - b[1]
out[2] = a[2] - b[2]
out[3] = a[3] - b[3]
out[4] = a[4] - b[4]
out[5] = a[5] - b[5]
out[6] = a[6] - b[6]
out[7] = a[7] - b[7]
out[8] = a[8] - b[8]
return out
}
export function add(out: Mat3, a: Mat3, b: Mat3) {
out[0] = a[0] + b[0]
out[1] = a[1] + b[1]
out[2] = a[2] + b[2]
out[3] = a[3] + b[3]
out[4] = a[4] + b[4]
out[5] = a[5] + b[5]
out[6] = a[6] + b[6]
out[7] = a[7] + b[7]
out[8] = a[8] + b[8]
return out
}
export function mul(out: Mat3, a: Mat3, b: Mat3) {
const a00 = a[0], a01 = a[1], a02 = a[2],
a10 = a[3], a11 = a[4], a12 = a[5],
a20 = a[6], a21 = a[7], a22 = a[8];
const b00 = b[0], b01 = b[1], b02 = b[2],
b10 = b[3], b11 = b[4], b12 = b[5],
b20 = b[6], b21 = b[7], b22 = b[8];
out[0] = b00 * a00 + b01 * a10 + b02 * a20;
out[1] = b00 * a01 + b01 * a11 + b02 * a21;
out[2] = b00 * a02 + b01 * a12 + b02 * a22;
out[3] = b10 * a00 + b11 * a10 + b12 * a20;
out[4] = b10 * a01 + b11 * a11 + b12 * a21;
out[5] = b10 * a02 + b11 * a12 + b12 * a22;
out[6] = b20 * a00 + b21 * a10 + b22 * a20;
out[7] = b20 * a01 + b21 * a11 + b22 * a21;
out[8] = b20 * a02 + b21 * a12 + b22 * a22;
return out;
}
export function subScalar(out: Mat3, a: Mat3, s: number) {
out[0] = a[0] - s
out[1] = a[1] - s
out[2] = a[2] - s
out[3] = a[3] - s
out[4] = a[4] - s
out[5] = a[5] - s
out[6] = a[6] - s
out[7] = a[7] - s
out[8] = a[8] - s
return out
}
export function addScalar(out: Mat3, a: Mat3, s: number) {
out[0] = a[0] + s
out[1] = a[1] + s
out[2] = a[2] + s
out[3] = a[3] + s
out[4] = a[4] + s
out[5] = a[5] + s
out[6] = a[6] + s
out[7] = a[7] + s
out[8] = a[8] + s
return out
}
export function mulScalar(out: Mat3, a: Mat3, s: number) {
out[0] = a[0] * s
out[1] = a[1] * s
out[2] = a[2] * s
out[3] = a[3] * s
out[4] = a[4] * s
out[5] = a[5] * s
out[6] = a[6] * s
out[7] = a[7] * s
out[8] = a[8] * s
return out
}
const piThird = Math.PI / 3
const tmpB = Mat3()
/**
* Given a real symmetric 3x3 matrix A, compute the eigenvalues
*
* From https://en.wikipedia.org/wiki/Eigenvalue_algorithm#3.C3.973_matrices
*/
export function symmetricEigenvalues(out: Vec3, a: Mat3) {
const p1 = a[1] * a[1] + a[2] * a[2] + a[5] * a[5]
if (p1 === 0) {
out[0] = a[0]
out[1] = a[4]
out[2] = a[8]
} else {
const q = trace(a) / 3
const a1 = a[0] - q
const a2 = a[4] - q
const a3 = a[8] - q
const p2 = a1 * a1 + a2 * a2 + a3 * a3 + 2 * p1
const p = Math.sqrt(p2 / 6)
mulScalar(tmpB, Identity, q)
sub(tmpB, a, tmpB)
mulScalar(tmpB, tmpB, (1 / p))
const r = determinant(tmpB) / 2
// In exact arithmetic for a symmetric matrix -1 <= r <= 1
// but computation error can leave it slightly outside this range.
const phi = r <= -1 ? piThird : r >= 1 ?
