#! /bin/sh # This is a shell archive, meaning: # 1. Remove everything above the #! /bin/sh line. # 2. Save the resulting text in a file. # 3. Execute the file with /bin/sh (not csh) to create the files: # C++/ # C++/DATA.c # C++/DATA.test # C++/Interp.cc # C++/Interp.h # C++/Interp_view.4000.nc.uu # C++/Interp_view.complete.nc.uu # C++/Net.cc # C++/Net.h # C++/Test11.nc.uu # C++/Test12.nc.uu # C++/Test21.nc.uu # C++/Test22.nc.uu # C++/Test31.nc.uu # C++/Test32.nc.uu # C++/Test41.nc.uu # C++/Test42.nc.uu # C++/Test51.nc.uu # C++/Test52.nc.uu # C++/Time.h # C++/input.3d.test # C++/input.5d # C++/main.cc # C++/netcdf/ # C++/netcdf/include/ # C++/netcdf/include/ncvalues.hh # C++/netcdf/include/netcdf-cpp.inc # C++/netcdf/include/netcdf.h # C++/netcdf/include/netcdf.hh # C++/netcdf/include/netcdf.inc # C++/resource.h # Doc/ # Doc/Makefile # Doc/README # This archive created: Mon May 20 18:07:51 2002 export PATH; PATH=/bin:$PATH if test ! -d 'C++' then mkdir 'C++' fi cd 'C++' if test -f 'DATA.c' then echo shar: will not over-write existing file "'DATA.c'" else cat << "SHAR_EOF" > 'DATA.c' 4000 1 1 1 4 7 -0.010234 1 1 1 5 9 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20 11 -0.000078 20 20 12 -0.000075 20 20 14 -0.000053 20 20 17 0.000008 20 20 18 0.000029 20 20 20 0.000063 SHAR_EOF fi # end of overwriting check if test -f 'Interp.cc' then echo shar: will not over-write existing file "'Interp.cc'" else cat << "SHAR_EOF" > 'Interp.cc' /*********************************************************************** ROBERT RENKA UNIV. OF NORTH TEXAS (817) 565-2767 10/25/87 Translated into C++ by Karen Minser Univ. of Tennessee 7/6/98 CLASS Interpolator The following functions contain the C++ code translated from Renka's Fortran interpolation code based on the Modified Shepard's Method. Many of the variables and parameters used and passed around through the Renka's fortran subroutines have been changed to class variables so a lot of the parameter passing has been eliminated. *************************************************************************/ #include #include #include #include "Interp.h" /************************************************************************ Interpolator::Interpolator Constructor function for Interpolator. Sets up many of the arrays that were established as global variables in Renka's original QSMTST3 subroutine. Input Parameters: DIM -dimensions of hypervolume, assigned to M ************************************************************************/ Interpolator::Interpolator(int DIM) : M(DIM) { int i,j, // loop indices // LIW, LWS; // size of WS array = NT**2 // LA; // size of A array NT = (M+1) * (M+2)/2; // LIW = 5 * M; LWS = NT * NT; // LA = NMAX * (NT-1); // IW = new int[LIW]; // define arrays IW = new int*[M+1]; // integer work space array >= 5*M if(!IW){ cerr << "IW array not allocated\n"; exit(1); } for(i=1;i= NT**2 if(!WS){ cerr << "WS array not allocated\n"; exit(1); } for(i=0;i NMAX)){ cout << " *** ERROR -- N = " << N << " MAXIMUM VALUE = "; cout << NMAX << " ***" << endl; exit(1); } // allocate array for cartesian coordinates of known nodes X = new float*[M+1]; if(!X){ cerr << "X array not allocated\n"; exit(1); } for(i=1;i NWMAX)) { cout << "QSMTST3: N = " << N << endl; cout << "Specify the number of nodes NQ for the least squares fit\n"; cout << "NQ = 17 is recommended. 9 < NQ < Min(50,N-1) or NQ = 0 to\n"; cout << "terminate.\n"; scanf("%d",&NQ); cout << "NQ = " << NQ << endl; if(NQ==0) exit(0); } NW=0; while((1 > NW)||(NW > NWMAX)){ cout << "Specify the number of nodes NW for the weights\n"; cout << "NW = 32 is recommended. 