public static HessMatrix GetMulImpl(ILinAlg ila, bool warning, params HessMatrix[] mats)
{
if (ila != null)
{
if (HDebug.Selftest())
{
Matrix h0 = new double[, ] {
{ 0, 1, 2, 3, 4, 5 }
, { 1, 2, 3, 4, 5, 6 }
, { 2, 3, 4, 5, 6, 7 }
, { 3, 4, 5, 6, 7, 8 }
, { 4, 5, 6, 7, 8, 9 }
, { 5, 6, 7, 8, 9, 0 }
};
HessMatrix h1 = HessMatrixDense.FromMatrix(h0);
HessMatrix h2 = HessMatrixSparse.FromMatrix(h0);
Matrix t0 = Matrix.GetMul(Matrix.GetMul(h1, h1), h1);
{
Matrix t1 = GetMulImpl(ila, false, h1, h1, h1); double d1 = (t0 - t1).HAbsMax(); HDebug.Assert(0 == d1);
Matrix t2 = GetMulImpl(ila, false, h1, h1, h2); double d2 = (t0 - t2).HAbsMax(); HDebug.Assert(0 == d2);
Matrix t3 = GetMulImpl(ila, false, h1, h2, h1); double d3 = (t0 - t3).HAbsMax(); HDebug.Assert(0 == d3);
Matrix t4 = GetMulImpl(ila, false, h1, h2, h2); double d4 = (t0 - t4).HAbsMax(); HDebug.Assert(0 == d4);
Matrix t5 = GetMulImpl(ila, false, h2, h1, h1); double d5 = (t0 - t5).HAbsMax(); HDebug.Assert(0 == d5);
Matrix t6 = GetMulImpl(ila, false, h2, h1, h2); double d6 = (t0 - t6).HAbsMax(); HDebug.Assert(0 == d6);
Matrix t7 = GetMulImpl(ila, false, h2, h2, h1); double d7 = (t0 - t7).HAbsMax(); HDebug.Assert(0 == d7);
Matrix t8 = GetMulImpl(ila, false, h2, h2, h2); double d8 = (t0 - t8).HAbsMax(); HDebug.Assert(0 == d8);
}
{
Matrix t1 = GetMulImpl(null, false, h1, h1, h1); double d1 = (t0 - t1).HAbsMax(); HDebug.Assert(0 == d1);
Matrix t2 = GetMulImpl(null, false, h1, h1, h2); double d2 = (t0 - t2).HAbsMax(); HDebug.Assert(0 == d2);
Matrix t3 = GetMulImpl(null, false, h1, h2, h1); double d3 = (t0 - t3).HAbsMax(); HDebug.Assert(0 == d3);
Matrix t4 = GetMulImpl(null, false, h1, h2, h2); double d4 = (t0 - t4).HAbsMax(); HDebug.Assert(0 == d4);
Matrix t5 = GetMulImpl(null, false, h2, h1, h1); double d5 = (t0 - t5).HAbsMax(); HDebug.Assert(0 == d5);
Matrix t6 = GetMulImpl(null, false, h2, h1, h2); double d6 = (t0 - t6).HAbsMax(); HDebug.Assert(0 == d6);
Matrix t7 = GetMulImpl(null, false, h2, h2, h1); double d7 = (t0 - t7).HAbsMax(); HDebug.Assert(0 == d7);
Matrix t8 = GetMulImpl(null, false, h2, h2, h2); double d8 = (t0 - t8).HAbsMax(); HDebug.Assert(0 == d8);
}
}
}
HessMatrix mul = null;
foreach (HessMatrix mat in mats)
{
if (mul == null)
{
mul = mat;
}
else
{
mul = GetMulImpl(mul, mat, ila, warning);
}
}
return(mul);
}
public HessMatrix SubMatrixByAtomsImpl0(IList <int> idxColAtoms, IList <int> idxRowAtoms)
{
if (SubMatrixByAtomsImpl0_selftest2)
{
SubMatrixByAtomsImpl0_selftest2 = false;
Matrix thess1 = new double[, ] {
{ 0, 1, 2, 3, 4, 5 }
, { 1, 2, 3, 4, 5, 6 }
, { 2, 3, 4, 5, 6, 7 }
, { 3, 4, 5, 6, 7, 8 }
, { 4, 5, 6, 7, 8, 9 }
, { 5, 6, 7, 8, 9, 0 }
};
HessMatrix thess2 = HessMatrixDense.FromMatrix(thess1);
HessMatrix thess3 = thess2.SubMatrixByAtomsImpl0(new int[] { 0 }, new int[] { 1 });
Matrix thess4 = new double[, ] {
{ 3, 4, 5 }
, { 4, 5, 6 }
, { 5, 6, 7 }
};
HDebug.AssertToleranceMatrix(0, thess3 - thess4);
}
HessMatrix nhess = Zeros(idxColAtoms.Count * 3, idxRowAtoms.Count * 3);
