#define UNUSED(x) (void) x
-static double sqr(double x) { return x * x; }
+static double sqr(double x)
+{
+ return x * x;
+}
int testfuncs_verbose = 0;
int testfuncs_counter = 0;
static double testfuncs_status(unsigned n, const double *x, double f)
{
- ++testfuncs_counter;
- if (testfuncs_verbose) {
- unsigned i;
- printf("f_%d (%g", testfuncs_counter, x[0]);
- for (i = 1; i < n; ++i) printf(", %g", x[i]);
- printf(") = %g\n", f);
- }
- return f;
+ ++testfuncs_counter;
+ if (testfuncs_verbose) {
+ unsigned i;
+ printf("f_%d (%g", testfuncs_counter, x[0]);
+ for (i = 1; i < n; ++i)
+ printf(", %g", x[i]);
+ printf(") = %g\n", f);
+ }
+ return f;
}
#define RETURN(f) return testfuncs_status(n, x, f);
-#define PI2 6.283185307179586 /* 2*pi */
-#define PI3 9.424777960769379 /* 3*pi */
-#define PI4 12.5663706143592 /* 4*pi */
+#define PI2 6.283185307179586 /* 2*pi */
+#define PI3 9.424777960769379 /* 3*pi */
+#define PI4 12.5663706143592 /* 4*pi */
/****************************************************************************/
static double rosenbrock_f(unsigned n, const double *x, double *grad, void *data)
{
- double a = x[1] - x[0] * x[0], b = 1 - x[0];
- UNUSED(data);
- if (grad) {
- grad[0] = -400 * a * x[0] - 2*b;
- grad[1] = 200 * a;
- }
- RETURN(100 * sqr(a) + sqr(b));
+ double a = x[1] - x[0] * x[0], b = 1 - x[0];
+ UNUSED(data);
+ if (grad) {
+ grad[0] = -400 * a * x[0] - 2 * b;
+ grad[1] = 200 * a;
+ }
+ RETURN(100 * sqr(a) + sqr(b));
}
-static const double rosenbrock_lb[2] = {-2, -2};
-static const double rosenbrock_ub[2] = {2, 2};
-static const double rosenbrock_xmin[2] = {1, 1};
+static const double rosenbrock_lb[2] = { -2, -2 };
+static const double rosenbrock_ub[2] = { 2, 2 };
+static const double rosenbrock_xmin[2] = { 1, 1 };
/****************************************************************************/
static double mccormic_f(unsigned n, const double *x, double *grad, void *data)
{
- double a = x[0] + x[1], b = x[0] - x[1];
- UNUSED(data);
- if (grad) {
- grad[0] = cos(a) + 2*b - 1.5;
- grad[1] = cos(a) - 2*b + 2.5;
- }
- RETURN(sin(a) + sqr(b) - 1.5*x[0] + 2.5*x[1] + 1);
+ double a = x[0] + x[1], b = x[0] - x[1];
+ UNUSED(data);
+ if (grad) {
+ grad[0] = cos(a) + 2 * b - 1.5;
+ grad[1] = cos(a) - 2 * b + 2.5;
+ }
+ RETURN(sin(a) + sqr(b) - 1.5 * x[0] + 2.5 * x[1] + 1);
}
-static const double mccormic_lb[2] = {-1.5, -3};
-static const double mccormic_ub[2] = {4, 4};
-static const double mccormic_xmin[2] = {-0.547197553, -1.54719756};
+static const double mccormic_lb[2] = { -1.5, -3 };
+static const double mccormic_ub[2] = { 4, 4 };
+static const double mccormic_xmin[2] = { -0.547197553, -1.54719756 };
/****************************************************************************/
static double boxbetts_f(unsigned n, const double *x, double *grad, void *data)
{
- unsigned i;
- double f = 0;
- UNUSED(data);
- if (grad)
- grad[0] = grad[1] = grad[2] = 0;
- for (i = 1; i <= 10; ++i) {
- double e0 = exp(-0.1*i*x[0]);
- double e1 = exp(-0.1*i*x[1]);
- double e2 = exp(-0.1*i) - exp(-1.0*i);
- double g = e0 - e1 - e2 * x[2];
- f += sqr(g);
- if (grad) {
- grad[0] += (2 * g) * (-0.1*i*e0);
- grad[1] += (2 * g) * (0.1*i*e1);
- grad[2] += -(2 * g) * e2;
- }
- }
- RETURN(f);
+ unsigned i;
+ double f = 0;
+ UNUSED(data);
+ if (grad)
+ grad[0] = grad[1] = grad[2] = 0;
+ for (i = 1; i <= 10; ++i) {
+ double e0 = exp(-0.1 * i * x[0]);
+ double e1 = exp(-0.1 * i * x[1]);
+ double e2 = exp(-0.1 * i) - exp(-1.0 * i);
+ double g = e0 - e1 - e2 * x[2];
+ f += sqr(g);
+ if (grad) {
+ grad[0] += (2 * g) * (-0.1 * i * e0);
+ grad[1] += (2 * g) * (0.1 * i * e1);
+ grad[2] += -(2 * g) * e2;
+ }
+ }
+ RETURN(f);
}
-static const double boxbetts_lb[3] = {0.9,9,0.9};
-static const double boxbetts_ub[3] = {1.2,11.2,1.2};
