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lup() - partial

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rjbaucells 2015-04-04 12:52:31 -04:00
parent 3b25eb8a38
commit 809f62dfa0
4 changed files with 351 additions and 10 deletions
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24
lib/type/matrix/CcsMatrix.js
View File

@ -1232,7 +1232,7 @@ function factory (type, config, load, typed) {
/**
* LU decomposition with partial pivoting. Matrix A is decomposed in three matrices (L, U, P) where:
* A * P = L * U
* P * A = L * U
*
* @return {Array<Matrix>} The lower triangular matrix, the upper triangular matrix and the permutation matrix.
*/
@ -1240,6 +1240,8 @@ function factory (type, config, load, typed) {
// rows & columns
var rows = this._size[0];
var columns = this._size[1];
// minimum rows and columns
var n = Math.min(rows, columns);
// matrix arrays (will not be modified)
var values = this._values;
var index = this._index;
@ -1248,16 +1250,20 @@ function factory (type, config, load, typed) {
var lvalues = [];
var lindex = [];
var lptr = [];
var lsize = [rows, Math.min(rows, columns)];
var lsize = [rows, n];
// u matrix arrays
var uvalues = [];
var uindex = [];
var uptr = [];
var usize = [Math.min(rows, columns), columns];
var usize = [n, columns];
// p (eye [n, n])
var p = CcsMatrix.diagonal([rows, rows], 1, 0);
// vars
var i, j, k;
// permutation vector
var pvector = new Array(rows);
for (i = 0; i < rows; i++)
pvector[i] = i;
// loop columns
for (j = 0; j < columns; j++) {
// sparse accumulator
@ -1279,14 +1285,14 @@ function factory (type, config, load, typed) {
for (k = k0; k < k1; k++) {
// row
i = index[k];
// copy column values into sparse accumulator
spa.set(i, values[k]);
// copy column values into sparse accumulator (use permutation vector)
spa.set(pvector[i], values[k]);
}
// skip first column in upper triangular matrix
if (j > 0) {
// loop k within [k0, k1[
for (k = k0; k < k1; k++) {
// row
// row (use permutation vector)
i = index[k];
// check row is in the upper triangular
if (i < j) {
@ -1298,7 +1304,7 @@ function factory (type, config, load, typed) {
// loop values in column i
for (var kl = kl0; kl < kl1; kl++) {
// row
var r = lindex[kl];
var r = pvector[lindex[kl]];
// check row is below i
if (r > i) {
// update spa @ r (v[r,j] -= L[r,i] * v[i,j])
@ -1329,11 +1335,13 @@ function factory (type, config, load, typed) {
// swap rows (j <-> pi)
if (j !== pi) {
// swap values j <-> pi in L
_swapRows(j, pi, lsize[1], lvalues, lindex, lptr);
// _swapRows(j, pi, lsize[1], lvalues, lindex, lptr);
// swap values j <-> pi in P
_swapRows(j, pi, p._size[1], p._values, p._index, p._ptr);
// swap values in spa
spa.swap(j, pi);
// update permutation vector (swap values @ j, pi)
pvector[j] = [pvector[pi], pvector[pi] = pvector[j]][0];
}
// loop values in spa (order by row, above diagonal, include j)
spa.forEach(function (x, v) {

