Merge pull request #140 from vais-ral/constrdiff

Edge constrained nonlinear diffusion

4 files changed, 213 insertions, 52 deletions

diff --git a/Readme.md b/Readme.md
index 13e182b..077d2f2 100644
--- a/Readme.md
+++ b/Readme.md
@@ -101,13 +101,13 @@ conda install ccpi-regulariser -c ccpi -c conda-forge
 
 #### Python (conda-build)
 ```
-	export CIL_VERSION=19.10 (Unix) / set CIL_VERSION=19.10 (Windows)
-	conda build recipe/ --numpy 1.15 --python 3.7
-	conda install ccpi-regulariser=${CIL_VERSION} --use-local --force-reinstall # doesn't work?
-	conda install -c file://${CONDA_PREFIX}/conda-bld/ ccpi-regulariser=${CIL_VERSION} --force-reinstall # try this one
-	cd demos/
-	python demo_cpu_regularisers.py # to run CPU demo
-	python demo_gpu_regularisers.py # to run GPU demo
+export CIL_VERSION=19.10.1 (Unix) / set CIL_VERSION=19.10 (Windows)
+conda build recipe/ --numpy 1.15 --python 3.7
+conda install ccpi-regulariser=${CIL_VERSION} --use-local --force-reinstall # doesn't work?
+conda install -c file://${CONDA_PREFIX}/conda-bld/ ccpi-regulariser=${CIL_VERSION} --force-reinstall # try this one
+cd demos/
+python demo_cpu_regularisers.py # to run CPU demo
+python demo_gpu_regularisers.py # to run GPU demo
 ```
 
 #### Python build
diff --git a/build/run.sh b/build/run.sh
index f0b3d3e..91c5f05 100755
--- a/build/run.sh
+++ b/build/run.sh
@@ -6,11 +6,11 @@ rm -r ../build_proj
 mkdir ../build_proj
 cd ../build_proj/
 #make clean
-export CIL_VERSION=19.10
+export CIL_VERSION=19.10.1
 # install Python modules without CUDA
 #cmake ../ -DBUILD_PYTHON_WRAPPER=ON -DBUILD_MATLAB_WRAPPER=OFF -DBUILD_CUDA=OFF -DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX=./install
 # install Python modules with CUDA
-cmake ../ -DBUILD_PYTHON_WRAPPER=ON -DBUILD_MATLAB_WRAPPER=OFF -DBUILD_CUDA=ON -DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX=./install
+ cmake ../ -DBUILD_PYTHON_WRAPPER=ON -DBUILD_MATLAB_WRAPPER=OFF -DBUILD_CUDA=ON -DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX=./install
 # install Matlab modules without CUDA
 # cmake ../ -DBUILD_PYTHON_WRAPPER=OFF -DMatlab_ROOT_DIR=/dls_sw/apps/matlab/r2014a/ -DBUILD_MATLAB_WRAPPER=ON -DBUILD_CUDA=OFF -DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX=./install
 # install Matlab modules with CUDA
diff --git a/src/Core/regularisers_CPU/Diffusion_core.c b/src/Core/regularisers_CPU/Diffusion_core.c
index f0039c7..bd23a15 100644
--- a/src/Core/regularisers_CPU/Diffusion_core.c
+++ b/src/Core/regularisers_CPU/Diffusion_core.c
@@ -38,7 +38,7 @@ int signNDFc(float x) {
  * 3. Edge-preserving parameter (sigma), when sigma equals to zero nonlinear diffusion -> linear diffusion
  * 4. Number of iterations, for explicit scheme >= 150 is recommended
  * 5. tau - time-marching step for explicit scheme
- * 6. Penalty type: 1 - Huber, 2 - Perona-Malik, 3 - Tukey Biweight
+ * 6. Penalty type: 1 - Huber, 2 - Perona-Malik, 3 - Tukey Biweight, 4 - Threshold-constrained Linear, , 5 - modified Huber with a dead stop on edge
  * 7. eplsilon - tolerance constant
  *
  * Output:
@@ -60,14 +60,14 @@ float Diffusion_CPU_main(float *Input, float *Output, float *infovector, float l
     re = 0.0f; re1 = 0.0f;
     int count = 0;
     DimTotal = (long)(dimX*dimY*dimZ);
-    
+
     if (epsil != 0.0f) Output_prev = calloc(DimTotal, sizeof(float));
-    
+
     /* copy into output */
     copyIm(Input, Output, (long)(dimX), (long)(dimY), (long)(dimZ));
-    
+
     for(i=0; i < iterationsNumb; i++) {
-        
+
         if ((epsil != 0.0f)  && (i % 5 == 0)) copyIm(Output, Output_prev, (long)(dimX), (long)(dimY), (long)(dimZ));
         if (dimZ == 1) {
             /* running 2D diffusion iterations */
@@ -93,7 +93,7 @@ float Diffusion_CPU_main(float *Input, float *Output, float *infovector, float l
             if (count > 3) break;
