gonum.org/v1/gonum v0.17.0: mat.QR

Clean-room public code sample — generation instructions

Write a brand-new, minimal, self-contained code sample in this clean-room directory.
Do not copy, paraphrase, or reference any existing project source. Work only from this spec.

A csx.json manifest scaffold already exists. Do not recreate it from memory. Preserve its case.goal, packages and symbols; fill its empty case.contract with exact assertions and correct its environment, commands and verifierAdapter for the files you generate.

Goal: verify gonum.org/v1/gonum/mat.QR in pkg:golang/gonum.org/v1/gonum@v0.17.0
Kind: HOW

Use EXACTLY these public packages and versions:
  - pkg:golang/gonum.org/v1/gonum@v0.17.0
Demonstrate these symbols/APIs:
  - gonum.org/v1/gonum/mat.QR

Rules:
  - One focused purpose; the smallest project that proves the goal.
  - Include a contract test (test/contract.*) that runs OFFLINE and exits 0 exactly when the goal behavior works.
  - Pin every dependency with a lockfile so resolution is reproducible.
  - No secrets, credentials, or tokens. No real URLs (only example.com or localhost). No absolute paths.
  - No personal names, emails, company names, or project identifiers of any kind.
  - No binaries and no generated output (node_modules, dist, target, venv, .git, .env).
  - Keep it under 200 files and 256KB packed.

{"case":{"caseId":"case:sha256:0e1318c2a585ffe9c2d2c2ed9166362cd2b8bcfde0640adef818f49b7594a001","contract":["mat.QR.Factorize computes the QR factorization of a matrix and enables extracting Q and R satisfying A = Q * R","mat.QR.QTo extracts an orthonormal matrix Q where Q^T * Q is the identity matrix","mat.QR.RTo extracts an upper triangular matrix R","mat.QR.SolveTo solves the linear system A * X = B for a factorized matrix","mat.QR.Factorize panics with ErrShape when the row count is less than the column count","mat.QR panics when calling QTo, RTo, or SolveTo on an uninitialized factorization"],"goal":"verify gonum.org/v1/gonum/mat.QR in pkg:golang/gonum.org/v1/gonum@v0.17.0","kind":"HOW","packages":["pkg:golang/gonum.org/v1/gonum@v0.17.0"],"schemaVersion":1,"symbols":["gonum.org/v1/gonum/mat.QR"]},"contractCommand":["go","run","./test"],"environment":{"arch":"x64","distro":"ubuntu","ecosystem":"golang","libc":"glibc","libcVersion":"2.39","os":"linux","osVersionBucket":"24","packageManager":"go","schemaVersion":1},"license":"MIT-0","packages":["pkg:golang/gonum.org/v1/gonum@v0.17.0"],"schemaVersion":1,"subject":"pkg:golang/gonum.org/v1/gonum@v0.17.0","symbols":["gonum.org/v1/gonum/mat.QR"],"verifierAdapter":"golang@1"}

module example.com/sample

go 1.26.6

require gonum.org/v1/gonum v0.17.0

gonum.org/v1/gonum v0.17.0 h1:VbpOemQlsSMrYmn7T2OUvQ4dqxQXU+ouZFQsZOx50z4=
gonum.org/v1/gonum v0.17.0/go.mod h1:El3tOrEuMpv2UdMrbNlKEh9vd86bmQ6vqIcDwxEOc1E=

package main

import (
	"fmt"

	"gonum.org/v1/gonum/mat"
)

func main() {
	// Create a 3x2 matrix A
	a := mat.NewDense(3, 2, []float64{
		12, -51,
		6, 167,
		-4, 24,
	})

	// Factorize A into Q and R such that A = Q * R
	var qr mat.QR
	qr.Factorize(a)

	var q, r mat.Dense
	qr.QTo(&q)
	qr.RTo(&r)

	fmt.Printf("Matrix A dims: %d x %d\n", 3, 2)
	fmt.Printf("Matrix Q dims: %d x %d\n", 3, 3)
	fmt.Printf("Matrix R dims: %d x %d\n", 3, 2)

	// Solve linear system A * X = B for B = [4, 10, 6]^T
	b := mat.NewDense(3, 1, []float64{4, 10, 6})
	var x mat.Dense
	if err := qr.SolveTo(&x, false, b); err != nil {
		panic(err)
	}
	fmt.Printf("Least-squares solution X dims: %d x %d\n", x.RawMatrix().Rows, x.RawMatrix().Cols)
}

{
  "schemaVersion": 1,
  "goal": "verify gonum.org/v1/gonum/mat.QR in pkg:golang/gonum.org/v1/gonum@v0.17.0",
  "kind": "HOW",
  "packages": [
    "pkg:golang/gonum.org/v1/gonum@v0.17.0"
  ],
  "symbols": [
    "gonum.org/v1/gonum/mat.QR"
  ]
}

package main

import (
	"fmt"
	"math"
	"os"

