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210 lines
6.9 KiB
Go
210 lines
6.9 KiB
Go
// Copyright ©2016 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package stat
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import (
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"math"
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"testing"
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"gonum.org/v1/gonum/floats/scalar"
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"gonum.org/v1/gonum/mat"
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)
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func TestPrincipalComponents(t *testing.T) {
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// Threshold for detecting zero variances.
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const epsilon = 1e-15
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tests:
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for i, test := range []struct {
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data mat.Matrix
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weights []float64
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wantVecs *mat.Dense
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wantVars []float64
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epsilon float64
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}{
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// Test results verified using R.
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{
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data: mat.NewDense(3, 3, []float64{
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1, 2, 3,
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4, 5, 6,
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7, 8, 9,
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}),
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wantVecs: mat.NewDense(3, 3, []float64{
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0.5773502691896258, 0.8164965809277261, 0,
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0.577350269189626, -0.4082482904638632, -0.7071067811865476,
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0.5773502691896258, -0.4082482904638631, 0.7071067811865475,
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}),
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wantVars: []float64{27, 0, 0},
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epsilon: 1e-12,
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},
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{ // Truncated iris data.
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data: mat.NewDense(10, 4, []float64{
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5.1, 3.5, 1.4, 0.2,
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4.9, 3.0, 1.4, 0.2,
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4.7, 3.2, 1.3, 0.2,
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4.6, 3.1, 1.5, 0.2,
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5.0, 3.6, 1.4, 0.2,
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5.4, 3.9, 1.7, 0.4,
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4.6, 3.4, 1.4, 0.3,
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5.0, 3.4, 1.5, 0.2,
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4.4, 2.9, 1.4, 0.2,
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4.9, 3.1, 1.5, 0.1,
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}),
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wantVecs: mat.NewDense(4, 4, []float64{
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-0.6681110197952722, 0.7064764857539533, -0.14026590216895132, -0.18666578956412125,
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-0.7166344774801547, -0.6427036135482664, -0.135650285905254, 0.23444848208629923,
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-0.164411275166307, 0.11898477441068218, 0.9136367900709548, 0.35224901970831746,
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-0.11415613655453069, -0.2714141920887426, 0.35664028439226514, -0.8866286823515034,
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}),
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wantVars: []float64{0.1665786313282786, 0.02065509475412993, 0.007944620317765855, 0.0019327647109368329},
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epsilon: 1e-12,
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},
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{ // Truncated iris data to form wide matrix.
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data: mat.NewDense(3, 4, []float64{
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5.1, 3.5, 1.4, 0.2,
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4.9, 3.0, 1.4, 0.2,
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4.7, 3.2, 1.3, 0.2,
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}),
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wantVecs: mat.NewDense(4, 3, []float64{
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-0.5705187254552365, -0.7505979435049239, 0.08084520834544455,
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-0.8166537769529318, 0.5615147645527523, -0.032338083338177705,
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-0.08709186238359454, -0.3482870890450082, -0.22636658336724505,
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0, 0, -0.9701425001453315,
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}),
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wantVars: []float64{0.0844692361537822, 0.022197430512884326, 0},
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epsilon: 1e-12,
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},
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{ // Truncated iris data transposed to check for operation on fat input.
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data: mat.NewDense(10, 4, []float64{
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5.1, 3.5, 1.4, 0.2,
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4.9, 3.0, 1.4, 0.2,
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4.7, 3.2, 1.3, 0.2,
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4.6, 3.1, 1.5, 0.2,
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5.0, 3.6, 1.4, 0.2,
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5.4, 3.9, 1.7, 0.4,
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4.6, 3.4, 1.4, 0.3,
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5.0, 3.4, 1.5, 0.2,
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4.4, 2.9, 1.4, 0.2,
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4.9, 3.1, 1.5, 0.1,
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}).T(),
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wantVecs: mat.NewDense(10, 4, []float64{
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-0.3366602459946619, -0.1373634006401213, 0.3465102523547623, -0.10290179303893479,
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-0.31381852053861975, 0.5197145790632827, 0.5567296129086686, -0.15923062170153618,
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-0.30857197637565165, -0.07670930360819002, 0.36159923003337235, 0.3342301027853355,
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-0.29527124351656137, 0.16885455995353074, -0.5056204762881208, 0.32580913261444344,
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-0.3327611073694004, -0.39365834489416474, 0.04900050959307464, 0.46812879383236555,
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-0.34445484362044815, -0.2985206914561878, -0.1009714701361799, -0.16803618186050803,
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-0.2986246350957691, -0.4222037823717799, -0.11838613462182519, -0.580283530375069,
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-0.325911246223126, 0.024366468758217238, -0.12082035131864265, 0.16756027181337868,
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-0.2814284432361538, 0.240812316260054, -0.24061437569068145, -0.365034616264623,
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-0.31906138507685167, 0.4423912824105986, -0.2906412122303604, 0.027551046870337714,
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}),
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wantVars: []float64{41.8851906634233, 0.07762619213464989, 0.010516477775373585, 0},
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epsilon: 1e-12,
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},
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{ // Truncated iris data unitary weights.