         }
     }
-    
+
     free(Output_prev);
     /*adding info into info_vector */
     infovector[0] = (float)(i);  /*iterations number (if stopped earlier based on tolerance)*/
@@ -109,7 +109,7 @@ float LinearDiff2D(float *Input, float *Output, float lambdaPar, float tau, long
 {
     long i,j,i1,i2,j1,j2,index;
     float e,w,n,s,e1,w1,n1,s1;
-    
+
 #pragma omp parallel for shared(Input) private(index,i,j,i1,i2,j1,j2,e,w,n,s,e1,w1,n1,s1)
     for(j=0; j<dimY; j++) {
         /* symmetric boundary conditions (Neuman) */
@@ -120,17 +120,17 @@ float LinearDiff2D(float *Input, float *Output, float lambdaPar, float tau, long
             i1 = i+1; if (i1 == dimX) i1 = i-1;
             i2 = i-1; if (i2 < 0) i2 = i+1;
             index = j*dimX+i;
-            
+
             e = Output[j*dimX+i1];
             w = Output[j*dimX+i2];
             n = Output[j1*dimX+i];
             s = Output[j2*dimX+i];
-            
+
             e1 = e - Output[index];
             w1 = w - Output[index];
             n1 = n - Output[index];
             s1 = s - Output[index];
-            
+
             Output[index] += tau*(lambdaPar*(e1 + w1 + n1 + s1) - (Output[index] - Input[index]));
         }}
     return *Output;
@@ -141,7 +141,7 @@ float NonLinearDiff2D(float *Input, float *Output, float lambdaPar, float sigmaP
 {
     long i,j,i1,i2,j1,j2,index;
     float e,w,n,s,e1,w1,n1,s1;
-    
+
 #pragma omp parallel for shared(Input) private(index,i,j,i1,i2,j1,j2,e,w,n,s,e1,w1,n1,s1)
     for(j=0; j<dimY; j++) {
         /* symmetric boundary conditions (Neuman) */
@@ -152,37 +152,37 @@ float NonLinearDiff2D(float *Input, float *Output, float lambdaPar, float sigmaP
             i1 = i+1; if (i1 == dimX) i1 = i-1;
             i2 = i-1; if (i2 < 0) i2 = i+1;
             index = j*dimX+i;
-            
+
             e = Output[j*dimX+i1];
             w = Output[j*dimX+i2];
             n = Output[j1*dimX+i];
             s = Output[j2*dimX+i];
-            
+
             e1 = e - Output[index];
             w1 = w - Output[index];
             n1 = n - Output[index];
             s1 = s - Output[index];
-            
+
             if (penaltytype == 1){
                 /* Huber penalty */
                 if (fabs(e1) > sigmaPar) e1 =  signNDFc(e1);
                 else e1 = e1/sigmaPar;
-                
+
                 if (fabs(w1) > sigmaPar) w1 =  signNDFc(w1);
                 else w1 = w1/sigmaPar;
-                
+
                 if (fabs(n1) > sigmaPar) n1 =  signNDFc(n1);
                 else n1 = n1/sigmaPar;
-                
+
                 if (fabs(s1) > sigmaPar) s1 =  signNDFc(s1);
                 else s1 = s1/sigmaPar;
             }
             else if (penaltytype == 2) {
                 /* Perona-Malik */
-                e1 = (e1)/(1.0f + powf((e1/sigmaPar),2));
-                w1 = (w1)/(1.0f + powf((w1/sigmaPar),2));
-                n1 = (n1)/(1.0f + powf((n1/sigmaPar),2));
-                s1 = (s1)/(1.0f + powf((s1/sigmaPar),2));
+                e1 /= (1.0f + powf((e1/sigmaPar),2));
+                w1 /= (1.0f + powf((w1/sigmaPar),2));
+                n1 /= (1.0f + powf((n1/sigmaPar),2));
+                s1 /= (1.0f + powf((s1/sigmaPar),2));
             }
             else if (penaltytype == 3) {
                 /* Tukey Biweight */
@@ -195,8 +195,42 @@ float NonLinearDiff2D(float *Input, float *Output, float lambdaPar, float sigmaP
                 if (fabs(s1) <= sigmaPar) s1 =  s1*powf((1.0f - powf((s1/sigmaPar),2)), 2);
                 else s1 = 0.0f;
             }
+            else if (penaltytype == 4) {
+                /* Threshold-constrained linear diffusion
+                This means that the linear diffusion will be performed on pixels with
+                absolute difference less than the threshold.