1 < NW < Min(50,N-1)\n"; scanf("%d",&NW); cout << "NW = " << NW << endl; } NR=0; while((NR < 1)||(NR > NRMAX)){ cout << "Specify the number of rows, columns, and planes NR in the\n"; cout << "uniform grid of cells used to locate nearest neighbors.\n"; cout << "NR = (N/3)**(1/M) is recommended. 1 < NR < NRMAX\n"; scanf("%d",&NR); cout << "NR = " << NR << endl; } //allocate Axes_Ticks array Axes_Ticks = new float*[M+1]; if(!Axes_Ticks){ cerr << "Axes_Ticks array not allocated\n"; exit(1); } for(i=1;i NQ NQWMAX, // MAX0(NQ,NW) NTT, // Number of terms in each quadratic nodal function Q(K). // Note: Changed from original NT so won't conflict // with class var NT NTM1, // NT-1 (the number of coefficients which, along with F(K), // define Q(K)) NTM1NT, // (NT-1)*NT NTP1, // NT+1 (offset between diagonal elements in WS) necessary, // conditional for do-while loop necessary4, // conditional for do-while loop necessary7, // conditional for do-while loop brk; // indicates if necessary to break out of loop double AV, // Root-mean-square distance between K and the // nodes in the least squares system (unless // additional nodes are introduced for stability). // The first MT columns of the matrix (quadratic terms) // are scaled by 1/AVSQ, the last M (linear terms) by 1/AV AVSQ, // AV*AV C, // First component of the plane rotation used to // zero the lower triangle of the regression // matrix; computed by GIVENS DMIN, // Minimum of the magnitudes of the diagonal elements of // the regression matrix after zeros are introduced // below the diagonal DTOL = 0.01, // Tolerance for detecting an ill-conditioned system. // The system is accepted when DMIN*RQ >= DTOL. FK, // Data value at node K - F(K) RQ, // Radius of influence which enters into the weights for // Q(K) (see subroutine SETUPM) RS, // Squared distance between K and NPTS[LNP]; used to // compute RQ and RSQ[K] RSMX, // Maximum RSQ element encountered RSOLD, // Squared distance between K and NPTS[LNP-1]; used to // compute a relative change in RS between succeeding // NPTS elements. RTOL = 1.0E-05, // Tolerance for detecting a sufficiently large relative // change in RS. If the change is not greater than RTOL, // the nodes are treated as being the same distance from K RWS, // Current value of RSQ[K]. S, // Second component of the plane Givens rotation SF = 1.0, // Marquardt stabilization factor used to damp out the // first MT solution components (second partials // of the quadratic) when the system is ill-conditioned. // As SF increases the fitting function approaches a // linear SUM, // Sum of squared Euclidean distances between node K and // the nodes used in the least squares fit (unless // additional nodes are added for stability) T; // Temporary variable for accumulating a scalar product in // the back substitution loop. NQWMAX = MAX0(NQ,NW); LMAX = MIN0(50,N-1); NTM1 = (M*(M+3))/2; NTT = NTM1 + 1; NTP1 = NTT + 1; MT = NTM1 - M; NTM1NT = NTM1*NTT; C=0; S=0; // make sure variables are legit - if not, exit the program if((M<1)||(NQLMAX)||(NR<1)){ IER = 1; return; } // Create the cell data structure, and initialize RSMX. STOREM(IERR); if(IERR!=0){ IER = 3; // All nodes are coplanar return; // Return from QSHEPM now } RSMX = 0; // OUTER LOOP on node K for(K=1;K NW)){ RWS = RS; } if((RQ == 0)&&(LNP > NQ)){ //RQ=0 (not yet computed) and //LNP>NQ. RQ=SQRT(RS) is //sufficiently large to (strictly) //include NQ nodes. The least squares //fit will include NEQ=LNP-1 //equations for //NT-1 <= NQ < LMAX <= N-1 RQ = (float)sqrt((double)RS); NEQ = LNP - 1; AVSQ = SUM/(float)NEQ; } // Test for termination on LNP > NQ and LNP > NW if(LNP > NQWMAX){ brk = 1; necessary = 0; // GO TO 3 } else{ SUM = SUM + RS; } } if(LNP == LMAX){ // #2 - loop conditional necessary = 0; } } while(necessary); // end