einsum-ndarray 0.1.0

Einstein summation for dynamically shaped ndarray arrays
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148

use einsum_ndarray::{einsum, einsum_path, EinsumError, EinsumPlan, Strategy};
use ndarray::{array, ArrayD, ArrayViewD, IxDyn};

#[test]
fn defect_fixed_left_to_right_order_selects_the_lower_cost_chain() {
    let shapes: [&[usize]; 4] = [&[16, 16], &[16, 16], &[16, 16], &[16, 1]];
    let path = einsum_path("ab,bc,cd,de->ae", &shapes).unwrap();
    assert_eq!(path.optimized_flops, 1536);
    assert!(path.optimized_flops < path.naive_flops);
}

#[test]
fn defect_generic_iteration_dispatches_matrix_contractions() {
    let matmul_shapes: [&[usize]; 2] = [&[3, 4], &[4, 5]];
    let matmul = einsum_path("ij,jk->ik", &matmul_shapes).unwrap();
    assert!(matmul.steps.iter().all(|step| step.gemm));

    let batch_shapes: [&[usize]; 2] = [&[2, 3, 4], &[2, 4, 5]];
    let batch = einsum_path("bij,bjk->bik", &batch_shapes).unwrap();
    assert!(batch.steps.iter().all(|step| step.gemm));

    let bilinear_shapes: [&[usize]; 3] = [&[3], &[3, 4], &[4]];
    let bilinear = einsum_path("i,ij,j->", &bilinear_shapes).unwrap();
    assert!(bilinear.steps.iter().any(|step| step.gemm));
}

#[test]
fn defect_missing_ellipsis_support_broadcasts_batch_axes() {
    let left =
        ArrayD::from_shape_vec(IxDyn(&[1, 2, 3]), vec![1.0, 2.0, 3.0, 4.0, 5.0, 6.0]).unwrap();
    let right =
        ArrayD::from_shape_vec(IxDyn(&[2, 3, 1]), vec![1.0, 2.0, 3.0, 4.0, 5.0, 6.0]).unwrap();
    let operands = [left.view(), right.view()];
    let result = einsum("...ij,...jk->...ik", &operands).unwrap();
    assert_eq!(result.shape(), &[2, 2, 1]);
    assert_eq!(result.as_slice().unwrap(), &[14.0, 32.0, 32.0, 77.0]);
}

#[test]
fn defect_unpinned_diagonal_broadcast_and_empty_axes_are_defined() {
    let matrix = array![[1_i64, 2, 3], [4, 5, 6], [7, 8, 9]].into_dyn();
    let diagonal = einsum("ii->i", &[matrix.view()]).unwrap();
    assert_eq!(diagonal.as_slice().unwrap(), &[1, 5, 9]);

    let left = array![1_i64, 2, 3].into_dyn();
    let one = array![4_i64].into_dyn();
    let broadcast = einsum("i,i->i", &[left.view(), one.view()]).unwrap();
    assert_eq!(broadcast.as_slice().unwrap(), &[4, 8, 12]);

    let empty = ArrayD::<i64>::zeros(IxDyn(&[2, 0]));
    let other = ArrayD::<i64>::zeros(IxDyn(&[0, 3]));
    let product = einsum("ij,jk->ik", &[empty.view(), other.view()]).unwrap();
    assert_eq!(product, ArrayD::<i64>::zeros(IxDyn(&[2, 3])));
}

#[test]
fn plan_rejects_execution_shapes_that_differ_from_the_bound_shapes() {
    let plan = EinsumPlan::new("ij->ji", &[&[2, 3]]).unwrap();
    let wrong = ArrayD::<f64>::zeros(IxDyn(&[3, 2]));
    let error = plan.execute(&[wrong.view()]).unwrap_err();
    assert!(matches!(
        error,
        einsum_ndarray::EinsumError::ShapeMismatch { .. }
    ));
}

#[test]
fn scalar_operands_and_results_keep_zero_rank() {
    let scalar = ArrayD::from_shape_vec(IxDyn(&[]), vec![3_i64]).unwrap();
    let vector = array![2_i64, 4, 6].into_dyn();
    let scaled = einsum(",i->i", &[scalar.view(), vector.view()]).unwrap();
    assert_eq!(scaled.as_slice().unwrap(), &[6, 12, 18]);

    let dot = einsum("i,i->", &[vector.view(), vector.view()]).unwrap();
    assert_eq!(dot.ndim(), 0);
    assert_eq!(dot.as_slice().unwrap(), &[56]);
}

#[test]
fn one_shot_api_accepts_non_owned_dynamic_views() {
    let left = array![[1_i64, 2], [3, 4]];
    let right = array![[5_i64, 6], [7, 8]];
    let views: Vec<ArrayViewD<'_, i64>> = vec![left.view().into_dyn(), right.view().into_dyn()];
    let result = einsum("ij,jk->ik", &views).unwrap();
    assert_eq!(result, array![[19, 22], [43, 50]].into_dyn());
}

#[test]
fn integer_overflow_wraps_in_reduction_broadcast_and_matrix_kernels() {
    let maximum = array![i64::MAX].into_dyn();
    let two = array![2_i64].into_dyn();
    let product = einsum("i,i->i", &[maximum.view(), two.view()]).unwrap();
    assert_eq!(product.as_slice().unwrap(), &[-2]);

    let summands = array![i64::MAX, 1].into_dyn();
    let sum = einsum("i->", &[summands.view()]).unwrap();
    assert_eq!(sum.as_slice().unwrap(), &[i64::MIN]);

    let left = array![[i64::MAX]].into_dyn();
    let right = array![[2_i64]].into_dyn();
    let matrix = einsum("ij,jk->ik", &[left.view(), right.view()]).unwrap();
    assert_eq!(matrix.as_slice().unwrap(), &[-2]);
}

#[test]
fn parser_reports_too_many_labels_for_rank_one_operand() {
    let error = EinsumPlan::new("ij,j->i", &[&[2], &[2]]).unwrap_err();
    assert!(matches!(
        error,
        EinsumError::TooManyLabels { operand: 0, .. }
    ));
}

#[test]
fn explicit_intermediate_size_overflow_is_rejected_during_planning() {
    let large = usize::MAX / 2 + 1;
    let shapes: [&[usize]; 3] = [&[large], &[large], &[1, 1]];
    let error = EinsumPlan::with_strategy(
        "i,j,ij->",
        &shapes,
        Strategy::Explicit(vec![vec![0, 1], vec![0, 1]]),
    )
    .unwrap_err();
    assert_eq!(error, EinsumError::SizeOverflow);
}

#[test]
fn strategy_default_selects_auto() {
    assert_eq!(Strategy::default(), Strategy::Auto);
}

#[test]
fn public_greedy_and_optimal_strategies_execute_without_panicking() {
    let shapes: [&[usize]; 3] = [&[2, 3], &[3, 4], &[4, 2]];
    let arrays = [
        ArrayD::<i64>::ones(IxDyn(shapes[0])),
        ArrayD::<i64>::ones(IxDyn(shapes[1])),
        ArrayD::<i64>::ones(IxDyn(shapes[2])),
    ];
    let views = arrays.iter().map(|array| array.view()).collect::<Vec<_>>();
    for strategy in [Strategy::Greedy, Strategy::Optimal] {
        let plan = EinsumPlan::with_strategy("ij,jk,kl->il", &shapes, strategy).unwrap();
        assert_eq!(
            plan.execute(&views).unwrap(),
            ArrayD::from_elem(IxDyn(&[2, 2]), 12)
        );
    }
}