+                */
+                if (fabs(e1) > sigmaPar) e1 = 0.0f;
+                if (fabs(w1) > sigmaPar) w1 = 0.0f;
+                if (fabs(n1) > sigmaPar) n1 = 0.0f;
+                if (fabs(s1) > sigmaPar) s1 = 0.0f;
+            }
+            else if (penaltytype == 5) {
+                /*
+                Threshold constrained Huber diffusion
+                */
+                if (fabs(e1) <= 2.0f*sigmaPar) {
+                if (fabs(e1) > sigmaPar) e1 =  signNDFc(e1);
+                else e1 = e1/sigmaPar; }
+                else e1 = 0.0f;
+
+                if (fabs(w1) <= 2.0f*sigmaPar) {
+                if (fabs(w1) > sigmaPar) w1 =  signNDFc(w1);
+                else w1 = w1/sigmaPar; }
+                else w1 = 0.0f;
+
+                if (fabs(n1) <= 2.0f*sigmaPar) {
+                if (fabs(n1) > sigmaPar) n1 =  signNDFc(n1);
+                else n1 = n1/sigmaPar; }
+                else n1 = 0.0f;
+
+                if (fabs(s1) <= 2.0f*sigmaPar) {
+                if (fabs(s1) > sigmaPar) s1 =  signNDFc(s1);
+                else s1 = s1/sigmaPar; }
+                else s1 = 0.0f;
+            }
             else {
-                printf("%s \n", "No penalty function selected! Use 1,2 or 3.");
+                printf("%s \n", "No penalty function selected! Use 1,2,3,4 or 5.");
                 break;
             }
             Output[index] += tau*(lambdaPar*(e1 + w1 + n1 + s1) - (Output[index] - Input[index]));
@@ -211,7 +245,7 @@ float LinearDiff3D(float *Input, float *Output, float lambdaPar, float tau, long
 {
     long i,j,k,i1,i2,j1,j2,k1,k2,index;
     float e,w,n,s,u,d,e1,w1,n1,s1,u1,d1;
-    
+
 #pragma omp parallel for shared(Input) private(index,i,j,i1,i2,j1,j2,e,w,n,s,e1,w1,n1,s1,k,k1,k2,u1,d1,u,d)
     for(k=0; k<dimZ; k++) {
         k1 = k+1; if (k1 == dimZ) k1 = k-1;
@@ -225,21 +259,21 @@ float LinearDiff3D(float *Input, float *Output, float lambdaPar, float tau, long
                 i1 = i+1; if (i1 == dimX) i1 = i-1;
                 i2 = i-1; if (i2 < 0) i2 = i+1;
                 index = (dimX*dimY)*k + j*dimX+i;
-                
+
                 e = Output[(dimX*dimY)*k + j*dimX+i1];
                 w = Output[(dimX*dimY)*k + j*dimX+i2];
                 n = Output[(dimX*dimY)*k + j1*dimX+i];
                 s = Output[(dimX*dimY)*k + j2*dimX+i];
                 u = Output[(dimX*dimY)*k1 + j*dimX+i];
                 d = Output[(dimX*dimY)*k2 + j*dimX+i];
-                
+
                 e1 = e - Output[index];
                 w1 = w - Output[index];
                 n1 = n - Output[index];
                 s1 = s - Output[index];
                 u1 = u - Output[index];
                 d1 = d - Output[index];
-                
+
