public static void test5() {
MathFunc f = FX.x * FX.y * FX.z + 1;
System.out.println(f);
System.out.println(f.getVarNames());
System.out.println(f.apply(2, 3, 4));
CompiledFunc cf = f.compile();
System.out.println(cf.apply(2, 3, 4));
}
public static void test1() {
MathFunc x = FX.x;
MathFunc y = FX.y;
MathFunc xy = x.S(y);
FuncClassLoader<CompiledFunc> fcl = new FuncClassLoader<CompiledFunc>();
ClassGen genClass = BytecodeUtils.genClass(xy, null, "add", true, false);
CompiledFunc fxy = fcl.newInstance(genClass);
System.out.println(fxy.apply(1.0, 2.0));
System.out.println(xy.compile(new String[] {"y", "x"}).apply(1.0, 2.0));
}
public static void test7() {
FSin sin = new FSin();
MathFunc fun = FMath.pow(sin, 2);
System.out.println(fun.toString());
System.out.println(fun.diff("x"));
System.out.println(FMath.sqrt(sin));
System.out.println(FMath.sqrt(sin).diff("x"));
FSqrt sqrt = new FSqrt();
System.out.println(sqrt.compile().apply(16));
System.out.println(FMath.sqrt(FX.x).compile().apply(16));
}
public static void test4() {
FSin sin = new FSin("x");
FCos cos = new FCos("y");
MathFunc f = sin * cos;
System.out.println(f);
System.out.println(f.getVarNames());
System.out.println(f.apply(Math.PI / 2, Math.PI / 4));
CompiledFunc cf = f.compile();
System.out.println(cf.apply(Math.PI / 2, Math.PI / 4));
// bug in order of args
System.out.println(f.compile(new String[] {"y", "x"}).apply(Math.PI / 2, Math.PI / 4));
}
/**
* 构造下列形函数中的一个： N1 = L1 = r N2 = L2 = s N3 = L3 = t
*
* @param funID = 1,2,3
*/
public void Create(int funID, double coef) {
funIndex = funID - 1;
if (funID < 1 || 3 < funID) {
throw new FutureyeException("ERROR: funID should be 1,2 or 3.");
}
this.varNames = new String[] {"r", "s", "t"};
innerVarNames = new ObjList<String>("x", "y");
// Compose function: r = r(x,y), s = s(x,y), t = t(x,y)
Map<String, MathFunc> fInners = new HashMap<String, MathFunc>();
final String varName = varNames[funIndex];
fInners.put(
varName,
new AbstractMathFunc(innerVarNames.toList()) {
public MathFunc diff(String var) {
if (area < 0.0) {
throw new FutureyeException("Check nodes order: area < 0.0");
} else {
if (varName.equals("r")) { // r对应三角形高h的负倒数
if (var.equals("x")) return new FC(b[0] / (2 * area));
if (var.equals("y")) return new FC(c[0] / (2 * area));
} else if (varName.equals("s")) { // s对应三角形高h的负倒数
if (var.equals("x")) return new FC(b[1] / (2 * area));
if (var.equals("y")) return new FC(c[1] / (2 * area));
} else if (varName.equals("t")) { // t对应三角形高h的负倒数
if (var.equals("x")) return new FC(b[2] / (2 * area));
if (var.equals("y")) return new FC(c[2] / (2 * area));
}
}
return null;
}
@Override
public double apply(double... args) {
throw new UnsupportedOperationException();
}
});
// 使用复合函数构造形函数
funOuter = new SF123();
this.coef = coef;
funCompose = FC.c(this.coef).M(funOuter.compose(fInners));
funCompose.setActiveVarNames(funOuter.getVarNames());
}
public static void testSFBilinearLocal2D() {
NodeList nodes = new NodeList();
nodes.add(new Node(1, -2.0, -2.0));
nodes.add(new Node(2, 2.0, -2.0));
nodes.add(new Node(3, 2.0, 2.0));