-static const double boxbetts_xmin[3] = {1,10,1};
+static const double boxbetts_lb[3] = { 0.9, 9, 0.9 };
+static const double boxbetts_ub[3] = { 1.2, 11.2, 1.2 };
+static const double boxbetts_xmin[3] = { 1, 10, 1 };
/****************************************************************************/
static double paviani_f(unsigned n, const double *x, double *grad, void *data)
{
- unsigned i;
- double f = 0, prod = 1;
- UNUSED(data);
- if (grad) for (i = 0; i < 10; ++i) grad[i] = 0;
- for (i = 0; i < 10; ++i) {
- double ln1 = log(x[i] - 2);
- double ln2 = log(10 - x[i]);
- f += sqr(ln1) + sqr(ln2);
- if (grad)
- grad[i] += 2 * ln1 / (x[i] - 2) - 2 * ln2 / (10 - x[i]);
- prod *= x[i];
- }
- f -= (prod = pow(prod, 0.2));
- if (grad)
- for (i = 0; i < 10; ++i)
- grad[i] -= 0.2 * prod / x[i];
- RETURN(f);
+ unsigned i;
+ double f = 0, prod = 1;
+ UNUSED(data);
+ if (grad)
+ for (i = 0; i < 10; ++i)
+ grad[i] = 0;
+ for (i = 0; i < 10; ++i) {
+ double ln1 = log(x[i] - 2);
+ double ln2 = log(10 - x[i]);
+ f += sqr(ln1) + sqr(ln2);
+ if (grad)
+ grad[i] += 2 * ln1 / (x[i] - 2) - 2 * ln2 / (10 - x[i]);
+ prod *= x[i];
+ }
+ f -= (prod = pow(prod, 0.2));
+ if (grad)
+ for (i = 0; i < 10; ++i)
+ grad[i] -= 0.2 * prod / x[i];
+ RETURN(f);
}
-static const double paviani_lb[10] = {2.001,2.001,2.001,2.001,2.001,2.001,2.001,2.001,2.001,2.001};
-static const double paviani_ub[10] = {9.999,9.999,9.999,9.999,9.999,9.999,9.999,9.999,9.999,9.999};
-static const double paviani_xmin[10] = {9.35026583,9.35026583,9.35026583,9.35026583,9.35026583,9.35026583,9.35026583,9.35026583,9.35026583,9.35026583};
+static const double paviani_lb[10] = { 2.001, 2.001, 2.001, 2.001, 2.001, 2.001, 2.001, 2.001, 2.001, 2.001 };
+static const double paviani_ub[10] = { 9.999, 9.999, 9.999, 9.999, 9.999, 9.999, 9.999, 9.999, 9.999, 9.999 };
+static const double paviani_xmin[10] = { 9.35026583, 9.35026583, 9.35026583, 9.35026583, 9.35026583, 9.35026583, 9.35026583, 9.35026583, 9.35026583, 9.35026583 };
/****************************************************************************/
static double grosenbrock_f(unsigned n, const double *x, double *grad, void *data)
{
- unsigned i;
- double f = 0;
- UNUSED(data);
- if (grad) grad[0] = 0;
- for (i = 0; i < 29; ++i) {
- double a = x[i+1] - x[i] * x[i], b = 1 - x[i];
- if (grad) {
- grad[i] += -400 * a * x[i] - 2*b;
- grad[i+1] = 200 * a;
- }
- f += 100 * sqr(a) + sqr(b);
- }
- RETURN(f);
+ unsigned i;
+ double f = 0;
+ UNUSED(data);
+ if (grad)
+ grad[0] = 0;
+ for (i = 0; i < 29; ++i) {
+ double a = x[i + 1] - x[i] * x[i], b = 1 - x[i];
+ if (grad) {
+ grad[i] += -400 * a * x[i] - 2 * b;
+ grad[i + 1] = 200 * a;
+ }
+ f += 100 * sqr(a) + sqr(b);
+ }
+ RETURN(f);
}
-static const double grosenbrock_lb[30] = {-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30,-30};
-static const double grosenbrock_ub[30] = {30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30};
-static const double grosenbrock_xmin[30] = {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1};
+static const double grosenbrock_lb[30] = { -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30, -30 };
+static const double grosenbrock_ub[30] = { 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30 };
+static const double grosenbrock_xmin[30] = { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 };
/****************************************************************************/
static double goldsteinprice_f(unsigned n, const double *x, double *grad, void *data)
{
- double x0, x1, a1, a12, a2, b1, b12, b2;
- x0 = x[0]; x1 = x[1];
- a1 = x0+x1+1; a12 = sqr(a1);
- a2 = 19 - 14*x0 + 3*x0*x0 - 14*x1 + 6*x0*x1 + 3*x1*x1;
- b1 = 2*x0-3*x1; b12 = sqr(b1);
- b2 = 18 - 32*x0 + 12*x0*x0 + 48*x1 - 36*x0*x1 + 27*x1*x1;