for (int nbc = 0; nbc < idxColAtoms.Count; nbc++)
{
for (int nbr = 0; nbr < idxRowAtoms.Count; nbr++)
{
int bc = idxColAtoms[nbc]; if (bc < 0)
{
continue;
}
int br = idxRowAtoms[nbr]; if (br < 0)
{
continue;
}
if (HasBlock(bc, br) == false)
{
continue;
}
MatrixByArr block = GetBlock(bc, br).CloneT(); // hessian matrix for interaction between atom i and j
HDebug.Assert(block.IsZero() == false);
nhess.SetBlock(nbc, nbr, block);
}
}
return(nhess);
}
private static HessMatrix GetHessCoarseResiIterImpl_Matlab_IterLowerTri_Get_BInvDC
(HessMatrix A
, HessMatrix C
, HessMatrix D
, bool process_disp_console
, string[] options
, double?thld_BinvDC = null
, bool parallel = false
)
{
HessMatrix B_invD_C;
Dictionary <int, int> Cbr_CCbr = new Dictionary <int, int>();
List <int> CCbr_Cbr = new List <int>();
foreach (ValueTuple <int, int, MatrixByArr> bc_br_bval in C.EnumBlocks())
{
int Cbr = bc_br_bval.Item2;
if (Cbr_CCbr.ContainsKey(Cbr) == false)
{
HDebug.Assert(Cbr_CCbr.Count == CCbr_Cbr.Count);
int CCbr = Cbr_CCbr.Count;
Cbr_CCbr.Add(Cbr, CCbr);
CCbr_Cbr.Add(Cbr);
HDebug.Assert(CCbr_Cbr[CCbr] == Cbr);
}
}
HessMatrix CC = HessMatrixSparse.ZerosSparse(C.ColSize, Cbr_CCbr.Count * 3);
{
Action <ValueTuple <int, int, MatrixByArr> > func = delegate(ValueTuple <int, int, MatrixByArr> bc_br_bval)
{
int Cbc = bc_br_bval.Item1; int CCbc = Cbc;
int Cbr = bc_br_bval.Item2; int CCbr = Cbr_CCbr[Cbr];
var bval = bc_br_bval.Item3;
lock (CC)
CC.SetBlock(CCbc, CCbr, bval);
};
if (parallel)
{
Parallel.ForEach(C.EnumBlocks(), func);
}
else
{
foreach (var bc_br_bval in C.EnumBlocks())
{
func(bc_br_bval);
}
}
}
if (process_disp_console)
{
System.Console.Write("squeezeC({0,6}->{1,6} blk), ", C.RowBlockSize, CC.RowBlockSize);
}
{
/// If a diagonal element of D is null, that row and column should be empty.
/// This assume that the atom is removed. In this case, the removed diagonal block
/// is replace as the 3x3 identity matrix.
///
/// [B1 0] [ A 0 ]^-1 [C1 C2 C3] = [B1 0] [ A^-1 0 ] [C1 C2 C3]
/// [B2 0] [ 0 I ] [ 0 0 0] [B2 0] [ 0 I^-1 ] [ 0 0 0]
/// [B3 0] [B3 0]
/// = [B1.invA 0] [C1 C2 C3]
/// [B2.invA 0] [ 0 0 0]
/// [B3.invA 0]
/// = [B1.invA.C1 B1.invA.C2 B1.invA.C3]
/// [B2.invA.C1 B2.invA.C2 B2.invA.C3]
/// [B3.invA.C1 B3.invA.C2 B3.invA.C3]
///
{
//HDebug.Exception(D.ColBlockSize == D.RowBlockSize);
for (int bi = 0; bi < D.ColBlockSize; bi++)
{
if (D.HasBlock(bi, bi) == true)
{
continue;
}
//for(int bc=0; bc< D.ColBlockSize; bc++) HDebug.Exception( D.HasBlock(bc, bi) == false);
//for(int br=0; br< D.RowBlockSize; br++) HDebug.Exception( D.HasBlock(bi, br) == false);
//for(int br=0; br<CC.RowBlockSize; br++) HDebug.Exception(CC.HasBlock(bi, br) == false);
D.SetBlock(bi, bi, new double[3, 3] {
{ 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 }
});
}
}
HessMatrix BB_invDD_CC;
using (new Matlab.NamedLock(""))
{
Matlab.Execute("clear;"); if (process_disp_console)
{
System.Console.Write("matlab(");
}
Matlab.PutMatrix("C", CC); if (process_disp_console)
{
System.Console.Write("C"); //Matlab.PutSparseMatrix("C", CC.GetMatrixSparse(), 3, 3);