nodes.add(new Node(4, -2.0, 2.0));
Element e = new Element(nodes);
System.out.println("Test coordinate transform and Jacbian on element " + e);
CoordinateTransform trans = new CoordinateTransform(2);
trans.transformLinear2D(e);
trans.computeJacobianMatrix();
trans.computeJacobian2D();
MathFunc jac = trans.getJacobian();
Variable v = new Variable();
v.set("r", 0);
v.set("s", 0);
check(jac.toString(), jac.apply(v), 4.0);
ScalarShapeFunction[] shapeFun = new ScalarShapeFunction[4];
shapeFun[0] = new SFBilinearLocal2D(1);
shapeFun[1] = new SFBilinearLocal2D(2);
shapeFun[2] = new SFBilinearLocal2D(3);
shapeFun[3] = new SFBilinearLocal2D(4);
System.out.println("Test the evaluation of SFBilinearLocal2D:");
double[] args = new double[] {0.1, 0.1};
Variable v0 = new Variable();
v0.set("r", args[0]);
v0.set("s", args[1]);
System.out.println(shapeFun[0]);
check(shapeFun[0].toString(), shapeFun[0].apply(v0), 0.2025);
check(shapeFun[0].toString(), shapeFun[0].apply(args), 0.2025);
check(shapeFun[0].toString(), shapeFun[0].compile().apply(args), 0.2025);
System.out.println("Test the derivatives of shape function SFBilinearLocal2D:");
e.updateJacobin();
double[] rlt = new double[] {-0.125, -0.125, 0.125, -0.125, 0.125, 0.125, -0.125, 0.125};
int j = 0;
for (int i = 0; i < 4; i++) {
System.out.println(shapeFun[i]);
shapeFun[i].assignElement(e);
MathFunc SFdx = shapeFun[i].diff("x");
MathFunc SFdy = shapeFun[i].diff("y");
check("shapeFun[" + i + "].diff(\"x\")=" + SFdy, SFdx.apply(v), rlt[j++]);
check("shapeFun[" + i + "].diff(\"y\")=" + SFdy, SFdy.apply(v), rlt[j++]);
}
}
public static void test2() {
MathFunc x = FX.x;
MathFunc y = FX.y;
MathFunc xy = x.M(y);
System.out.println(xy);
HashMap<String, MathFunc> map = new HashMap<String, MathFunc>();
map.put(x.getVarNames().get(0), FX.r.A(FX.s));
map.put(y.getVarNames().get(0), FX.r.S(FX.s));
MathFunc xy2 = xy.compose(map);
System.out.println(xy2);
System.out.println(FX.r.A(FX.s).M(FX.r.S(FX.s)));
FuncClassLoader<CompiledFunc> fcl = new FuncClassLoader<CompiledFunc>();
ClassGen genClass = BytecodeUtils.genClass(xy2, null, "add2", true, false);
CompiledFunc fxy2 = fcl.newInstance(genClass);
System.out.println(fxy2.apply(4.0, 2.0));
}
public String toString() {
if (this.coef < 1.0) return this.coef + "*" + funOuter.toString();
else return funOuter.toString();
}
@Override
public double[] applyAll(VariableArray v, Map<Object, Object> cache) {
return funCompose.applyAll(v, cache);
}
public double apply(Variable v) {
return funCompose.apply(v);
}
public MathFunc diff(String varName) {
return funCompose.diff(varName);
}
/**
* 构造下列形函数中的一个： Ni = (1+r*ri)*(1+s*si)*(1+t*ti)/8 where (ri,si,ti),i=1,...,8 are vertices
* coordinate of the hexahedron
*
* @param funID = 1,...,8
*/
public void Create(int funID, double coef) {
funIndex = funID - 1;
if (funID < 1 || funID > 8) {
System.out.println("ERROR: funID should be 1,...,8.");
return;
}
varNames.add("r");
varNames.add("s");
varNames.add("t");
innerVarNames = new ObjList<String>("x", "y", "z");
// 复合函数
Map<String, MathFunc> fInners = new HashMap<String, MathFunc>(4);