- UNUSED(data);
- if (grad) {
- grad[0] = (1 + a12 * a2) * (2 * b1 * 2 * b2
- + b12 * (-32 + 24*x0 - 36*x1))
- + (2 * a1 * a2 + a12 * (-14 + 6*x0 + 6*x1)) * (30 + b12 * b2);
- grad[1] = (1 + a12 * a2) * (2 * b1 * (-3) * b2
- + b12 * (48 - 36*x0 + 54 * x1))
- + (2 * a1 * a2 + a12 * (-14 + 6*x0 + 6*x1)) * (30 + b12 * b2);
- }
- RETURN((1 + a12 * a2) * (30 + b12 * b2));
+ double x0, x1, a1, a12, a2, b1, b12, b2;
+ x0 = x[0];
+ x1 = x[1];
+ a1 = x0 + x1 + 1;
+ a12 = sqr(a1);
+ a2 = 19 - 14 * x0 + 3 * x0 * x0 - 14 * x1 + 6 * x0 * x1 + 3 * x1 * x1;
+ b1 = 2 * x0 - 3 * x1;
+ b12 = sqr(b1);
+ b2 = 18 - 32 * x0 + 12 * x0 * x0 + 48 * x1 - 36 * x0 * x1 + 27 * x1 * x1;
+ UNUSED(data);
+ if (grad) {
+ grad[0] = (1 + a12 * a2) * (2 * b1 * 2 * b2 + b12 * (-32 + 24 * x0 - 36 * x1))
+ + (2 * a1 * a2 + a12 * (-14 + 6 * x0 + 6 * x1)) * (30 + b12 * b2);
+ grad[1] = (1 + a12 * a2) * (2 * b1 * (-3) * b2 + b12 * (48 - 36 * x0 + 54 * x1))
+ + (2 * a1 * a2 + a12 * (-14 + 6 * x0 + 6 * x1)) * (30 + b12 * b2);
+ }
+ RETURN((1 + a12 * a2) * (30 + b12 * b2));
}
-static const double goldsteinprice_lb[2] = {-2, -2};
-static const double goldsteinprice_ub[2] = {2, 2};
-static const double goldsteinprice_xmin[2] = {0, -1};
+static const double goldsteinprice_lb[2] = { -2, -2 };
+static const double goldsteinprice_ub[2] = { 2, 2 };
+static const double goldsteinprice_xmin[2] = { 0, -1 };
/****************************************************************************/
static double shekel_f(unsigned n, const double *x, double *grad, void *data)
{
- static const double A[10][4] = { {4,4,4,4},
- {1,1,1,1},
- {8,8,8,8},
- {6,6,6,6},
- {3,7,3,7},
- {2,9,2,9},
- {5,5,3,3},
- {8,1,8,1},
- {6,2,6,2},
- {7,3.6,7,3.6} };
- static const double c[10] = {.1,.2,.2,.4,.4,.6,.3,.7,.5,.5};
- unsigned i;
- double f = 0;
- unsigned m = *((unsigned *) data);
- if (grad) for (i = 0; i < n; ++i) grad[i] = 0;
- for (i = 0; i < m; ++i) {
- double fi = 1.0 / (c[i]
- + sqr(x[0]-A[i][0])
- + sqr(x[1]-A[i][1])
- + sqr(x[2]-A[i][2])
- + sqr(x[3]-A[i][3]));
- f -= fi;
- if (grad) {
- grad[0] += (2*fi*fi) * (x[0]-A[i][0]);
- grad[1] += (2*fi*fi) * (x[1]-A[i][1]);
- grad[2] += (2*fi*fi) * (x[2]-A[i][2]);
- grad[3] += (2*fi*fi) * (x[3]-A[i][3]);
- }
- }
- RETURN(f);
+ static const double A[10][4] = { {4, 4, 4, 4},
+ {1, 1, 1, 1},
+ {8, 8, 8, 8},
+ {6, 6, 6, 6},
+ {3, 7, 3, 7},
+ {2, 9, 2, 9},
+ {5, 5, 3, 3},
+ {8, 1, 8, 1},
+ {6, 2, 6, 2},
+ {7, 3.6, 7, 3.6}
+ };
+ static const double c[10] = { .1, .2, .2, .4, .4, .6, .3, .7, .5, .5 };
+ unsigned i;
+ double f = 0;
+ unsigned m = *((unsigned *) data);
+ if (grad)
+ for (i = 0; i < n; ++i)
+ grad[i] = 0;
+ for (i = 0; i < m; ++i) {
+ double fi = 1.0 / (c[i]
+ + sqr(x[0] - A[i][0])
+ + sqr(x[1] - A[i][1])
+ + sqr(x[2] - A[i][2])
+ + sqr(x[3] - A[i][3]));
+ f -= fi;
+ if (grad) {
+ grad[0] += (2 * fi * fi) * (x[0] - A[i][0]);
+ grad[1] += (2 * fi * fi) * (x[1] - A[i][1]);
+ grad[2] += (2 * fi * fi) * (x[2] - A[i][2]);
+ grad[3] += (2 * fi * fi) * (x[3] - A[i][3]);
+ }
+ }
+ RETURN(f);
}
-static unsigned shekel_m[3] = {5,7,10};
-static const double shekel_lb[4] = {0,0,0,0};
-static const double shekel_ub[4] = {10,10,10,10};
-static const double shekel0_xmin[4] = {4.000037154,4.000133276,4.000037154,4.000133276};
-static const double shekel1_xmin[4] = {4.000572917,4.000689366,3.999489709,3.999606158};
-static const double shekel2_xmin[4] = {4.000746531,4.000592935,3.999663399,3.999509801};
+static unsigned shekel_m[3] = { 5, 7, 10 };
+static const double shekel_lb[4] = { 0, 0, 0, 0 };
+static const double shekel_ub[4] = { 10, 10, 10, 10 };
+static const double shekel0_xmin[4] = { 4.000037154, 4.000133276, 4.000037154, 4.000133276 };
+static const double shekel1_xmin[4] = { 4.000572917, 4.000689366, 3.999489709, 3.999606158 };
