{"id":"node_modules/mathjs/es/function/algebra/decomposition/qr.js","dependencies":[{"name":"/home/hernan/workspace/tests/test-simulador/package.json","includedInParent":true,"mtime":1597264365661},{"name":"/home/hernan/workspace/tests/test-simulador/node_modules/mathjs/package.json","includedInParent":true,"mtime":1593627585935},{"name":"../../../utils/factory","loc":{"line":3,"column":24},"parent":"/home/hernan/workspace/tests/test-simulador/node_modules/mathjs/es/function/algebra/decomposition/qr.js","resolved":"/home/hernan/workspace/tests/test-simulador/node_modules/mathjs/es/utils/factory.js"}],"generated":{"js":"\"use strict\";\n\nObject.defineProperty(exports, \"__esModule\", {\n value: true\n});\nexports.createQr = void 0;\n\nvar _factory = require(\"../../../utils/factory\");\n\nfunction _extends() {\n _extends = Object.assign || function (target) {\n for (var i = 1; i < arguments.length; i++) {\n var source = arguments[i];\n\n for (var key in source) {\n if (Object.prototype.hasOwnProperty.call(source, key)) {\n target[key] = source[key];\n }\n }\n }\n\n return target;\n };\n\n return _extends.apply(this, arguments);\n}\n\nvar name = 'qr';\nvar dependencies = ['typed', 'matrix', 'zeros', 'identity', 'isZero', 'equal', 'sign', 'sqrt', 'conj', 'unaryMinus', 'addScalar', 'divideScalar', 'multiplyScalar', 'subtract', 'complex'];\nvar createQr = /* #__PURE__ */(0, _factory.factory)(name, dependencies, function (_ref) {\n var typed = _ref.typed,\n matrix = _ref.matrix,\n zeros = _ref.zeros,\n identity = _ref.identity,\n isZero = _ref.isZero,\n equal = _ref.equal,\n sign = _ref.sign,\n sqrt = _ref.sqrt,\n conj = _ref.conj,\n unaryMinus = _ref.unaryMinus,\n addScalar = _ref.addScalar,\n divideScalar = _ref.divideScalar,\n multiplyScalar = _ref.multiplyScalar,\n subtract = _ref.subtract,\n complex = _ref.complex;\n /**\n * Calculate the Matrix QR decomposition. 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that\n *\n * 2 * v * tranpose(v) = tau * w * tranpose(w)\n */\n\n /*\n * -- calculate R = R - tau * w * tranpose(w) * R --\n * Only do calculation with rows k to (rows-1)\n * Additionally columns 0 to (k-1) will not be changed by this\n * multiplication so do not bother recalculating them\n */\n\n for (j = k; j < cols; j++) {\n s = 0.0; // calculate jth element of [tranpose(w) * R]\n\n for (i = k; i < rows; i++) {\n s = addScalar(s, multiplyScalar(conj(w[i]), Rdata[i][j]));\n } // calculate the jth element of [tau * transpose(w) * R]\n\n\n s = multiplyScalar(s, tau);\n\n for (i = k; i < rows; i++) {\n Rdata[i][j] = multiplyScalar(subtract(Rdata[i][j], multiplyScalar(w[i], s)), conjSgn);\n }\n }\n /*\n * -- calculate Q = Q - tau * Q * w * transpose(w) --\n * Q is a square matrix (rows x rows)\n * Only do calculation with columns k to (rows-1)\n * Additionally rows 0 to (k-1) will not be changed by this\n * multiplication so do not bother recalculating them\n */\n\n\n for (i = 0; i < rows; i++) {\n s = 0.0; // calculate ith element of [Q * w]\n\n for (j = k; j < rows; j++) {\n s = addScalar(s, multiplyScalar(Qdata[i][j], w[j]));\n } // calculate the ith element of [tau * Q * w]\n\n\n s = multiplyScalar(s, tau);\n\n for (j = k; j < rows; ++j) {\n Qdata[i][j] = divideScalar(subtract(Qdata[i][j], multiplyScalar(s, conj(w[j]))), conjSgn);\n }\n }\n }\n } // return matrices\n\n\n return {\n Q: Q,\n R: R,\n toString: function toString() {\n return 'Q: ' + this.Q.toString() + '\\nR: ' + this.R.toString();\n }\n };\n }\n\n function _denseQR(m) {\n var ret = _denseQRimpl(m);\n\n var Rdata = ret.R._data;\n\n if (m._data.length > 0) {\n var zero = Rdata[0][0].type === 'Complex' ? complex(0) : 0;\n\n for (var i = 0; i < Rdata.length; ++i) {\n for (var j = 0; j < i && j < (Rdata[0] || []).length; ++j) {\n Rdata[i][j] = zero;\n }\n }\n }\n\n return ret;\n }\n\n function _sparseQR(m) {\n throw new Error('qr not implemented for sparse matrices yet');\n }\n});\nexports.createQr = 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subtract = _ref.subtract,\n complex = _ref.complex;\n\n /**\n * Calculate the Matrix QR decomposition. Matrix `A` is decomposed in\n * two matrices (`Q`, `R`) where `Q` is an\n * orthogonal matrix and `R` is an upper triangular matrix.\n *\n * Syntax:\n *\n * math.qr(A)\n *\n * Example:\n *\n * const m = [\n * [1, -1, 4],\n * [1, 4, -2],\n * [1, 4, 2],\n * [1, -1, 0]\n * ]\n * const result = math.qr(m)\n * // r = {\n * // Q: [\n * // [0.5, -0.5, 0.5],\n * // [0.5, 0.5, -0.5],\n * // [0.5, 0.5, 0.5],\n * // [0.5, -0.5, -0.5],\n * // ],\n * // R: [\n * // [2, 3, 2],\n * // [0, 5, -2],\n * // [0, 0, 4],\n * // [0, 0, 0]\n * // ]\n * // }\n *\n * See also:\n *\n * lup, lusolve\n *\n * @param {Matrix | Array} A A two dimensional matrix or array\n * for which to get the QR decomposition.\n *\n * @return {{Q: Array | Matrix, R: Array | Matrix}} Q: the orthogonal\n * matrix and R: the upper triangular matrix\n */\n return _extends(typed(name, {\n DenseMatrix: function DenseMatrix(m) {\n return _denseQR(m);\n },\n SparseMatrix: function SparseMatrix(m) {\n return _sparseQR(m);\n },\n Array: function Array(a) {\n // create dense matrix from array\n var m = matrix(a); // lup, use matrix implementation\n\n var r = _denseQR(m); // result\n\n\n return {\n Q: r.Q.valueOf(),\n R: r.R.valueOf()\n };\n }\n }), {\n _denseQRimpl: _denseQRimpl\n });\n\n function _denseQRimpl(m) {\n // rows & columns (m x n)\n var rows = m._size[0]; // m\n\n var cols = m._size[1]; // n\n\n var Q = identity([rows], 'dense');\n var Qdata = Q._data;\n var R = m.clone();\n var Rdata = R._data; // vars\n\n var i, j, k;\n var w = zeros([rows], '');\n\n for (k = 0; k < Math.min(cols, rows); ++k) {\n /*\n * **k-th Household matrix**\n *\n * The matrix I - 2*v*transpose(v)\n * x = first column of A\n * x1 = first element of x\n * alpha = x1 / |x1| * |x|\n * e1 = tranpose([1, 0, 0, ...])\n * u = x - alpha * e1\n * v = u / |u|\n *\n * Household matrix = I - 2 * v * tranpose(v)\n *\n * * Initially Q = I and R = A.\n * * Household matrix is a reflection in a plane normal to v which\n * will zero out all but the top right element in R.