ENH: Allow `Splinterpolator` instances to be created from an existing set of spline coefficients, and extend extrapolation options

• The Splinterpolator class can now accept a pointer to an array of pre-calculated coefficients - in this case, a copy of the pointer is used (the data is not copied), and pre-filtering (coefficient calculation) is skipped
• New SoftZeros extrapolation method - out of bounds coefficients will be set to zero, but out-of-bounds coordinates will still be constructed via interpolation. This differs from the existing Zeros extrapolation method, where out-of-bounds coordinates are forced to zero.
• Adjustment to the coefficient initialisation method used when Constant extrapolation is requested; previously, a mirroring boundary condition was used.
• New Splinterpolator::Copy function, which allows the spline coefficients to be copied/extracted.

splinterpolator.h

@@ -22,7 +22,14 @@
 
 namespace SPLINTERPOLATOR {
 
-enum ExtrapolationType {Zeros, Constant, Mirror, Periodic};
+// Controls how the field behaves outside of the FOV:
+//  - Zeros:     Out-of-bounds coordinates are set to zero
+//  - Constant:  Out-of-bounds coordinates are set to the boundary voxels
+//  - Mirror:    The field is mirrored in all directions
+//  - Periodic:  The field is repeated in all directions
+//  - SoftZeros: The field boundary is set to zero, but out-of-bounds voxels
+//               are calculated via interpolation
+enum ExtrapolationType {Zeros, Constant, Mirror, Periodic, SoftZeros};
 
 class SplinterpolatorException: public std::exception
 {
@@ -657,27 +664,35 @@ double Splinterpolator<T>::value_at(const double *coord) const
 
   double       iwgt[8], jwgt[8], kwgt[8], lwgt[8], mwgt[8];
   double       *wgts[] = {iwgt, jwgt, kwgt, lwgt, mwgt};
+  int          start_inds[5];
   int          inds[5];
   unsigned int ni = 0;
   const T      *cptr = coef_ptr();
 
-  ni = get_start_indicies(coord,inds);
-  get_wgts(coord,inds,wgts);
+  ni = get_start_indicies(coord,start_inds);
+  get_wgts(coord,start_inds,wgts);
 
   double val=0.0;
   for (unsigned int m=0, me=(_ndim>4)?ni:1; m<me; m++) {
+    inds[4] = start_inds[4] + m;
+
     for (unsigned int l=0, le=(_ndim>3)?ni:1; l<le; l++) {
+      inds[3] = start_inds[3] + l;
+
       for (unsigned int k=0, ke=(_ndim>2)?ni:1; k<ke; k++) {
+        inds[2] = start_inds[2] + k;
         double wgt1 = wgts[4][m]*wgts[3][l]*wgts[2][k];
-        unsigned int linear1 = indx2linear(inds[2]+k,inds[3]+l,inds[4]+m);
+
         for (unsigned int j=0, je=(_ndim>1)?ni:1; j<je; j++) {
+          inds[1] = start_inds[1] + j;
           double wgt2 = wgt1*wgts[1][j];
-          int linear2 = add2linear(linear1,inds[1]+j);
-          double *iiwgt=iwgt;
+          double *iiwgt = iwgt;
+
           for (unsigned int i=0; i<ni; i++, iiwgt++) {
-	    val += cptr[linear2+indx2indx(inds[0]+i,0)]*(*iiwgt)*wgt2;
+            inds[0] = start_inds[0] + i;
+            val += coef(inds) * (*iiwgt) * wgt2;
           }
-	}
+        }
       }
     }
   }
@@ -696,9 +711,9 @@ double Splinterpolator<T>::value_at(const double *coord) const
 
 template<class T>
 double Splinterpolator<T>::value_and_derivatives_at(const double       *coord,
-						    const unsigned int *deriv,
-						    double             *dval)
-const
+                                                    const unsigned int *deriv,
+                                                    double             *dval)
+  const
 {
   if (should_be_zero(coord)) { memset(dval,0,n_nonzero(deriv)*sizeof(double)); return(0.0); }
 
