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RBCD3.cpp
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#include <math.h>
#include "mex.h"
#define EPSILON 2.220446e-16
/**
* RBCD size 3 with general constraints
* random choose uniformly from [d/3] blocks without overlap
**/
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
/** input args
* [1] Matrix A
* [2] Vettor b
* [3] dimension d
* [4] max iters
* [5] precision of KKT conditions
* here the lower and upper bounds are
* set by the input parameters
* if the number of inputs is 5, then it has default constraint [0,1]
* if the number of inputs is 7, then the last two are constraints
* if lower is greater than upper, then there will be no constraints
* [6] lower bound l
* [7] upper bound u
* [8] initial value of out_x
*/
// first check the number of input values
if(nrhs!=8){mexErrMsgTxt("Input Value Error"); return;}
// [1]
double *in_A;
mwIndex *irs;// for sparse matrix
mwIndex *jcs;// for sparse matrix
// [2]
double *in_b;
// [3]
long int in_d;
// [4]
long int in_max_iter;
// [5]
double in_precision;
// [6]
double lower;
// [7]
double upper;
// [8]
double in_init;
/** ouput args
* [1] the minimizer out_x
* [2] the KKT condition residual
* the length will be adjusted in the end,
* and final output is *r
*/
// [1]
double *out_x;// the minimizer
// [2]
double residual;
// parameters in the function
long int i,j,epoch;//loop
double df;//gradient in KKT residual
double RV;//random variable for RBCD
/**
* get input args
**/
// [1]
in_A = mxGetPr(prhs[0]);if(in_A==NULL){mexErrMsgTxt("pointer in_A is null"); return;}
irs = mxGetIr(prhs[0]);if(irs==NULL){mexErrMsgTxt("pointer irs is null"); return;}
jcs = mxGetJc(prhs[0]);if(jcs==NULL){mexErrMsgTxt("pointer jcs is null"); return;}
// [2]
in_b = mxGetPr(prhs[1]);if(in_b==NULL){mexErrMsgTxt("pointer in_b is null"); return;}
// [3]
in_d = mxGetScalar(prhs[2]);if(in_d<3){mexErrMsgTxt("dimension error"); return;}
// [4]
in_max_iter = mxGetScalar(prhs[3]);if(in_max_iter<=0){mexErrMsgTxt("max_iter error"); return;}
// [5]
in_precision = mxGetScalar(prhs[4]);if(in_precision<=0){mexErrMsgTxt("precision error"); return;}
// [6]
lower = mxGetScalar(prhs[5]);
// [7]
upper = mxGetScalar(prhs[6]);
// [8]
in_init = mxGetScalar(prhs[7]);
/* make sure that the upper bound is larger than the lower bound
* if the lower bound is greater,
* then we solve for an unconstrained problem
*/
if (lower>=upper){mexPrintf("Bounds Error, Results without constraints\n");}
/* if the in_init is out of the bound, set it as lower */
else if ((in_init<lower)||(in_init>upper)){mexPrintf("x_init Error, Default: lower\n");in_init=lower;}
// print begin
mexPrintf("RBCD size 3.cpp...\n");
/**
* allocate output
**/
// [1] init out_x as all in_init
plhs[0] = mxCreateDoubleMatrix(in_d,1,mxREAL);
out_x = mxGetPr(plhs[0]);if(out_x==NULL){mexErrMsgTxt("pointer out_x is null"); return;}
for (i=0;i<in_d;i++){
out_x[i] = in_init;
}
// [2] pre-allocate output of residual, length as max_iter
double* out_r=new double[in_max_iter]; if(out_r==NULL){mexErrMsgTxt("pointer out_r is null"); return;}
/**
* in-code parameters
**/
// allocate gradient, will delete later
// in the function gradient is A*x, without -b
double* grad=new double[in_d]; if(grad==NULL){mexErrMsgTxt("pointer grad is null"); return;}
/* allocate diagonal, for solving small block problem,
* diag_A0 is the main diagonal, diag_A1/2 are the one below(and above, as symmetric)
* although the length of diag_A1/2 is in_d-1/in_d-2, set them as in_d,
* the in_d th element will be 0 and not be used.