                 Output[index] += tau*(lambdaPar*(e1 + w1 + n1 + s1 + u1 + d1) - (Output[index] - Input[index]));
             }}}
     return *Output;
@@ -249,7 +283,7 @@ float NonLinearDiff3D(float *Input, float *Output, float lambdaPar, float sigmaP
 {
     long i,j,k,i1,i2,j1,j2,k1,k2,index;
     float e,w,n,s,u,d,e1,w1,n1,s1,u1,d1;
-    
+
 #pragma omp parallel for shared(Input) private(index,i,j,i1,i2,j1,j2,e,w,n,s,e1,w1,n1,s1,k,k1,k2,u1,d1,u,d)
     for(k=0; k<dimZ; k++) {
         k1 = k+1; if (k1 == dimZ) k1 = k-1;
@@ -263,38 +297,38 @@ float NonLinearDiff3D(float *Input, float *Output, float lambdaPar, float sigmaP
                 i1 = i+1; if (i1 == dimX) i1 = i-1;
                 i2 = i-1; if (i2 < 0) i2 = i+1;
                 index = (dimX*dimY)*k + j*dimX+i;
-                
+
                 e = Output[(dimX*dimY)*k + j*dimX+i1];
                 w = Output[(dimX*dimY)*k + j*dimX+i2];
                 n = Output[(dimX*dimY)*k + j1*dimX+i];
                 s = Output[(dimX*dimY)*k + j2*dimX+i];
                 u = Output[(dimX*dimY)*k1 + j*dimX+i];
                 d = Output[(dimX*dimY)*k2 + j*dimX+i];
-                
+
                 e1 = e - Output[index];
                 w1 = w - Output[index];
                 n1 = n - Output[index];
                 s1 = s - Output[index];
                 u1 = u - Output[index];
                 d1 = d - Output[index];
-                
+
                 if (penaltytype == 1){
                     /* Huber penalty */
                     if (fabs(e1) > sigmaPar) e1 =  signNDFc(e1);
                     else e1 = e1/sigmaPar;
-                    
+
                     if (fabs(w1) > sigmaPar) w1 =  signNDFc(w1);
                     else w1 = w1/sigmaPar;
-                    
+
                     if (fabs(n1) > sigmaPar) n1 =  signNDFc(n1);
                     else n1 = n1/sigmaPar;
-                    
+
                     if (fabs(s1) > sigmaPar) s1 =  signNDFc(s1);
                     else s1 = s1/sigmaPar;
-                    
+
                     if (fabs(u1) > sigmaPar) u1 =  signNDFc(u1);
                     else u1 = u1/sigmaPar;
-                    
+
                     if (fabs(d1) > sigmaPar) d1 =  signNDFc(d1);
                     else d1 = d1/sigmaPar;
                 }
@@ -322,11 +356,57 @@ float NonLinearDiff3D(float *Input, float *Output, float lambdaPar, float sigmaP
                     if (fabs(d1) <= sigmaPar) d1 =  d1*powf((1.0f - powf((d1/sigmaPar),2)), 2);
                     else d1 = 0.0f;
                 }
+                else if (penaltytype == 4) {
+                    /* Threshold-constrained linear diffusion
+                    This means that the linear diffusion will be performed on pixels with
+                    absolute difference less than the threshold.
