public void Alloc(PZMath_multimin_fminimizer_type T, int n)
{
type = T;
x = new PZMath_vector(n);
state = new nmsimplex_state_t();
T.alloc(state, n);
}
public PZMath_permutation(PZMath_permutation p)
{
size = p.Size;
data = new PZMath_vector(size);
for (int i = 0; i < size; i ++)
data[i] = p[i];
}
public static int ContractByBest(nmsimplex_state_t state, int best, PZMath_vector xc,
PZMath_multimin_function f)
{
/* Function contracts the simplex in respect to
best valued corner. That is, all corners besides the
best corner are moved. */
/* the xc vector is simply work space here */
PZMath_matrix x1 = state.x1;
PZMath_vector y1 = state.y1;
int i, j;
double newval;
for (i = 0; i < x1.RowCount; i++)
{
if (i != best)
{
for (j = 0; j < x1.ColumnCount; j++)
{
newval = 0.5 * (x1[i, j] + x1[best, j]);
x1[i, j] = newval;
}
/* evaluate function in the new point */
x1.CopyRow2(i, xc);
newval = f.FN_EVAL(xc);
y1[i] = newval;
}
}
return PZMath_errno.PZMath_SUCCESS;
}
public static int expb_df(PZMath_vector x, object param, PZMath_matrix J)
{
int n = (param as TestNonlinearLeastSquareFitParam).n;
double[] sigma = (param as TestNonlinearLeastSquareFitParam).sigma;
double A = x[0];
double lambda = x[1];
int i;
for (i = 0; i < n; i++)
{
// Jacobian matrix J(i, j) = dfi / dxj
// where fi = (Yi - yi) / sigma[i]
// Yi = A * exp(-lambda * i) + b
// and the xj are the parameters (A, lambda, b)
double t = (double)i;
double s = sigma[i];
double e = System.Math.Exp(-lambda * t);
J[i, 0] = e / s;
J[i, 1] = -t * A * e / s;
J[i, 2] = 1 / s;
}
return PZMath_errno.PZMath_SUCCESS;
}
public static int BidiagDecomp(PZMath_matrix A, PZMath_vector tau_U, PZMath_vector tau_V)
{
if (A.RowCount < A.ColumnCount)
PZMath_errno.ERROR ("PZMath_linalg::BidiagDecomp(), bidiagonal decomposition requires M>=N", PZMath_errno.PZMath_EBADLEN);
else if (tau_U.Size != A.ColumnCount)
PZMath_errno.ERROR ("PZMath_linalg::BidiagDecomp(),size of tau_U must be N", PZMath_errno.PZMath_EBADLEN);
else if (tau_V.Size + 1 != A.ColumnCount)
PZMath_errno.ERROR ("PZMath_linalg::BidiagDecomp(),size of tau_V must be (N - 1)", PZMath_errno.PZMath_EBADLEN);
else
{
int M = A.RowCount;
int N = A.ColumnCount;
int i;
for (i = 0 ; i < N; i++)
{
/* Apply Householder transformation to current column */
{
PZMath_vector c = A.Column(i);
PZMath_vector v = c.SubVector(i, M - i);
double tau_i = PZMath_linalg.HouseholderTransform(v);
/* Apply the transformation to the remaining columns */
if (i + 1 < N)
{
PZMath_matrix m = A.Submatrix(i, i + 1, M - i, N - (i + 1));
PZMath_linalg.HouseholderHM(tau_i, v, m);
}
tau_U[i] = tau_i;
}
/* Apply Householder transformation to current row */
if (i + 1 < N)
{
PZMath_vector r = A.Row(i);
PZMath_vector v = r.SubVector(i + 1, N - (i + 1));
double tau_i = PZMath_linalg.HouseholderTransform (v);
/* Apply the transformation to the remaining rows */
if (i + 1 < M)
{
PZMath_matrix m = A.Submatrix(i+1, i+1, M - (i+1), N - (i+1));
PZMath_linalg.HouseholderMH(tau_i, v, m);