}
Matlab.PutMatrix("D", D); if (process_disp_console)
{
System.Console.Write("D");
}
{ // Matlab.Execute("BinvDC = (C' / D) * C;");
if (options != null && options.Contains("pinv(D)"))
{
string msg = Matlab.Execute("BinvDC = (C' / D) * C;", true);
if (msg != "")
{
Matlab.Execute("BinvDC = C' * pinv(D) * C;");
}
}
else
{
Matlab.Execute("BinvDC = (C' / D) * C;");
}
} if (process_disp_console)
{
System.Console.Write("X");
}
/// » whos
/// Name Size Bytes Class Attributes
/// // before compressing C matrix
/// C 1359x507 5512104 double // C 1359x1545 16797240 double
/// CC 1359x507 198464 double sparse // CC 1359x1545 206768 double sparse
/// D 1359x1359 14775048 double // D 1359x1359 14775048 double
/// DD 1359x1359 979280 double sparse // DD 1359x1359 979280 double sparse
/// ans 1x1 8 double
///
/// » tic; for i=1:30; A=(C' / D) * C; end; toc dense * dense * dense => 8.839463 seconds. (win)
/// Elapsed time is 8.839463 seconds.
/// » tic; for i=1:30; AA=(CC' / DD) * CC; end; toc sparse * sparse * sparse => 27.945534 seconds.
/// Elapsed time is 27.945534 seconds.
/// » tic; for i=1:30; AAA=(C' / DD) * C; end; toc sparse * dense * sparse => 29.136144 seconds.
/// Elapsed time is 29.136144 seconds.
/// »
/// » tic; for i=1:30; A=(C' / D) * C; end; toc dense * dense * dense => 8.469071 seconds. (win)
/// Elapsed time is 8.469071 seconds.
/// » tic; for i=1:30; AA=(CC' / DD) * CC; end; toc sparse * sparse * sparse => 28.309953 seconds.
/// Elapsed time is 28.309953 seconds.
/// » tic; for i=1:30; AAA=(C' / DD) * C; end; toc sparse * dense * sparse => 28.586375 seconds.
/// Elapsed time is 28.586375 seconds.
//Matrix BBinvDDCC = Matlab.GetMatrix("BinvDC", true);
if (thld_BinvDC != null)
{
Matlab.Execute("BinvDC(find(BinvDC < " + thld_BinvDC.ToString() + ")) = 0;");
}
if (Matlab.GetValue("nnz(BinvDC)/numel(BinvDC)") > 0.5)
{
double[,] arr = Matlab.GetMatrix("BinvDC", true);
BB_invDD_CC = HessMatrixDense.FromMatrix(arr);
if (process_disp_console)
{
System.Console.Write("Y), ");
}
}
else
{
Matlab.Execute("[i,j,s] = find(sparse(BinvDC));");
TVector <int> listi = Matlab.GetVectorLargeInt("i", true);
TVector <int> listj = Matlab.GetVectorLargeInt("j", true);
TVector <double> lists = Matlab.GetVectorLarge("s", true);
int colsize = Matlab.GetValueInt("size(BinvDC,1)");
int rowsize = Matlab.GetValueInt("size(BinvDC,2)");
Dictionary <ValueTuple <int, int>, MatrixByArr> lst_bc_br_bval = new Dictionary <ValueTuple <int, int>, MatrixByArr>();
for (long i = 0; i < listi.SizeLong; i++)
{
int c = listi[i] - 1; int bc = c / 3; int ic = c % 3;
int r = listj[i] - 1; int br = r / 3; int ir = r % 3;
double v = lists[i];
ValueTuple <int, int> bc_br = new ValueTuple <int, int>(bc, br);
if (lst_bc_br_bval.ContainsKey(bc_br) == false)
{
lst_bc_br_bval.Add(bc_br, new double[3, 3]);
}
lst_bc_br_bval[bc_br][ic, ir] = v;
}
// Matrix BBinvDDCC = Matrix.Zeros(colsize, rowsize);
// for(int i=0; i<listi.Length; i++)
// BBinvDDCC[listi[i]-1, listj[i]-1] = lists[i];
// //GC.Collect(0);
