jsketcher/web/app/sketcher/constr/polynomial.ts

import {eqEps} from "geom/tolerance";
import {compositeFn} from "gems/func";
import {SolverParam} from "./solverParam";

export class Polynomial {

  monomials = [];
  constant = 0;

  constructor(constant = 0) {
    this.constant = constant;
  }

  get lastMonomial() {
    return this.monomials[this.monomials.length - 1];
  }

  term(p, fn) {
    this.lastMonomial.addParam(p, fn);
    return this;
  }

  monomial(k = 1) {
    this.monomials.push(new Monomial(k));
    return this;
  }

  eliminate(param, value) {
    let touched = false;
    for (let m of this.monomials) {
      for (let i = 0; i < m.terms.length; ++i) {
        if (m.terms[i].param === param) {
          m.eliminate(i, value);
          touched = true;
        }
      }
    }
    return touched;
  }

  substitute(param, toParam, dotConstant) {
    for (let m of this.monomials) {
      let touched = false;
      for (let i = 0; i < m.terms.length; ++i) {
        if (m.terms[i].param === param) {
          m.substitute(i, toParam, dotConstant);
          touched = true;
        }
      }
      if (touched) {
        m.mergeTerms();
      }
    }
  }

  linearSubstitution(param, toParam, k, b) {
    const transaction = compositeFn();
    for (let mi = this.monomials.length - 1; mi >= 0 ; --mi) {
      const m = this.monomials[mi];
      for (let i = 0; i < m.terms.length; ++i) {
        if (m.terms[i].param === param) {
          const polynomial = m.terms[i].fn.linearSubstitution(k, toParam, b);
          if (polynomial) {
            transaction.push(() => {
              for (let k = 0; k < polynomial.monomials.length; ++k) {
                let monomialToExpand = polynomial.monomials[k];
                this.monomial(monomialToExpand.constant * m.constant);
                this.lastMonomial.terms = monomialToExpand.terms.slice();

                for (let termToJoin of m.terms) {
                  if (termToJoin !== m.terms[i]) {
                    this.lastMonomial.terms.push({...termToJoin});
                  }
                }
                this.lastMonomial.sort();
              }
              m.constant *= polynomial.constant;
              m.terms.splice(i, 1);
            });
          } else {
            return null;
          }
        }
      }
    }
    return transaction;
  }

  compact() {
    for (let i = 0; i < this.monomials.length; ++i) {
      const m1 = this.monomials[i];
      if (m1 === null) {
        continue;
      }
      for (let j = i + 1; j < this.monomials.length; ++j) {
        const m2 = this.monomials[j];
        if (m2 === null) {
          continue;
        }

        if (m1.equalVars(m2)) {
          m1.constant += m2.constant;
          this.monomials[j] = null;
        }
      }
      if (eqEps(m1.constant, 0)) {
        this.monomials[i] = null;
      } else if (m1.terms.length === 0) {
        this.constant += m1.constant;
        this.monomials[i] = null;
      }
    }
    this.monomials = this.monomials.filter(m => m !== null);
  }

  get isLinear() {
    for (let m of this.monomials) {
      if (m.terms.length !== 1 || m.terms[0].fn.degree !== 1) {
        return false;
      }
    }
    return true;
  }

  value(valueFn = GET_VALUE) {
    let res = this.constant;
    for (let m of this.monomials) {
      res += m.value(valueFn);
    }
    return res;
  }

  asResidual() {

    const paramsSet: Set<SolverParam> = new Set();

    for (let m of this.monomials) {
      for (let t of m.terms) {
        paramsSet.add(t.param.solverParam);
      }
    }

    const params = Array.from(paramsSet);

    const solverValue = p => p.solverParam.get();

    return {

      params,

      error: () => this.value(solverValue),

      gradient: out => {

        for (let i = 0; i < params.length; i++) {

          out[i] = 0;

          for (let m of this.monomials) {
            out[i] += m.differentiate(params[i].objectParam, solverValue);
          }
        }

      },

    };