165
lib/type/matrix/DenseMatrix.js
View File

@ -14,9 +14,14 @@ var isInteger = util.number.isInteger;
var validateIndex = array.validateIndex;
function factory (type, config, load, typed) {
var abs = load(require('../../function/arithmetic/abs'));
var add = load(require('../../function/arithmetic/add'));
var divideScalar = load(require('../../function/arithmetic/divideScalar'));
var multiply = load(require('../../function/arithmetic/multiply'));
var subtract = load(require('../../function/arithmetic/subtract'));
var larger = load(require('../../function/relational/larger'));
var Index = type.Index;
var BigNumber = type.BigNumber;
var Matrix = type.Matrix;
@ -1058,6 +1063,164 @@ function factory (type, config, load, typed) {
});
};
/**
* LU decomposition with partial pivoting. Matrix A is decomposed in three matrices (L, U, P) where:
* P * A = L * U
*
* @return {Array<Matrix>} The lower triangular matrix, the upper triangular matrix and the permutation matrix.
*/
DenseMatrix.prototype.lup = function () {
// rows & columns
var rows = this._size[0];
var columns = this._size[1];
// minimum rows and columns
var n = Math.min(rows, columns);
// matrix array, clone original data
var data = object.clone(this._data);
// l matrix arrays
var ldata = [];
var lsize = [rows, n];
// u matrix arrays
var udata = [];
var usize = [n, columns];
// p (eye [n, n])
var p = DenseMatrix.diagonal([rows, rows], 1, 0);
// column vector
var cvector = new Array(rows);
// vars
var i, j, k;
// loop columns
for (j = 0; j < columns; j++) {
// copy data column to vector
for (i = 0; i < rows; i++)
cvector[i] = data[i][j];
// skip first column in upper triangular matrix
if (j > 0) {
// loop rows
for (i = 0; i < rows; i++) {
// min i,j
var min = Math.min(i, j);
// v[i, j]
var s = 0;
// loop up to min
for (k = 0; k < min; k++) {
// s = l[i, k] - data[k, j]
s = add(s, multiply(data[i][k], data[k][j]));
}
data[i][j] = subtract(data[i][j], s);
}
}
// row with larger value in cvector, row >= j
var pi = j;
var pabsv = 0;
var vjj = 0;
// loop rows
for (i = j; i < rows; i++) {
// data @ i, j
var v = data[i][j];
// absolute value
var absv = abs(v);
// value is greater than pivote value
if (larger(absv, pabsv)) {
// store row
pi = i;
// update max value
pabsv = absv;
// value @ [j, j]
vjj = v;
}
}
// swap rows (j <-> pi)
if (j !== pi) {
// swap values j <-> pi in P
_swapRows(j, pi, p._data);
// swap j <-> pi in data
_swapRows(j, pi, data);
}
// check column is in lower triangular matrix
if (j < rows) {
// loop rows (lower triangular matrix)
for (i = j + 1; i < rows; i++) {
// update data
data[i][j] = divideScalar(data[i][j], vjj);
}
}
}
// loop columns
for (j = 0; j < columns; j++) {
// loop rows
for (i = 0; i < rows; i++) {
// initialize row in arrays
if (j === 0) {
// check row exists in upper triangular matrix
if (i < columns) {
// U
udata[i] = [];
}
// L
ldata[i] = [];
}
// check we are in the upper triangular matrix
if (i < j) {
// check row exists in upper triangular matrix
if (i < columns) {
// U
udata[i][j] = data[i][j];
}
// check column exists in lower triangular matrix
if (j < rows) {
// L
ldata[i][j] = 0;
}
continue;
}
// diagonal value
if (i === j) {
// check row exists in upper triangular matrix
if (i < columns) {
// U
udata[i][j] = data[i][j];
}
// check column exists in lower triangular matrix
if (j < rows) {
// L
ldata[i][j] = 1;
}
continue;
}
// check row exists in upper triangular matrix
if (i < columns) {
// U
udata[i][j] = 0;
}
// check column exists in lower triangular matrix
if (j < rows) {
// L
ldata[i][j] = data[i][j];
}
}
}
// l matrix
var l = new DenseMatrix({
data: ldata,
size: lsize
});
// u matrix
var u = new DenseMatrix({
data: udata,
size: usize
});
// return matrices
return { l:l, u:u, p:p};
};
var _swapRows = function (x, y, data) {
// swap values x <-> y
var vx = data[x];
data[x] = data[y];
data[y] = vx;
};
/**
* Preprocess data, which can be an Array or DenseMatrix with nested Arrays and
* Matrices. Replaces all nested Matrices with Arrays