+static const double shekel2_xmin[4] = { 4.000746531, 4.000592935, 3.999663399, 3.999509801 };
/****************************************************************************/
static double levy_f(unsigned n, const double *x, double *grad, void *data)
{
- unsigned i;
- double a = x[n-1] - 1, b = 1 + sqr(sin(PI2*x[n-1]));
- double f = sqr(sin(PI3*x[0])) + a * b;
- UNUSED(data);
- if (grad) {
- for (i = 0; i < n; ++i) grad[i] = 0;
- grad[0] = 2 * PI3 * sin(PI3*x[0]) * cos(PI3*x[0]);
- grad[n-1] += b + a * 2 * PI2 * sin(PI2*x[n-1]) * cos(PI2*x[n-1]);
- }
- for (i = 0; i < n-1; ++i) {
- a = x[i] - 1;
- b = 1 + sqr(sin(PI3*x[i+1]));
- f += sqr(a) * b;
- if (grad) {
- grad[i] += 2 * a * b;
- grad[i+1] += 2*PI3 * sqr(a) * sin(PI3*x[i+1])*cos(PI3*x[i+1]);
- }
- }
- RETURN(f);
+ unsigned i;
+ double a = x[n - 1] - 1, b = 1 + sqr(sin(PI2 * x[n - 1]));
+ double f = sqr(sin(PI3 * x[0])) + a * b;
+ UNUSED(data);
+ if (grad) {
+ for (i = 0; i < n; ++i)
+ grad[i] = 0;
+ grad[0] = 2 * PI3 * sin(PI3 * x[0]) * cos(PI3 * x[0]);
+ grad[n - 1] += b + a * 2 * PI2 * sin(PI2 * x[n - 1]) * cos(PI2 * x[n - 1]);
+ }
+ for (i = 0; i < n - 1; ++i) {
+ a = x[i] - 1;
+ b = 1 + sqr(sin(PI3 * x[i + 1]));
+ f += sqr(a) * b;
+ if (grad) {
+ grad[i] += 2 * a * b;
+ grad[i + 1] += 2 * PI3 * sqr(a) * sin(PI3 * x[i + 1]) * cos(PI3 * x[i + 1]);
+ }
+ }
+ RETURN(f);
}
-static const double levy_lb[7] = {-5,-5,-5,-5,-5,-5,-5};
-static const double levy_ub[7] = {5,5,5,5,5,5,5};
-static const double levy_xmin[7] = {1,1,1,1,1,1,-4.75440246};
-static const double levy4_lb[4] = {-10,-10,-10,-10};
-static const double levy4_ub[4] = {10,10,10,10};
-static const double levy4_xmin[4] = {1,1,1,-9.75235596};
+static const double levy_lb[7] = { -5, -5, -5, -5, -5, -5, -5 };
+static const double levy_ub[7] = { 5, 5, 5, 5, 5, 5, 5 };
+static const double levy_xmin[7] = { 1, 1, 1, 1, 1, 1, -4.75440246 };
+static const double levy4_lb[4] = { -10, -10, -10, -10 };
+static const double levy4_ub[4] = { 10, 10, 10, 10 };
+static const double levy4_xmin[4] = { 1, 1, 1, -9.75235596 };
/****************************************************************************/
static double griewank_f(unsigned n, const double *x, double *grad, void *data)
{
- unsigned i;
- double f = 1, p = 1;
- UNUSED(data);
- for (i = 0; i < n; ++i) {
- f += sqr(x[i]) * 0.00025;
- p *= cos(x[i] / sqrt(i + 1.));
- if (grad) grad[i] = x[i] * 0.0005;
- }
- f -= p;
- if (grad)
- for (i = 0; i < n; ++i)
- grad[i] += p * tan(x[i] / sqrt(i + 1.)) / sqrt(i + 1.);
- RETURN(f);
+ unsigned i;
+ double f = 1, p = 1;
+ UNUSED(data);
+ for (i = 0; i < n; ++i) {
+ f += sqr(x[i]) * 0.00025;
+ p *= cos(x[i] / sqrt(i + 1.));
+ if (grad)
+ grad[i] = x[i] * 0.0005;
+ }
+ f -= p;
+ if (grad)
+ for (i = 0; i < n; ++i)
+ grad[i] += p * tan(x[i] / sqrt(i + 1.)) / sqrt(i + 1.);
+ RETURN(f);
}
-static const double griewank_lb[10] = {-500,-500,-500,-500,-500,-500,-500,-500,-500,-500};
-static const double griewank_ub[10] = {600,600,600,600,600,600,600,600,600,600};
-static const double griewank_xmin[10] = {0,0,0,0,0,0,0,0,0,0};
+static const double griewank_lb[10] = { -500, -500, -500, -500, -500, -500, -500, -500, -500, -500 };
+static const double griewank_ub[10] = { 600, 600, 600, 600, 600, 600, 600, 600, 600, 600 };
+static const double griewank_xmin[10] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
/****************************************************************************/
static double sixhumpcamel_f(unsigned n, const double *x, double *grad, void *data)
{
- UNUSED(data);
- if (grad) {
- grad[0] = 8*x[0] - 2.1*4*pow(x[0],3.) + 2*pow(x[0],5.) + x[1];
- grad[1] = x[0] - 8*x[1] + 16*pow(x[1],3.);
- }
- RETURN(4*sqr(x[0]) - 2.1 * pow(x[0],4.) + pow(x[0],6.)/3.