@@ -708,38 +723,47 @@ const
   double       *dwgts[] = {diwgt, djwgt, dkwgt, dlwgt, dmwgt};
   double       dwgt1[5];
   double       dwgt2[5];
+  int          start_inds[5];
   int          inds[5];
   unsigned int dd[5];
   unsigned int nd = 0;
   unsigned int ni = 0;
   const T      *cptr = coef_ptr();
 
-  ni = get_start_indicies(coord,inds);
-  get_wgts(coord,inds,wgts);
-  get_dwgts(coord,inds,deriv,dwgts);
+  ni = get_start_indicies(coord,start_inds);
+  get_wgts(coord,start_inds,wgts);
+  get_dwgts(coord,start_inds,deriv,dwgts);
   for (unsigned int i=0; i<_ndim; i++) if (deriv[i]) { dd[nd] = i; dval[nd++] = 0.0; }
 
   double val=0.0;
   for (unsigned int m=0, me=(_ndim>4)?ni:1; m<me; m++) {
+    inds[4] = start_inds[4] + m;
+
     for (unsigned int l=0, le=(_ndim>3)?ni:1; l<le; l++) {
+      inds[3] = start_inds[3] + l;
+
       for (unsigned int k=0, ke=(_ndim>2)?ni:1; k<ke; k++) {
+        inds[2] = start_inds[2] + k;
         double wgt1 = wgts[4][m]*wgts[3][l]*wgts[2][k];
         get_dwgt1(wgts,dwgts,dd,nd,k,l,m,wgt1,dwgt1);
-        unsigned int linear1 = indx2linear(inds[2]+k,inds[3]+l,inds[4]+m);
+
         for (unsigned int j=0, je=(_ndim>1)?ni:1; j<je; j++) {
+          inds[1] = start_inds[1] + j;
           double wgt2 = wgt1*wgts[1][j];
           for (unsigned int d=0; d<nd; d++) dwgt2[d] = (dd[d]==1) ? dwgt1[d]*dwgts[1][j] : dwgt1[d]*wgts[1][j];
-          int linear2 = add2linear(linear1,inds[1]+j);
           double *iiwgt=iwgt;
+
           for (unsigned int i=0; i<ni; i++, iiwgt++) {
-            double c = cptr[linear2+indx2indx(inds[0]+i,0)];
+            inds[0] = start_inds[0] + i;
+            double c = coef(inds);
             val += c*(*iiwgt)*wgt2;
+
             for (unsigned int d=0; d<nd; d++) {
               double add = (dd[d]==0) ? c*diwgt[i]*dwgt2[d] : c*(*iiwgt)*dwgt2[d];
               dval[d] += add;
-	    }
-	  }
-	}
+            }
+          }
+        }
       }
     }
   }
@@ -812,18 +836,10 @@ unsigned int Splinterpolator<T>::get_start_indicies(const double *coord, int *si
 {
   unsigned int ni = _order+1;
 
-  if (odd(ni)) {
-    for (unsigned int i=0; i<_ndim; i++) {
-      sinds[i] = static_cast<int>(coord[i]+0.5) - ni/2;
-    }
-  }
-  else {
-    for (unsigned int i=0; i<_ndim; i++) {
-      int ix = static_cast<int>(coord[i]+0.5);
-      if (ix < coord[i]) sinds[i] = ix - (ni-1)/2;
-      else sinds[i] = ix -ni/2;
-    }
+  for (unsigned int i=0; i<_ndim; i++) {
+    sinds[i] = std::ceil(coord[i]) - ni/2;
   }
+
   for (unsigned int i=_ndim; i<5; i++) sinds[i] = 0;
 