*/
double* diag_A0=new double[in_d]; if(diag_A0==NULL){mexErrMsgTxt("pointer diag_A0 is null"); return;}
double* diag_A1=new double[in_d]; if(diag_A1==NULL){mexErrMsgTxt("pointer diag_A1 is null"); return;}
double* diag_A2=new double[in_d]; if(diag_A2==NULL){mexErrMsgTxt("pointer diag_A2 is null"); return;}
/* grad and residual of init loop
* out_x is initialized as in_init
* in the loop the elements from the diagonal are also extracted
*/
// init gradient as 0s
// extract i th element in diagonal and below
for (i=0;i<in_d;i++){
grad[i]=0;
// i th element in diagonal and below
diag_A0[i]=0;
diag_A1[i]=0;
diag_A2[i]=0;
for (j=jcs[i];j<jcs[i+1];j++){
if (irs[j]==i){
diag_A0[i]=in_A[j];
}
else if (irs[j]==i+1){
diag_A1[i]=in_A[j];
}
else if (irs[j]==i+2){
diag_A2[i]=in_A[j];
}
}
}
// update gradient
for (j=0;j<in_d;j++){
for (i=jcs[j];i<jcs[j+1];i++){
grad[irs[i]] += in_A[i]*in_init;
}
}
// get the residual of KKT condition
residual = 0;
// if with constraints
if (lower<upper){
for (i=0;i<in_d;i++){
// i th residual
df = grad[i]-in_b[i];
if (in_init<=lower+2*EPSILON){
if (df<0){
residual += df*df;
}
}
else if (in_init>=upper-2*EPSILON){
if (df>0){
residual += df*df;
}
}
else {
residual += df*df;
}
}
}
// if without constraints
else{
for (i=0;i<in_d;i++){
// i th residual
df = grad[i]-in_b[i];
residual += df*df;
}
}
residual = sqrt(residual);
out_r[0] = residual;
mexPrintf("init: 0, residual=%.15f\n",residual);
epoch=1;
// parameters for size 3 matrix
double a11,a12,a13,a21,a22,a23,a31,a32,a33;
double b1,b2,b3,x1,x2,x3,detA;
// FLAG stores the label of last choice of each block
int FLAG;
// labels stores the last choice of all the blocks in last epoch
long int* labels=new long int[in_d]; if(labels==NULL){mexErrMsgTxt("pointer labels is null"); return;} ;
for (i=0;i<in_d;i++){
labels[i]=0;
}
/* if the bounds are defined, and lower<upper
* we take them as [lower,upper]
* then do the following
*/
if (lower<upper){
while ((residual>in_precision)&&(epoch<in_max_iter)){
// KKT condition is calculated every in_d/2 updates, i.e. one epoch
for (long int loop_number=0;loop_number<in_d/3;loop_number++){
// get the random index, in the range of [0,in_d-3]
// i=[0,3,6,9....]
RV = ((double)rand())/((double)RAND_MAX+1.0);
i= 3 * (int) (RV*(in_d/3.0));
if (i<in_d-2){
// calc temporal grad
// sparse g=g-A(:,i)*x(i) and i+1
// three for loops to reuse current memory
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] -= in_A[j]*out_x[i];
}
for (j=jcs[i+1];j<jcs[i+2];j++){
grad[irs[j]] -= in_A[j]*out_x[i+1];
}
for (j=jcs[i+2];j<jcs[i+3];j++){
grad[irs[j]] -= in_A[j]*out_x[i+2];
}
// update x(i)
// define size 3 block
a11=diag_A0[i ]; a12=diag_A1[i ]; a13=diag_A2[i ];
a21=diag_A1[i ]; a22=diag_A0[i+1]; a23=diag_A1[i+1];
a31=diag_A2[i ]; a32=diag_A1[i+1]; a33=diag_A0[i+2];
b1 =in_b[i] -grad[i];
b2 =in_b[i+1]-grad[i+1];
b3 =in_b[i+2]-grad[i+2];
// decission tree
FLAG = labels[i];
switch (FLAG){
case 1: {