- + x[0]*x[1] - 4*sqr(x[1]) + 4*pow(x[1],4.));
+ UNUSED(data);
+ if (grad) {
+ grad[0] = 8 * x[0] - 2.1 * 4 * pow(x[0], 3.) + 2 * pow(x[0], 5.) + x[1];
+ grad[1] = x[0] - 8 * x[1] + 16 * pow(x[1], 3.);
+ }
+ RETURN(4 * sqr(x[0]) - 2.1 * pow(x[0], 4.) + pow(x[0], 6.) / 3. + x[0] * x[1] - 4 * sqr(x[1]) + 4 * pow(x[1], 4.));
}
-static const double sixhumpcamel_lb[2] = {-5,-5};
-static const double sixhumpcamel_ub[2] = {5,5};
-static const double sixhumpcamel_xmin[2] = {0.08984201317, -0.7126564032};
+static const double sixhumpcamel_lb[2] = { -5, -5 };
+static const double sixhumpcamel_ub[2] = { 5, 5 };
+static const double sixhumpcamel_xmin[2] = { 0.08984201317, -0.7126564032 };
/****************************************************************************/
static double convexcosh_f(unsigned n, const double *x, double *grad, void *data)
{
- unsigned i;
- double f = 1;
- UNUSED(data);
- for (i = 0; i < n; ++i)
- f *= cosh((x[i] - i) * (i+1));
- if (grad)
- for (i = 0; i < n; ++i)
- grad[i] = f * tanh((x[i] - i) * (i+1)) * (i+1);
- RETURN(f);
+ unsigned i;
+ double f = 1;
+ UNUSED(data);
+ for (i = 0; i < n; ++i)
+ f *= cosh((x[i] - i) * (i + 1));
+ if (grad)
+ for (i = 0; i < n; ++i)
+ grad[i] = f * tanh((x[i] - i) * (i + 1)) * (i + 1);
+ RETURN(f);
}
-static const double convexcosh_lb[10] = {-1,0,0,0,0,0,0,0,0,0};
-static const double convexcosh_ub[10] = {2,3,6,7,8,10,11,13,14,16};
-static const double convexcosh_xmin[10] = {0,1,2,3,4,5,6,7,8,9};
+static const double convexcosh_lb[10] = { -1, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
+static const double convexcosh_ub[10] = { 2, 3, 6, 7, 8, 10, 11, 13, 14, 16 };
+static const double convexcosh_xmin[10] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
/****************************************************************************/
static double branin_f(unsigned n, const double *x, double *grad, void *data)
{
- double a = 1 - 2*x[1] + 0.05 * sin(PI4 * x[1]) - x[0];
- double b = x[1] - 0.5 * sin(PI2 * x[0]);
- UNUSED(data);
- if (grad) {
- grad[0] = -2*a - cos(PI2 * x[0]) * PI2 * b;
- grad[1] = 2*a*(0.05 * PI4 * cos(PI4*x[1]) - 2) + 2*b;
- }
- RETURN(sqr(a) + sqr(b));
+ double a = 1 - 2 * x[1] + 0.05 * sin(PI4 * x[1]) - x[0];
+ double b = x[1] - 0.5 * sin(PI2 * x[0]);
+ UNUSED(data);
+ if (grad) {
+ grad[0] = -2 * a - cos(PI2 * x[0]) * PI2 * b;
+ grad[1] = 2 * a * (0.05 * PI4 * cos(PI4 * x[1]) - 2) + 2 * b;
+ }
+ RETURN(sqr(a) + sqr(b));
}
-static const double branin_lb[2] = {-10,-10};
-static const double branin_ub[2] = {10,10};
-static const double branin_xmin[2] = {1,0};
+static const double branin_lb[2] = { -10, -10 };
+static const double branin_ub[2] = { 10, 10 };
+static const double branin_xmin[2] = { 1, 0 };
/****************************************************************************/
static double shubert_f(unsigned n, const double *x, double *grad, void *data)
{
- unsigned i, j;
- double f = 0;
- UNUSED(data);
- for (j = 1; j <= 5; ++j)
- for (i = 0; i < n; ++i)
- f -= j * sin((j+1) * x[i] + j);
- if (grad) {
- for (i = 0; i < n; ++i) {
- grad[i] = 0;
- for (j = 1; j <= 5; ++j)
- grad[i] -= j * (j+1) * cos((j+1) * x[i] + j);
- }
- }
- RETURN(f);
+ unsigned i, j;
+ double f = 0;
+ UNUSED(data);
+ for (j = 1; j <= 5; ++j)
+ for (i = 0; i < n; ++i)
+ f -= j * sin((j + 1) * x[i] + j);
+ if (grad) {
+ for (i = 0; i < n; ++i) {
+ grad[i] = 0;
+ for (j = 1; j <= 5; ++j)
+ grad[i] -= j * (j + 1) * cos((j + 1) * x[i] + j);
+ }
+ }
+ RETURN(f);
}
-static const double shubert_lb[2] = {-10,-10};
-static const double shubert_ub[2] = {10,10};
-static const double shubert_xmin[2] = {-6.774576143, -6.774576143};
+static const double shubert_lb[2] = { -10, -10 };
+static const double shubert_ub[2] = { 10, 10 };