of do-while #1 // If brk==0 then no GO TO's (or breaks) encountered and // all LMAX nodes are included in NPTS. RWS and/or RQ**2 is // (arbitrarily) taken to be 10% larger than the distance RS to the // last node included. if(!brk){ if(RWS == 0){ RWS = 1.1*RS; } if(RQ == 0){ RQ = (float)sqrt((double)(1.1*RS)); NEQ = LMAX; AVSQ = SUM/(float)NEQ; } } // Store RSQ[K], update RSMX if necessary, and compute AV. RSQ[K] = RWS; // #3 if(RWS > RSMX){ RSMX = RWS; } AV = (float)sqrt((double)AVSQ); //cout << "QSHEPM: AV = " << AV << endl; // Set up the augmented regression matrix (stored by rows in WS, and // zero out the lower triangle and Givens rotations - QR decomposition // with orthogonal matrix Q not stored. brk = 0; necessary4 = 1; I = 0; do { //do-while #4 I++; NP = NPTS[I]; IROW = MIN0(I,NTT); IRM1 = IROW-1; IJ = IRM1*NTT + 1; SETUPM(K,FK,NP,AV,AVSQ,RQ,IJ); if(I != 1){ // else go back to top of do-while #4. Same // as GO TO 4 JJ = 1; for(J=1;J= NEQ){ // else go back to top of do-while #4. Same // as GO TO 4 //Test the system for ill-conditioning DMIN = abs(WS[1]); JJ = 1; for(J=2;J= RTOL){ RQ = (float)sqrt((double)RS); necessary7 = 0; //break out of #7 and GO TO top of #4 } } else{ // NEQ==LMAX RQ = (float)sqrt((double)(1.1*RS)); necessary7 = 0; } } // end of do-while #7 while(necessary7); } else{ necessary4 = 0; brk = 9; //GOTO #9 } } else{ necessary4 = 0; //GOTO #13 } } // end of if I>=NEQ } // end of if I!=1 } // end of do-while #4 while(necessary4); if(brk == 9){ //#9 //Stabilize the system by damping second // partials - add multiples of the first MT // unit vectors to the first MT equations, // where MT=M*(M+1)/2 is the number of // quadratic terms. NI = NTM1NT; for(I=1;I IMAX = IW[I][2] for any I. IW[][3] is initial- // ized to IW[][1], and LCI is initialized to the index // associated with IW[][3] by Horner's method. LCI = 0; for(I=M;I>0;I--){ //Loop #1 if(DX[I] <= 0){ return -0; } IMIN = (int)((P[I]-XMIN[I]-RM)/DX[I]) + 1; if(IMIN < 1){ IMIN = 1; } IMAX = (int)((P[I]-XMIN[I]+RM)/DX[I]) + 1; if(IMAX > NNR){ IMAX = NNR; } if(IMIN > IMAX){ qsmval = 0; return qsmval; } LCI = LCI*NNR + IMIN - 1; IW[I][1] = IMIN; IW[I][2] = IMAX; IW[I][3] = IMIN; } //end of Loop #1 LCI++; // Accumulate weight values in SW and weighted nodal function // values in SWQ. The weights are W(K) = ((R-D)+/(R*D))**2 // for R**2 = RSQ[K] and D = distance between P and node K. SW = 0.0; SWQ = 0.0; // outer loop on on cells LCI cells = 1; do{ //do-while #2 brk = 0; // break out variable to allow for GO TO's K = LCELL[LCI]; if(K != 0){ // else break out to #8 nodes = 1; // Inner loop on nodes K. Compute WW = W(K) and update SW. do{ //#3 DS = 0.0; for(I=1;I DS){ // GOTO #7 if(DS != 0){ // GOTO #10 RDS = RS * DS; RD = (float)sqrt((double)RDS); WW = (RS+DS-RD-RD)/RDS; SW += WW; // Compute QK = Q(K) (P) and update SWQ QK = W[K]; L = 0; for(J=1;J0;J--){ // DO-LOOP #7 LCI = LCI*NR + IW[J][3] - 1; } // end of DO-LOOP #7 LCI++; L = LCELL[LCI]; if(L != 0){ // Else GO TO #12 nodes = 1; // Loop on nodes in cell LCI do{ // Do-While #8 LN = LNEXT[L]; if(LN >= 0) { // Else GO TO #11 // Node L is not marked. Set RSQ to its squared distance from P RRSQ = 0.0; for(J=1;J=0 ) // Test for termination of loop on nodes in cell LCI. if((int)abs((float)LN) != L){ L = (int)abs((float)LN); } else{ nodes = 0; // terminate the loop } } while(nodes); } // end if(L != 0) // #12 - Bottom of loop on cells. Update the current cell indices. brk = 0; for(J=1;J IW[I][4])||(IW[I][2] < IW[I][5])) { // Update IW[I][1] and IW[I][2] to the next layer out for(J=1;J abs(BB)){ U = AA + AA; V = BB/U; R = (float)sqrt((double)(0.25+V*V)) * U; C = AA/R; S = V * (C+C); // Note: R has the sign of A, C > 0, and S has SIGN(A)*SIGN(B) *B = S; *A = R; return; } else{ // abs(AA) <= abs(BB) if(BB == 0.0){ // #1 C = 1; // #2 - A = B = 0 S = 0; return; } else{ // BB != 0 U = BB + BB; V = AA/U; // Store R in A *A = (float)sqrt((double)(0.25+V*V)) * U; S = BB/(*A); C = V * (S+S); // Note: R has the sign of B, S > 0, and C has SIGN(A)*SIGN(B). *B = 1.0; if(C != 0.0) *B = 1.0/C; return; } } } // end of GIVENS /***************************************************************************** ROBERT RENKA UNIV. OF NORTH TEXAS (817) 565-2767 10/25/87 Translated into C++ by Karen Minser Univ. of Tennessee 7/6/98 ROTATE ( C S) This routine applies the Givens rotation ( ) to the (-S C) (X[1] ... X[N]) 2 by N matrix ( ). (Y[1] ... Y[N]) On input: N = Number of columns to be rotated. C,S = Elements of the Givens rotation. These may be determined by subroutine GIVENS. II,JJ = Indices into arrays of length .GE. N containing the vectors to be rotated. Parameters N, C, and S are not altered by this routine. On output: IJ,JJ = Rotated vectors at indices IJ and JJ. Note: instead of passing vectors which are part of a larger vector as was done in the original fortran code, the indices marking the smaller vectors were passed instead. The larger vector, WS, is a class variable. ****************************************************************************/ void Interpolator::ROTATE(int NN,double C,double S,int IJ,int JJ){ int I; // Loop index float XI, // X_PTR[I] YI, // Y_PTR[I] *X_PTR, // Points to vector in WS at IJ *Y_PTR; // Points to vector in WS at JJ X_PTR = &WS[IJ-1]; Y_PTR = &WS[JJ-1]; if((NN <= 0)||((C == 1)&&(S == 0))){ return; } else{ for(I=1;I D, or W = 0 if R <= D, where D is the distance between nodes L and K. On input: K = current node and column of X which contains the Cartesian coordinates of node K FK = interpolated value at node K NP = index marking column of X which contains the coordinates of node L. Also, the index in array W which is the data value at node L. S1,S2 = Reciprocals of the scale factors for the linear and quadratic terms, respectively. R = Radius of influence about node K defining the weight W. ROW = Array of length NT = (M+1)(M+2)/2. On output: ROW = Array containing row L of the augmented re- gression matrix as described above, or zero vector if M < 1 or nodes K and L coincide. *********************************************************************/ void Interpolator::SETUPM(int K,double FK,int NP,double S1,double S2,double R,int ROW){ int I,J, // Loop indices IJ, // Counter and index MT, // Number of quadratic terms in the nodal functions Q(K) NNT; // Total number of terms in Q(K) float D, // Distance between nodes L and K W0,W1,W2, // Weight values DXJ, // Difference between respective coordinates of L and K *WS_PTR; // Pointer into array WS WS_PTR = &WS[ROW-1]; MT = (M*(M+1))/2; NNT = MT + M + 1; if(M >= 1){ // else "GO TO 4" // Compute distance D , weights W=(R-D)/(R*D), W1=W/S1 D = 0.0; for(I=1;I 0)&&(D < R)){ // else "GO TO 4" W0 = (R-D)/R/D; W1 = W0/S1; W2 = W0/S2; // Store the row IJ = 0; for(J=1;J DX[I]) DX[I] = X[I][K]; } } // Compute the interval widths, and test for a zero width. RNR = (float)NR; for(I=1;I0;I--){ LI = (int)( (X[I][K]-XMIN[I])/DX[I] ) + 1; if(LI > NR) LI=NR; LCI = LCI*NR + LI-1; } LCI++; // Add K to the data structure as the last node in cell LCI. LN = LCELL[LCI]; if(LN==0){ // K is the first node in cell LCI. LCELL[LCI] = K; } else { // Find the index L such that LNEXT[L] = L do { L = LN; LN = LNEXT[L]; } while(LN!