}
tau_V[i] = tau_i;
}
}
}
return PZMath_errno.PZMath_SUCCESS;
}
public static double Dasum(PZMath_vector X)
{
double r = 0.0;
int i;
int N = X.Size;
for (i = 0; i < N; i++)
r += System.Math.Abs(X[i]);
return r;
}
public int Alloc(PZMath_multifit_fdfsolver_type T, int n, int p)
{
x = new PZMath_vector(p);
f = new PZMath_vector(n);
J = new PZMath_matrix(n, p);
dx = new PZMath_vector(p);
type = T;
state = new lmder_state_t();
return (this.type.alloc) (this.state, n, p);
}
// copy constructor
public PZMath_vector(PZMath_vector v)
{
size = v.Size;
offset = v.offset;
stride = v.stride;
length = v.length;
data = new double [length];
Array.Copy(v.data, data, length);
_mean = v._mean;
_stddev = v._stddev;
}
static double my_f(PZMath_vector v, object parms)
{
double x, y;
double dp1 = (parms as TestMultiminNMSimplexParms).dp1;
double dp2 = (parms as TestMultiminNMSimplexParms).dp2;
x = v[0];
y = v[1];
return 10.0 * (x - dp1) * (x - dp1) + 20.0 * (y - dp2) * (y - dp2) + 30.0;
}
/// <summary>
/// N(mu, sigma)
/// </summary>
/// <param name="l">lower bound</param>
/// <param name="u">upper bound</param>
public MultivariateNormalDistribution(PZMath_vector m, PZMath_matrix s)
{
dimension = m.Size;
mu = new PZMath_vector(dimension);
mu.MemCopyFrom(m);
sigma = new PZMath_matrix(dimension, dimension);
sigma.MemCopyFrom(s);
if (dimension != sigma.RowCount || dimension != sigma.ColumnCount)
throw new ApplicationException("MultivariateNormalDistribution::MultivariateNormalDistribution(), mu and sigma in different dimension!");
Init();
}
// vector sum, i.e. Y = aX + Y
public static int Daxpy(double alpha, PZMath_vector X, PZMath_vector Y)
{
if (X.Size == Y.Size)
{
for (int i = 0; i < X.Size; i ++)
Y[i] = alpha * X[i] + Y[i];
return PZMath_errno.PZMath_SUCCESS;
}
else
{
PZMath_errno.ERROR("invalid length", PZMath_errno.PZMath_EBADLEN);
}
return 0;
}
// scalar product of vector X and Y, i.e. (X ^ T) Y = Sum(X[i] * Y[i]);
// out result
public static int Ddot(PZMath_vector X, PZMath_vector Y, out double result)
{
result = 0.0;
if (X.Size == Y.Size)
{
for (int i = 0; i < X.Size; i ++)
result += X[i] * Y[i];
return PZMath_errno.PZMath_SUCCESS;
}
else
{
PZMath_errno.ERROR("invalid length", PZMath_errno.PZMath_EBADLEN);
}
return 0;
}
/// <summary>
/// sigma is a diagonal matrix
/// </summary>
/// <param name="m"></param>
/// <param name="diag"></param>
public MultivariateNormalDistribution(PZMath_vector m, PZMath_vector diag)
{
if (m.Size != diag.Size)
throw new ApplicationException("MultivariateNormalDistribution::MultivariateNormalDistribution(), mu and sigma in different dimension!");
dimension = m.Size;
mu = new PZMath_vector(dimension);
mu.MemCopyFrom(m);
sigma = new PZMath_matrix(dimension, dimension);
for (int i = 0; i < dimension; i ++)
sigma[i, i] = diag[i];
Init();
}
public static int BalanceColumns(PZMath_matrix A, PZMath_vector D)
{
int N = A.ColumnCount;
int j;
if (D.Size != N)
{
