ocn_g02.h

图像处理的压缩算法

	printf("Variable       Parameter           Estimate Standard error\n\n");
	for (j=0; j<ip; j++)
		printf("%6ld%20.4e%20.4e\n", j+1, b[j], se[j]);
	
	printf("\n");
	printf("Obs            Residuals           h\n\n");
	for (i=0; i<n; i++)
		printf("%6ld%20.4e%20.4e\n", i+1, res[i], h[i]);		
}


	The output is as follows:
	
	The  input data are as follows
	n = 12, m = 4, tol = 0.000001e0
	x
	1.0, 0.0, 0.0, 0.0, 
	0.0, 0.0, 0.0, 1.0, 
	0.0, 1.0, 0.0, 0.0, 
	0.0, 0.0, 1.0, 0.0, 
	0.0, 0.0, 0.0, 1.0, 
	0.0, 1.0, 0.0, 0.0, 
	0.0, 0.0, 0.0, 1.0, 
	1.0, 0.0, 0.0, 0.0, 
	0.0, 0.0, 1.0, 0.0, 
	1.0, 0.0, 0.0, 0.0, 
	0.0, 0.0, 1.0, 0.0, 
	0.0, 1.0, 0.0, 0.0, 

	y
	33.630, 39.620, 38.180, 41.460, 38.020, 35.830, 35.990, 
	36.580, 42.920, 37.800, 40.430, 37.890, 
	Model not of full rank, rank =    4
	Residual sum of squares =  2.2227e+001
	Degrees of freedom = 8.0

	Variable       Parameter           Estimate Standard error
	
     	 1         3.0557e+001         3.8494e-001
         2         5.4467e+000         8.3896e-001
    	 3         6.7433e+000         8.3896e-001
    	 4         1.1047e+001         8.3896e-001
    	 5         7.3200e+000         8.3896e-001

	Obs            Residuals           h

    	 1        -2.3733e+000         3.3333e-001
     	 2         1.7433e+000         3.3333e-001
    	 3         8.8000e-001         3.3333e-001
    	 4        -1.4333e-001         3.3333e-001
    	 5         1.4333e-001         3.3333e-001
    	 6        -1.4700e+000         3.3333e-001
    	 7        -1.8867e+000         3.3333e-001
    	 8         5.7667e-001         3.3333e-001
    	 9         1.3167e+000         3.3333e-001
   		10         1.7967e+000         3.3333e-001
    	11        -1.1733e+000         3.3333e-001
    	12         5.9000e-001         3.3333e-001
	
Return:
	The function returns NAG error code or 0 if no error.
	
	11: On entry, n must not be less than 2: n = _value_.  On entry, m must not be less than 1: m = _value_.  On entry, ip must not be less than 1: ip = _value_.  On entry, sx[_value_] must not be less than 0: sx[_value_] = _value_.
	17: On entry, tdx = _value_ while m = _value_. These parameters must satisfy tdx = m.  On entry, tdq = _value_ while ip+1 = _value_. These parameters must satisfy tdq = ip+1.  On entry, n = _value_ while ip = _value_. These parameters must satisfy n = ip.
	5: On entry, tol must not be less than 0.0: tol = _value_.  On entry, wt[_value_] must not be less than 0.0: wt[_value_] = _value_.
	70: On entry, parameter mean had an illegal value.
	425: Either a value of sx is < 0, or ip is incompatible with mean and sx, or ip > the effective number of observations.
	427: The singular value decomposition has failed to converge.
	426: The degrees of freedom for the residuals are zero, i.e., the designated number of parameters = the effective number of observations.  In this case the parameter estimates will be returned along with the diagonal elements of H, but neither standard errors nor the variance-covariance matrix will be calculated.
	73: Memory allocation failed.
	