if (b1<=(a11+a12+a13)*lower && b2<=(a21+a22+a23)*lower && b3<=(a31+a32+a33)*lower){
out_x[i] =lower;
out_x[i+1]=lower;
out_x[i+2]=lower;
FLAG=1;
}
else {FLAG=0;}
break;
}
case 2: {
if (b1<=(a11+a12)*lower+a13*upper && b2<=(a21+a22)*lower+a23*upper && b3>=(a31+a32)*lower+a33*upper){
out_x[i] =lower;
out_x[i+1]=lower;
out_x[i+2]=upper;
FLAG=2;
}
else {FLAG=0;}
break;
}
case 3: {
if (b1<=(a11+a13)*lower+a12*upper && b2>=(a21+a23)*lower+a22*upper && b3<=(a31+a33)*lower+a32*upper){
out_x[i] =lower;
out_x[i+1]=upper;
out_x[i+2]=lower;
FLAG=3;
}
else {FLAG=0;}
break;
}
case 4: {
if (b1<=a11*lower+(a12+a13)*upper && b2>=a21*lower+(a22+a23)*upper && b3>=a31*lower+(a32+a33)*upper){
out_x[i] =lower;
out_x[i+1]=upper;
out_x[i+2]=upper;
FLAG=4;
}
else {FLAG=0;}
break;
}
case 5: {
if (b1>=a11*upper+(a12+a13)*lower && b2<=a21*upper+(a22+a23)*lower && b3<=a31*upper+(a32+a33)*lower){
out_x[i] =upper;
out_x[i+1]=lower;
out_x[i+2]=lower;
FLAG=5;
}
else {FLAG=0;}
break;
}
case 6: {
if (b1>=(a11+a12)*upper+a13*lower && b2>=(a21+a22)*upper+a23*lower && b3<=(a31+a32)*upper+a33*lower){
out_x[i] =upper;
out_x[i+1]=upper;
out_x[i+2]=lower;
FLAG=7;
}
else {FLAG=0;}
break;
}
case 7: {
if (b1>=(a11+a12)*upper+a13*lower && b2>=(a21+a22)*upper+a23*lower && b3<=(a31+a32)*upper+a33*lower){
out_x[i] =upper;
out_x[i+1]=upper;
out_x[i+2]=lower;
FLAG=7;
}
else {FLAG=0;}
break;
}
case 8: {
if (b1>=(a11+a12+a13)*upper && b2>=(a21+a22+a23)*upper && b3>=(a31+a32+a33)*upper){
out_x[i] =upper;
out_x[i+1]=upper;
out_x[i+2]=upper;
FLAG=8;
}
else {FLAG=0;}
break;
}
case 9: {
x3 = (b3-(a31+a32)*lower)/a33;
if (x3>=lower && x3<=upper && (a11+a12)*lower+a13*x3>=b1 && (a21+a22)*lower+a23*x3>=b2){
out_x[i] =lower;
out_x[i+1]=lower;
out_x[i+2]=x3;
FLAG=9;
}
else {FLAG=0;}
break;
}
case 10: {
x2 = (b2-(a21+a23)*lower)/a22;
if (x2>=lower && x2<=upper && (a11+a13)*lower+a12*x2>=b1 && (a31+a33)*lower+a32*x2>=b3){
out_x[i] =lower;
out_x[i+1]=x2;
out_x[i+2]=lower;
FLAG=10;
}
else {FLAG=0;}
break;
}
case 11: {
x1 = (b1-(a12+a13)*lower)/a11;
if (x1>=lower && x1<=upper && (a22+a23)*lower+a21*x1>=b2 && (a32+a33)*lower+a31*x1>=b3){
out_x[i] =x1;
out_x[i+1]=lower;
out_x[i+2]=lower;
FLAG=11;
}
else {FLAG=0;}
break;
}
case 12: {
x1=(b1-(a12+a13)*upper)/a11;
if (x1>=lower && x1<=upper && a21*x1+(a22+a23)*upper<=b2 && a31*x1+(a32+a33)*upper<=b3){
out_x[i] =x1;
out_x[i+1]=upper;
out_x[i+2]=upper;
FLAG=12;
}
else {FLAG=0;}
break;
}
case 13: {
x2=(b2-(a21+a23)*upper)/a22;
if (x2>=lower && x2<=upper && (a11+a13)*upper+a12*x2<=b1 && (a31+a33)*upper+a32*x2<=b3){
out_x[i] =upper;
out_x[i+1]=x2;
out_x[i+2]=upper;
FLAG=13;
}
else {FLAG=0;}
break;
}
case 14: {
x3=(b3-(a31+a32)*upper)/a33;
if (x3>=lower && x3<=upper && (a11+a12)*upper+a13*x3<=b1 && (a21+a22)*upper+a23*x3<=b2){
out_x[i] =upper;
out_x[i+1]=upper;
out_x[i+2]=x3;
FLAG=14;
}
else {FLAG=0;}
break;
}
case 15: {
x1=(b1-a12*lower-a13*upper)/a11;
if (x1>=lower && x1<=upper && a21*x1+a22*lower+a23*upper>=b2 && a31*x1+a32*lower+a33*upper<=b3){
out_x[i] =x1;
out_x[i+1]=lower;