for (final String varName : varNames) {
fInners.put(
varName,
new AbstractMathFunc(innerVarNames.toList()) {
// r_x,r_y,r_z, s_x,s_y,s_z, t_x,t_y,t_z
public MathFunc diff(String var) {
/**
* f(x,y,z) = g(r,s,t) f_x = g_r*r_x + g_s*s_x + g_t*t_x ---(1) f_y = g_r*r_y +
* g_s*s_y + g_t*t_y ---(2) f_z = g_r*r_z + g_s*s_z + g_t*t_z ---(3)
*
* <p>for (1) let f=x,f=y,f=z we get 3 equations, solve them: (x_r x_s x_t) (r_x) (1)
* (y_r y_s y_z) * (s_x) = (0) (z_r z_s z_t) (t_x) (0)
*
* <p>similarly, for (2): (x_r x_s x_t) (r_y) (0) (y_r y_s y_z) * (s_y) = (1) (z_r z_s
* z_t) (t_y) (0)
*
* <p>for (3): (x_r x_s x_t) (r_z) (0) (y_r y_s y_z) * (s_z) = (0) (z_r z_s z_t) (t_z)
* (1)
*
* <p>(x_r x_s x_t) Let J = (y_r y_s y_z) (z_r z_s z_t)
*
* <p>from the above 9 equations, we have: (r_x r_y r_z) (s_x s_y s_z) = inv(J) (t_x
* t_y t_z)
*/
return new InvJ(varName, var);
}
@Override
public double apply(Variable v) {
// TODO Auto-generated method stub
return 0;
}
});
}
// funOuter = new FAxpb("r",vt[funIndex][0]/2.0,0.5).M(
// new FAxpb("s",vt[funIndex][1]/2.0,0.5)).M(
// new FAxpb("t",vt[funIndex][2]/2.0,0.5));
// 速度提高1倍
funOuter = new FOuter(varNames, funIndex);
// 使用复合函数构造形函数
this.coef = coef;
funCompose = FC.c(this.coef).M(funOuter.compose(fInners));
}
public static void testSFLinearLocal2D() {
NodeList nodes = new NodeList();
nodes.add(new Node(1, 0.0, 0.0));
nodes.add(new Node(2, 0.2, 0.0));
nodes.add(new Node(3, 0.0, 0.2));
Element e = new Element(nodes);
System.out.println("Test coordinate transform and Jacbian on element " + e);
CoordinateTransform trans = new CoordinateTransform(2);
trans.transformLinear2D(e);
trans.computeJacobianMatrix();
trans.computeJacobian2D();
MathFunc jac = trans.getJacobian();
Variable v = new Variable();
v.set("r", 0);
v.set("s", 0);
check(jac.toString(), jac.apply(v), 0.04);
ScalarShapeFunction[] shapeFun = new ScalarShapeFunction[3];
shapeFun[0] = new SFLinearLocal2DRS(1);
shapeFun[1] = new SFLinearLocal2DRS(2);
shapeFun[2] = new SFLinearLocal2DRS(3);
System.out.println("Test the derivatives of shape function SFLinearLocal2DRS:");
double[] rlt = new double[] {-5, -5, 5, 0, 0, 5};
int j = 0;
for (int i = 0; i < 3; i++) {
System.out.println(shapeFun[i]);
shapeFun[i].assignElement(e);
MathFunc SFdx = shapeFun[i].diff("x");
MathFunc SFdy = shapeFun[i].diff("y");
check("shapeFun[" + i + "].diff(\"x\")", SFdx.apply(), rlt[j++]);
check("shapeFun[" + i + "].diff(\"y\")", SFdy.apply(), rlt[j++]);
}
System.out.println("Test the derivatives of shape function SFLinearLocal2D:");
shapeFun[0] = new SFLinearLocal2D(1);
shapeFun[1] = new SFLinearLocal2D(2);
shapeFun[2] = new SFLinearLocal2D(3);
j = 0;
for (int i = 0; i < 3; i++) {
System.out.println(shapeFun[i]);
shapeFun[i].assignElement(e);
MathFunc SFdx = shapeFun[i].diff("x");
MathFunc SFdy = shapeFun[i].diff("y");
check("shapeFun[" + i + "].diff(\"x\")=" + SFdy, SFdx.apply(v), rlt[j++]);
check("shapeFun[" + i + "].diff(\"y\")=" + SFdy, SFdy.apply(v), rlt[j++]);
}
}
public String toString() {
return "N" + (funIndex + 1) + "(r,s,t) = " + funOuter.getExpr();
}