PZMath_errno.ERROR ("PZMath_linalg::BalanceColumns(), length of D must match second dimension of A", PZMath_errno.PZMath_EINVAL);
}
D.SetAll(1.0);
for (j = 0; j < N; j++)
{
PZMath_vector A_j = A.Column(j);
double s = PZMath_blas.Dasum (A_j);
double f = 1.0;
if (s == 0.0 || !PZMath_sys.Finite(s))
{
D[j] = f;
continue;
}
while (s > 1.0)
{
s /= 2.0;
f *= 2.0;
}
while (s < 0.5)
{
s *= 2.0;
f /= 2.0;
}
D[j] = f;
if (f != 1.0)
PZMath_blas.Dscal(1.0/f, A_j);
}
return PZMath_errno.PZMath_SUCCESS;
}
public static int expb_f(PZMath_vector x, object param, PZMath_vector f)
{
int n = (param as TestNonlinearLeastSquareFitParam).n;
double[] y = (param as TestNonlinearLeastSquareFitParam).y;
double[] sigma = (param as TestNonlinearLeastSquareFitParam).sigma;
double A = x[0];
double lambda = x[1];
double b = x[2];
int i;
for (i = 0; i < n; i++)
{
// Model Yi = A * exp(-lambda * i) + b
double t = (double)i;
double Yi = A * System.Math.Exp(-lambda * t) + b;
f[i] = (Yi - y[i]) / sigma[i];
}
return PZMath_errno.PZMath_SUCCESS;
}
public static int CalcCenter(nmsimplex_state_t state, PZMath_vector mp)
{
/* calculates the center of the simplex to mp */
PZMath_matrix x1 = state.x1;
int i, j;
double val;
for (j = 0; j < x1.ColumnCount; j++)
{
val = 0.0;
for (i = 0; i < x1.RowCount; i++)
{
val += x1[i, j];
}
val /= x1.RowCount;
mp[j] = val;
}
return PZMath_errno.PZMath_SUCCESS;
}
public static double MoveCorner(double coeff, nmsimplex_state_t state, int corner,
PZMath_vector xc, PZMath_multimin_function f)
{
/* moves a simplex corner scaled by coeff (negative value represents
mirroring by the middle point of the "other" corner points)
and gives new corner in xc and function value at xc as a
return value
*/
PZMath_matrix x1 = state.x1;
int i, j;
double newval, mp;
if (x1.RowCount < 2)
{
PZMath_errno.ERROR ("nmsimplex::MoveCorner(), simplex cannot have less than two corners!", PZMath_errno.PZMath_FAILURE);
}
for (j = 0; j < x1.ColumnCount; j++)
{
mp = 0.0;
for (i = 0; i < x1.RowCount; i++)
{
if (i != corner)
{
mp += (x1[i, j]);
}
}
mp /= (double) (x1.RowCount - 1);
newval = mp - coeff * (mp - x1[corner, j]);
xc[j] = newval;
}
newval = f.FN_EVAL(xc);
return newval;
}
// return the index of max element of X, in absolut magtitude
public static int Idamax(PZMath_vector X)
{
double max = 0.0;
double t;
int index = 0;
for (int i = 0; i < X.Size; i ++)
{
t = System.Math.Abs(X[i]);
if (t > max)
{
max = t;
index = i;
}
}
return index;
}
public static int Dtrsv(CBLAS_UPLO Uplo, CBLAS_TRANSPOSE TransA, CBLAS_DIAG Diag, PZMath_matrix A, PZMath_vector x)
{
int M = A.RowCount;
int N = A.ColumnCount;
if (M != N)
{
PZMath_errno.ERROR("PZMath_blas::Dtrsv(), matrix must be square", PZMath_errno.PZMath_ENOTSQR);
}
else if (N != x.Size)
{
PZMath_errno.ERROR("PZMath_blas::Dtrsv(), invalid length", PZMath_errno.PZMath_EBADLEN);
}
bool nonunit = (Diag == CBLAS_DIAG.CblasNonUnit);
int ix, jx;
int i, j;
CBLAS_TRANSPOSE Trans = (TransA != CBLAS_TRANSPOSE.CblasConjTrans) ? TransA : CBLAS_TRANSPOSE.CblasTrans;