out_x[i+2]=upper;
FLAG=15;
}
else {FLAG=0;}
break;
}
case 16: {
x1 = (b1-a12*upper-a13*lower)/a11;
if (x1>=lower && x1<=upper && a21*x1+a22*upper+a23*lower<=b2 && a31*x1+a32*upper+a33*lower>=b3){
out_x[i] =x1;
out_x[i+1]=upper;
out_x[i+2]=lower;
FLAG=16;
}
else {FLAG=0;}
break;
}
case 17: {
x2 = (b2-a23*upper-a21*lower)/a22;
if (x2>=lower && x2<=upper && a12*x2+a13*upper+a11*lower>=b1 && a32*x2+a33*upper+a31*lower<=b3){
out_x[i] =lower;
out_x[i+1]=x2;
out_x[i+2]=upper;
FLAG=17;
}
else {FLAG=0;}
break;
}
case 18: {
x2=(b2-a21*upper-a23*lower)/a22;
if (x2>=lower && x2<=upper && a11*upper+a13*lower+a12*x2<=b1 && a31*upper+a33*lower+a32*x2>=b3){
out_x[i] =upper;
out_x[i+1]=x2;
out_x[i+2]=lower;
FLAG=18;
}
else {FLAG=0;}
break;
}
case 19: {
x3=(b3-a32*upper-a31*lower)/a33;
if (x3>=lower && x3<=upper && a11*lower+a12*upper+a13*x3>=b1 && a21*lower+a22*upper+a23*x3<=b2){
out_x[i] =lower;
out_x[i+1]=upper;
out_x[i+2]=x3;
FLAG=19;
}
else {FLAG=0;}
break;
}
case 20: {
x3=(b3-a31*upper-a32*lower)/a33;
if (x3>=lower && x3<=upper && a11*upper+a12*lower+a13*x3<=b1 && a21*upper+a22*lower+a23*x3>=b2){
out_x[i] =upper;
out_x[i+1]=lower;
out_x[i+2]=x3;
FLAG=20;
}
else {FLAG=0;}
break;
}
case 21: {
detA = a22*a33-a23*a32;
x2 = (a33*(b2-a21*lower)-a23*(b3-a31*lower))/detA;
x3 = (a22*(b3-a31*lower)-a32*(b2-a21*lower))/detA;
if (x2>=lower && x2<=upper && x3>=lower && x3<=upper && a11*lower+a12*x2+a13*x3>=b1){
out_x[i] =lower;
out_x[i+1]=x2;
out_x[i+2]=x3;
FLAG=21;
}
else {FLAG=0;}
break;
}
case 22: {
detA = a22*a33-a23*a32;
x2 = (a33*(b2-a21*upper)-a23*(b3-a31*upper))/detA;
x3 = (a22*(b3-a31*upper)-a32*(b2-a21*upper))/detA;
if (x2>=lower && x2<=upper && x3>=lower && x3<=upper && a11*upper+a12*x2+a13*x3<=b1){
out_x[i] =upper;
out_x[i+1]=x2;
out_x[i+2]=x3;
FLAG=22;
}
else {FLAG=0;}
break;
}
case 23: {
detA = a11*a33-a13*a31;
x1 = (a33*(b1-a12*lower)-a13*(b3-a32*lower))/detA;
x3 = (a11*(b3-a32*lower)-a31*(b1-a12*lower))/detA;
if (x1>=lower && x1<=upper && x3>=lower && x3<=upper && a22*lower+a21*x1+a23*x3>=b2){
out_x[i] =x1;
out_x[i+1]=lower;
out_x[i+2]=x3;
FLAG=23;
}
else {FLAG=0;}
break;
}
case 24: {
detA = a11*a33-a13*a31;
x1 = (a33*(b1-a12*upper)-a13*(b3-a32*upper))/detA;
x3 = (a11*(b3-a32*upper)-a31*(b1-a12*upper))/detA;
if (x1>=lower && x1<=upper && x3>=lower && x3<=upper && a21*x1+a22*upper+a23*x3<=b2){
out_x[i] =x1;
out_x[i+1]=upper;
out_x[i+2]=x3;
FLAG=24;
}
else {FLAG=0;}
break;
}
case 25: {
detA = a11*a22-a12*a21;
x1 = (a22*(b1-a13*lower)-a12*(b2-a23*lower))/detA;
x2 = (a11*(b2-a23*lower)-a21*(b1-a13*lower))/detA;
if (x1>=lower && x1<=upper && x2>=lower && x2<=upper && a31*x1+a32*x2+a33*lower>=b3){
out_x[i] =x1;
out_x[i+1]=x2;
out_x[i+2]=lower;
FLAG=25;
}
else {FLAG=0;}
break;
}
case 26: {
detA = a11*a22-a12*a21;
x1 = (a22*(b1-a13*upper)-a12*(b2-a23*upper))/detA;
x2 = (a11*(b2-a23*upper)-a21*(b1-a13*upper))/detA;
if (x1>=lower && x1<=upper && x2>=lower && x2<=upper && a31*x1+a32*x2+a33*upper<=b3){
out_x[i] =x1;
out_x[i+1]=x2;
