forked from M-Labs/nalgebra
688 lines
19 KiB
Rust
688 lines
19 KiB
Rust
#[cfg(feature = "arbitrary")]
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#[macro_use]
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extern crate quickcheck;
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#[macro_use]
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extern crate approx;
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extern crate num_traits as num;
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extern crate alga;
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extern crate nalgebra as na;
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use num::{Zero, One};
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use std::fmt::Display;
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use alga::linear::FiniteDimInnerSpace;
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use na::{U8, U15,
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DVector, DMatrix,
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Vector1, Vector2, Vector3, Vector4, Vector5, Vector6,
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RowVector4,
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Matrix1, Matrix2, Matrix3, Matrix4, Matrix5, Matrix6,
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MatrixNM, Matrix2x3, Matrix3x2, Matrix3x4, Matrix4x3, Matrix2x4, Matrix4x5, Matrix4x6};
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#[test]
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fn is_column_major() {
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let a = Matrix2x3::new(1.0, 2.0, 3.0,
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4.0, 5.0, 6.0);
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let expected = &[ 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ];
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assert_eq!(a.as_slice(), expected);
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let a = Matrix2x3::from_row_slice(&[1.0, 2.0, 3.0,
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4.0, 5.0, 6.0]);
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assert_eq!(a.as_slice(), expected);
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let a = Matrix2x3::from_column_slice(&[1.0, 4.0,
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2.0, 5.0,
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3.0, 6.0]);
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assert_eq!(a.as_slice(), expected);
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}
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#[test]
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fn linear_index() {
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let a = Matrix2x3::new(1, 2, 3,
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4, 5, 6);
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assert_eq!(a[0], 1);
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assert_eq!(a[1], 4);
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assert_eq!(a[2], 2);
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assert_eq!(a[3], 5);
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assert_eq!(a[4], 3);
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assert_eq!(a[5], 6);
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let b = Vector4::new(1, 2, 3, 4);
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assert_eq!(b[0], 1);
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assert_eq!(b[1], 2);
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assert_eq!(b[2], 3);
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assert_eq!(b[3], 4);
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let c = RowVector4::new(1, 2, 3, 4);
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assert_eq!(c[0], 1);
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assert_eq!(c[1], 2);
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assert_eq!(c[2], 3);
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assert_eq!(c[3], 4);
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}
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#[test]
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fn identity() {
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let id1 = Matrix3::<f64>::identity();
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let id2 = Matrix3x4::new(1.0, 0.0, 0.0, 0.0,
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0.0, 1.0, 0.0, 0.0,
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0.0, 0.0, 1.0, 0.0);
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let id2bis = Matrix3x4::identity();
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let id3 = Matrix4x3::new(1.0, 0.0, 0.0,
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0.0, 1.0, 0.0,
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0.0, 0.0, 1.0,
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0.0, 0.0, 0.0);
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let id3bis = Matrix4x3::identity();
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let not_id1 = Matrix3::identity() * 2.0;
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let not_id2 = Matrix3x4::new(1.0, 0.0, 0.0, 0.0,
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0.0, 1.0, 0.0, 0.0,
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0.0, 0.0, 1.0, 1.0);
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let not_id3 = Matrix4x3::new(1.0, 0.0, 0.0,
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0.0, 1.0, 0.0,
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0.0, 0.0, 1.0,
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0.0, 1.0, 0.0);
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assert_eq!(id2, id2bis);
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assert_eq!(id3, id3bis);
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assert!(id1.is_identity(0.0));
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assert!(id2.is_identity(0.0));
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assert!(id3.is_identity(0.0));
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assert!(!not_id1.is_identity(0.0));
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assert!(!not_id2.is_identity(0.0));
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assert!(!not_id3.is_identity(0.0));
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}
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#[test]
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fn coordinates() {
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let a = Matrix3x4::new(11, 12, 13, 14,
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21, 22, 23, 24,
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31, 32, 33, 34);
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assert_eq!(a.m11, 11);
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assert_eq!(a.m12, 12);
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assert_eq!(a.m13, 13);
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assert_eq!(a.m14, 14);
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assert_eq!(a.m21, 21);
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assert_eq!(a.m22, 22);
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assert_eq!(a.m23, 23);
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assert_eq!(a.m24, 24);
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assert_eq!(a.m31, 31);
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assert_eq!(a.m32, 32);
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assert_eq!(a.m33, 33);
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assert_eq!(a.m34, 34);
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}
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#[test]
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fn from_diagonal() {
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let diag = Vector3::new(1, 2, 3);