  }

  visitParams(callback) {
    for (let m of this.monomials) {
      for (let t of m.terms) {
        callback(t.param);
      }
    }
  }

  toString() {

    return this.monomials.map(m => {

        let out = '';
        if (m.constant === 1) {
          out += '+';
        } else if (m.constant === -1) {
          out += '-';
        } else {
          out += (m.constant >= 0 ? '+' : '') + m.constant.toFixed(2);
          if (m.terms.length) {
            out += '*';
          }
        }

        out += m.terms.map(t => {
          let out = t.param.debugSymbol + t.param.id;
          if (t.fn.degree === 1) {

          } else if (t.fn.degree !== Infinity) {
            out += t.fn.id;
          } else if (t.fn.render) {
            out = t.fn.render(out);
          } else {
            out = t.fn.id + '(' + out + ')';
          }
          return out;
        }).join('*');

        return out;
      }
    ).join(' ') + (this.constant >= 0 ? ' + ' : ' ') + this.constant.toFixed(2);

  }

}

export class Monomial {

  terms = [];
  constant = 1;

  constructor(constant = 1) {
    this.constant = constant;
  }

  get linearParam() {
    return this.terms[0].param;
  }

  addParam(param, fn) {
    this.terms.push({param, fn});
    this.sort();
  }

  sort() {
    this.terms.sort(t => t.param.id);
  }

  eliminate(i, value) {
    const fn = this.terms[i].fn;
    this.constant *= fn.apply(value);
    this.terms.splice(i, 1);
  }

  substitute(index, toParam, dotConstant) {
    this.terms[index].param = toParam;
    this.constant *= dotConstant;
  }

  mergeTerms() {
    let wasMerge = false;
    for (let i = 0; i < this.terms.length; ++i) {
      const merger = this.terms[i];
      if (!merger) {
        continue;
      }
      for (let j = i + 1; j < this.terms.length; ++j) {
        const term = this.terms[j];
        if (merger.param === term.param) {
          let mergedFn = merger.fn.merge(term.fn);
          if (mergedFn) {
            merger.fn = mergedFn;
            this.terms[j] = null;
            wasMerge = true;
          }
        }
      }
    }
    if (wasMerge) {
      this.terms = this.terms.filter(t => t);
    }
  }

  equalVars(other) {
    if (this.terms.length !== other.terms.length) {
      return false;
    }

    for (let i = 0; i < this.terms.length; ++i) {
      const t1 = this.terms[i];
      const t2 = other.terms[i];
      if (t1.fn.id !== t2.fn.id || t1.param.id !== t2.param.id) {
        return false;
      }
    }
    return true;
  }

  differentiate(partialParam, valueFn = GET_VALUE) {

    let cnst = this.constant;

    let diffProduct = 0;
    let freeProduct = 1;

    for (let term of this.terms) {
      const pVal = valueFn(term.param);
      const d0 = term.fn.apply(pVal);
      if (partialParam === term.param) {
        const d1 = term.fn.derivative1(pVal);
        diffProduct = diffProduct*d0 + freeProduct * d1;
        freeProduct *= d0;
      } else {
        cnst *= d0;
      }
    }

    return cnst * diffProduct;
  }

  value(valueFn) {
    let res = this.constant;
    for (let t of this.terms) {
      res *= t.fn.apply(valueFn(t.param));
    }
    return res;
  }
}

export abstract class PolynomialFunction {

  id: string;
  abstract get degree(): number;
  abstract apply(x: number): number;
  abstract merge(fn: PolynomialFunction): PolynomialFunction;
  abstract derivative1(x: number): number
}

export class ToThePowerFunction extends PolynomialFunction {

  static get(degree) {
    switch (degree) {
      case 0: return POW_0_FN;
      case 1: return POW_1_FN;
      case 2: return POW_2_FN;
      case 3: return POW_3_FN;
      case 4: return POW_4_FN;
      default: return new ToThePowerFunction(degree,
        x => {
          let val = 1;
          for (let i = 0; i < degree; ++i) {
            val *= x;
          }
          return val
        },
        x => {
          let val = 1;
          for (let i = 0; i < degree - 1; ++i) {
            val *= x;
          }
          return degree * val
        }
      )
    }
  }