out_x[i+2]=upper;
FLAG=26;
}
else {FLAG=0;}
break;
}
case 27: {
detA = a11*a22*a33+a21*a32*a13+a31*a12*a23-a11*a32*a23-a22*a13*a31-a33*a12*a21;
if(detA==0){mexErrMsgTxt("Input Matrix is not positive definite"); return;}
x1 = ( (a22*a33-a32*a23)*b1-(a12*a33-a32*a13)*b2+(a12*a23-a22*a13)*b3)/detA;
x2 = (-(a21*a33-a31*a23)*b1+(a11*a33-a31*a13)*b2-(a11*a23-a21*a13)*b3)/detA;
x3 = ( (a21*a32-a31*a22)*b1-(a11*a32-a31*a12)*b2+(a11*a22-a21*a12)*b3)/detA;
if (x1>=lower && x1<=upper && x2>=lower && x2<=upper && x3>=lower && x3<=upper){
out_x[i] =x1;
out_x[i+1]=x2;
out_x[i+2]=x3;
FLAG=27;
}
else {FLAG=0;}
break;
}
}
// if the last choice does not match this time, 27 cases again
if (FLAG==0){
// first discuss three lower or upper, 8 cases
if (b1<=(a11+a12+a13)*lower && b2<=(a21+a22+a23)*lower && b3<=(a31+a32+a33)*lower){
out_x[i] =lower;
out_x[i+1]=lower;
out_x[i+2]=lower;
FLAG=1;
}
else if (b1<=(a11+a12)*lower+a13*upper && b2<=(a21+a22)*lower+a23*upper && b3>=(a31+a32)*lower+a33*upper){
out_x[i] =lower;
out_x[i+1]=lower;
out_x[i+2]=upper;
FLAG=2;
}
else if (b1<=(a11+a13)*lower+a12*upper && b2>=(a21+a23)*lower+a22*upper && b3<=(a31+a33)*lower+a32*upper){
out_x[i] =lower;
out_x[i+1]=upper;
out_x[i+2]=lower;
FLAG=3;
}
else if (b1<=a11*lower+(a12+a13)*upper && b2>=a21*lower+(a22+a23)*upper && b3>=a31*lower+(a32+a33)*upper){
out_x[i] =lower;
out_x[i+1]=upper;
out_x[i+2]=upper;
FLAG=4;
}
else if (b1>=a11*upper+(a12+a13)*lower && b2<=a21*upper+(a22+a23)*lower && b3<=a31*upper+(a32+a33)*lower){
out_x[i] =upper;
out_x[i+1]=lower;
out_x[i+2]=lower;
FLAG=5;
}
else if (b1>=(a11+a13)*upper+a12*lower && b2<=(a21+a23)*upper+a22*lower && b3>=(a31+a33)*upper+a32*lower){
out_x[i] =upper;
out_x[i+1]=lower;
out_x[i+2]=upper;
FLAG=6;
}
else if (b1>=(a11+a12)*upper+a13*lower && b2>=(a21+a22)*upper+a23*lower && b3<=(a31+a32)*upper+a33*lower){
out_x[i] =upper;
out_x[i+1]=upper;
out_x[i+2]=lower;
FLAG=7;
}
else if (b1>=(a11+a12+a13)*upper && b2>=(a21+a22+a23)*upper && b3>=(a31+a32+a33)*upper){
out_x[i] =upper;
out_x[i+1]=upper;
out_x[i+2]=upper;
FLAG=8;
}
// second discuss two lower and two upper, 6 cases
if (FLAG==0){
x3 = (b3-(a31+a32)*lower)/a33;
if (x3>=lower && x3<=upper && (a11+a12)*lower+a13*x3>=b1 && (a21+a22)*lower+a23*x3>=b2){
out_x[i] =lower;
out_x[i+1]=lower;
out_x[i+2]=x3;
FLAG=9;
}
if (FLAG==0){
x2 = (b2-(a21+a23)*lower)/a22;
if (x2>=lower && x2<=upper && (a11+a13)*lower+a12*x2>=b1 && (a31+a33)*lower+a32*x2>=b3){
out_x[i] =lower;
out_x[i+1]=x2;
out_x[i+2]=lower;
FLAG=10;
}
if (FLAG==0){
x1 = (b1-(a12+a13)*lower)/a11;
if (x1>=lower && x1<=upper && (a22+a23)*lower+a21*x1>=b2 && (a32+a33)*lower+a31*x1>=b3){
out_x[i] =x1;
out_x[i+1]=lower;
out_x[i+2]=lower;
FLAG=11;
}
if (FLAG==0){
x1=(b1-(a12+a13)*upper)/a11;
if (x1>=lower && x1<=upper && a21*x1+(a22+a23)*upper<=b2 && a31*x1+(a32+a33)*upper<=b3){
out_x[i] =x1;
out_x[i+1]=upper;
out_x[i+2]=upper;
FLAG=12;
}
if (FLAG==0){
x2=(b2-(a21+a23)*upper)/a22;
