int Ifpack_AnalyzeMatrixElements(const Epetra_RowMatrix& A,
const bool abs, const int steps)
{
bool verbose = (A.Comm().MyPID() == 0);
double min_val = DBL_MAX;
double max_val = -DBL_MAX;
std::vector<int> colInd(A.MaxNumEntries());
std::vector<double> colVal(A.MaxNumEntries());
for (int i = 0 ; i < A.NumMyRows() ; ++i) {
int Nnz;
IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz,
&colVal[0],&colInd[0]));
for (int j = 0 ; j < Nnz ; ++j) {
double v = colVal[j];
if (abs)
if (v < 0) v = -v;
if (v < min_val)
min_val = v;
if (v > max_val)
max_val = v;
}
}
if (verbose) {
cout << endl;
Ifpack_PrintLine();
cout << "Label of matrix = " << A.Label() << endl;
cout << endl;
}
double delta = (max_val - min_val) / steps;
for (int k = 0 ; k < steps ; ++k) {
double below = delta * k + min_val;
double above = below + delta;
int MyBelow = 0, GlobalBelow;
for (int i = 0 ; i < A.NumMyRows() ; ++i) {
int Nnz;
IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz,
&colVal[0],&colInd[0]));
for (int j = 0 ; j < Nnz ; ++j) {
double v = colVal[j];
if (abs)
if (v < 0) v = -v;
if (v >= below && v < above) MyBelow++;
}
}
A.Comm().SumAll(&MyBelow, &GlobalBelow, 1);
if (verbose) {
printf("Elements in [%+7e, %+7e) = %10d ( = %5.2f %%)\n",
below, above, GlobalBelow,
100.0 * GlobalBelow / A.NumGlobalNonzeros64());
}
}
if (verbose) {
Ifpack_PrintLine();
cout << endl;
}
return(0);
}
// ======================================================================
int Ifpack_PrintSparsity(const Epetra_RowMatrix& A, const char* InputFileName,
const int NumPDEEqns)
{
int ltit;
long long m,nc,nr,maxdim;
double lrmrgn,botmrgn,xtit,ytit,ytitof,fnstit,siz = 0.0;
double xl,xr, yb,yt, scfct,u2dot,frlw,delt,paperx;
bool square = false;
/*change square to .true. if you prefer a square frame around
a rectangular matrix */
double conv = 2.54;
char munt = 'E'; /* put 'E' for centimeters, 'U' for inches */
int ptitle = 0; /* position of the title, 0 under the drawing,
else above */
FILE* fp = NULL;
int NumMyRows;
//int NumMyCols;
long long NumGlobalRows;
long long NumGlobalCols;
int MyPID;
int NumProc;
char FileName[1024];
char title[1024];
const Epetra_Comm& Comm = A.Comm();
/* --------------------- execution begins ---------------------- */
if (strlen(A.Label()) != 0)
strcpy(title, A.Label());
else
sprintf(title, "%s", "matrix");
if (InputFileName == 0)
sprintf(FileName, "%s.ps", title);
else
strcpy(FileName, InputFileName);
MyPID = Comm.MyPID();
NumProc = Comm.NumProc();
NumMyRows = A.NumMyRows();
//NumMyCols = A.NumMyCols();
NumGlobalRows = A.NumGlobalRows64();
NumGlobalCols = A.NumGlobalCols64();
if (NumGlobalRows != NumGlobalCols)
IFPACK_CHK_ERR(-1); // never tested
/* to be changed for rect matrices */
maxdim = (NumGlobalRows>NumGlobalCols)?NumGlobalRows:NumGlobalCols;
maxdim /= NumPDEEqns;
m = 1 + maxdim;
nr = NumGlobalRows / NumPDEEqns + 1;