CBLAS_ORDER order = CBLAS_ORDER.CblasRowMajor;
if (N == 0)
return PZMath_errno.PZMath_SUCCESS;
/* form x := inv( A )*x */
if ((order == CBLAS_ORDER.CblasRowMajor && Trans == CBLAS_TRANSPOSE.CblasNoTrans
&& Uplo == CBLAS_UPLO.CblasUpper)
|| (order == CBLAS_ORDER.CblasColMajor && Trans == CBLAS_TRANSPOSE.CblasTrans
&& Uplo == CBLAS_UPLO.CblasLower))
{
/* backsubstitution */
ix = N - 1;
if (nonunit)
x[ix] = x[ix] / A[N - 1, N - 1];
ix--;
for (i = N - 1; i > 0 && (i-- > 0); )
{
double tmp = x[ix];
jx = ix + 1;
for (j = i + 1; j < N; j++)
{
double Aij = A[i, j];
tmp -= Aij * x[jx];
jx++;
}
if (nonunit)
{
x[ix] = tmp / A[i, i];
}
else
{
x[ix] = tmp;
}
ix--;
}
}
else if ((order == CBLAS_ORDER.CblasRowMajor && Trans == CBLAS_TRANSPOSE.CblasNoTrans
&& Uplo == CBLAS_UPLO.CblasLower)
|| (order == CBLAS_ORDER.CblasColMajor && Trans == CBLAS_TRANSPOSE.CblasTrans
&& Uplo == CBLAS_UPLO.CblasUpper))
{
/* forward substitution */
ix = 0;
if (nonunit)
{
x[ix] = x[ix] / A[0, 0];
}
ix++;
for (i = 1; i < N; i++)
{
double tmp = x[ix];
jx = 0;
for (j = 0; j < i; j++)
{
double Aij = A[i, j];
tmp -= Aij * x[jx];
jx++;
}
if (nonunit)
{
x[ix] = tmp / A[i, i];
}
else
{
x[ix] = tmp;
}
ix++;
}
}
else if ((order == CBLAS_ORDER.CblasRowMajor && Trans == CBLAS_TRANSPOSE.CblasTrans
&& Uplo == CBLAS_UPLO.CblasUpper)
|| (order == CBLAS_ORDER.CblasColMajor && Trans == CBLAS_TRANSPOSE.CblasNoTrans
&& Uplo == CBLAS_UPLO.CblasLower))
{
/* form x := inv( A' )*x */
/* forward substitution */
ix = 0;
if (nonunit)
{
x[ix] = x[ix] / A[0, 0];
}
ix++;
for (i = 1; i < N; i++)
{
double tmp = x[ix];
jx = 0;
for (j = 0; j < i; j++)
{
double Aji = A[j, i];
tmp -= Aji * x[jx];
jx++;
}
if (nonunit)
{
x[ix] = tmp / A[i, i];
}
else
{
x[ix] = tmp;
}
ix++;
}
}
else if ((order == CBLAS_ORDER.CblasRowMajor && Trans == CBLAS_TRANSPOSE.CblasTrans
&& Uplo == CBLAS_UPLO.CblasLower)
|| (order == CBLAS_ORDER.CblasColMajor && Trans == CBLAS_TRANSPOSE.CblasNoTrans
&& Uplo == CBLAS_UPLO.CblasUpper))
{
/* backsubstitution */
ix = N - 1;
if (nonunit)
{
x[ix] = x[ix] / A[(N - 1), (N - 1)];
}
ix--;
for (i = N - 1; i > 0 && (i-- > 0); )
{
double tmp = x[ix];
jx = ix + 1;
for (j = i + 1; j < N; j++)
{
double Aji = A[j, i];
tmp -= Aji * x[jx];
jx++;
}
if (nonunit)
{
x[ix] = tmp / A[i, i];
}
else
{
x[ix] = tmp;
}
ix--;
}
}
else
{
PZMath_errno.ERROR("PZMath_blas::Dtrsv(), unrecognized operation");
}
return PZMath_errno.PZMath_SUCCESS;
}
// rescale X by the multicative factor alpha, X = alpha * X
public static void Dscal(double alpha, PZMath_vector X)
{
for (int i = 0; i < X.Size; i ++)
X[i] = alpha * X[i];
}
// return Norm 2 of vector f i.e. Sqrt(Sum(f[i] ^ 2))
public static double Dnrm2(PZMath_vector f)
{
double scale = 0.0;
double ssq = 1.0;
int i;
if (f.Size <= 0 || f.stride <= 0)
{
return 0;
}
else if (f.size == 1)
{
return System.Math.Abs(f[0]);
}
for (i = 0; i < f.size; i++)
{
double x = f[i];
if (x != 0.0)
{
double ax = System.Math.Abs(x);
if (scale < ax)
{