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let expected = Matrix3::new(
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1, 0, 0,
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0, 2, 0,
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0, 0, 3);
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let a = Matrix3::from_diagonal(&diag);
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assert_eq!(a, expected);
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}
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#[test]
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fn from_rows() {
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let rows = &[
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RowVector4::new(11, 12, 13, 14),
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RowVector4::new(21, 22, 23, 24),
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RowVector4::new(31, 32, 33, 34)
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];
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let expected = Matrix3x4::new(
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11, 12, 13, 14,
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21, 22, 23, 24,
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31, 32, 33, 34);
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let a = Matrix3x4::from_rows(rows);
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assert_eq!(a, expected);
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}
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#[test]
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fn from_columns() {
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let columns = &[
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Vector3::new(11, 21, 31),
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Vector3::new(12, 22, 32),
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Vector3::new(13, 23, 33),
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Vector3::new(14, 24, 34)
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];
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let expected = Matrix3x4::new(
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11, 12, 13, 14,
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21, 22, 23, 24,
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31, 32, 33, 34);
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let a = Matrix3x4::from_columns(columns);
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assert_eq!(a, expected);
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}
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#[test]
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fn from_columns_dynamic() {
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let columns = &[
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DVector::from_row_slice(3, &[11, 21, 31]),
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DVector::from_row_slice(3, &[12, 22, 32]),
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DVector::from_row_slice(3, &[13, 23, 33]),
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DVector::from_row_slice(3, &[14, 24, 34])
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];
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let expected = DMatrix::from_row_slice(3, 4,
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&[ 11, 12, 13, 14,
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21, 22, 23, 24,
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31, 32, 33, 34 ]);
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let a = DMatrix::from_columns(columns);
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assert_eq!(a, expected);
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}
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#[test]
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#[should_panic]
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fn from_too_many_rows() {
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let rows = &[
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RowVector4::new(11, 12, 13, 14),
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RowVector4::new(21, 22, 23, 24),
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RowVector4::new(31, 32, 33, 34),
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RowVector4::new(31, 32, 33, 34)
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];
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let _ = Matrix3x4::from_rows(rows);
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}
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#[test]
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#[should_panic]
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fn from_not_enough_columns() {
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let columns = &[
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Vector3::new(11, 21, 31),
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Vector3::new(14, 24, 34)
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];
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let _ = Matrix3x4::from_columns(columns);
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}
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#[test]
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#[should_panic]
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fn from_rows_with_different_dimensions() {
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let columns = &[
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DVector::from_row_slice(3, &[11, 21, 31]),
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DVector::from_row_slice(3, &[12, 22, 32, 33])
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];
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let _ = DMatrix::from_columns(columns);
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}
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#[test]
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fn to_homogeneous() {
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let a = Vector3::new(1.0, 2.0, 3.0);
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let expected_a = Vector4::new(1.0, 2.0, 3.0, 0.0);
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let b = DVector::from_row_slice(3, &[1.0, 2.0, 3.0]);
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let expected_b = DVector::from_row_slice(4, &[1.0, 2.0, 3.0, 0.0]);
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assert_eq!(a.to_homogeneous(), expected_a);
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assert_eq!(b.to_homogeneous(), expected_b);
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}
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#[test]
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fn simple_add() {
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let a = Matrix2x3::new(1.0, 2.0, 3.0,
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4.0, 5.0, 6.0);
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let b = Matrix2x3::new(10.0, 20.0, 30.0,
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40.0, 50.0, 60.0);
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let c = DMatrix::from_row_slice(2, 3, &[ 10.0, 20.0, 30.0,
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40.0, 50.0, 60.0 ]);
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let expected = Matrix2x3::new(11.0, 22.0, 33.0,
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44.0, 55.0, 66.0);
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assert_eq!(expected, &a + &b);
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assert_eq!(expected, &a + b);
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assert_eq!(expected, a + &b);
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assert_eq!(expected, a + b);
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// Sum of a static matrix with a dynamic one.
