Find Root of System of Equations

Find a solution to a system of nonlinear equations F(x) = 0 where F and x are vectors. Supports built-in systems: linear_2x2 (system of two linear equations), nonlinear_2x2 (nonlinear system like x^2 + y^2 = 4, xy = 1). Methods: newton (multidimensional Newton-Raphson with Jacobian), broyden (quasi-Newton method, approximates Jacobian). Essential for finding equilibrium points, solving nonlinear systems in economics, and multi-asset calibration. [Tier: BASIC, Credits: 1]

POST /quantlib/numerical/roots/find-nd

Find Root of System of Equations

cURL

curl --request POST \
  --url https://api.fincept.in/quantlib/numerical/roots/find-nd \
  --header 'Content-Type: application/json' \
  --header 'X-API-Key: <api-key>' \
  --data '
{
  "system": "nonlinear_2x2",
  "x0": [
    1.5,
    1
  ],
  "method": "newton",
  "tol": 1e-10
}
'

import requests

url = "https://api.fincept.in/quantlib/numerical/roots/find-nd"

payload = {
    "system": "nonlinear_2x2",
    "x0": [1.5, 1],
    "method": "newton",
    "tol": 1e-10
}
headers = {
    "X-API-Key": "<api-key>",
    "Content-Type": "application/json"
}

response = requests.post(url, json=payload, headers=headers)

print(response.text)

const options = {
  method: 'POST',
  headers: {'X-API-Key': '<api-key>', 'Content-Type': 'application/json'},
  body: JSON.stringify({system: 'nonlinear_2x2', x0: [1.5, 1], method: 'newton', tol: 1e-10})
};

fetch('https://api.fincept.in/quantlib/numerical/roots/find-nd', options)
  .then(res => res.json())
  .then(res => console.log(res))
  .catch(err => console.error(err));

<?php

$curl = curl_init();

curl_setopt_array($curl, [
  CURLOPT_URL => "https://api.fincept.in/quantlib/numerical/roots/find-nd",
  CURLOPT_RETURNTRANSFER => true,
  CURLOPT_ENCODING => "",
  CURLOPT_MAXREDIRS => 10,
  CURLOPT_TIMEOUT => 30,
  CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
  CURLOPT_CUSTOMREQUEST => "POST",
  CURLOPT_POSTFIELDS => json_encode([
    'system' => 'nonlinear_2x2',
    'x0' => [
        1.5,
        1
    ],
    'method' => 'newton',
    'tol' => 1e-10
  ]),
  CURLOPT_HTTPHEADER => [
    "Content-Type: application/json",
    "X-API-Key: <api-key>"
  ],
]);

$response = curl_exec($curl);
$err = curl_error($curl);

curl_close($curl);

if ($err) {
  echo "cURL Error #:" . $err;
} else {
  echo $response;
}

package main

import (
	"fmt"
	"strings"
	"net/http"
	"io"
)

func main() {

	url := "https://api.fincept.in/quantlib/numerical/roots/find-nd"

	payload := strings.NewReader("{\n  \"system\": \"nonlinear_2x2\",\n  \"x0\": [\n    1.5,\n    1\n  ],\n  \"method\": \"newton\",\n  \"tol\": 1e-10\n}")

	req, _ := http.NewRequest("POST", url, payload)

	req.Header.Add("X-API-Key", "<api-key>")
	req.Header.Add("Content-Type", "application/json")

	res, _ := http.DefaultClient.Do(req)

	defer res.Body.Close()
	body, _ := io.ReadAll(res.Body)

	fmt.Println(string(body))

}

HttpResponse<String> response = Unirest.post("https://api.fincept.in/quantlib/numerical/roots/find-nd")
  .header("X-API-Key", "<api-key>")
  .header("Content-Type", "application/json")
  .body("{\n  \"system\": \"nonlinear_2x2\",\n  \"x0\": [\n    1.5,\n    1\n  ],\n  \"method\": \"newton\",\n  \"tol\": 1e-10\n}")
  .asString();

require 'uri'
require 'net/http'

url = URI("https://api.fincept.in/quantlib/numerical/roots/find-nd")

http = Net::HTTP.new(url.host, url.port)
http.use_ssl = true

request = Net::HTTP::Post.new(url)
request["X-API-Key"] = '<api-key>'
request["Content-Type"] = 'application/json'
request.body = "{\n  \"system\": \"nonlinear_2x2\",\n  \"x0\": [\n    1.5,\n    1\n  ],\n  \"method\": \"newton\",\n  \"tol\": 1e-10\n}"

response = http.request(request)
puts response.read_body

200

{
  "success": true,
  "data": {
    "root": [
      1.7320508,
      0.5773503
    ],
    "iterations": 5,
    "converged": true
  }
}

{
  "detail": "Invalid API key"
}

{
  "detail": "Endpoint requires Basic tier or higher"
}

Authorizations

X-API-Key · string · header · required

API key for authentication. Get your key at https://api.fincept.in/auth/register

Body

application/json

system · enum<string> · required

System of equations to solve

Available options: linear_2x2, nonlinear_2x2

Example:

"nonlinear_2x2"

x0 · number[] · required

Initial guess for the solution (number of elements = number of equations)

Example:

[1.5, 1]

method · enum<string> · default: newton

Solution method

Available options: newton, broyden

Example:

"newton"

tol · number · default: 1e-10

Convergence tolerance

Example:

1e-10

params · number[]

System-specific parameters (for linear_2x2: [a,b,c,d,e,f] for ax+by+c=0, dx+ey+f=0)

Example:

[1, 1, -3, 2, -1, -1]

Response

200

application/json

Successful Response

success · boolean

Example:

true

data · object

Show child attributes