	successful call of the nag_regsn_mult_linear function
	
*/
    int nag_regsn_mult_linear(
    Nag_IncludeMean mean,
    int n, 		  // the number of observations 
    double x[],   	//the variable for which ith observation for the jth potential indepent variable.
    int tdx, 	  	// the second dimension of the array x.
    int m, 		  	// the total number of independent variables in the data set.
    int sx[], 	  	// indicates which of the potential independent variables are to be included in the model.
    int ip, 	  	// the number p of independent variables in the model, including the mean or intercept if present.
    double y[],   	// the observations on the dependent variable.
    double wt[],  	// an (optional) weight is specified to be used in the weighted regression. 
    double *rss,  	// the residual sum of squares for the regression.
    double *df,   	// the degree of freedom associated with the residual sum of squares.
    double b[],   	// return the least-squares estimates of the parameters of the regression model.
    double se[],  	// return the standard errors of the ip parameter estimates given in b.
    double cov[], 	// return the variance-covariance matrix of estimated parameters in b.
    double res[], 	// return the (weighted) residuals.
    double h[],   	// return the diagonal elements of H.
    double q[],   	// return the results of the QR decomposition.
    int tdq, 	  	// the second dimension of the array q. 
    Boolean *svd, 	  	// return TRUE if a singular value decomposition has been performed, otherwise FALSE
    int *rank, 	  	// return the rank of the independent variables.
    double p[],   	// details of the QR decomposition and SVD if used.
    double tol,   	// the value of tol is used to decide what is the rank of the independent variables. 
    double com_ar[] // return information which is needed by nag_regsn_mult_linear_newyvar_if svd = TRUE.
  );//  Parameter estimates, standard errors, residuals ... 

/** g02dcc
		adds or deletes an observation from a general regression model fitted by nag_regsn_mult_linear.
	
	
Example:  
	A data set consisting of 12 observations with four independent variables is read in 
	and a general linear regression model fitted by nag_regsn_mult_linear (g02dac) and 
	parameter estimates printed. The last observation is then dropped and the parameter 
	estimates recalculated, using nag_regsn_mult_linear_upd model (g02ddc), and printed.


void test_nag_regsn_mult_linear_addrem_obs()
{
	
	double rss, tol;
	int i, ip, rank, j, m, n;
	double df;
	Boolean svd;
	char meanc, weight;
	Nag_IncludeMean mean;
	Nag_UpdateObserv update;
	double b[5]; 
	double cov[15];
	double h[12];
	double  p[35];
	double  res[12], se[5];
	double com_ar[45], wt[12];
	matrix q;
	q.SetSize(12,6);
	double *wtptr;
	int success;
	n = 12;
	m = 4;
	weight = 'u'; 
	meanc = 'z';

	if (meanc=='m')
		mean = Nag_MeanInclude;
	else
		mean = Nag_MeanZero;
	if (weight=='w')
		wtptr = wt;
	else
		wtptr = NULL;

	matrix xm = {{1.0, 0.0, 0.0, 0.0, 0}, {0.0, 0.0, 0.0, 1.0, 0},
				 {0.0, 1.0, 0.0, 0.0, 0}, {0.0, 0.0, 1.0, 0.0, 0},
				 {0.0, 0.0, 0.0, 1.0, 0}, {0.0, 1.0, 0.0, 0.0, 0},
				 {0.0, 0.0, 0.0, 1.0, 0}, {1.0, 0.0, 0.0, 0.0, 0},
				 {0.0, 0.0, 1.0, 0.0, 0}, {1.0, 0.0, 0.0, 0.0, 0},
				 {0.0, 0.0, 1.0, 0.0, 0}, {1.0, 1.0, 1.0, 1.0, 0}};		
	double y[12] = {33.63, 39.62, 38.18, 41.46, 38.02, 35.83,
					35.99, 36.58, 42.92, 37.80, 40.43, 37.89};
	
	int sx[5] =	{1, 1, 1, 1, 4};		

	ip = 4;
	
	tol = 0.00001e0;

	success = nag_regsn_mult_linear(mean, n, xm, 5, m, sx, ip, y, wtptr, &rss,
									&df, b, se, cov, res, h, q, 6, &svd, &rank,
									p, tol, com_ar);
	
	if(success ==0)
	{
		printf("Results from g02dac\n\n");
		if (svd)
			printf("Model not of full rank\n");
		printf("Residual sum of squares = %12.4e\n", rss);
		printf("Degrees of freedom = %3.1f\n\n", df);
		printf("Variable       Parameter           Estimate Standard error\n\n");
		for (j=0; j<ip; j++)
			printf("%6ld%20.4e%20.4e\n", j+1, b[j], se[j]);
		printf("\n");
		update = Nag_ObservDel;
		success = nag_regsn_mult_linear_addrem_obs(update, mean, m, sx, q, 6, ip,
													xm, 12, 5, 12, y[11], wtptr, &rss);
			printf("Results from dropping an observation using g02dcc\n");
			n = n - 1;
			nag_regsn_mult_linear_upd_model(n, ip, q, 6, &rss, &df, b, se, cov,
			&svd, &rank, p, tol);
			printf("Residual sum of squares = %12.4e\n", rss);
			printf("Degrees of freedom = %3.1f\n\n", df);
			printf("Variable       Parameter           Estimate Standard error\n\n");
			for (j=0; j<ip; j++)
				printf("%6ld%20.4e%20.4e\n", j+1, b[j], se[j]);
	}
	else
	{
		printf("There is some problem with the function nag_regsn_mult_linear\n");
	}