if (x2>=lower && x2<=upper && (a11+a13)*upper+a12*x2<=b1 && (a31+a33)*upper+a32*x2<=b3){
out_x[i] =upper;
out_x[i+1]=x2;
out_x[i+2]=upper;
FLAG=13;
}
if (FLAG==0){
x3=(b3-(a31+a32)*upper)/a33;
if (x3>=lower && x3<=upper && (a11+a12)*upper+a13*x3<=b1 && (a21+a22)*upper+a23*x3<=b2){
out_x[i] =upper;
out_x[i+1]=upper;
out_x[i+2]=x3;
FLAG=14;
}
}
}
}
}
}
}
// third discuss one lower and one upper
if (FLAG==0){
x1=(b1-a12*lower-a13*upper)/a11;
if (x1>=lower && x1<=upper && a21*x1+a22*lower+a23*upper>=b2 && a31*x1+a32*lower+a33*upper<=b3){
out_x[i] =x1;
out_x[i+1]=lower;
out_x[i+2]=upper;
FLAG=15;
}
if (FLAG==0){
x1 = (b1-a12*upper-a13*lower)/a11;
if (x1>=lower && x1<=upper && a21*x1+a22*upper+a23*lower<=b2 && a31*x1+a32*upper+a33*lower>=b3){
out_x[i] =x1;
out_x[i+1]=upper;
out_x[i+2]=lower;
FLAG=16;
}
if (FLAG==0){
x2 = (b2-a23*upper-a21*lower)/a22;
if (x2>=lower && x2<=upper && a12*x2+a13*upper+a11*lower>=b1 && a32*x2+a33*upper+a31*lower<=b3){
out_x[i] =lower;
out_x[i+1]=x2;
out_x[i+2]=upper;
FLAG=17;
}
if (FLAG==0){
x2=(b2-a21*upper-a23*lower)/a22;
if (x2>=lower && x2<=upper && a11*upper+a13*lower+a12*x2<=b1 && a31*upper+a33*lower+a32*x2>=b3){
out_x[i] =upper;
out_x[i+1]=x2;
out_x[i+2]=lower;
FLAG=18;
}
if (FLAG==0){
x3=(b3-a32*upper-a31*lower)/a33;
if (x3>=lower && x3<=upper && a11*lower+a12*upper+a13*x3>=b1 && a21*lower+a22*upper+a23*x3<=b2){
out_x[i] =lower;
out_x[i+1]=upper;
out_x[i+2]=x3;
FLAG=19;
}
if (FLAG==0){
x3=(b3-a31*upper-a32*lower)/a33;
if (x3>=lower && x3<=upper && a11*upper+a12*lower+a13*x3<=b1 && a21*upper+a22*lower+a23*x3>=b2){
out_x[i] =upper;
out_x[i+1]=lower;
out_x[i+2]=x3;
FLAG=20;
}
}
}
}
}
}
}
// fourth discuss one 1 or one 0
if (FLAG==0){
detA = a22*a33-a23*a32;
x2 = (a33*(b2-a21*lower)-a23*(b3-a31*lower))/detA;
x3 = (a22*(b3-a31*lower)-a32*(b2-a21*lower))/detA;
if (x2>=lower && x2<=upper && x3>=lower && x3<=upper && a11*lower+a12*x2+a13*x3>=b1){
out_x[i] =lower;
out_x[i+1]=x2;
out_x[i+2]=x3;
FLAG=21;
}
if (FLAG==0){
x2 = (a33*(b2-a21*upper)-a23*(b3-a31*upper))/detA;
x3 = (a22*(b3-a31*upper)-a32*(b2-a21*upper))/detA;
if (x2>=lower && x2<=upper && x3>=lower && x3<=upper && a11*upper+a12*x2+a13*x3<=b1){
out_x[i] =upper;
out_x[i+1]=x2;
out_x[i+2]=x3;
FLAG=22;
}
if (FLAG==0){
detA = a11*a33-a13*a31;
x1 = (a33*(b1-a12*lower)-a13*(b3-a32*lower))/detA;
x3 = (a11*(b3-a32*lower)-a31*(b1-a12*lower))/detA;
if (x1>=lower && x1<=upper && x3>=lower && x3<=upper && a22*lower+a21*x1+a23*x3>=b2){
out_x[i] =x1;
out_x[i+1]=lower;
out_x[i+2]=x3;
FLAG=23;
}
if (FLAG==0){
x1 = (a33*(b1-a12*upper)-a13*(b3-a32*upper))/detA;
x3 = (a11*(b3-a32*upper)-a31*(b1-a12*upper))/detA;
if (x1>=lower && x1<=upper && x3>=lower && x3<=upper && a21*x1+a22*upper+a23*x3<=b2){
out_x[i] =x1;
out_x[i+1]=upper;
out_x[i+2]=x3;
FLAG=24;
}
if (FLAG==0){
detA = a11*a22-a12*a21;
x1 = (a22*(b1-a13*lower)-a12*(b2-a23*lower))/detA;
x2 = (a11*(b2-a23*lower)-a21*(b1-a13*lower))/detA;
if (x1>=lower && x1<=upper && x2>=lower && x2<=upper && a31*x1+a32*x2+a33*lower>=b3){
out_x[i] =x1;
out_x[i+1]=x2;