nc = NumGlobalCols / NumPDEEqns + 1;
if (munt == 'E') {
u2dot = 72.0/conv;
paperx = 21.0;
siz = 10.0;
}
else {
u2dot = 72.0;
paperx = 8.5*conv;
siz = siz*conv;
}
/* left and right margins (drawing is centered) */
lrmrgn = (paperx-siz)/2.0;
/* bottom margin : 2 cm */
botmrgn = 2.0;
/* c scaling factor */
scfct = siz*u2dot/m;
/* matrix frame line witdh */
frlw = 0.25;
/* font size for title (cm) */
fnstit = 0.5;
/* mfh 23 Jan 2013: title is always nonnull, since it's an array of
fixed nonzero length. The 'if' test thus results in a compiler
warning. */
/*if (title) ltit = strlen(title);*/
/*else ltit = 0;*/
ltit = strlen(title);
/* position of title : centered horizontally */
/* at 1.0 cm vertically over the drawing */
ytitof = 1.0;
xtit = paperx/2.0;
ytit = botmrgn+siz*nr/m + ytitof;
/* almost exact bounding box */
xl = lrmrgn*u2dot - scfct*frlw/2;
xr = (lrmrgn+siz)*u2dot + scfct*frlw/2;
yb = botmrgn*u2dot - scfct*frlw/2;
yt = (botmrgn+siz*nr/m)*u2dot + scfct*frlw/2;
if (ltit == 0) {
yt = yt + (ytitof+fnstit*0.70)*u2dot;
}
/* add some room to bounding box */
delt = 10.0;
xl = xl-delt;
xr = xr+delt;
yb = yb-delt;
yt = yt+delt;
/* correction for title under the drawing */
if ((ptitle == 0) && (ltit == 0)) {
ytit = botmrgn + fnstit*0.3;
botmrgn = botmrgn + ytitof + fnstit*0.7;
}
/* begin of output */
if (MyPID == 0) {
fp = fopen(FileName,"w");
fprintf(fp,"%s","%%!PS-Adobe-2.0\n");
fprintf(fp,"%s","%%Creator: IFPACK\n");
fprintf(fp,"%%%%BoundingBox: %f %f %f %f\n",
xl,yb,xr,yt);
fprintf(fp,"%s","%%EndComments\n");
fprintf(fp,"%s","/cm {72 mul 2.54 div} def\n");
fprintf(fp,"%s","/mc {72 div 2.54 mul} def\n");
fprintf(fp,"%s","/pnum { 72 div 2.54 mul 20 string ");
fprintf(fp,"%s","cvs print ( ) print} def\n");
fprintf(fp,"%s","/Cshow {dup stringwidth pop -2 div 0 rmoveto show} def\n");
/* we leave margins etc. in cm so it is easy to modify them if
needed by editing the output file */
fprintf(fp,"%s","gsave\n");
if (ltit != 0) {
fprintf(fp,"/Helvetica findfont %e cm scalefont setfont\n",
fnstit);
fprintf(fp,"%f cm %f cm moveto\n",
xtit,ytit);
fprintf(fp,"(%s) Cshow\n", title);
fprintf(fp,"%f cm %f cm translate\n",
lrmrgn,botmrgn);
}
fprintf(fp,"%f cm %d div dup scale \n",
siz, (int) m);
/* draw a frame around the matrix */
fprintf(fp,"%f setlinewidth\n",
frlw);
fprintf(fp,"%s","newpath\n");
fprintf(fp,"%s","0 0 moveto ");
if (square) {
printf("------------------- %d\n", (int) m);
fprintf(fp,"%d %d lineto\n",
(int) m, 0);
fprintf(fp,"%d %d lineto\n",
(int) m, (int) m);
fprintf(fp,"%d %d lineto\n",
0, (int) m);
}
else {
fprintf(fp,"%d %d lineto\n",
(int) nc, 0);
fprintf(fp,"%d %d lineto\n",
(int) nc, (int) nr);
fprintf(fp,"%d %d lineto\n",
0, (int) nr);
}
fprintf(fp,"%s","closepath stroke\n");
/* plotting loop */
fprintf(fp,"%s","1 1 translate\n");
fprintf(fp,"%s","0.8 setlinewidth\n");