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assert_eq!(expected, &a + &c);
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assert_eq!(expected, a + &c);
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assert_eq!(expected, &c + &a);
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assert_eq!(expected, &c + a);
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}
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#[test]
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fn simple_scalar_mul() {
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let a = Matrix2x3::new(1.0, 2.0, 3.0,
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4.0, 5.0, 6.0);
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let expected = Matrix2x3::new(10.0, 20.0, 30.0,
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40.0, 50.0, 60.0);
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assert_eq!(expected, a * 10.0);
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assert_eq!(expected, &a * 10.0);
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assert_eq!(expected, 10.0 * a);
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assert_eq!(expected, 10.0 * &a);
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}
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#[test]
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fn simple_mul() {
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let a = Matrix2x3::new(1.0, 2.0, 3.0,
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4.0, 5.0, 6.0);
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let b = Matrix3x4::new(10.0, 20.0, 30.0, 40.0,
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50.0, 60.0, 70.0, 80.0,
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90.0, 100.0, 110.0, 120.0);
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let expected = Matrix2x4::new(380.0, 440.0, 500.0, 560.0,
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830.0, 980.0, 1130.0, 1280.0);
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assert_eq!(expected, &a * &b);
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assert_eq!(expected, a * &b);
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assert_eq!(expected, &a * b);
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assert_eq!(expected, a * b);
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}
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#[test]
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fn simple_scalar_conversion() {
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let a = Matrix2x3::new(1.0, 2.0, 3.0,
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4.0, 5.0, 6.0);
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let expected = Matrix2x3::new(1, 2, 3,
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4, 5, 6);
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let a_u32: Matrix2x3<u32> = na::try_convert(a).unwrap(); // f32 -> u32
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let a_f32: Matrix2x3<f32> = na::convert(a_u32); // u32 -> f32
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assert_eq!(a, a_f32);
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assert_eq!(expected, a_u32);
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}
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#[test]
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#[should_panic]
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fn trace_panic() {
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let m = DMatrix::<f32>::new_random(2, 3);
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let _ = m.trace();
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}
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#[test]
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fn trace() {
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let m = Matrix2::new(1.0, 20.0,
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30.0, 4.0);
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assert_eq!(m.trace(), 5.0);
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}
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#[test]
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fn simple_transpose() {
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let a = Matrix2x3::new(1.0, 2.0, 3.0,
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4.0, 5.0, 6.0);
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let expected = Matrix3x2::new(1.0, 4.0,
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2.0, 5.0,
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3.0, 6.0);
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assert_eq!(a.transpose(), expected);
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}
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#[test]
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fn simple_transpose_mut() {
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let mut a = Matrix3::new(1.0, 2.0, 3.0,
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4.0, 5.0, 6.0,
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7.0, 8.0, 9.0);
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let expected = Matrix3::new(1.0, 4.0, 7.0,
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2.0, 5.0, 8.0,
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3.0, 6.0, 9.0);
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a.transpose_mut();
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assert_eq!(a, expected);
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}
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#[test]
