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first approach to detecting conflicting redundant constraints
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Val Erastov
parent
51399a967f
commit
4cefadffd6
5 changed files with 211 additions and 36 deletions
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@ -207,6 +207,15 @@ TCAD.parametric.lock2Equals2 = function(constrs, locked) {
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TCAD.parametric._alg = 5;
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TCAD.parametric.diagnose = function(sys) {
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var jacobian = sys.makeJacobian();
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var qr = new TCAD.math.QR(jacobian);
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return {
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conflict : sys.constraints.length > qr.rank,
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dof : sys.params.length - qr.rank
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}
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};
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TCAD.parametric.prepare = function(constrs, locked, aux, alg) {
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this.lock1(constrs, aux);
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@ -234,10 +243,15 @@ TCAD.parametric.prepare = function(constrs, locked, aux, alg) {
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return sys.makeJacobian();
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};
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alg = TCAD.parametric._alg;
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var _point = [];
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function solve(fineLevel) {
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if (constrs.length == 0) return;
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if (sys.params.length == 0) return;
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if (TCAD.parametric.diagnose(sys).conflict) {
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console.log("Conflicting or redundant constraints. Please fix your system.");
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return;
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}
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if (alg > 0) {
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switch (alg) {
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case 1:
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@ -255,8 +269,8 @@ TCAD.parametric.prepare = function(constrs, locked, aux, alg) {
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break;
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case 5:
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if (optim.dog_leg(sys) !== 0) {
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alg = -5;
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solve(fineLevel);
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//alg = -5;
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//solve(fineLevel);
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}
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break;
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}
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@ -1,24 +1,33 @@
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TCAD.math.qr = function(matrix) {
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function arr(size) {
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var out = [];
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out.length = size;
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for (var i = 0; i < size; ++i) {
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out[i] = 0;
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}
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return out;
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TCAD.math.vec = function(size) {
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var out = [];
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out.length = size;
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for (var i = 0; i < size; ++i) {
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out[i] = 0;
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}
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return out;
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};
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TCAD.math.Arrays_fill = function(a, fromIndex, toIndex,val) {
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for (var i = fromIndex; i < toIndex; i++)
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a[i] = val;
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};
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TCAD.math.QR = function(matrix) {
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var vec = TCAD.math.vec;
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this.matrix = matrix;
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var nR = this.matrix.length;
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var nC = this.matrix[0].length;
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this.qrRankingThreshold = 1e-30; //??
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this.solvedCols = Math.min(nR, nC);
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this.diagR = arr(nC);
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this.norm = arr(nC);
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this.beta = arr(nC);
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this.permutation = arr(nC);
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this.diagR = vec(nC);
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this.norm = vec(nC);
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this.beta = vec(nC);
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this.permutation = vec(nC);
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this.rank = null;
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var nR = this.matrix.length;
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var nC = this.matrix[0].length;
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var k;
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var norm2;
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var akk;
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@ -88,3 +97,131 @@ TCAD.math.qr = function(matrix) {
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}
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this.rank = this.solvedCols;
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};
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TCAD.math.QR.prototype.qTy = function(y) {
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var nR = this.matrix.length;
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var nC = this.matrix[0].length;
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for (var k = 0; k < nC; ++k) {
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var pk = this.permutation[k];
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var gamma = 0;
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for (var i = k; i < nR; ++i) {
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gamma += this.matrix[i][pk] * y[i];
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}
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gamma *= this.beta[pk];
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for (var i = k; i < nR; ++i) {
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y[i] -= gamma * this.matrix[i][pk];
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}
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}
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};
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TCAD.math.QR.prototype.solve = function(qy) {
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var nR = this.matrix.length;
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var nC = this.matrix[0].length;
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var vec = TCAD.math.vec;
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var diag = vec(nC);
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var lmDiag = vec(nC);
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var work = vec(nC);
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var out = vec(nC);
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// copy R and Qty to preserve input and initialize s
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// in particular, save the diagonal elements of R in lmDir
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for (var j = 0; j < this.solvedCols; ++j) {
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var pj = this.permutation[j];
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for (var i = j + 1; i < this.solvedCols; ++i) {
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this.matrix[i][pj] = this.matrix[j][this.permutation[i]];
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}
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out[j] = this.diagR[pj];
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work[j] = qy[j];
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}
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// eliminate the diagonal matrix d using a Givens rotation
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for (var j = 0; j < this.solvedCols; ++j) {
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// prepare the row of d to be eliminated, locating the
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// diagonal element using p from the Q.R. factorization
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var pj = this.permutation[j];
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var dpj = diag[pj];
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if (dpj != 0) {
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TCAD.math.Arrays_fill(lmDiag, j + 1, lmDiag.length, 0);
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}
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lmDiag[j] = dpj;
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// the transformations to eliminate the row of d
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// modify only a single element of Qty
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// beyond the first n, which is initially zero.