fprintf(fp,"%s","/p {moveto 0 -.40 rmoveto \n");
fprintf(fp,"%s"," 0 .80 rlineto stroke} def\n");
fclose(fp);
}
int MaxEntries = A.MaxNumEntries();
std::vector<int> Indices(MaxEntries);
std::vector<double> Values(MaxEntries);
for (int pid = 0 ; pid < NumProc ; ++pid) {
if (pid == MyPID) {
fp = fopen(FileName,"a");
if( fp == NULL ) {
fprintf(stderr,"%s","ERROR\n");
exit(EXIT_FAILURE);
}
for (int i = 0 ; i < NumMyRows ; ++i) {
if (i % NumPDEEqns) continue;
int Nnz;
A.ExtractMyRowCopy(i,MaxEntries,Nnz,&Values[0],&Indices[0]);
long long grow = A.RowMatrixRowMap().GID64(i);
for (int j = 0 ; j < Nnz ; ++j) {
int col = Indices[j];
if (col % NumPDEEqns == 0) {
long long gcol = A.RowMatrixColMap().GID64(Indices[j]);
grow /= NumPDEEqns;
gcol /= NumPDEEqns;
fprintf(fp,"%lld %lld p\n",
gcol, NumGlobalRows - grow - 1);
}
}
}
fprintf(fp,"%s","%end of data for this process\n");
if( pid == NumProc - 1 )
fprintf(fp,"%s","showpage\n");
fclose(fp);
}
Comm.Barrier();
}
return(0);
}
int Ifpack_Analyze(const Epetra_RowMatrix& A, const bool Cheap,
const int NumPDEEqns)
{
int NumMyRows = A.NumMyRows();
long long NumGlobalRows = A.NumGlobalRows64();
long long NumGlobalCols = A.NumGlobalCols64();
long long MyBandwidth = 0, GlobalBandwidth;
long long MyLowerNonzeros = 0, MyUpperNonzeros = 0;
long long GlobalLowerNonzeros, GlobalUpperNonzeros;
long long MyDiagonallyDominant = 0, GlobalDiagonallyDominant;
long long MyWeaklyDiagonallyDominant = 0, GlobalWeaklyDiagonallyDominant;
double MyMin, MyAvg, MyMax;
double GlobalMin, GlobalAvg, GlobalMax;
long long GlobalStorage;
bool verbose = (A.Comm().MyPID() == 0);
GlobalStorage = sizeof(int*) * NumGlobalRows +
sizeof(int) * A.NumGlobalNonzeros64() +
sizeof(double) * A.NumGlobalNonzeros64();
if (verbose) {
print();
Ifpack_PrintLine();
print<const char*>("Label", A.Label());
print<long long>("Global rows", NumGlobalRows);
print<long long>("Global columns", NumGlobalCols);
print<long long>("Stored nonzeros", A.NumGlobalNonzeros64());
print<long long>("Nonzeros / row", A.NumGlobalNonzeros64() / NumGlobalRows);
print<double>("Estimated storage (Mbytes)", 1.0e-6 * GlobalStorage);
}
long long NumMyActualNonzeros = 0, NumGlobalActualNonzeros;
long long NumMyEmptyRows = 0, NumGlobalEmptyRows;
long long NumMyDirichletRows = 0, NumGlobalDirichletRows;
std::vector<int> colInd(A.MaxNumEntries());
std::vector<double> colVal(A.MaxNumEntries());
Epetra_Vector Diag(A.RowMatrixRowMap());
Epetra_Vector RowSum(A.RowMatrixRowMap());
Diag.PutScalar(0.0);
RowSum.PutScalar(0.0);
for (int i = 0 ; i < NumMyRows ; ++i) {
long long GRID = A.RowMatrixRowMap().GID64(i);
int Nnz;
IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz,
&colVal[0],&colInd[0]));
if (Nnz == 0)
NumMyEmptyRows++;
if (Nnz == 1)
NumMyDirichletRows++;
for (int j = 0 ; j < Nnz ; ++j) {
double v = colVal[j];
if (v < 0) v = -v;
if (colVal[j] != 0.0)