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fn vector_index_mut() {
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let mut v = Vector3::new(1, 2, 3);
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assert_eq!(v[0], 1);
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assert_eq!(v[1], 2);
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assert_eq!(v[2], 3);
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v[0] = 10;
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v[1] = 20;
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v[2] = 30;
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assert_eq!(v, Vector3::new(10, 20, 30));
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}
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#[test]
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fn components_mut() {
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let mut m2 = Matrix2::from_element(1.0);
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let mut m3 = Matrix3::from_element(1.0);
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let mut m4 = Matrix4::from_element(1.0);
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let mut m5 = Matrix5::from_element(1.0);
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let mut m6 = Matrix6::from_element(1.0);
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m2.m11 = 0.0; m2.m12 = 0.0;
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m2.m21 = 0.0; m2.m22 = 0.0;
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m3.m11 = 0.0; m3.m12 = 0.0; m3.m13 = 0.0;
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m3.m21 = 0.0; m3.m22 = 0.0; m3.m23 = 0.0;
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m3.m31 = 0.0; m3.m32 = 0.0; m3.m33 = 0.0;
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m4.m11 = 0.0; m4.m12 = 0.0; m4.m13 = 0.0; m4.m14 = 0.0;
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m4.m21 = 0.0; m4.m22 = 0.0; m4.m23 = 0.0; m4.m24 = 0.0;
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m4.m31 = 0.0; m4.m32 = 0.0; m4.m33 = 0.0; m4.m34 = 0.0;
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m4.m41 = 0.0; m4.m42 = 0.0; m4.m43 = 0.0; m4.m44 = 0.0;
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m5.m11 = 0.0; m5.m12 = 0.0; m5.m13 = 0.0; m5.m14 = 0.0; m5.m15 = 0.0;
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m5.m21 = 0.0; m5.m22 = 0.0; m5.m23 = 0.0; m5.m24 = 0.0; m5.m25 = 0.0;
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m5.m31 = 0.0; m5.m32 = 0.0; m5.m33 = 0.0; m5.m34 = 0.0; m5.m35 = 0.0;
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m5.m41 = 0.0; m5.m42 = 0.0; m5.m43 = 0.0; m5.m44 = 0.0; m5.m45 = 0.0;
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m5.m51 = 0.0; m5.m52 = 0.0; m5.m53 = 0.0; m5.m54 = 0.0; m5.m55 = 0.0;
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m6.m11 = 0.0; m6.m12 = 0.0; m6.m13 = 0.0; m6.m14 = 0.0; m6.m15 = 0.0; m6.m16 = 0.0;
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m6.m21 = 0.0; m6.m22 = 0.0; m6.m23 = 0.0; m6.m24 = 0.0; m6.m25 = 0.0; m6.m26 = 0.0;
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m6.m31 = 0.0; m6.m32 = 0.0; m6.m33 = 0.0; m6.m34 = 0.0; m6.m35 = 0.0; m6.m36 = 0.0;
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m6.m41 = 0.0; m6.m42 = 0.0; m6.m43 = 0.0; m6.m44 = 0.0; m6.m45 = 0.0; m6.m46 = 0.0;
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m6.m51 = 0.0; m6.m52 = 0.0; m6.m53 = 0.0; m6.m54 = 0.0; m6.m55 = 0.0; m6.m56 = 0.0;
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m6.m61 = 0.0; m6.m62 = 0.0; m6.m63 = 0.0; m6.m64 = 0.0; m6.m65 = 0.0; m6.m66 = 0.0;
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assert!(m2.is_zero());
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assert!(m3.is_zero());
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assert!(m4.is_zero());
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assert!(m5.is_zero());
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assert!(m6.is_zero());
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let mut v1 = Vector1::from_element(1.0);
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let mut v2 = Vector2::from_element(1.0);
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let mut v3 = Vector3::from_element(1.0);
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let mut v4 = Vector4::from_element(1.0);
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let mut v5 = Vector5::from_element(1.0);
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let mut v6 = Vector6::from_element(1.0);
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v1.x = 0.0;
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v2.x = 0.0; v2.y = 0.0;
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v3.x = 0.0; v3.y = 0.0; v3.z = 0.0;
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v4.x = 0.0; v4.y = 0.0; v4.z = 0.0; v4.w = 0.0;
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v5.x = 0.0; v5.y = 0.0; v5.z = 0.0; v5.w = 0.0; v5.a = 0.0;
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v6.x = 0.0; v6.y = 0.0; v6.z = 0.0; v6.w = 0.0; v6.a = 0.0; v6.b = 0.0;
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assert!(v1.is_zero());
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assert!(v2.is_zero());
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assert!(v3.is_zero());
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assert!(v4.is_zero());
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assert!(v5.is_zero());
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assert!(v6.is_zero());
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// Check that the components order is correct.