+                    */
+                    if (fabs(e1) > sigmaPar) e1 = 0.0f;
+                    if (fabs(w1) > sigmaPar) w1 = 0.0f;
+                    if (fabs(n1) > sigmaPar) n1 = 0.0f;
+                    if (fabs(s1) > sigmaPar) s1 = 0.0f;
+                    if (fabs(u1) > sigmaPar) u1 = 0.0f;
+                    if (fabs(d1) > sigmaPar) d1 = 0.0f;
+                }
+                else if (penaltytype == 5) {
+                    /*
+                    Threshold constrained Huber diffusion
+                    */
+                    if (fabs(e1) <= 2.0f*sigmaPar) {
+                    if (fabs(e1) > sigmaPar) e1 =  signNDFc(e1);
+                    else e1 = e1/sigmaPar; }
+                    else e1 = 0.0f;
+
+                    if (fabs(w1) <= 2.0f*sigmaPar) {
+                    if (fabs(w1) > sigmaPar) w1 =  signNDFc(w1);
+                    else w1 = w1/sigmaPar; }
+                    else w1 = 0.0f;
+
+                    if (fabs(n1) <= 2.0f*sigmaPar) {
+                    if (fabs(n1) > sigmaPar) n1 =  signNDFc(n1);
+                    else n1 = n1/sigmaPar; }
+                    else n1 = 0.0f;
+
+                    if (fabs(s1) <= 2.0f*sigmaPar) {
+                    if (fabs(s1) > sigmaPar) s1 =  signNDFc(s1);
+                    else s1 = s1/sigmaPar; }
+                    else s1 = 0.0f;
+
+                    if (fabs(u1) <= 2.0f*sigmaPar) {
+                    if (fabs(u1) > sigmaPar) u1 =  signNDFc(u1);
+                    else u1 = u1/sigmaPar; }
+                    else u1 = 0.0f;
+
+                    if (fabs(d1) <= 2.0f*sigmaPar) {
+                    if (fabs(d1) > sigmaPar) d1 =  signNDFc(d1);
+                    else d1 = d1/sigmaPar; }
+                    else d1 = 0.0f;
+                }
                 else {
-                    printf("%s \n", "No penalty function selected! Use 1,2 or 3.");
+                    printf("%s \n", "No penalty function selected! Use 1,2,3,4 or 5.");
                     break;
                 }
-                
+
                 Output[index] += tau*(lambdaPar*(e1 + w1 + n1 + s1 + u1 + d1) - (Output[index] - Input[index]));
             }}}
     return *Output;
diff --git a/src/Core/regularisers_GPU/NonlDiff_GPU_core.cu b/src/Core/regularisers_GPU/NonlDiff_GPU_core.cu
index de9abd4..d7a6bac 100644
--- a/src/Core/regularisers_GPU/NonlDiff_GPU_core.cu
+++ b/src/Core/regularisers_GPU/NonlDiff_GPU_core.cu
@@ -32,7 +32,7 @@ limitations under the License.
  * 3. Edge-preserving parameter (sigma), when sigma equals to zero nonlinear diffusion -> linear diffusion
  * 4. Number of iterations, for explicit scheme >= 150 is recommended
  * 5. tau - time-marching step for explicit scheme
- * 6. Penalty type: 1 - Huber, 2 - Perona-Malik, 3 - Tukey Biweight
+ * 6. Penalty type: 1 - Huber, 2 - Perona-Malik, 3 - Tukey Biweight, 4 - Threshold-constrained Linear, 5 - modified Huber with a dead stop on edge
  * 7. eplsilon: tolerance constant
 
   * Output:
@@ -108,8 +108,8 @@ __global__ void LinearDiff2D_kernel(float *Input, float *Output, float lambdaPar
         if ((i >= 0) && (i < N) && (j >= 0) && (j < M)) {
 
             /* boundary conditions (Neumann reflections) */
-			i1 = i+1; if (i1 == N) i1 = i-1;
-			i2 = i-1; if (i2 < 0) i2 = i+1;
+			      i1 = i+1; if (i1 == N) i1 = i-1;
+			      i2 = i-1; if (i2 < 0) i2 = i+1;
             j1 = j+1; if (j1 == M) j1 = j-1;
             j2 = j-1; if (j2 < 0) j2 = j+1;
 
@@ -155,7 +155,42 @@ __global__ void LinearDiff2D_kernel(float *Input, float *Output, float lambdaPar
             if (abs(s1) <= sigmaPar) s1 =  s1*pow((1.0f - pow((s1/sigmaPar),2)), 2);
             else s1 = 0.0f;
             }
-            else printf("%s \n", "No penalty function selected! Use 1,2 or 3.");
+            else if (penaltytype == 4) {
+                /* Threshold-constrained linear diffusion
+                This means that the linear diffusion will be performed on pixels with
+                absolute difference less than the threshold.
+                */
+                if (abs(e1) > sigmaPar) e1 = 0.0f;
+                if (abs(w1) > sigmaPar) w1 = 0.0f;
+                if (abs(n1) > sigmaPar) n1 = 0.0f;
+                if (abs(s1) > sigmaPar) s1 = 0.0f;
+            }
+            else if (penaltytype == 5) {
+                /* Threshold-constrained Huber nonlinear diffusion
+                This means that the linear diffusion will be performed on pixels with
+                absolute difference less than the threshold.