NumMyActualNonzeros++;
long long GCID = A.RowMatrixColMap().GID64(colInd[j]);
if (GCID != GRID)
RowSum[i] += v;
else
Diag[i] = v;
if (GCID < GRID)
MyLowerNonzeros++;
else if (GCID > GRID)
MyUpperNonzeros++;
long long b = GCID - GRID;
if (b < 0) b = -b;
if (b > MyBandwidth)
MyBandwidth = b;
}
if (Diag[i] > RowSum[i])
MyDiagonallyDominant++;
if (Diag[i] >= RowSum[i])
MyWeaklyDiagonallyDominant++;
RowSum[i] += Diag[i];
}
// ======================== //
// summing up global values //
// ======================== //
A.Comm().SumAll(&MyDiagonallyDominant,&GlobalDiagonallyDominant,1);
A.Comm().SumAll(&MyWeaklyDiagonallyDominant,&GlobalWeaklyDiagonallyDominant,1);
A.Comm().SumAll(&NumMyActualNonzeros, &NumGlobalActualNonzeros, 1);
A.Comm().SumAll(&NumMyEmptyRows, &NumGlobalEmptyRows, 1);
A.Comm().SumAll(&NumMyDirichletRows, &NumGlobalDirichletRows, 1);
A.Comm().SumAll(&MyBandwidth, &GlobalBandwidth, 1);
A.Comm().SumAll(&MyLowerNonzeros, &GlobalLowerNonzeros, 1);
A.Comm().SumAll(&MyUpperNonzeros, &GlobalUpperNonzeros, 1);
A.Comm().SumAll(&MyDiagonallyDominant, &GlobalDiagonallyDominant, 1);
A.Comm().SumAll(&MyWeaklyDiagonallyDominant, &GlobalWeaklyDiagonallyDominant, 1);
double NormOne = A.NormOne();
double NormInf = A.NormInf();
double NormF = Ifpack_FrobeniusNorm(A);
if (verbose) {
print();
print<long long>("Actual nonzeros", NumGlobalActualNonzeros);
print<long long>("Nonzeros in strict lower part", GlobalLowerNonzeros);
print<long long>("Nonzeros in strict upper part", GlobalUpperNonzeros);
print();
print<long long>("Empty rows", NumGlobalEmptyRows,
100.0 * NumGlobalEmptyRows / NumGlobalRows);
print<long long>("Dirichlet rows", NumGlobalDirichletRows,
100.0 * NumGlobalDirichletRows / NumGlobalRows);
print<long long>("Diagonally dominant rows", GlobalDiagonallyDominant,
100.0 * GlobalDiagonallyDominant / NumGlobalRows);
print<long long>("Weakly diag. dominant rows",
GlobalWeaklyDiagonallyDominant,
100.0 * GlobalWeaklyDiagonallyDominant / NumGlobalRows);
print();
print<long long>("Maximum bandwidth", GlobalBandwidth);
print();
print("", "one-norm", "inf-norm", "Frobenius", false);
print("", "========", "========", "=========", false);
print();
print<double>("A", NormOne, NormInf, NormF);
}
if (Cheap == false) {
// create A + A^T and A - A^T
Epetra_FECrsMatrix AplusAT(Copy, A.RowMatrixRowMap(), 0);
Epetra_FECrsMatrix AminusAT(Copy, A.RowMatrixRowMap(), 0);
#ifndef EPETRA_NO_32BIT_GLOBAL_INDICES
if(A.RowMatrixRowMap().GlobalIndicesInt()) {
for (int i = 0 ; i < NumMyRows ; ++i) {
int GRID = A.RowMatrixRowMap().GID(i);
assert (GRID != -1);
int Nnz;
IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz,
&colVal[0],&colInd[0]));
for (int j = 0 ; j < Nnz ; ++j) {
int GCID = A.RowMatrixColMap().GID(colInd[j]);
assert (GCID != -1);
double plus_val = colVal[j];
double minus_val = -colVal[j];