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m3.m11 = 11.0; m3.m12 = 12.0; m3.m13 = 13.0;
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m3.m21 = 21.0; m3.m22 = 22.0; m3.m23 = 23.0;
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m3.m31 = 31.0; m3.m32 = 32.0; m3.m33 = 33.0;
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let expected_m3 = Matrix3::new(11.0, 12.0, 13.0,
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21.0, 22.0, 23.0,
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31.0, 32.0, 33.0);
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assert_eq!(expected_m3, m3);
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}
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#[test]
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fn kronecker() {
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let a = Matrix2x3::new(
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11, 12, 13,
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21, 22, 23);
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let b = Matrix4x5::new(
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110, 120, 130, 140, 150,
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210, 220, 230, 240, 250,
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310, 320, 330, 340, 350,
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410, 420, 430, 440, 450);
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||
|
||
let expected = MatrixNM::<_, U8, U15>::from_row_slice(&[
|
||
1210, 1320, 1430, 1540, 1650, 1320, 1440, 1560, 1680, 1800, 1430, 1560, 1690, 1820, 1950,
|
||
2310, 2420, 2530, 2640, 2750, 2520, 2640, 2760, 2880, 3000, 2730, 2860, 2990, 3120, 3250,
|
||
3410, 3520, 3630, 3740, 3850, 3720, 3840, 3960, 4080, 4200, 4030, 4160, 4290, 4420, 4550,
|
||
4510, 4620, 4730, 4840, 4950, 4920, 5040, 5160, 5280, 5400, 5330, 5460, 5590, 5720, 5850,
|
||
2310, 2520, 2730, 2940, 3150, 2420, 2640, 2860, 3080, 3300, 2530, 2760, 2990, 3220, 3450,
|
||
4410, 4620, 4830, 5040, 5250, 4620, 4840, 5060, 5280, 5500, 4830, 5060, 5290, 5520, 5750,
|
||
6510, 6720, 6930, 7140, 7350, 6820, 7040, 7260, 7480, 7700, 7130, 7360, 7590, 7820, 8050,
|
||
8610, 8820, 9030, 9240, 9450, 9020, 9240, 9460, 9680, 9900, 9430, 9660, 9890, 10120, 10350 ]);
|
||
|
||
let computed = a.kronecker(&b);
|
||
|
||
assert_eq!(computed, expected);
|
||
|
||
let a = Vector2::new(1, 2);
|
||
let b = Vector3::new(10, 20, 30);
|
||
let expected = Vector6::new(10, 20, 30, 20, 40, 60);
|
||
|
||
assert_eq!(a.kronecker(&b), expected);
|
||
|
||
let a = Vector2::new(1, 2);
|
||
let b = RowVector4::new(10, 20, 30, 40);
|
||
let expected = Matrix2x4::new(
|
||
10, 20, 30, 40,
|
||
20, 40, 60, 80);
|
||
|
||
assert_eq!(a.kronecker(&b), expected);
|
||
}
|
||
|
||
#[cfg(feature = "arbitrary")]
|
||
quickcheck!{
|
||
/*
|
||
*
|
||
* Transposition.