+                */
+                if (abs(e1) <= 2.0f*sigmaPar) {
+                if (abs(e1) > sigmaPar) e1 =  signNDF(e1);
+                else e1 = e1/sigmaPar;}
+                else e1 = 0.0f;
+
+                if (abs(w1) <= 2.0f*sigmaPar) {
+                if (abs(w1) > sigmaPar) w1 =  signNDF(w1);
+                else w1 = w1/sigmaPar;}
+                else w1 = 0.0f;
+
+                if (abs(n1) <= 2.0f*sigmaPar) {
+                if (abs(n1) > sigmaPar) n1 =  signNDF(n1);
+                else n1 = n1/sigmaPar; }
+                else n1 = 0.0f;
+
+                if (abs(s1) <= 2.0f*sigmaPar) {
+                if (abs(s1) > sigmaPar) s1 =  signNDF(s1);
+                else s1 = s1/sigmaPar; }
+                else s1 = 0.0f;
+            }
+            else printf("%s \n", "No penalty function selected! Use 1,2,3, 4 or 5.");
 
             Output[index] += tau*(lambdaPar*(e1 + w1 + n1 + s1) - (Output[index] - Input[index]));
 		}
@@ -281,8 +316,54 @@ __global__ void NonLinearDiff3D_kernel(float *Input, float *Output, float lambda
             if (abs(d1) <= sigmaPar) d1 =  d1*pow((1.0f - pow((d1/sigmaPar),2)), 2);
             else d1 = 0.0f;
             }
-            else printf("%s \n", "No penalty function selected! Use 1,2 or 3.");
-
+            else if (penaltytype == 4) {
+                /* Threshold-constrained linear diffusion
+                This means that the linear diffusion will be performed on pixels with
+                absolute difference less than the threshold.
+                */
+                if (abs(e1) > sigmaPar) e1 = 0.0f;
+                if (abs(w1) > sigmaPar) w1 = 0.0f;
+                if (abs(n1) > sigmaPar) n1 = 0.0f;
+                if (abs(s1) > sigmaPar) s1 = 0.0f;
+                if (abs(u1) > sigmaPar) u1 = 0.0f;
+                if (abs(d1) > sigmaPar) d1 = 0.0f;
+            }
+            else if (penaltytype == 5) {
+                /* Threshold-constrained Huber nonlinear diffusion
+                This means that the linear diffusion will be performed on pixels with
+                absolute difference less than the threshold.
+                */
+                if (abs(e1) <= 2.0f*sigmaPar) {
+                if (abs(e1) > sigmaPar) e1 =  signNDF(e1);
+                else e1 = e1/sigmaPar;}
+                else e1 = 0.0f;
+
+                if (abs(w1) <= 2.0f*sigmaPar) {
+                if (abs(w1) > sigmaPar) w1 =  signNDF(w1);
+                else w1 = w1/sigmaPar;}
+                else w1 = 0.0f;
+
+                if (abs(n1) <= 2.0f*sigmaPar) {
+                if (abs(n1) > sigmaPar) n1 =  signNDF(n1);
+                else n1 = n1/sigmaPar; }
+                else n1 = 0.0f;
+
+                if (abs(s1) <= 2.0f*sigmaPar) {
+                if (abs(s1) > sigmaPar) s1 =  signNDF(s1);
+                else s1 = s1/sigmaPar; }
+                else s1 = 0.0f;
+
+                if (abs(u1) <= 2.0f*sigmaPar) {
+                if (abs(u1) > sigmaPar) u1 =  signNDF(u1);
+                else u1 = u1/sigmaPar; }
+                else u1 = 0.0f;
+
+                if (abs(d1) <= 2.0f*sigmaPar) {
+                if (abs(d1) > sigmaPar) d1 =  signNDF(d1);
+                else d1 = d1/sigmaPar; }
+                else d1 = 0.0f;
+            }
+            else printf("%s \n", "No penalty function selected! Use 1,2,3,4, or 5.");
             Output[index] += tau*(lambdaPar*(e1 + w1 + n1 + s1 + u1 + d1) - (Output[index] - Input[index]));
 		}
 	}