}


	The output is as follows:
	
	Results from g02dac
	
	Residual sum of squares =  5.2748e+003
	Degrees of freedom = 8.0
	
	Variable       Parameter           Estimate Standard error

    	 1         2.0724e+001         1.3801e+001
    	 2         1.4085e+001         1.6240e+001
    	 3         2.6324e+001         1.3801e+001
    	 4         2.2597e+001         1.3801e+001

	Results from dropping an observation using g02dcc
	Residual sum of squares =  2.1705e+001
	Degrees of freedom = 7.0

	Variable       Parameter           Estimate Standard error

    	 1         3.6003e+001         1.0166e+000
    	 2         3.7005e+001         1.2451e+000
    	 3         4.1603e+001         1.0166e+000
    	 4         3.7877e+001         1.0166e+000
Return:
	The function returns NAG error code or 0 if no error.
	11: On entry, ip must not be less than 1: ip = _value_.  On entry, m must not be less than 1: m = _value_.  On entry, ix must not be less than 1: ix = _value_.  On entry, nr must not be less than 1: nr = _value_.
	17: On entry tdq = _value_ while ip + 1 = _value_. These parameters must satisfy tdq = ip + 1.  On entry tdx = _value_ while m = _value_. These parameters must satisfy tdx = m.
	19: On entry ix = _value_ while nr = _value_. These parameters must satisfy ix = nr.
	5: On entry, wt must not be less than 0.0: wt = _value_.  On entry, rss must not be less than 0.0: rss = _value_.
	70: On entry, update had an illegal value.  On entry, mean had an illegal value.
	437: On entry, for mean = Nag MeanInclude, number of non-zero values of sx must be equal to ip - 1: number of non-zero values of sx = _value_, ip - 1 = _value_.  On entry, for mean = Nag MeanZero, number of non-zero values of sx must be equal to ip: number of non-zero values of sx = _value_, ip = _value_.
	429: The rss could not be updated because the input rss was less than the calculated decrease in rss when the new observation was deleted.
	428: The R matrix could not be updated: to, either, delete non-existent observation, or, add an observation to R matrix with zero diagonal element.
	73: Memory allocation failed.
		
	successful call of the int nag_regsn_mult_linear_addrem_obs function.
	
	

*/ 
  int nag_regsn_mult_linear_addrem_obs(
    Nag_UpdateObserv update,
    Nag_IncludeMean mean,
    int m, 		// the total number of independent variables in the data set.
    int sx[], 	// indicates which of the potential independent variables are to be included in the model.
    double q[],	// array q taken from output by_nag_regsn_mult_linear 
    int tdq, 	// the last dimension of the array q. 
    int ip, 	// the number of linear terms in general linear regression model (including mean if there is one).
    double x[], // the ip values for the dependent variables of the observation to be added or deleted.
    int nr, 	// the number of rows of the notional two dimensional array x.
    int tdx, 	// the trailing dimension of the notional two dimensional array x.
    int ix, 	// the row of the two dimensional array x that contains the values for the dependent variables of the observation to be added or deleted.
    double y, 	// the value of the dependent variable for the observation to be added or deleted.
    double *wt, // an (optional) weight for a new observation.
    double *rss // the value of the residual sums of squares for the original set of observations.
  ); // Regression coefficients, standard errors and variance-covariance matrix.
  
/** g02ddc
		calculates the regression parameters for a general linear regression model. It is intended to 
		be called after nag_regsn_mult_linear_addrem_obs, nag_regsn_mult_linear_add_var or 
		nag_regsn_mult_linear_delete_var.
	

Example:
	A data set consisting of 12 observations and four independent variables is input and 
	a regression model fitted by calls to nag_regsn_mult_linear_add_var (g02dec).  The 
	parameters are then calculated by nag_regsn_mult_linear_upd_model and the results printed.
	