+static const double shubert_xmin[2] = { -6.774576143, -6.774576143 };
/****************************************************************************/
static double hansen_f(unsigned n, const double *x, double *grad, void *data)
{
- unsigned i;
- double a = 0, b = 0;
- UNUSED(data);
- for (i = 1; i <= 5; ++i)
- a += i * cos((i-1) * x[0] + i);
- for (i = 1; i <= 5; ++i)
- b += i * cos((i+1) * x[1] + i);
- if (grad) {
- grad[0] = 0;
- for (i = 1; i <= 5; ++i)
- grad[0] -= i * (i-1) * sin((i-1) * x[0] + i);
- grad[0] *= b;
- grad[1] = 0;
- for (i = 1; i <= 5; ++i)
- grad[1] -= i * (i+1) * sin((i+1) * x[1] + i);
- grad[1] *= a;
- }
- RETURN(a*b);
+ unsigned i;
+ double a = 0, b = 0;
+ UNUSED(data);
+ for (i = 1; i <= 5; ++i)
+ a += i * cos((i - 1) * x[0] + i);
+ for (i = 1; i <= 5; ++i)
+ b += i * cos((i + 1) * x[1] + i);
+ if (grad) {
+ grad[0] = 0;
+ for (i = 1; i <= 5; ++i)
+ grad[0] -= i * (i - 1) * sin((i - 1) * x[0] + i);
+ grad[0] *= b;
+ grad[1] = 0;
+ for (i = 1; i <= 5; ++i)
+ grad[1] -= i * (i + 1) * sin((i + 1) * x[1] + i);
+ grad[1] *= a;
+ }
+ RETURN(a * b);
}
-static const double hansen_lb[2] = {-10,-10};
-static const double hansen_ub[2] = {10,10};
-static const double hansen_xmin[2] = {-1.306707704,-1.425128429};
+static const double hansen_lb[2] = { -10, -10 };
+static const double hansen_ub[2] = { 10, 10 };
+static const double hansen_xmin[2] = { -1.306707704, -1.425128429 };
/****************************************************************************/
static double osc1d_f(unsigned n, const double *x, double *grad, void *data)
{
- double y = *x - 1.23456789;
- UNUSED(data);
- if (grad) grad[0] = y*0.02 + sin(y - 2*sin(3*y)) * (1 - 6*cos(3*y));
- RETURN(sqr(y*0.1) - cos(y - 2*sin(3*y)));
+ double y = *x - 1.23456789;
+ UNUSED(data);
+ if (grad)
+ grad[0] = y * 0.02 + sin(y - 2 * sin(3 * y)) * (1 - 6 * cos(3 * y));
+ RETURN(sqr(y * 0.1) - cos(y - 2 * sin(3 * y)));
}
-static const double osc1d_lb[1] = {-5};
-static const double osc1d_ub[1] = {5};
-static const double osc1d_xmin[1] = {1.23456789};
+static const double osc1d_lb[1] = { -5 };
+static const double osc1d_ub[1] = { 5 };
+static const double osc1d_xmin[1] = { 1.23456789 };
/****************************************************************************/
static double corner4d_f(unsigned n, const double *x, double *grad, void *data)
{
- double u = x[0] + x[1] * x[2] * sin(2 * x[3]);
- double v = x[0] + 2*sin(u);
- UNUSED(data);
- UNUSED(n);
- if (grad) {
- grad[0] = 2*v * (1 + 2*cos(u));
- grad[1] = 2*v * 2*cos(u) * x[2] * sin(2*x[3]) + 0.1;
- grad[2] = 2*v * 2*cos(u) * x[1] * sin(2*x[3]) + 0.1;
- grad[3] = 2*v * 2*cos(u) * x[1]*x[2] * cos(2*x[3]) * 2 + 0.1;
- }
- RETURN(1 + v*v + 0.1*(x[1]+x[2]+x[3]));
+ double u = x[0] + x[1] * x[2] * sin(2 * x[3]);
+ double v = x[0] + 2 * sin(u);
+ UNUSED(data);
+ UNUSED(n);
+ if (grad) {
+ grad[0] = 2 * v * (1 + 2 * cos(u));
+ grad[1] = 2 * v * 2 * cos(u) * x[2] * sin(2 * x[3]) + 0.1;
+ grad[2] = 2 * v * 2 * cos(u) * x[1] * sin(2 * x[3]) + 0.1;
+ grad[3] = 2 * v * 2 * cos(u) * x[1] * x[2] * cos(2 * x[3]) * 2 + 0.1;
+ }
+ RETURN(1 + v * v + 0.1 * (x[1] + x[2] + x[3]));
}
-static const double corner4d_lb[4] = {0,0,0,0};
-static const double corner4d_ub[4] = {1,1,1,1};
-static const double corner4d_xmin[4] = {0,0,0,0};
+static const double corner4d_lb[4] = { 0, 0, 0, 0 };
+static const double corner4d_ub[4] = { 1, 1, 1, 1 };
+static const double corner4d_xmin[4] = { 0, 0, 0, 0 };
/****************************************************************************/
static double side4d_f(unsigned n, const double *x, double *grad, void *data)
{
- double x0, x1, x2, x3, d0,d1,d2,d3;
- const double w0 = 0.1, w1 = 0.2, w2 = 0.3, w3 = 0.4;
- UNUSED(data);