|
||
*
|
||
*/
|
||
fn transpose_transpose_is_self(m: Matrix2x3<f64>) -> bool {
|
||
m.transpose().transpose() == m
|
||
}
|
||
|
||
fn transpose_mut_transpose_mut_is_self(m: Matrix3<f64>) -> bool {
|
||
let mut mm = m;
|
||
mm.transpose_mut();
|
||
mm.transpose_mut();
|
||
m == mm
|
||
}
|
||
|
||
fn transpose_transpose_is_id_dyn(m: DMatrix<f64>) -> bool {
|
||
m.transpose().transpose() == m
|
||
}
|
||
|
||
fn check_transpose_components_dyn(m: DMatrix<f64>) -> bool {
|
||
let tr = m.transpose();
|
||
let (nrows, ncols) = m.shape();
|
||
|
||
if nrows != tr.shape().1 || ncols != tr.shape().0 {
|
||
return false
|
||
}
|
||
|
||
for i in 0 .. nrows {
|
||
for j in 0 .. ncols {
|
||
if m[(i, j)] != tr[(j, i)] {
|
||
return false
|
||
}
|
||
}
|
||
}
|
||
|
||
true
|
||
}
|
||
|
||
fn tr_mul_is_transpose_then_mul(m: Matrix4x6<f64>, v: Vector4<f64>) -> bool {
|
||
m.transpose() * v == m.tr_mul(&v)
|
||
}
|
||
|
||
/*
|
||
*
|
||
*
|
||
* Inversion.
|
||
*
|
||
*
|
||
*/
|
||
fn self_mul_inv_is_id_dim1(m: Matrix1<f64>) -> bool {
|
||
if let Some(im) = m.try_inverse() {
|
||
let id = Matrix1::one();
|
||
relative_eq!(im * m, id, epsilon = 1.0e-7) &&
|
||
relative_eq!(m * im, id, epsilon = 1.0e-7)
|
||
}
|
||
else {
|
||
true
|
||
}
|
||
}
|
||
|
||
fn self_mul_inv_is_id_dim2(m: Matrix2<f64>) -> bool {
|
||
if let Some(im) = m.try_inverse() {
|
||
let id = Matrix2::one();
|
||
relative_eq!(im * m, id, epsilon = 1.0e-7) &&
|
||
relative_eq!(m * im, id, epsilon = 1.0e-7)
|
||
}
|
||
else {
|
||
true
|
||
}
|
||
}
|
||
|
||
fn self_mul_inv_is_id_dim3(m: Matrix3<f64>) -> bool {
|
||
if let Some(im) = m.try_inverse() {
|
||
let id = Matrix3::one();
|
||
relative_eq!(im * m, id, epsilon = 1.0e-7) &&
|
||
relative_eq!(m * im, id, epsilon = 1.0e-7)
|
||
}
|
||
else {
|
||
true
|
||
}
|
||
}
|
||
|
||
fn self_mul_inv_is_id_dim6(m: Matrix6<f64>) -> bool {
|
||
if let Some(im) = m.try_inverse() {
|
||
let id = Matrix6::one();
|
||
relative_eq!(im * m, id, epsilon = 1.0e-7) &&
|
||
relative_eq!(m * im, id, epsilon = 1.0e-7)
|
||
}
|
||
else {
|
||
true
|
||
}
|
||
}
|
||
|
||
/*
|
||
*
|
||
* Normalization.
|
||
*
|
||
*/
|
||
fn normalized_vec_norm_is_one(v: Vector3<f64>) -> bool {
|
||
if let Some(nv) = v.try_normalize(1.0e-10) {
|
||
relative_eq!(nv.norm(), 1.0, epsilon = 1.0e-7)
|
||
}
|
||
else {
|
||
true
|
||
}
|
||
}
|
||
|
||
fn normalized_vec_norm_is_one_dyn(v: DVector<f64>) -> bool {
|
||
if let Some(nv) = v.try_normalize(1.0e-10) {
|
||
relative_eq!(nv.norm(), 1.0)
|
||
}
|
||
else {
|
||
true
|
||
}
|
||
}
|
||
}
|
||
|
||
// FIXME: move this to alga ?