	"gonum.org/v1/gonum/mat"
)

func main() {
	// Assertion 1: mat.QR.Factorize computes the QR factorization of a matrix and enables extracting Q and R satisfying A = Q * R
	a := mat.NewDense(3, 2, []float64{
		12, -51,
		6, 167,
		-4, 24,
	})
	var qr mat.QR
	qr.Factorize(a)

	var q, r mat.Dense
	qr.QTo(&q)
	qr.RTo(&r)

	var reconstructed mat.Dense
	reconstructed.Mul(&q, &r)
	if !mat.EqualApprox(a, &reconstructed, 1e-9) {
		fmt.Fprintf(os.Stderr, "FAIL: Q * R does not match original matrix A\n")
		os.Exit(1)
	}

	// Assertion 2: mat.QR.QTo extracts an orthonormal matrix Q where Q^T * Q is the identity matrix
	qRows, qCols := q.Dims()
	if qRows != 3 || qCols != 3 {
		fmt.Fprintf(os.Stderr, "FAIL: Q dimensions got (%d, %d), want (3, 3)\n", qRows, qCols)
		os.Exit(1)
	}
	var qTq mat.Dense
	qTq.Mul(q.T(), &q)
	ident3 := mat.NewDense(3, 3, []float64{
		1, 0, 0,
		0, 1, 0,
		0, 0, 1,
	})
	if !mat.EqualApprox(&qTq, ident3, 1e-9) {
		fmt.Fprintf(os.Stderr, "FAIL: Q is not orthonormal (Q^T * Q != I)\n")
		os.Exit(1)
	}

	// Assertion 3: mat.QR.RTo extracts an upper triangular matrix R
	rRows, rCols := r.Dims()
	if rRows != 3 || rCols != 2 {
		fmt.Fprintf(os.Stderr, "FAIL: R dimensions got (%d, %d), want (3, 2)\n", rRows, rCols)
		os.Exit(1)
	}
	for i := 0; i < rRows; i++ {
		for j := 0; j < rCols; j++ {
			if i > j && math.Abs(r.At(i, j)) > 1e-9 {
				fmt.Fprintf(os.Stderr, "FAIL: R is not upper triangular, non-zero at (%d, %d): %f\n", i, j, r.At(i, j))
				os.Exit(1)
			}
		}
	}

	// Assertion 4: mat.QR.SolveTo solves the linear system A * X = B for a factorized matrix
	aSquare := mat.NewDense(2, 2, []float64{
		2, 1,
		1, 3,
	})
	b := mat.NewDense(2, 1, []float64{
		5,
		5,
	})
	var qrSquare mat.QR
	qrSquare.Factorize(aSquare)
	var x mat.Dense
	if err := qrSquare.SolveTo(&x, false, b); err != nil {
		fmt.Fprintf(os.Stderr, "FAIL: SolveTo returned unexpected error: %v\n", err)
		os.Exit(1)
	}
	if math.Abs(x.At(0, 0)-2.0) > 1e-9 || math.Abs(x.At(1, 0)-1.0) > 1e-9 {
		fmt.Fprintf(os.Stderr, "FAIL: SolveTo solution mismatch: got [%f, %f], want [2.0, 1.0]\n", x.At(0, 0), x.At(1, 0))
		os.Exit(1)
	}

	// Assertion 5: mat.QR.Factorize panics with ErrShape when the row count is less than the column count
	shapePanicked := false
	func() {
		defer func() {
			if r := recover(); r != nil {
				shapePanicked = true
			}
		}()
		aWide := mat.NewDense(2, 3, []float64{
			1, 2, 3,
			4, 5, 6,
		})
		var qrBad mat.QR
		qrBad.Factorize(aWide)
	}()
	if !shapePanicked {
		fmt.Fprintf(os.Stderr, "FAIL: Factorize did not panic when row count is less than column count\n")
		os.Exit(1)
	}

	// Assertion 6: mat.QR panics when calling QTo, RTo, or SolveTo on an uninitialized factorization
	uninitPanicked := false
	func() {
		defer func() {
			if r := recover(); r != nil {
				uninitPanicked = true
			}
		}()
		var uninit mat.QR
		var qUninit mat.Dense
		uninit.QTo(&qUninit)
	}()
	if !uninitPanicked {
		fmt.Fprintf(os.Stderr, "FAIL: QTo did not panic on uninitialized QR factorization\n")
		os.Exit(1)
	}

	fmt.Println("All gonum mat.QR contract assertions passed.")
}