   return(ni);
@@ -1203,7 +1219,7 @@ inline unsigned int Splinterpolator<T>::indx2indx(int indx, unsigned int d) cons
     if (indx < 0) indx = 0;
     else if (indx >= dim) indx = dim-1;
   }
-  else if (_et[d] == Zeros || _et[d] == Mirror) {
+  else if (_et[d] == Zeros || _et[d] == SoftZeros || _et[d] == Mirror) {
     while (indx < 0) indx = 2*dim*((indx+1)/dim) - 1 - indx;
     while (indx >= dim) indx = 2*dim*(indx/dim) - 1 - indx;
   }
@@ -1326,36 +1342,38 @@ T Splinterpolator<T>::coef(int *indx) const
   for (unsigned int i=0; i<_ndim; i++) {
     if (indx[i] < 0) {
       switch (_et[i]) {
+      case SoftZeros:
       case Zeros:
-	return(static_cast<T>(0));
+        return(static_cast<T>(0));
       case Constant:
-	indx[i] = 0;
-	break;
+        indx[i] = 0;
+        break;
       case Mirror:
-	indx[i] = 1-indx[i];
-	break;
+        indx[i] = 1-indx[i];
+        break;
       case Periodic:
-	indx[i] = _dim[i]+indx[i];
-	break;
+        indx[i] = _dim[i]+indx[i];
+        break;
       default:
-	break;
+        break;
       }
     }
     else if (indx[i] >= static_cast<int>(_dim[i])) {
       switch (_et[i]) {
+      case SoftZeros:
       case Zeros:
-	return(static_cast<T>(0));
+        return(static_cast<T>(0));
       case Constant:
-	indx[i] = _dim[i]-1;
-	break;
+        indx[i] = _dim[i]-1;
+        break;
       case Mirror:
-	indx[i] = 2*_dim[i]-indx[i]-1;
-	break;
+        indx[i] = 2*_dim[i]-indx[i]-1;
+        break;
       case Periodic:
-	indx[i] = indx[i]-_dim[i];
-	break;
+        indx[i] = indx[i]-_dim[i];
+        break;
       default:
-	break;
+        break;
       }
     }
   }
@@ -1506,7 +1524,7 @@ void Splinterpolator<T>::deconv_along(unsigned int dim)
     ss *= _dim[i];
   }
 
-  if (_nthr==1) { // If we are to run single-threaded
+  if (_nthr<=1) { // If we are to run single-threaded
     SplineColumn  col(mdim,mstep);          // Column helps us do the job
     for (unsigned int l=0; l<rdim[3]; l++) {
       for (unsigned int k=0; k<rdim[2]; k++) {
@@ -1646,11 +1664,17 @@ double Splinterpolator<T>::SplineColumn::init_fwd_sweep(double z, ExtrapolationT
     double z2i=z;
     for (unsigned int i=1; i<n; i++, ptr--, z2i*=z) iv += z2i * *ptr;
   }
-  else {
+  else if (et == Mirror) {
     double *ptr=&_col[1];
     double z2i=z;
     for (unsigned int i=1; i<n; i++, ptr++, z2i*=z) iv += z2i * *ptr;
   }
+  // et == Constant || et == Zeros || et == SoftZeros
+  else {
+    double *ptr=&_col[0];
+    double z2i=z;
+    for (unsigned int i=0; i<n; i++, ptr++, z2i*=z) iv += z2i * *ptr;
+  }
   return(iv);
 }
 
@@ -1677,9 +1701,14 @@ double Splinterpolator<T>::SplineColumn::init_bwd_sweep(double z, double lv, Ext
     }
     iv /= (z2i-1.0);
   }
-  else {
+  else if (et == Mirror) {
     iv = -z/(1.0-z*z) * (2.0*_col[_sz-1] - lv);
   }
+  // et == Constant || et == Zeros || et == SoftZeros
+  else  {
+    iv = z / (z - 1) * _col[_sz-1];
+  }
+
   return(iv);
 }