|
||
macro_rules! finite_dim_inner_space_test(
|
||
($($Vector: ident, $orthonormal_subspace: ident, $orthonormalization: ident);* $(;)*) => {$(
|
||
#[cfg(feature = "arbitrary")]
|
||
quickcheck!{
|
||
fn $orthonormal_subspace(vs: Vec<$Vector<f64>>) -> bool {
|
||
let mut given_basis = vs.clone();
|
||
let given_basis_dim = $Vector::orthonormalize(&mut given_basis[..]);
|
||
let mut ortho_basis = Vec::new();
|
||
$Vector::orthonormal_subspace_basis(
|
||
&given_basis[.. given_basis_dim],
|
||
|e| { ortho_basis.push(*e); true }
|
||
);
|
||
|
||
if !is_subspace_basis(&ortho_basis[..]) {
|
||
return false;
|
||
}
|
||
|
||
for v in vs {
|
||
for b in &ortho_basis {
|
||
if !relative_eq!(v.dot(b), 0.0, epsilon = 1.0e-7) {
|
||
println!("Found dot product: {} · {} = {}", v, b, v.dot(b));
|
||
return false;
|
||
}
|
||
}
|
||
}
|
||
|
||
true
|
||
}
|
||
|
||
fn $orthonormalization(vs: Vec<$Vector<f64>>) -> bool {
|
||
let mut basis = vs.clone();
|
||
let subdim = $Vector::orthonormalize(&mut basis[..]);
|
||
|
||
if !is_subspace_basis(&basis[.. subdim]) {
|
||
return false;
|
||
}
|
||
|
||
for mut e in vs {
|
||
for b in &basis[.. subdim] {
|
||
e -= e.dot(b) * b
|
||
}
|
||
|
||
// Any element of `e` must be a linear combination of the basis elements.
|
||
if !relative_eq!(e.norm(), 0.0, epsilon = 1.0e-7) {
|
||
println!("Orthonormalization; element decomposition failure: {}", e);
|
||
println!("... the non-zero norm is: {}", e.norm());
|
||
return false;
|
||
}
|
||
}
|
||
|
||
true
|
||
}
|
||
}
|
||
)*}
|
||
);
|
||
|
||
finite_dim_inner_space_test!(
|
||
Vector1, orthonormal_subspace_basis1, orthonormalize1;
|
||
Vector2, orthonormal_subspace_basis2, orthonormalize2;
|
||
Vector3, orthonormal_subspace_basis3, orthonormalize3;
|
||
Vector4, orthonormal_subspace_basis4, orthonormalize4;
|
||
Vector5, orthonormal_subspace_basis5, orthonormalize5;
|
||
Vector6, orthonormal_subspace_basis6, orthonormalize6;
|
||
);
|
||
|
||
/*
|
||
*
|
||
* Helper functions.
|
||
*
|
||
*/
|
||
fn is_subspace_basis<T: FiniteDimInnerSpace<Real = f64> + Display>(vs: &[T]) -> bool {
|
||
for i in 0 .. vs.len() {
|
||
// Basis elements must be normalized.
|
||
if !relative_eq!(vs[i].norm(), 1.0, epsilon = 1.0e-7) {
|
||
println!("Non-zero basis element norm: {}", vs[i].norm());
|
||
return false;
|
||
}
|
||
|
||
for j in 0 .. i {
|
||
// Basis elements must be orthogonal.
|
||
if !relative_eq!(vs[i].dot(&vs[j]), 0.0, epsilon = 1.0e-7) {
|
||
println!("Non-orthogonal basis elements: {} · {} = {}", vs[i], vs[j], vs[i].dot(&vs[j]));
|
||
return false
|
||
}
|
||
}
|
||
}
|
||
|
||
true
|
||
}
|