\n * * Appplying reflection to both Q and R will not change product.\n * * Repeat this process on the (1,1) minor to get R as an upper\n * triangular matrix.\n * * Reflections leave the magnitude of the columns of Q unchanged\n * so Q remains othoganal.\n *\n */\n var pivot = Rdata[k][k];\n var sgn = unaryMinus(equal(pivot, 0) ? 1 : sign(pivot));\n var conjSgn = conj(sgn);\n var alphaSquared = 0;\n\n for (i = k; i < rows; i++) {\n alphaSquared = addScalar(alphaSquared, multiplyScalar(Rdata[i][k], conj(Rdata[i][k])));\n }\n\n var alpha = multiplyScalar(sgn, sqrt(alphaSquared));\n\n if (!isZero(alpha)) {\n // first element in vector u\n var u1 = subtract(pivot, alpha); // w = v * u1 / |u| (only elements k to (rows-1) are used)\n\n w[k] = 1;\n\n for (i = k + 1; i < rows; i++) {\n w[i] = divideScalar(Rdata[i][k], u1);\n } // tau = - conj(u1 / alpha)\n\n\n var tau = unaryMinus(conj(divideScalar(u1, alpha)));\n var s = void 0;\n /*\n * tau and w have been choosen so that\n *\n * 2 * v * tranpose(v) = tau * w * tranpose(w)\n */\n\n /*\n * -- calculate R = R - tau * w * tranpose(w) * R --\n * Only do calculation with rows k to (rows-1)\n * Additionally columns 0 to (k-1) will not be changed by this\n * multiplication so do not bother recalculating them\n */\n\n for (j = k; j < cols; j++) {\n s = 0.0; // calculate jth element of [tranpose(w) * R]\n\n for (i = k; i < rows; i++) {\n s = addScalar(s, multiplyScalar(conj(w[i]), Rdata[i][j]));\n } // calculate the jth element of [tau * transpose(w) * R]\n\n\n s = multiplyScalar(s, tau);\n\n for (i = k; i < rows; i++) {\n Rdata[i][j] = multiplyScalar(subtract(Rdata[i][j], multiplyScalar(w[i], s)), conjSgn);\n }\n }\n /*\n * -- calculate Q = Q - tau * Q * w * transpose(w) --\n * Q is a square matrix (rows x rows)\n * Only do calculation with columns k to (rows-1)\n * Additionally rows 0 to (k-1) will not be changed by this\n * multiplication so do not bother recalculating them\n */\n\n\n for (i = 0; i < rows; i++) {\n s = 0.0; // calculate ith element of [Q * w]\n\n for (j = k; j < rows; j++) {\n s = addScalar(s, multiplyScalar(Qdata[i][j], w[j]));\n } // calculate the ith element of [tau * Q * w]\n\n\n s = multiplyScalar(s, tau);\n\n for (j = k; j < rows; ++j) {\n Qdata[i][j] = divideScalar(subtract(Qdata[i][j], multiplyScalar(s, conj(w[j]))), conjSgn);\n }\n }\n }\n } // return matrices\n\n\n return {\n Q: Q,\n R: R,\n toString: function toString() {\n return 'Q: ' + this.Q.toString() + '\\nR: ' + this.R.toString();\n }\n };\n }\n\n function _denseQR(m) {\n var ret = _denseQRimpl(m);\n\n var Rdata = ret.R._data;\n\n if (m._data.length > 0) {\n var zero = Rdata[0][0].type === 'Complex' ? complex(0) : 0;\n\n for (var i = 0; i < Rdata.length; ++i) {\n for (var j = 0; j < i && j < (Rdata[0] || []).length; ++j) {\n Rdata[i][j] = zero;\n }\n }\n }\n\n return ret;\n }\n\n function _sparseQR(m) {\n throw new Error('qr not implemented for sparse matrices yet');\n }\n});"},"lineCount":null}},"error":null,"hash":"a3d5ee92a68ac5c0be3cbd54c875e6db","cacheData":{"env":{}}}