simple-squiggle

usolveAll.js (5389B)

---

 import { factory } from '../../../utils/factory.js';
 import { createSolveValidation } from './utils/solveValidation.js';
 var name = 'usolveAll';
 var dependencies = ['typed', 'matrix', 'divideScalar', 'multiplyScalar', 'subtract', 'equalScalar', 'DenseMatrix'];
 export var createUsolveAll = /* #__PURE__ */factory(name, dependencies, _ref => {
   var {
     typed,
     matrix,
     divideScalar,
     multiplyScalar,
     subtract,
     equalScalar,
     DenseMatrix
   } = _ref;
   var solveValidation = createSolveValidation({
     DenseMatrix
   });
   /**
    * Finds all solutions of a linear equation system by backward substitution. Matrix must be an upper triangular matrix.
    *
    * `U * x = b`
    *
    * Syntax:
    *
    *    math.usolveAll(U, b)
    *
    * Examples:
    *
    *    const a = [[-2, 3], [2, 1]]
    *    const b = [11, 9]
    *    const x = usolveAll(a, b)  // [ [[8], [9]] ]
    *
    * See also:
    *
    *    usolve, lup, slu, usolve, lusolve
    *
    * @param {Matrix, Array} U       A N x N matrix or array (U)
    * @param {Matrix, Array} b       A column vector with the b values
    *
    * @return {DenseMatrix[] | Array[]}  An array of affine-independent column vectors (x) that solve the linear system
    */
 
   return typed(name, {
     'SparseMatrix, Array | Matrix': function SparseMatrixArrayMatrix(m, b) {
       return _sparseBackwardSubstitution(m, b);
     },
     'DenseMatrix, Array | Matrix': function DenseMatrixArrayMatrix(m, b) {
       return _denseBackwardSubstitution(m, b);
     },
     'Array, Array | Matrix': function ArrayArrayMatrix(a, b) {
       var m = matrix(a);
 
       var R = _denseBackwardSubstitution(m, b);
 
       return R.map(r => r.valueOf());
     }
   });
 
   function _denseBackwardSubstitution(m, b_) {
     // the algorithm is derived from
     // https://www.overleaf.com/read/csvgqdxggyjv
     // array of right-hand sides
     var B = [solveValidation(m, b_, true)._data.map(e => e[0])];
     var M = m._data;
     var rows = m._size[0];
     var columns = m._size[1]; // loop columns backwards
 
     for (var i = columns - 1; i >= 0; i--) {
       var L = B.length; // loop right-hand sides
 
       for (var k = 0; k < L; k++) {
         var b = B[k];
 
         if (!equalScalar(M[i][i], 0)) {
           // non-singular row
           b[i] = divideScalar(b[i], M[i][i]);
 
           for (var j = i - 1; j >= 0; j--) {
             // b[j] -= b[i] * M[j,i]
             b[j] = subtract(b[j], multiplyScalar(b[i], M[j][i]));
           }
         } else if (!equalScalar(b[i], 0)) {
           // singular row, nonzero RHS
           if (k === 0) {
             // There is no valid solution
             return [];
           } else {
             // This RHS is invalid but other solutions may still exist
             B.splice(k, 1);
             k -= 1;
             L -= 1;
           }
         } else if (k === 0) {
           // singular row, RHS is zero
           var bNew = [...b];
           bNew[i] = 1;
 
           for (var _j = i - 1; _j >= 0; _j--) {
             bNew[_j] = subtract(bNew[_j], M[_j][i]);
           }
 
           B.push(bNew);
         }
       }
     }
 
     return B.map(x => new DenseMatrix({
       data: x.map(e => [e]),
       size: [rows, 1]
     }));
   }
 
   function _sparseBackwardSubstitution(m, b_) {
     // array of right-hand sides
     var B = [solveValidation(m, b_, true)._data.map(e => e[0])];
     var rows = m._size[0];
     var columns = m._size[1];
     var values = m._values;
     var index = m._index;
     var ptr = m._ptr; // loop columns backwards
 
     for (var i = columns - 1; i >= 0; i--) {
       var L = B.length; // loop right-hand sides
 
       for (var k = 0; k < L; k++) {
         var b = B[k]; // values & indices (column i)
 
         var iValues = [];
         var iIndices = []; // first & last indeces in column
 
         var firstIndex = ptr[i];
         var lastIndex = ptr[i + 1]; // find the value at [i, i]
 
         var Mii = 0;
 
         for (var j = lastIndex - 1; j >= firstIndex; j--) {
           var J = index[j]; // check row
 
           if (J === i) {
             Mii = values[j];
           } else if (J < i) {
             // store upper triangular
             iValues.push(values[j]);
             iIndices.push(J);
           }
         }
 
         if (!equalScalar(Mii, 0)) {
           // non-singular row
           b[i] = divideScalar(b[i], Mii); // loop upper triangular
 
           for (var _j2 = 0, _lastIndex = iIndices.length; _j2 < _lastIndex; _j2++) {
             var _J = iIndices[_j2];
             b[_J] = subtract(b[_J], multiplyScalar(b[i], iValues[_j2]));
           }
         } else if (!equalScalar(b[i], 0)) {
           // singular row, nonzero RHS
           if (k === 0) {
             // There is no valid solution
             return [];
           } else {
             // This RHS is invalid but other solutions may still exist
             B.splice(k, 1);
             k -= 1;
             L -= 1;
           }
         } else if (k === 0) {
           // singular row, RHS is zero
           var bNew = [...b];
           bNew[i] = 1; // loop upper triangular
 
           for (var _j3 = 0, _lastIndex2 = iIndices.length; _j3 < _lastIndex2; _j3++) {
             var _J2 = iIndices[_j3];
             bNew[_J2] = subtract(bNew[_J2], iValues[_j3]);
           }
 
           B.push(bNew);
         }
       }
     }
 
     return B.map(x => new DenseMatrix({
       data: x.map(e => [e]),
       size: [rows, 1]
     }));
   }
 });