if (AplusAT.SumIntoGlobalValues(1,&GRID,1,&GCID,&plus_val) != 0) {
IFPACK_CHK_ERR(AplusAT.InsertGlobalValues(1,&GRID,1,&GCID,&plus_val));
}
if (AplusAT.SumIntoGlobalValues(1,&GCID,1,&GRID,&plus_val) != 0) {
IFPACK_CHK_ERR(AplusAT.InsertGlobalValues(1,&GCID,1,&GRID,&plus_val));
}
if (AminusAT.SumIntoGlobalValues(1,&GRID,1,&GCID,&plus_val) != 0) {
IFPACK_CHK_ERR(AminusAT.InsertGlobalValues(1,&GRID,1,&GCID,&plus_val));
}
if (AminusAT.SumIntoGlobalValues(1,&GCID,1,&GRID,&minus_val) != 0) {
IFPACK_CHK_ERR(AminusAT.InsertGlobalValues(1,&GCID,1,&GRID,&minus_val));
}
}
}
}
else
#endif
#ifndef EPETRA_NO_64BIT_GLOBAL_INDICES
if(A.RowMatrixRowMap().GlobalIndicesLongLong()) {
for (int i = 0 ; i < NumMyRows ; ++i) {
long long GRID = A.RowMatrixRowMap().GID64(i);
assert (GRID != -1);
int Nnz;
IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz,
&colVal[0],&colInd[0]));
for (int j = 0 ; j < Nnz ; ++j) {
long long GCID = A.RowMatrixColMap().GID64(colInd[j]);
assert (GCID != -1);
double plus_val = colVal[j];
double minus_val = -colVal[j];
if (AplusAT.SumIntoGlobalValues(1,&GRID,1,&GCID,&plus_val) != 0) {
IFPACK_CHK_ERR(AplusAT.InsertGlobalValues(1,&GRID,1,&GCID,&plus_val));
}
if (AplusAT.SumIntoGlobalValues(1,&GCID,1,&GRID,&plus_val) != 0) {
IFPACK_CHK_ERR(AplusAT.InsertGlobalValues(1,&GCID,1,&GRID,&plus_val));
}
if (AminusAT.SumIntoGlobalValues(1,&GRID,1,&GCID,&plus_val) != 0) {
IFPACK_CHK_ERR(AminusAT.InsertGlobalValues(1,&GRID,1,&GCID,&plus_val));
}
if (AminusAT.SumIntoGlobalValues(1,&GCID,1,&GRID,&minus_val) != 0) {
IFPACK_CHK_ERR(AminusAT.InsertGlobalValues(1,&GCID,1,&GRID,&minus_val));
}
}
}
}
else
#endif
throw "Ifpack_Analyze: GlobalIndices type unknown";
AplusAT.FillComplete();
AminusAT.FillComplete();
AplusAT.Scale(0.5);
AminusAT.Scale(0.5);
NormOne = AplusAT.NormOne();
NormInf = AplusAT.NormInf();
NormF = Ifpack_FrobeniusNorm(AplusAT);
if (verbose) {
print<double>("A + A^T", NormOne, NormInf, NormF);
}
NormOne = AminusAT.NormOne();
NormInf = AminusAT.NormInf();
NormF = Ifpack_FrobeniusNorm(AminusAT);
if (verbose) {
print<double>("A - A^T", NormOne, NormInf, NormF);
}
}
if (verbose) {
print();
print<const char*>("", "min", "avg", "max", false);
print<const char*>("", "===", "===", "===", false);
}
MyMax = -DBL_MAX;
MyMin = DBL_MAX;
MyAvg = 0.0;
for (int i = 0 ; i < NumMyRows ; ++i) {
int Nnz;
IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz,
&colVal[0],&colInd[0]));
for (int j = 0 ; j < Nnz ; ++j) {
MyAvg += colVal[j];
if (colVal[j] > MyMax) MyMax = colVal[j];
if (colVal[j] < MyMin) MyMin = colVal[j];
}
}
A.Comm().MaxAll(&MyMax, &GlobalMax, 1);
A.Comm().MinAll(&MyMin, &GlobalMin, 1);
A.Comm().SumAll(&MyAvg, &GlobalAvg, 1);
GlobalAvg /= A.NumGlobalNonzeros64();
if (verbose) {
print();
print<double>(" A(i,j)", GlobalMin, GlobalAvg, GlobalMax);
}
MyMax = 0.0;
MyMin = DBL_MAX;
MyAvg = 0.0;