ssq = 1.0 + ssq * (scale / ax) * (scale / ax);
scale = ax;
}
else
{
ssq += (ax / scale) * (ax / scale);
}
}
}
return scale * System.Math.Sqrt(ssq);
}
// These functions compute the matrix-vector product and sum
// y = \alpha op(A) x + \beta y,
// where op(A) = A, A^T, A^H for method =
// 0 - CblasNoTrans,
// 1 - CblasTrans
public static int Dgemv(int method, double alpha, PZMath_matrix A, PZMath_vector X, double beta, PZMath_vector Y)
{
int M = A.RowCount;
int N = A.ColumnCount;
if ((method == 0 && N == X.Size && M == Y.Size)
|| (method == 1 && M == X.Size && N == Y.Size))
{
if (method == 0)
// no trans
{
for (int i = 0; i < M; i ++)
// each element of Y
{
double temp = 0;
for (int j = 0; j < N; j ++)
// each element of A
temp += A[i, j] * X[j];
Y[i] = alpha * temp + beta * Y[i];
}
}
else
// trans
{
for (int i = 0; i < N; i ++)
// each element of Y
{
double temp = 0;
for (int j = 0; j < M; j ++)
// each element of A
temp += A[j, i] * X[j];
Y[i] = alpha * temp + beta * Y[i];
}
}
return PZMath_errno.PZMath_SUCCESS;
}
else
{
PZMath_errno.ERROR ("PZMath_blas::Dgemv(), invalid length", PZMath_errno.PZMath_EBADLEN);
return 0;
}
}
public static void TestNonlinearLeastSquareFit()
{
PZMath_multifit_fdfsolver_type T = new PZMath_multifit_fdfsolver_type();
PZMath_multifit_fdfsolver s = new PZMath_multifit_fdfsolver();
int N = 40;
int status;
int i, iter = 0;
int n = N;
int p = 3;
PZMath_matrix covar = new PZMath_matrix(p, p);
double[] y = new double[N];
double[] sigma = new double[N];
double h = 1e-2; // step-size
TestNonlinearLeastSquareFitParam d = new TestNonlinearLeastSquareFitParam(n, p, y, sigma, h);
PZMath_multifit_function_fdf f = new PZMath_multifit_function_fdf();
double[] x_init = new double[3];
x_init[0] = 1.0;
x_init[1] = 0.0;
x_init[2] = 0.0;
PZMath_vector x = new PZMath_vector(x_init);
f.f = new multifit_delegate_f(TestPZMathMultifit.expb_f);
f.df = new multifit_delegate_df(TestPZMathMultifit.expb_df);
f.fdf = new multifit_delegate_fdf(TestPZMathMultifit.expb_fdf);
f.n = n;
f.p = p;
f.parms = d;
ParkMillerNormal r = new ParkMillerNormal();
// this is the data to be fiitted
for (i = 0; i < n; i++)
{
double t = i;
double tt = System.Math.Exp(-0.1 * t);
d.y[i] = 1.0 + 5 * System.Math.Exp(-0.1 * t);// + r.NextVariate();
d.sigma[i] = 0.1;
System.Diagnostics.Debug.WriteLine("data: " + i + " " + d.y[i] + " " + d.sigma[i]);
}
T.Init("PZMath_multifit_fdfsolver_lmsder");
s.Alloc(T, n, p);
s.Init(f, x);
s.PrintState(iter);
do
{
iter++;
status = s.Iterate();
System.Diagnostics.Debug.WriteLine("status = " + status);
//printf ("status = %s \n", gsl_strerror(status));
s.PrintState(iter);
if (status > 0)
break;
status = s.TestDelta(s.dx, s.x, 1e-4, 1e-4);
}
while (status == PZMath_errno.PZMath_CONTINUE && iter < 500);
s.Covar(0.0, covar);
covar.DebugWriteLine();
System.Console.WriteLine("A = " + s.FIT(0) + " +/- " + s.ERR(0, covar));
System.Console.WriteLine("lambda = " + s.FIT(1) + " +/- " + s.ERR(1, covar));