  _degree: number;
  fn: (number) => number;
  d1: (number) => number;

  constructor(degree, fn, d1) {
    super();
    this._degree = degree;
    this.fn = fn;
    this.d1 = d1;
    this.id = '^' + degree;
  }

  get degree() {
    return this._degree;
  }

  apply(x) {
    return this.fn(x);
  }

  merge(fn) {
    if (fn.constructor.name === this.constructor.name) {
      return ToThePowerFunction.get(fn.degree + this.degree);
    }
    return null;
  }

  derivative1(x) {
    return this.d1(x)
  }

  linearSubstitution(k, x, b) {
    if (this.degree === 1) {
      return new Polynomial(b).monomial(k).term(x, POW_1_FN);
    } else if (this.degree === 2) {
      return new Polynomial(b*b).monomial(k*k).term(x, POW_2_FN).monomial(2*k*b).term(x, POW_1_FN);
    } else {
      return null;
    }
  }

}


export class FreeFunction extends PolynomialFunction {

  fn: (number) => number;
  d1: (number) => number;
  linearSubstitutionFn: (k: number, param: any, b :number) => Polynomial;

  constructor(fn, d1, id, linearSubstitutionFn) {
    super();
    this.fn = fn;
    this.d1 = d1;
    this.id = id;
    this.linearSubstitutionFn = linearSubstitutionFn || null;
  }

  apply(x) {
    return this.fn(x);
  }

  get degree() {
    return Infinity;
  }

  merge(fn) {
    return null;
  }

  derivative1(x) {
    return this.d1(x)
  }

  linearSubstitution(k, x, b) {
    return this.linearSubstitutionFn(k, x, b);
  }

}

export class CosineOfSum extends PolynomialFunction {

  k: number;
  b: number;

  constructor(k, b) {
    super();
    this.k = k;
    this.b = b;
    this.id = 'cos(' + k + 'x + ' + b + ')';
  }

  apply(x) {
    return Math.cos(this.k * x + this.b);
  }

  get degree() {
    return Infinity;
  }

  merge(fn) {
    return null;
  }

  derivative1(x) {
    return - this.k * Math.sin(this.k * x + this.b);
  }

  linearSubstitution(k, x, b) {
    return new Polynomial(0).monomial(1).term(x, new CosineOfSum(this.k * k, this.k * b + this.b));
  }

  render(x) {
    return 'cos(' + this.k.toFixed(2) + '*' + x + ' + ' + this.b.toFixed(2) + ')';
  }

}

export class SineOfSum extends PolynomialFunction {

  k: number;
  b: number;

  constructor(k, b) {
    super();
    this.k = k;
    this.b = b;
    this.id = 'sin(' + k + 'x + ' + b + ')';
  }

  apply(x) {
    return Math.sin(this.k * x + this.b);
  }

  get degree() {
    return Infinity;
  }

  merge(fn) {
    return null;
  }

  derivative1(x) {
    return this.k * Math.cos(this.k * x + this.b);
  }

  linearSubstitution(k, x, b) {
    return new Polynomial(0).monomial(1).term(x, new SineOfSum(this.k * k, this.k * b + this.b));
  }

  render(x) {
    return 'sin(' + this.k.toFixed(2) + '*' + x + ' + ' + this.b.toFixed(2) + ')';
  }
}

const GET_VALUE = param => param.get();

export const POW_0_FN = new ToThePowerFunction(0, x => 1, x => 0);
export const POW_1_FN = new ToThePowerFunction(1, x => x,  x => 1);
export const POW_2_FN = new ToThePowerFunction(2, x => x*x, x => 2*x);
export const POW_3_FN = new ToThePowerFunction(3, x => x*x*x, x => 3*x*x);
export const POW_4_FN = new ToThePowerFunction(3, x => x*x*x*x, x => 4*x*x*x);

export const COS_FN = new FreeFunction(x => Math.cos(x), x => -Math.sin(x) ,'cos', (k, x, b) => new Polynomial(0).monomial(1).term(x, new CosineOfSum(k, b)));
export const SIN_FN = new FreeFunction(x => Math.sin(x), x =>  Math.cos(x), 'sin', (k, x, b) => new Polynomial(0).monomial(1).term(x, new SineOfSum(k, b)));