for (int i = 0 ; i < NumMyRows ; ++i) {
int Nnz;
IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz,
&colVal[0],&colInd[0]));
for (int j = 0 ; j < Nnz ; ++j) {
double v = colVal[j];
if (v < 0) v = -v;
MyAvg += v;
if (colVal[j] > MyMax) MyMax = v;
if (colVal[j] < MyMin) MyMin = v;
}
}
A.Comm().MaxAll(&MyMax, &GlobalMax, 1);
A.Comm().MinAll(&MyMin, &GlobalMin, 1);
A.Comm().SumAll(&MyAvg, &GlobalAvg, 1);
GlobalAvg /= A.NumGlobalNonzeros64();
if (verbose) {
print<double>("|A(i,j)|", GlobalMin, GlobalAvg, GlobalMax);
}
// ================= //
// diagonal elements //
// ================= //
Diag.MinValue(&GlobalMin);
Diag.MaxValue(&GlobalMax);
Diag.MeanValue(&GlobalAvg);
if (verbose) {
print();
print<double>(" A(k,k)", GlobalMin, GlobalAvg, GlobalMax);
}
Diag.Abs(Diag);
Diag.MinValue(&GlobalMin);
Diag.MaxValue(&GlobalMax);
Diag.MeanValue(&GlobalAvg);
if (verbose) {
print<double>("|A(k,k)|", GlobalMin, GlobalAvg, GlobalMax);
}
// ============================================== //
// cycle over all equations for diagonal elements //
// ============================================== //
if (NumPDEEqns > 1 ) {
if (verbose) print();
for (int ie = 0 ; ie < NumPDEEqns ; ie++) {
MyMin = DBL_MAX;
MyMax = -DBL_MAX;
MyAvg = 0.0;
for (int i = ie ; i < Diag.MyLength() ; i += NumPDEEqns) {
double d = Diag[i];
MyAvg += d;
if (d < MyMin)
MyMin = d;
if (d > MyMax)
MyMax = d;
}
A.Comm().MinAll(&MyMin, &GlobalMin, 1);
A.Comm().MaxAll(&MyMax, &GlobalMax, 1);
A.Comm().SumAll(&MyAvg, &GlobalAvg, 1);
// does not really work fine if the number of global
// elements is not a multiple of NumPDEEqns
GlobalAvg /= (Diag.GlobalLength64() / NumPDEEqns);
if (verbose) {
char str[80];
sprintf(str, " A(k,k), eq %d", ie);
print<double>(str, GlobalMin, GlobalAvg, GlobalMax);
}
}
}
// ======== //
// row sums //
// ======== //
RowSum.MinValue(&GlobalMin);
RowSum.MaxValue(&GlobalMax);
RowSum.MeanValue(&GlobalAvg);
if (verbose) {
print();
print<double>(" sum_j A(k,j)", GlobalMin, GlobalAvg, GlobalMax);
}
// ===================================== //
// cycle over all equations for row sums //
// ===================================== //
if (NumPDEEqns > 1 ) {
if (verbose) print();
for (int ie = 0 ; ie < NumPDEEqns ; ie++) {
MyMin = DBL_MAX;
MyMax = -DBL_MAX;
MyAvg = 0.0;
for (int i = ie ; i < Diag.MyLength() ; i += NumPDEEqns) {
double d = RowSum[i];
MyAvg += d;
if (d < MyMin)
MyMin = d;
if (d > MyMax)
MyMax = d;
}
A.Comm().MinAll(&MyMin, &GlobalMin, 1);
A.Comm().MaxAll(&MyMax, &GlobalMax, 1);
A.Comm().SumAll(&MyAvg, &GlobalAvg, 1);
// does not really work fine if the number of global
// elements is not a multiple of NumPDEEqns
GlobalAvg /= (Diag.GlobalLength64() / NumPDEEqns);
if (verbose) {
char str[80];
sprintf(str, " sum_j A(k,j), eq %d", ie);
print<double>(str, GlobalMin, GlobalAvg, GlobalMax);
}
}
}
if (verbose)
Ifpack_PrintLine();
return(0);
}