System.Console.WriteLine("b = " + s.FIT(2) + " +/- " + s.ERR(2, covar));
double chi = s.Chi();
System.Console.WriteLine("chisq/dof = " + (System.Math.Pow(chi, 2.0) / (double)(n - p)));
System.Console.WriteLine("state = " + status);
//printf ("status = %s \n", gsl_strerror(status));
}
public double FN_EVAL(PZMath_vector x)
{
return f(x, parms);
}
//This function copies the elements of the i-th row of the matrix m
// into the vector v.
// The length of the vector must be the same as the length of the row.
public void CopyRow2(int indexRow, PZMath_vector v)
{
if (indexRow < 0 || indexRow > row)
{
PZMath_errno.ERROR("PZMath_matrix::GetRow(), Index Out Of Range", PZMath_errno.PZMath_EFAILED);
}
if (v.size != col)
PZMath_errno.ERROR("PZMath_matrix::GetRow(), vector does not match the row");
for (int i = 0; i < col; i ++)
v[i] = this[indexRow, i];
}
public static int expb_fdf(PZMath_vector x, object param, PZMath_vector f, PZMath_matrix J)
{
expb_f(x, param, f);
expb_df(x, param, J);
return PZMath_errno.PZMath_SUCCESS;
}
public static int Iterate(object vstate, PZMath_multimin_function f,
PZMath_vector x, out double size, out double fval)
{
/* Simplex iteration tries to minimize function f value */
/* Includes corrections from Ivo Alxneit <*****@*****.**> */
/* xc and xc2 vectors store tried corner point coordinates */
PZMath_vector xc = (vstate as nmsimplex_state_t).ws1;
PZMath_vector xc2 = (vstate as nmsimplex_state_t).ws2;
PZMath_vector y1 = (vstate as nmsimplex_state_t).y1;
PZMath_matrix x1 = (vstate as nmsimplex_state_t).x1;
int n = y1.size;
int i;
int hi = 0, s_hi = 0, lo = 0;
double dhi, ds_hi, dlo;
int status;
double val, val2;
/* get index of highest, second highest and lowest point */
dhi = ds_hi = dlo = y1[0];
for (i = 1; i < n; i++)
{
val = y1[i];
if (val < dlo)
{
dlo = val;
lo = i;
}
else if (val > dhi)
{
ds_hi = dhi;
s_hi = hi;
dhi = val;
hi = i;
}
else if (val > ds_hi)
{
ds_hi = val;
s_hi = i;
}
}
/* reflect the highest value */
val = MoveCorner (-1.0, vstate as nmsimplex_state_t, hi, xc, f);
if (val < y1[lo])
{
/* reflected point becomes lowest point, try expansion */
val2 = MoveCorner (-2.0, vstate as nmsimplex_state_t, hi, xc2, f);
if (val2 < y1[lo])
{
x1.SetRow(hi, xc2);
y1[hi] = val2;
}
else
{
x1.SetRow(hi, xc);
y1[hi] = val;
}
}
/* reflection does not improve things enough */
else if (val > y1[s_hi])
{
if (val <= y1[hi])
{
/* if trial point is better than highest point, replace
highest point */
x1.SetRow(hi, xc);
y1[hi] = val;
}
/* try one dimensional contraction */
val2 = MoveCorner (0.5, vstate as nmsimplex_state_t, hi, xc2, f);
if (val2 <= y1[hi])
{
x1.SetRow(hi, xc2);
y1[hi] = val2;
}
else
{
/* contract the whole simplex in respect to the best point */
status = ContractByBest (vstate as nmsimplex_state_t, lo, xc, f);
if (status != 0)
{
PZMath_errno.ERROR("nmsimplex::Iterate(), nmsimplex_contract_by_best failed", PZMath_errno.PZMath_FAILURE);
}
}
}
else
{
/* trial point is better than second highest point.