0 : Math.acos(r) / 3
// the eigenvalues satisfy eig3 <= eig2 <= eig1
out[0] = q + 2 * p * Math.cos(phi)
out[2] = q + 2 * p * Math.cos(phi + (2 * piThird))
out[1] = 3 * q - out[0] - out[2] // since trace(A) = eig1 + eig2 + eig3
}
return out
}
const tmpR0 = [0.1, 0.0, 0.0] as Vec3
const tmpR1 = [0.1, 0.0, 0.0] as Vec3
const tmpR2 = [0.1, 0.0, 0.0] as Vec3
const tmpR0xR1 = [0.1, 0.0, 0.0] as Vec3
const tmpR0xR2 = [0.1, 0.0, 0.0] as Vec3
const tmpR1xR2 = [0.1, 0.0, 0.0] as Vec3
/**
* Calculates the eigenvector for the given eigenvalue `e` of matrix `a`
*/
export function eigenvector(out: Vec3, a: Mat3, e: number) {
Vec3.set(tmpR0, a[0] - e, a[1], a[2])
Vec3.set(tmpR1, a[1], a[4] - e, a[5])
Vec3.set(tmpR2, a[2], a[5], a[8] - e)
Vec3.cross(tmpR0xR1, tmpR0, tmpR1)
Vec3.cross(tmpR0xR2, tmpR0, tmpR2)
Vec3.cross(tmpR1xR2, tmpR1, tmpR2)
const d0 = Vec3.dot(tmpR0xR1, tmpR0xR1)
const d1 = Vec3.dot(tmpR0xR2, tmpR0xR2)
const d2 = Vec3.dot(tmpR1xR2, tmpR1xR2)
let dmax = d0
let imax = 0
if (d1 > dmax) {
dmax = d1
imax = 1
}
if (d2 > dmax) imax = 2
if (imax === 0) {
Vec3.scale(out, tmpR0xR1, 1 / Math.sqrt(d0))
} else if (imax === 1) {
Vec3.scale(out, tmpR0xR2, 1 / Math.sqrt(d1))
} else {
Vec3.scale(out, tmpR1xR2, 1 / Math.sqrt(d2))
}
return out
}
export const Identity: ReadonlyMat3 = identity()
}
export default Mat3
\ No newline at end of file
src/mol-math/linear-algebra/_spec/mat3.spec.ts 0 → 100644
+ 35
− 0
View file @ 80506448
/**
* Copyright (c) 2019 mol* contributors, licensed under MIT, See LICENSE file for more info.
*
* @author Alexander Rose <alexander.rose@weirdbyte.de>
*/
import { Mat3, Vec3 } from '../3d'
describe('Mat3', () => {
it('symmetricEigenvalues', () => {
const m = Mat3.create(
0.1945, -0.0219, -0.0416,
-0.0219, 0.1995, -0.0119,
-0.0416, -0.0119, 0.3673
)
const e = Vec3.create(0.377052701425898, 0.21713981522725134, 0.1671074833468507)
expect(Vec3.equals(e, Mat3.symmetricEigenvalues(Vec3(), m))).toBe(true);
});
it('eigenvectors', () => {
const m = Mat3.create(
0.1945, -0.0219, -0.0416,
-0.0219, 0.1995, -0.0119,
-0.0416, -0.0119, 0.3673
)
const e = Vec3.create(0.377052701425898, 0.21713981522725134, 0.1671074833468507)
const v0 = Vec3.create(-0.2176231019882068, -0.038522620041966125, 0.9752723687391808)
const v1 = Vec3.create(-0.5905636938047126, 0.8007524989198634, -0.10014968314142503)
const v2 = Vec3.create(0.7770937582036648, 0.5977553372576602, 0.19701230352667118)
expect(Vec3.equals(v0, Mat3.eigenvector(Vec3(), m, e[0]))).toBe(true);
expect(Vec3.equals(v1, Mat3.eigenvector(Vec3(), m, e[1]))).toBe(true);
expect(Vec3.equals(v2, Mat3.eigenvector(Vec3(), m, e[2]))).toBe(true);
});
});
\ No newline at end of file
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Please register or to comment