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var qtbpj = 0;
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for (var k = j; k < this.solvedCols; ++k) {
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var pk = this.permutation[k];
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// determine a Givens rotation which eliminates the
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// appropriate element in the current row of d
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if (lmDiag[k] != 0) {
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var sin;
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var cos;
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var rkk = this.matrix[k][pk];
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if (Math.abs(rkk) < Math.abs(lmDiag[k])) {
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var cotan = rkk / lmDiag[k];
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sin = 1.0 / Math.sqrt(1.0 + cotan * cotan);
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cos = sin * cotan;
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} else {
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var tan = lmDiag[k] / rkk;
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cos = 1.0 / Math.sqrt(1.0 + tan * tan);
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sin = cos * tan;
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}
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// compute the modified diagonal element of R and
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// the modified element of (Qty,0)
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this.matrix[k][pk] = cos * rkk + sin * lmDiag[k];
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var temp = cos * work[k] + sin * qtbpj;
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qtbpj = -sin * work[k] + cos * qtbpj;
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work[k] = temp;
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// accumulate the tranformation in the row of s
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for (var i = k + 1; i < this.solvedCols; ++i) {
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var rik = this.matrix[i][pk];
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var temp2 = cos * rik + sin * lmDiag[i];
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lmDiag[i] = -sin * rik + cos * lmDiag[i];
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this.matrix[i][pk] = temp2;
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}
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}
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}
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// store the diagonal element of s and restore
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// the corresponding diagonal element of R
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lmDiag[j] = this.matrix[j][this.permutation[j]];
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this.matrix[j][this.permutation[j]] = out[j];
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}
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// solve the triangular system for z, if the system is
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// singular, then obtain a least squares solution
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var nSing = this.solvedCols;
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for (var j = 0; j < this.solvedCols; ++j) {
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if ((lmDiag[j] == 0) && (nSing == this.solvedCols)) {
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nSing = j;
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}
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if (nSing < this.solvedCols) {
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work[j] = 0;
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}
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}
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if (nSing > 0) {
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for (var j = nSing - 1; j >= 0; --j) {
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var pj = this.permutation[j];
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var sum = 0;
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for (var i = j + 1; i < nSing; ++i) {
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sum += this.matrix[i][pj] * work[i];
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}
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work[j] = (work[j] - sum) / lmDiag[j];
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}
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}
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// permute the components of z back to components of lmDir
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for (var j = 0; j < out.length; ++j) {
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out[this.permutation[j]] = work[j];
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}
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return out;
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};
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@ -55,13 +55,19 @@ function testCompare() {
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function lsolve() {
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var n = numeric;
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A = [[1, 0, 0], [2,3,0]]
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b = [10,25]
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var A = [[2,3], [1,1]];
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var b = [13,5];
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// var At = n.transpose(A);
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// var A = n.dot(At, A);
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// var b = n.dot(At, b);
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// var res = n.dot(n.dot(At, n.inv(n.dot(A, At)) ), b);
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var res = optim.cg(A, [100, 100, 0], b, 1e-8, 800);
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// var res = optim.cg(A, [100, 100, 0], b, 1e-8, 800);
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//var qr = new TCAD.math.QR(A);
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//qr.qTy(b);
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//var res = qr.solve(b);
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var res = n.solve(A, b);
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console.log(res);
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}
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@ -192,6 +192,7 @@
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<script src="app/vector.js"></script>
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<script src="app/math/math.js"></script>
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<script src="app/math/qr.js"></script>
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<script src="app/math/matrix.js"></script>
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<script src="app/math/optim.js"></script>
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<script src="app/math/noptim.js"></script>
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@ -1,27 +1,44 @@
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<html>
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<head>
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<title>Test Suite</title>
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<title>TCAD</title>
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<style>
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body {
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font-family: Monospace;
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margin: 0px;
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overflow: hidden;
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}
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</style>
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<script> TCAD = {} </script>
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<script src="lib/three/three.js"></script>
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<script src="lib/three/TrackballControls.js"></script>
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<script src="lib/three/OrbitControls.js"></script>
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<script src="lib/dat.gui.min.js"></script>
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<script src="lib/csg.js"></script>
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<script src="lib/pnltri.js"></script>
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<script src="app/main.js"></script>
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<script src="app/ctrl.js"></script>
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<script src="app/viewer.js"></script>
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<script src="app/engine.js"></script>
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<script src="lib/numeric-1.2.6.js"></script>
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<script src="app/canvas.js"></script>
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<script src="app/vector.js"></script>
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<script src="app/math/math.js"></script>
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<script src="app/workbench.js"></script>
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<script src="app/math/graph.js"></script>
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<script src="app/struct.js"></script>
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<script src="app/struct-tests.js"></script>
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<script src="app/math/qr.js"></script>
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<script src="app/engine.js"></script>
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<script src="app/math/matrix.js"></script>
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<script src="app/math/optim.js"></script>
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<script src="app/math/noptim.js"></script>
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<script>window.onload = function() {
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TCAD.struct.tests.testHashTable();
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}</script>
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<script src="app/math/lm.js"></script>
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<script src="app/constr/constraints.js"></script>
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<script src="app/constr/solver.js"></script>
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<script src="app/engine.js"></script>
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<script src="app/math/test.js"></script>
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<script>
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function start() {
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new TCAD.App2D();
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}
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window.onload = function() {
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// testCompare();
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lsolve();
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}
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</script>
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</head>
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<body>
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