out_x[i+2]=lower;
FLAG=25;
}
if (FLAG==0){
x1 = (a22*(b1-a13*upper)-a12*(b2-a23*upper))/detA;
x2 = (a11*(b2-a23*upper)-a21*(b1-a13*upper))/detA;
if (x1>=lower && x1<=upper && x2>=lower && x2<=upper && a31*x1+a32*x2+a33*upper<=b3){
out_x[i] =x1;
out_x[i+1]=x2;
out_x[i+2]=upper;
FLAG=26;
}
}
}
}
}
}
}
// last case, no 0 or 1
if (FLAG==0){
// solve 3 dim linear system
detA = a11*a22*a33+a21*a32*a13+a31*a12*a23-a11*a32*a23-a22*a13*a31-a33*a12*a21;
x1 = ( (a22*a33-a32*a23)*b1-(a12*a33-a32*a13)*b2+(a12*a23-a22*a13)*b3)/detA;
x2 = (-(a21*a33-a31*a23)*b1+(a11*a33-a31*a13)*b2-(a11*a23-a21*a13)*b3)/detA;
x3 = ( (a21*a32-a31*a22)*b1-(a11*a32-a31*a12)*b2+(a11*a22-a21*a12)*b3)/detA;
if (x1>=lower && x1<=upper && x2>=lower && x2<=upper && x3>=lower && x3<=upper){
out_x[i] =x1;
out_x[i+1]=x2;
out_x[i+2]=x3;
FLAG=27;
}
else {
mexPrintf("no update, check code\n");
}
}
}
// update the labels of blocks
labels[i] = FLAG;
// update temporal grad
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] += in_A[j]*out_x[i];
}
for (j=jcs[i+1];j<jcs[i+2];j++){
grad[irs[j]] += in_A[j]*out_x[i+1];
}
for (j=jcs[i+2];j<jcs[i+3];j++){
grad[irs[j]] += in_A[j]*out_x[i+2];
}
}
else if (i==in_d-1){
// calc temporal grad
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] -= in_A[j]*out_x[i];
}
// descent
out_x[i] = (in_b[i]-grad[i])/diag_A0[i];
// bounds
if (out_x[i]>upper){
out_x[i] = upper;
}
if (out_x[i]<lower){
out_x[i] = lower;
}
// update temporal grad
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] += in_A[j]*out_x[i];
}
}
else if (i==in_d-2){
// calc temporal grad
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] -= in_A[j]*out_x[i];
}
// descent
out_x[i] = (in_b[i]-grad[i])/diag_A0[i];
// bounds
if (out_x[i]>upper){
out_x[i] = upper;
}
if (out_x[i]<lower){
out_x[i] = lower;
}
// update temporal grad
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] += in_A[j]*out_x[i];
}
i++;
// calc temporal grad
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] -= in_A[j]*out_x[i];
}
// descent
out_x[i] = (in_b[i]-grad[i])/diag_A0[i];
// bounds
if (out_x[i]>upper){
out_x[i] = upper;
}
if (out_x[i]<lower){
out_x[i] = lower;
}
// update temporal grad
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] += in_A[j]*out_x[i];
}
}
}
//get the residual
residual = 0;
for (i=0;i<in_d;i++){
// i th residual
df = grad[i]-in_b[i];
if (out_x[i]<=lower+2*EPSILON){
if (df<0){
residual += df*df;
}
}
else if (out_x[i]>=upper-2*EPSILON){
if (df>0){
residual += df*df;
}
}
else {
residual += df*df;
}
}
residual = sqrt(residual);
out_r[epoch] = residual;
epoch++;
}
}
/* if the bounds are defined, but lower>=upper
* we take them as unconstrained
* then do the following
*/
else if (lower>=upper){
while ((residual>in_precision)&&(epoch<in_max_iter)){
// KKT condition is calculated every in_d/2 updates, i.e. one epoch
for (long int loop_number=0;loop_number<in_d/3;loop_number++){
// get the random index, in the range of [0,in_d-3]
// i=[0,3,6,9....]