- UNUSED(n);
- x0 = +0.4977 * x[0] - 0.3153 * x[1] - 0.5066 * x[2] - 0.4391 * x[3];
- x1 = -0.3153 * x[0] + 0.3248 * x[1] - 0.4382 * x[2] - 0.4096 * x[3];
- x2 = -0.5066 * x[0] - 0.4382 * x[1] + 0.3807 * x[2] - 0.4543 * x[3];
- x3 = -0.4391 * x[0] - 0.4096 * x[1] - 0.4543 * x[2] + 0.5667 * x[3];
-
- d0 = -1. / (x0*x0 + w0*w0);
- d1 = -1. / (x1*x1 + w1*w1);
- d2 = -1. / (x2*x2 + w2*w2);
- d3 = -1. / (x3*x3 + w3*w3);
-
- if (grad) {
- grad[0] = 2 * (x0*d0*d0 * +0.4977 +
- x1*d1*d1 * -0.3153 +
- x2*d2*d2 * -0.5066 +
- x3*d3*d3 * -0.4391);
- grad[1] = 2 * (x0*d0*d0 * -0.3153 +
- x1*d1*d1 * +0.3248 +
- x2*d2*d2 * -0.4382 +
- x3*d3*d3 * -0.4096);
- grad[2] = 2 * (x0*d0*d0 * -0.5066 +
- x1*d1*d1 * -0.4382 +
- x2*d2*d2 * +0.3807 +
- x3*d3*d3 * -0.4543);
- grad[3] = 2 * (x0*d0*d0 * -0.4391 +
- x1*d1*d1 * -0.4096 +
- x2*d2*d2 * -0.4543 +
- x3*d3*d3 * +0.5667);
- }
- RETURN(d0 + d1 + d2 + d3);
+ double x0, x1, x2, x3, d0, d1, d2, d3;
+ const double w0 = 0.1, w1 = 0.2, w2 = 0.3, w3 = 0.4;
+ UNUSED(data);
+ UNUSED(n);
+ x0 = +0.4977 * x[0] - 0.3153 * x[1] - 0.5066 * x[2] - 0.4391 * x[3];
+ x1 = -0.3153 * x[0] + 0.3248 * x[1] - 0.4382 * x[2] - 0.4096 * x[3];
+ x2 = -0.5066 * x[0] - 0.4382 * x[1] + 0.3807 * x[2] - 0.4543 * x[3];
+ x3 = -0.4391 * x[0] - 0.4096 * x[1] - 0.4543 * x[2] + 0.5667 * x[3];
+
+ d0 = -1. / (x0 * x0 + w0 * w0);
+ d1 = -1. / (x1 * x1 + w1 * w1);
+ d2 = -1. / (x2 * x2 + w2 * w2);
+ d3 = -1. / (x3 * x3 + w3 * w3);
+
+ if (grad) {
+ grad[0] = 2 * (x0 * d0 * d0 * +0.4977 + x1 * d1 * d1 * -0.3153 + x2 * d2 * d2 * -0.5066 + x3 * d3 * d3 * -0.4391);
+ grad[1] = 2 * (x0 * d0 * d0 * -0.3153 + x1 * d1 * d1 * +0.3248 + x2 * d2 * d2 * -0.4382 + x3 * d3 * d3 * -0.4096);
+ grad[2] = 2 * (x0 * d0 * d0 * -0.5066 + x1 * d1 * d1 * -0.4382 + x2 * d2 * d2 * +0.3807 + x3 * d3 * d3 * -0.4543);
+ grad[3] = 2 * (x0 * d0 * d0 * -0.4391 + x1 * d1 * d1 * -0.4096 + x2 * d2 * d2 * -0.4543 + x3 * d3 * d3 * +0.5667);
+ }
+ RETURN(d0 + d1 + d2 + d3);
}
-static const double side4d_lb[4] = {0.1,-1,-1,-1};
-static const double side4d_ub[4] = {1,1,1,1};
-static const double side4d_xmin[4] = {0.1,0.102971169,0.0760520641,-0.0497098571};
+static const double side4d_lb[4] = { 0.1, -1, -1, -1 };
+static const double side4d_ub[4] = { 1, 1, 1, 1 };
+static const double side4d_xmin[4] = { 0.1, 0.102971169, 0.0760520641, -0.0497098571 };
/****************************************************************************/
/****************************************************************************/
const testfunc testfuncs[NTESTFUNCS] = {
- { rosenbrock_f, NULL, 1, 2,
- rosenbrock_lb, rosenbrock_ub, rosenbrock_xmin,
- 0.0, "Rosenbrock function" },
- { mccormic_f, NULL, 1, 2,
- mccormic_lb, mccormic_ub, mccormic_xmin,
- -1.91322295, "McCormic function" },
- { boxbetts_f, NULL, 1, 3,
- boxbetts_lb, boxbetts_ub, boxbetts_xmin,
- 0.0, "Box and Betts exponential quadratic sum" },
- { paviani_f, NULL, 1, 10,
- paviani_lb, paviani_ub, paviani_xmin,
- -45.7784697, "Paviani function" },
- { grosenbrock_f, NULL, 1, 30,
- grosenbrock_lb, grosenbrock_ub, grosenbrock_xmin,
- 0.0, "Generalized Rosenbrock function" },
- { goldsteinprice_f, NULL, 1, 2,
- goldsteinprice_lb, goldsteinprice_ub, goldsteinprice_xmin,
- 3.0, "Goldstein and Price function" },
- { shekel_f, shekel_m + 0, 1, 4,
- shekel_lb, shekel_ub, shekel0_xmin,
- -10.15319968, "Shekel m=5 function" },
- { shekel_f, shekel_m + 1, 1, 4,
- shekel_lb, shekel_ub, shekel1_xmin,
- -10.40294057, "Shekel m=7 function" },
- { shekel_f, shekel_m + 2, 1, 4,
- shekel_lb, shekel_ub, shekel2_xmin,
- -10.53640982, "Shekel m=10 function" },
- { levy_f, NULL, 1, 4,
- levy4_lb, levy4_ub, levy4_xmin,
- -21.50235596, "Levy n=4 function" },
- { levy_f, NULL, 1, 5,