=L); LNEXT[L] = K; } // Bottom of loop: set LNEXT[K] = K to indicate that K is // the last node in the cell LNEXT[K] = K; } IER = 0; // No errors encountered } // end of STOREM /************************************************************************* get_node_coords This function gets the coordinates of node K from matrix X and stores them in vector PP. Input Parameters: PP -vector of length M which will obtain the coordinates of K K -current node - column in X where coordinates are found ****************************************************************************/ void Interpolator::get_node_coords(float *PP, int K){ int i; // loop index for(i=1;i 'Interp.h' /*********************************************************************** CLASS Interpolator This class contains all of the variables and functions related to the interpolation process. This code was directly translated from Renka's Fortran code. ************************************************************************/ #include #include //#define NMAX 10700 #define NMAX 26000 //maximum number of known nodes #define NRMAX 6 //maximum number number of cells = NR //#define LLC (NRMAX*NRMAX) #define MIN0(a,b) a < b ? a : b //min. macro #define MAX0(a,b) a > b ? a : b //max. macro #define NFUN 5 //number of test functions class Interpolator { protected: int M, //Dimensions of hypervolume N, //Number of known nodes NT, //Number of terms in quadratic equation // with M variables: NT=(M+1)(M+2)/2 NQ, //Number of data points to be used in // the least squares fit for // coefficients defining the nodal fxns. // Q(K). // NT-1=M(M+3)/2 <= NQ <= MIN0(50,N-1) NW, //Number of nodes within (and defining) // the radii of influence R(K) which enter // into the weights W(K). // 1 <= NW <= MIN0(50,N-1) NR, //Number of intervals along each // coordinate axis defining the cell grid // described in function STOREM. // Recommended value is nearest integer to // (N/3)**(1/M) with NR >=1. **IW, //Integer work space array of length >= 5*M. LCELL[NMAX+1], //Array of length NR**M containing nodal // indices associated with cells. See STOREM. LNEXT[NMAX+1]; //Array of length N containing next-node // indices. See STOREM. float *WS, //Work space array of length >= NT**2 for // NT=(M+1)(M+2)/2. *XMIN, *DX, //Arrays of length M containing minimum nodal // coordinates and cell dimensions, // respectively. See STOREM. **A, //N by NT-1 array containing the coefficients // for quadratic nodal function Q(K) in row // K. **X, //M by N array whose Kth column contains the // cartesian coordinates of node K. The // actual row dimension in the calling // program must be M. Q, //Weighted sum of quadratic nodal fxns. // defined in QSHEPM. RMAX, //Square root of the largest element in RSQ - // maximum radius R(K). W[NMAX+1], //stores values at known nodes RSQ[NMAX+1]; //Array of length N containing the squares of // the radii R(K) which enter into the // weights W(K). // DQ; public: Interpolator (int); ~Interpolator (); float **QSMTST3(int*, float[][3], char); void QSHEPM(int&); double QSMVAL(float*); void QSMGRD(); void GETNPM(int,int&,double&); void GIVENS(float*,float*,double&,double&); void ROTATE(int,double,double,int,int); void SETUPM(int,double,int,double,double,double,int); void STOREM(int&); void get_node_coords(float*,int); float **getX(){ return X;}; // returns array of coordinates float *getW(){ return W;}; // returns array of weights int getN(){ return N; }; // returns number of known nodes void TFUN3(int,int,float*,int,int,float*,float,float,float); }; SHAR_EOF fi # end of overwriting check if test -f 'Interp_view.4000.nc.uu' then echo shar: will not over-write existing file "'Interp_view.4000.nc.uu'" else cat << "SHAR_EOF" > 'Interp_view.4000.nc.uu' begin 644 Interp_view.4000.nc M0T1&`0`````````*````!0````)/,P``````"@````-#3S(`````"@````%. 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