RV = ((double)rand())/((double)RAND_MAX+1.0);
i= 3 * (int) (RV*(in_d/3.0));
if (i<in_d-2){
// calc temporal grad
// sparse g=g-A(:,i)*x(i) and i+1, i+2
for (j=jcs[i ];j<jcs[i+1];j++){
grad[irs[j]] -= in_A[j]*out_x[i];
}
for (j=jcs[i+1];j<jcs[i+2];j++){
grad[irs[j]] -= in_A[j]*out_x[i+1];
}
for (j=jcs[i+2];j<jcs[i+3];j++){
grad[irs[j]] -= in_A[j]*out_x[i+2];
}
// update x(i)
// define size 3 block
a11=diag_A0[i ]; a12=diag_A1[i ]; a13=diag_A2[i ];
a21=diag_A1[i ]; a22=diag_A0[i+1]; a23=diag_A1[i+1];
a31=diag_A2[i ]; a32=diag_A1[i+1]; a33=diag_A0[i+2];
b1 =in_b[i] -grad[i];
b2 =in_b[i+1]-grad[i+1];
b3 =in_b[i+2]-grad[i+2];
// solve 3 dim linear system
detA = a11*a22*a33+a21*a32*a13+a31*a12*a23-a11*a32*a23-a22*a13*a31-a33*a12*a21;
if(detA==0){mexErrMsgTxt("Input Matrix is not positive definite"); return;}
out_x[i ] = ( (a22*a33-a32*a23)*b1-(a12*a33-a32*a13)*b2+(a12*a23-a22*a13)*b3)/detA;
out_x[i+1] = (-(a21*a33-a31*a23)*b1+(a11*a33-a31*a13)*b2-(a11*a23-a21*a13)*b3)/detA;
out_x[i+2] = ( (a21*a32-a31*a22)*b1-(a11*a32-a31*a12)*b2+(a11*a22-a21*a12)*b3)/detA;
// update temporal grad
for (j=jcs[i ];j<jcs[i+1];j++){
grad[irs[j]] += in_A[j]*out_x[i];
}
for (j=jcs[i+1];j<jcs[i+2];j++){
grad[irs[j]] += in_A[j]*out_x[i+1];
}
for (j=jcs[i+2];j<jcs[i+3];j++){
grad[irs[j]] += in_A[j]*out_x[i+2];
}
}
else if (i==in_d-1){
// calc temporal grad
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] -= in_A[j]*out_x[i];
}
// descent
// without bounds
out_x[i] = (in_b[i]-grad[i])/diag_A0[i];
// update temporal grad
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] += in_A[j]*out_x[i];
}
}
else if (i==in_d-2){
// calc temporal grad
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] -= in_A[j]*out_x[i];
}
// descent
// without bounds
out_x[i] = (in_b[i]-grad[i])/diag_A0[i];
// update temporal grad
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] += in_A[j]*out_x[i];
}
i++;
// calc temporal grad
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] -= in_A[j]*out_x[i];
}
// descent
// without bounds
out_x[i] = (in_b[i]-grad[i])/diag_A0[i];
// update temporal grad, actually not needed
for (j=jcs[i];j<jcs[i+1];j++){
grad[irs[j]] += in_A[j]*out_x[i];
}
}
}
// get the residual
residual = 0;
for (i=0;i<in_d;i++){
// i th residual
df = grad[i]-in_b[i];
residual += df*df;
}
residual = sqrt(residual);
out_r[epoch] = residual;
epoch++;
}
}
plhs[1] = mxCreateDoubleMatrix(epoch,1,mxREAL);
double *r = mxGetPr(plhs[1]);if(r==NULL){mexErrMsgTxt("pointer r is null"); return;}
for (i=0;i<epoch;i++){
r[i]=out_r[i];
}
delete [] grad; delete [] out_r; delete [] diag_A0;
delete [] diag_A1; delete [] diag_A2;delete [] labels;
mexPrintf("epoch:%5d, residual=%.15f\nEnd of RBCD size 3.cpp\n",epoch-1,residual);
}