void test_nag_regsn_mult_linear_upd_model()
{

	double rss, tol;
	int i, ip, rank, j, m, n;
	double df;
	Boolean svd;
	char weight;
	double cov[15];
	double p[35];
	
	double b[5];
	matrix q;
	q.SetSize(12, 6);
	int success;
 	double se[5], wt[12],  xe[12];
	double *wtptr;
	n = 12;
	m = 4; 
	weight = 'u';
	if (weight=='w')
	wtptr = wt;
	else
	wtptr = NULL;
	
	matrix x = {{1.0, 0.0, 0.0, 0.0, 0}, {0.0, 0.0, 0.0, 1.0, 0},
				{0.0, 1.0, 0.0, 0.0, 0}, {0.0, 0.0, 1.0, 0.0, 0},
				{0.0, 0.0, 0.0, 1.0, 0}, {0.0, 1.0, 0.0, 0.0, 0},
				{0.0, 0.0, 0.0, 1.0, 0}, {1.0, 0.0, 0.0, 0.0, 0},
				{0.0, 0.0, 1.0, 0.0, 0}, {1.0, 0.0, 0.0, 0.0, 0},
				{0.0, 0.0, 1.0, 0.0, 0}, {0.0, 1.0, 0.0, 0.0, 0}};
	q[0][0] = 33.63;
	q[1][0] = 39.62;
	q[2][0] = 38.18;
	q[3][0] = 41.46;
	q[4][0] = 38.02;
	q[5][0] = 35.83;
	q[6][0] = 35.99;
	q[7][0] = 36.58;
	q[8][0] = 42.92;
	q[9][0] = 37.80;
	q[10][0] = 40.43;
	q[11][0] = 37.89;


	printf("\nThe input data are as follows\n");
	printf("n = 12, m = 4, wtptr = NULL, tol = 0.000001e0, tdq = 6\n");
	printf("x\n");
	for(i = 0; i < 12; i ++)
	{
		for(j = 0; j < 3; j++)
			printf("%2.1f, ",x[i][j]);
		printf("\n");
	}
	printf("q[i][0]\n");
	for(i = 0; i < 12; i++)
		printf("%4.2f, ", q[i][0]);
	
	printf("\n\nThe results are follows\n\n");
	
	tol = 0.000001e0;
	ip = 0;
	for (j=0; j<m; ++j)
	{
		for (i=0; i<n; i++)
		xe[i] = x[i][j];
		success = nag_regsn_mult_linear_add_var(n, ip, q, 6, p, wtptr, xe, &rss, tol);
		if( success == 0)
				ip += 1;
		else if (success ==NE_NVAR_NOT_IND)
			printf(" *New variable not added *\n");
		else
			printf("This function has some problem\n");
		
	}
	rss = 0.0;
	success = nag_regsn_mult_linear_upd_model(n, ip, q, 6, &rss, &df, b, se, cov, &svd,
					&rank, p, tol);
	if(success  == 0)
	{
		printf("\n");
		if (svd)
			printf("Model not of full rank\n\n");
		printf("Residual sum of squares = %12.4e\n", rss);
		printf("Degrees of freedom = %3.1f\n\n", df);

		printf("Variable       Parameter           Estimate Standard error\n\n");
		for (j=0; j<ip; j++)
			printf("%6ld%20.4e%20.4e\n", j+1, b[j], se[j]);
		printf("\n");
	}	
	else
		printf("\nThe function of g02ddc has some problem\n");


}


	The output is as follows:
	
	The input data are as follows
	n = 12, m = 4, wtptr = NULL, tol = 0.000001e0, tdq = 6
	x
	1.0, 0.0, 0.0, 
	0.0, 0.0, 0.0, 
	0.0, 1.0, 0.0, 
	0.0, 0.0, 1.0, 
	0.0, 0.0, 0.0, 
	0.0, 1.0, 0.0, 
	0.0, 0.0, 0.0, 
	1.0, 0.0, 0.0, 
	0.0, 0.0, 1.0, 
	1.0, 0.0, 0.0, 
	0.0, 0.0, 1.0, 
	0.0, 1.0, 0.0, 
	q[i][0]
	33.63, 39.62, 38.18, 41.46, 38.02, 35.83, 35.99, 36.58, 42.92, 37.80, 40.43, 37.89, 
	
	The results are follows
	
	
	Residual sum of squares =  2.2227e+001
	Degrees of freedom = 8.0
	
	Variable       Parameter           Estimate Standard error
	
    	 1         3.6003e+001         9.6235e-001
    	 2         3.7300e+001         9.6235e-001
    	 3         4.1603e+001         9.6235e-001
    	 4         3.7877e+001         9.6235e-001
    	 
Return:
	The function returns NAG error code or 0 if no error.
	
	11: On entry, n must not be less than 1: n = _value_.  On entry, ip must not be less than 1: ip = _value_.
	17: On entry tdq = _value_ while ip + 1 = _value_. These parameters must satisfy tdq = ip + 1.  On entry, n = _value_ while ip = _value_. These parameters must satisfy n = ip.
	430: The degrees of freedom for error are less than or equal to 0. In this case the estimates,