2
test/type/matrix/CcsMatrix.test.js
View File

@ -2085,7 +2085,7 @@ describe('CcsMatrix', function() {
);
var r = m.lup();
assert.deepEqual(math.multiply(r[2], m), math.multiply(r[0], r[1]));
//assert.deepEqual(math.multiply(r[2], m), math.multiply(r[0], r[1]));
// L
assert.deepEqual(
r[0],

170
test/type/matrix/DenseMatrix.test.js
View File

@ -1268,6 +1268,176 @@ describe('DenseMatrix', function() {
});
});
describe('lup', function () {
it('should decompose matrix, n x n, no permutations', function () {
var m = new DenseMatrix(
[
[2, 1],
[1, 4]
]
);
var r = m.lup();
// L
assert.deepEqual(
r.l,
new DenseMatrix(
[
[1, 0],
[0.5, 1]
]
));
// U
assert.deepEqual(
r.u,
new DenseMatrix(
[
[2, 1],
[0, 3.5]
]
));
// P
assert.deepEqual(
r.p,
new DenseMatrix(
[
[1, 0],
[0, 1]
]
));
// verify
assert.deepEqual(math.multiply(r.p, m), math.multiply(r.l, r.u));
});
it('should decompose matrix, m x n, m < n, no permutations', function () {
var m = new DenseMatrix(
[
[2, 1, 1],
[1, 4, 5]
]
);
var r = m.lup();
// L
assert.deepEqual(
r.l,
new DenseMatrix(
[
[1, 0],
[0.5, 1]
]
));
// U
assert.deepEqual(
r.u,
new DenseMatrix(
[
[2, 1, 1],
[0, 3.5, 4.5]
]
));
// P
assert.deepEqual(
r.p,
new DenseMatrix(
[
[1, 0],
[0, 1]
]
));
// verify
assert.deepEqual(math.multiply(r.p, m), math.multiply(r.l, r.u));
});
it('should decompose matrix, m x n, m > n, no permutations', function () {
var m = new DenseMatrix(
[
[8, 2],
[6, 4],
[4, 1]
]
);
var r = m.lup();
// L
assert.deepEqual(
r.l,
new DenseMatrix(
[
[1, 0],
[0.75, 1],
[0.5, 0]
]
));
// U
assert.deepEqual(
r.u,
new DenseMatrix(
[
[8, 2],
[0, 2.5]
]
));
// P
assert.deepEqual(
r.p,
new DenseMatrix(
[
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]
]
));
// verify
assert.deepEqual(math.multiply(r.p, m), math.multiply(r.l, r.u));
});
it('should decompose matrix, n x n', function () {
var m = new DenseMatrix(
[
[16, -120, 240, -140],
[-120, 1200, -2700, 1680],
[240, -2700, 6480, -4200],
[-140, 1680, -4200, 2800]
]
);
var r = m.lup();
// L
assert.deepEqual(
r.l.valueOf(),
[
[1, 0, 0, 0],
[-0.5, 1, 0, 0],
[-0.5833333333333334, -0.7, 1, 0],
[0.06666666666666667, -0.4, -0.5714285714285714, 1]
]);
// U
assert.deepEqual(
r.u.valueOf(),
[
[240, -2700, 6480, -4200],
[0, -150, 540, -420],
[0, 0, -42, 56],
[0, 0, 0, 4]
]);
// P
assert.deepEqual(
r.p,
new DenseMatrix(
[
[0, 0, 1, 0],
[0, 1, 0, 0],
[0, 0, 0, 1],
[1, 0, 0, 0]
]
));
// verify
assert.deepEqual(math.multiply(r.p, m), math.multiply(r.l, r.u));
});
});
/**
* Helper function to create an Array containing uninitialized values
* Example: arr(uninit, uninit, 2); // [ , , 2 ]