Replace highest point by it */
x1.SetRow(hi, xc);
y1[hi] = val;
}
/* return lowest point of simplex as x */
lo = y1.MinIndex();
x1.CopyRow2(lo, x);
fval = y1[lo];
/* Update simplex size */
size = Size (vstate as nmsimplex_state_t);
return PZMath_errno.PZMath_SUCCESS;
}
public int Init(PZMath_multimin_function f, PZMath_vector x, PZMath_vector step_size)
{
this.f = f;
this.x.MemCopyFrom(x);
return type.init(state, this.f, this.x, out this.size, step_size);
}
// fit data from y = exp(x), x :[0 : 2]
public static void TestLinearLeastSquareFit()
{
int i, n;
n = 19;
// -- prepare model parameters
double xi, yi, chisq;
PZMath_matrix X, cov;
PZMath_vector y, w, c;
X = new PZMath_matrix(n, 3);
y = new PZMath_vector(n);
w = new PZMath_vector(n);
c = new PZMath_vector(3);
cov = new PZMath_matrix(3, 3);
// -- data to be fitted
//PZMath_random_ParkMiller_Normal r = new PZMath_random_ParkMiller_Normal();
for (i = 0; i < n; i++)
{
xi = 0.1 + 0.1 * i;
yi = System.Math.Exp(xi); // f(x)
System.Console.WriteLine(xi + " " + yi);
X[i, 0] = 1.0;
X[i, 1] = xi;
X[i, 2] = xi * xi;
y[i] = yi;
w[i] = 1.0;
}
PZMath_multifit_linear l = new PZMath_multifit_linear();
l.Alloc(n, 3);
l.Wlinear(X, w, y, c, cov, out chisq);
System.Console.WriteLine("# best fit: Y = " + c[0] + " + " + c[1] + " X + " + c[2] + " X ^ 2");
System.Console.WriteLine("# covariance matrix:");
cov.ScreenWriteLine();
System.Console.WriteLine("# chisq = " + chisq);
}
public static int Init(object vstate, PZMath_multimin_function f, PZMath_vector x,
out double size, PZMath_vector step_size)
{
int i;
double val;
PZMath_vector xtemp = (vstate as nmsimplex_state_t).ws1;
/* first point is the original x0 */
val = f.FN_EVAL(x);
(vstate as nmsimplex_state_t).x1.SetRow(0, x);
(vstate as nmsimplex_state_t).y1[0] = val;
/* following points are initialized to x0 + step_size */
for (i = 0; i < x.size; i++)
{
xtemp.MemCopyFrom(x);
val = xtemp[i] + step_size[i];
xtemp[i] = val;
val = f.FN_EVAL(xtemp);
(vstate as nmsimplex_state_t).x1.SetRow(i + 1, xtemp);
(vstate as nmsimplex_state_t).y1[i + 1] = val;
}
/* Initialize simplex size */
size = Size (vstate as nmsimplex_state_t);
return PZMath_errno.PZMath_SUCCESS;
}