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140 lines
3.2 KiB
Go
140 lines
3.2 KiB
Go
// Copyright ©2015 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 testlapack
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import (
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"testing"
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"golang.org/x/exp/rand"
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/blas/blas64"
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)
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type Dgeqp3er interface {
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Dlapmter
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Dgeqp3(m, n int, a []float64, lda int, jpvt []int, tau, work []float64, lwork int)
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}
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func Dgeqp3Test(t *testing.T, impl Dgeqp3er) {
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rnd := rand.New(rand.NewSource(1))
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for c, test := range []struct {
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m, n, lda int
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}{
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{1, 1, 0},
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{2, 2, 0},
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{3, 2, 0},
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{2, 3, 0},
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{1, 12, 0},
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{2, 6, 0},
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{3, 4, 0},
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{4, 3, 0},
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{6, 2, 0},
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{12, 1, 0},
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{1, 1, 20},
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{2, 2, 20},
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{3, 2, 20},
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{2, 3, 20},
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{1, 12, 20},
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{2, 6, 20},
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{3, 4, 20},
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{4, 3, 20},
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{6, 2, 20},
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{12, 1, 20},
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{129, 256, 0},
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{256, 129, 0},
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{129, 256, 266},
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{256, 129, 266},
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} {
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n := test.n
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m := test.m
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lda := test.lda
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if lda == 0 {
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lda = test.n
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}
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const (
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all = iota
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some
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none
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)
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for _, free := range []int{all, some, none} {
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// Allocate m×n matrix A and fill it with random numbers.
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a := make([]float64, m*lda)
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for i := range a {
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a[i] = rnd.Float64()
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}
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// Store a copy of A for later comparison.
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aCopy := make([]float64, len(a))
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copy(aCopy, a)
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// Allocate a slice of column pivots.
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jpvt := make([]int, n)
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for j := range jpvt {
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switch free {
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case all:
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// All columns are free.
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jpvt[j] = -1
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case some:
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// Some columns are free, some are leading columns.
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jpvt[j] = rnd.Intn(2) - 1 // -1 or 0
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case none:
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// All columns are leading.
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jpvt[j] = 0
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default:
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panic("bad freedom")
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}
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}
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// Allocate a slice for scalar factors of elementary
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// reflectors and fill it with random numbers. Dgeqp3
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// will overwrite them with valid data.
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k := min(m, n)
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tau := make([]float64, k)
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for i := range tau {
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tau[i] = rnd.Float64()
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}
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// Get optimal workspace size for Dgeqp3.
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work := make([]float64, 1)
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impl.Dgeqp3(m, n, a, lda, jpvt, tau, work, -1)
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lwork := int(work[0])
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work = make([]float64, lwork)
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for i := range work {
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work[i] = rnd.Float64()
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}
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// Compute a QR factorization of A with column pivoting.
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impl.Dgeqp3(m, n, a, lda, jpvt, tau, work, lwork)
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// Compute Q based on the elementary reflectors stored in A.
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q := constructQ("QR", m, n, a, lda, tau)
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// Check that Q is orthogonal.
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if !isOrthogonal(q) {
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t.Errorf("Case %v, Q not orthogonal", c)
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}
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// Copy the upper triangle of A into R.
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r := blas64.General{
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Rows: m,
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Cols: n,
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Stride: n,
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Data: make([]float64, m*n),
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}
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for i := 0; i < m; i++ {
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for j := i; j < n; j++ {
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r.Data[i*n+j] = a[i*lda+j]
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}
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}
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// Compute Q * R.
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got := nanGeneral(m, n, lda)
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blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, r, 0, got)
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// Compute A * P: rearrange the columns of A based on the permutation in jpvt.
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want := blas64.General{Rows: m, Cols: n, Stride: lda, Data: aCopy}
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impl.Dlapmt(true, want.Rows, want.Cols, want.Data, want.Stride, jpvt)
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// Check that A * P = Q * R.
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if !equalApproxGeneral(got, want, 1e-13) {
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t.Errorf("Case %v, Q*R != A*P\nQ*R=%v\nA*P=%v", c, got, want)
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}
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}
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}
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}
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