- levy_lb, levy_ub, levy_xmin+2,
- -11.50440302, "Levy n=5 function" },
- { levy_f, NULL, 1, 6,
- levy_lb, levy_ub, levy_xmin+1,
- -11.50440302, "Levy n=6 function" },
- { levy_f, NULL, 1, 7,
- levy_lb, levy_ub, levy_xmin,
- -11.50440302, "Levy n=7 function" },
- { griewank_f, NULL, 1, 10,
- griewank_lb, griewank_ub, griewank_xmin,
- 0.0, "Griewank function" },
- { sixhumpcamel_f, NULL, 1, 2,
- sixhumpcamel_lb, sixhumpcamel_ub, sixhumpcamel_xmin,
- -1.031628453, "Six-hump camel back function" },
- { convexcosh_f, NULL, 1, 10,
- convexcosh_lb, convexcosh_ub, convexcosh_xmin,
- 1.0, "Convex product of cosh functions" },
- { branin_f, NULL, 1, 2,
- branin_lb, branin_ub, branin_xmin,
- -.0, "Branin function" },
- { shubert_f, NULL, 1, 2,
- shubert_lb, shubert_ub, shubert_xmin,
- -24.06249888, "Shubert function" },
- { hansen_f, NULL, 1, 2,
- hansen_lb, hansen_ub, hansen_xmin,
- -176.5417931367, "Hansen function" },
- { osc1d_f, NULL, 1, 1,
- osc1d_lb, osc1d_ub, osc1d_xmin,
- -1.0, "1d oscillating function with a single minimum" },
- { corner4d_f, NULL, 1, 4,
- corner4d_lb, corner4d_ub, corner4d_xmin,
- 1.0, "4d function with minimum at corner" },
- { side4d_f, NULL, 1, 4,
- side4d_lb, side4d_ub, side4d_xmin,
- -141.285020472, "4d function with minimum at side" }
+ {rosenbrock_f, NULL, 1, 2,
+ rosenbrock_lb, rosenbrock_ub, rosenbrock_xmin,
+ 0.0, "Rosenbrock function"},
+ {mccormic_f, NULL, 1, 2,
+ mccormic_lb, mccormic_ub, mccormic_xmin,
+ -1.91322295, "McCormic function"},
+ {boxbetts_f, NULL, 1, 3,
+ boxbetts_lb, boxbetts_ub, boxbetts_xmin,
+ 0.0, "Box and Betts exponential quadratic sum"},
+ {paviani_f, NULL, 1, 10,
+ paviani_lb, paviani_ub, paviani_xmin,
+ -45.7784697, "Paviani function"},
+ {grosenbrock_f, NULL, 1, 30,
+ grosenbrock_lb, grosenbrock_ub, grosenbrock_xmin,
+ 0.0, "Generalized Rosenbrock function"},
+ {goldsteinprice_f, NULL, 1, 2,
+ goldsteinprice_lb, goldsteinprice_ub, goldsteinprice_xmin,
+ 3.0, "Goldstein and Price function"},
+ {shekel_f, shekel_m + 0, 1, 4,
+ shekel_lb, shekel_ub, shekel0_xmin,
+ -10.15319968, "Shekel m=5 function"},
+ {shekel_f, shekel_m + 1, 1, 4,
+ shekel_lb, shekel_ub, shekel1_xmin,
+ -10.40294057, "Shekel m=7 function"},
+ {shekel_f, shekel_m + 2, 1, 4,
+ shekel_lb, shekel_ub, shekel2_xmin,
+ -10.53640982, "Shekel m=10 function"},
+ {levy_f, NULL, 1, 4,
+ levy4_lb, levy4_ub, levy4_xmin,
+ -21.50235596, "Levy n=4 function"},
+ {levy_f, NULL, 1, 5,
+ levy_lb, levy_ub, levy_xmin + 2,
+ -11.50440302, "Levy n=5 function"},
+ {levy_f, NULL, 1, 6,
+ levy_lb, levy_ub, levy_xmin + 1,
+ -11.50440302, "Levy n=6 function"},
+ {levy_f, NULL, 1, 7,
+ levy_lb, levy_ub, levy_xmin,
+ -11.50440302, "Levy n=7 function"},
+ {griewank_f, NULL, 1, 10,
+ griewank_lb, griewank_ub, griewank_xmin,
+ 0.0, "Griewank function"},
+ {sixhumpcamel_f, NULL, 1, 2,
+ sixhumpcamel_lb, sixhumpcamel_ub, sixhumpcamel_xmin,
+ -1.031628453, "Six-hump camel back function"},
+ {convexcosh_f, NULL, 1, 10,
+ convexcosh_lb, convexcosh_ub, convexcosh_xmin,
+ 1.0, "Convex product of cosh functions"},
+ {branin_f, NULL, 1, 2,
+ branin_lb, branin_ub, branin_xmin,
+ -.0, "Branin function"},
+ {shubert_f, NULL, 1, 2,
+ shubert_lb, shubert_ub, shubert_xmin,
+ -24.06249888, "Shubert function"},
+ {hansen_f, NULL, 1, 2,
+ hansen_lb, hansen_ub, hansen_xmin,
+ -176.5417931367, "Hansen function"},
+ {osc1d_f, NULL, 1, 1,
+ osc1d_lb, osc1d_ub, osc1d_xmin,
+ -1.0, "1d oscillating function with a single minimum"},
+ {corner4d_f, NULL, 1, 4,
+ corner4d_lb, corner4d_ub, corner4d_xmin,
+ 1.0, "4d function with minimum at corner"},
+ {side4d_f, NULL, 1, 4,
+ side4d_lb, side4d_ub, side4d_xmin,
+ -141.285020472, "4d function with minimum at side"}
};
~ianmdlvl / nlopt.git / blobdiff