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data: mat.NewDense(10, 4, []float64{
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5.1, 3.5, 1.4, 0.2,
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4.9, 3.0, 1.4, 0.2,
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4.7, 3.2, 1.3, 0.2,
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4.6, 3.1, 1.5, 0.2,
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5.0, 3.6, 1.4, 0.2,
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5.4, 3.9, 1.7, 0.4,
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4.6, 3.4, 1.4, 0.3,
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5.0, 3.4, 1.5, 0.2,
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4.4, 2.9, 1.4, 0.2,
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4.9, 3.1, 1.5, 0.1,
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}),
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weights: []float64{1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
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wantVecs: mat.NewDense(4, 4, []float64{
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-0.6681110197952722, 0.7064764857539533, -0.14026590216895132, -0.18666578956412125,
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-0.7166344774801547, -0.6427036135482664, -0.135650285905254, 0.23444848208629923,
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-0.164411275166307, 0.11898477441068218, 0.9136367900709548, 0.35224901970831746,
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-0.11415613655453069, -0.2714141920887426, 0.35664028439226514, -0.8866286823515034,
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}),
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wantVars: []float64{0.1665786313282786, 0.02065509475412993, 0.007944620317765855, 0.0019327647109368329},
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epsilon: 1e-12,
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},
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{ // Truncated iris data non-unitary weights.
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data: mat.NewDense(10, 4, []float64{
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5.1, 3.5, 1.4, 0.2,
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4.9, 3.0, 1.4, 0.2,
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4.7, 3.2, 1.3, 0.2,
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4.6, 3.1, 1.5, 0.2,
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5.0, 3.6, 1.4, 0.2,
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5.4, 3.9, 1.7, 0.4,
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4.6, 3.4, 1.4, 0.3,
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5.0, 3.4, 1.5, 0.2,
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4.4, 2.9, 1.4, 0.2,
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4.9, 3.1, 1.5, 0.1,
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}),
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weights: []float64{2, 3, 1, 1, 1, 1, 1, 1, 1, 2},
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wantVecs: mat.NewDense(4, 4, []float64{
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-0.618936145422414, 0.763069301531647, 0.124857741232537, 0.138035623677211,
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-0.763958271606519, -0.603881770702898, 0.118267155321333, -0.194184052457746,
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-0.143552119754944, 0.090014599564871, -0.942209377020044, -0.289018426115945,
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-0.112599271966947, -0.212012782487076, -0.287515067921680, 0.927203898682805,
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}),
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wantVars: []float64{0.129621985550623, 0.022417487771598, 0.006454461065715, 0.002495076601075},
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epsilon: 1e-12,
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},
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} {
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var pc PC
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vecs := &mat.Dense{}
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var vars []float64
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for j := 0; j < 2; j++ {
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ok := pc.PrincipalComponents(test.data, test.weights)
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pc.VectorsTo(vecs)
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vars = pc.VarsTo(vars)
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if !ok {
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t.Errorf("unexpected SVD failure for test %d use %d", i, j)
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continue tests
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}
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// Find the number of non-zero variances to handle
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// non-uniqueness in SVD result (issue #21).
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nnz := len(vars)
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for k, v := range vars {
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if math.Abs(v) < epsilon {
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nnz = k
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break
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}
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}
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r, c := vecs.Dims()
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if !mat.EqualApprox(vecs.Slice(0, r, 0, nnz), test.wantVecs.Slice(0, r, 0, nnz), test.epsilon) {
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t.Errorf("%d use %d: unexpected PCA result got:\n%v\nwant:\n%v",
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i, j, mat.Formatted(vecs), mat.Formatted(test.wantVecs))
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}
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if !approxEqual(vars, test.wantVars, test.epsilon) {
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t.Errorf("%d use %d: unexpected variance result got:%v, want:%v",
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i, j, vars, test.wantVars)
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}
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// Check that the set of principal vectors is
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// orthonormal by comparing Vᵀ*V to the identity matrix.
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I := mat.NewDiagDense(c, nil)
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for k := 0; k < c; k++ {
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I.SetDiag(k, 1)
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}
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var vv mat.Dense
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vv.Mul(vecs.T(), vecs)
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if !mat.EqualApprox(&vv, I, test.epsilon) {
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t.Errorf("%d use %d: vectors not orthonormal\n%v", i, j, mat.Formatted(I))
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}
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}
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}
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}
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func approxEqual(a, b []float64, epsilon float64) bool {
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if len(a) != len(b) {
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return false
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}
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for i, v := range a {
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if !scalar.EqualWithinAbsOrRel(v, b[i], epsilon, epsilon) {
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return false
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}
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}
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return true
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}
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