BB_invDD_CC = HessMatrixSparse.ZerosSparse(colsize, rowsize);
foreach (var bc_br_bval in lst_bc_br_bval)
{
int bc = bc_br_bval.Key.Item1;
int br = bc_br_bval.Key.Item2;
var bval = bc_br_bval.Value;
BB_invDD_CC.SetBlock(bc, br, bval);
}
if (process_disp_console)
{
System.Console.Write("Z), ");
}
if (HDebug.IsDebuggerAttached)
{
for (int i = 0; i < listi.Size; i++)
{
int c = listi[i] - 1;
int r = listj[i] - 1;
double v = lists[i];
HDebug.Assert(BB_invDD_CC[c, r] == v);
}
}
}
Matlab.Execute("clear;");
}
//GC.Collect(0);
B_invD_C = HessMatrixSparse.ZerosSparse(C.RowSize, C.RowSize);
{
// for(int bcc=0; bcc<CCbr_Cbr.Count; bcc++)
// {
// int bc = CCbr_Cbr[bcc];
// for(int brr=0; brr<CCbr_Cbr.Count; brr++)
// {
// int br = CCbr_Cbr[brr];
// HDebug.Assert(B_invD_C.HasBlock(bc, br) == false);
// if(BB_invDD_CC.HasBlock(bcc, brr) == false)
// continue;
// var bval = BB_invDD_CC.GetBlock(bcc, brr);
// B_invD_C.SetBlock(bc, br, bval);
// HDebug.Exception(A.HasBlock(bc, bc));
// HDebug.Exception(A.HasBlock(br, br));
// }
// }
Action <ValueTuple <int, int, MatrixByArr> > func = delegate(ValueTuple <int, int, MatrixByArr> bcc_brr_bval)
{
int bcc = bcc_brr_bval.Item1;
int brr = bcc_brr_bval.Item2;
var bval = bcc_brr_bval.Item3;
int bc = CCbr_Cbr[bcc];
int br = CCbr_Cbr[brr];
lock (B_invD_C)
B_invD_C.SetBlock(bc, br, bval);
};
if (parallel)
{
Parallel.ForEach(BB_invDD_CC.EnumBlocks(), func);
}
else
{
foreach (var bcc_brr_bval in BB_invDD_CC.EnumBlocks())
{
func(bcc_brr_bval);
}
}
}
}
GC.Collect(0);
return(B_invD_C);
}
public HessMatrix SubMatrixByAtomsImpl
(bool ignNegIdx // [false]
, IList <int> idxColAtoms
, IList <int> idxRowAtoms
, bool bCloneBlock
, bool parallel = false
)
{
Dictionary <int, int[]> col_idx2nidx = new Dictionary <int, int[]>();
HashSet <int> col_idxs = new HashSet <int>();
for (int nidx = 0; nidx < idxColAtoms.Count; nidx++)
{
int idx = idxColAtoms[nidx];
if (idx < 0)
{
if (ignNegIdx)
{
continue;
}
throw new IndexOutOfRangeException();
}
if (col_idx2nidx.ContainsKey(idx) == false)
{
col_idx2nidx.Add(idx, new int[0]);
}
col_idx2nidx[idx] = col_idx2nidx[idx].HAdd(nidx);
col_idxs.Add(idx);
}
Dictionary <int, int[]> row_idx2nidx = new Dictionary <int, int[]>();
for (int nidx = 0; nidx < idxRowAtoms.Count; nidx++)
{
int idx = idxRowAtoms[nidx];
if (idx < 0)
{
if (ignNegIdx)
{
continue;
}
throw new IndexOutOfRangeException();
}
if (row_idx2nidx.ContainsKey(idx) == false)
{
row_idx2nidx.Add(idx, new int[0]);
}
row_idx2nidx[idx] = row_idx2nidx[idx].HAdd(nidx);
}
HessMatrix nhess = Zeros(idxColAtoms.Count * 3, idxRowAtoms.Count * 3);
{
Action <ValueTuple <int, int, MatrixByArr> > func = delegate(ValueTuple <int, int, MatrixByArr> bc_br_bval)
{
int bc = bc_br_bval.Item1; if (col_idx2nidx.ContainsKey(bc) == false)
{
return;
}
int br = bc_br_bval.Item2; if (row_idx2nidx.ContainsKey(br) == false)
{
return;
}
var bval = bc_br_bval.Item3;
if (bCloneBlock)
{
foreach (int nbc in col_idx2nidx[bc])
{
foreach (int nbr in row_idx2nidx[br])
{
lock (nhess)
nhess.SetBlock(nbc, nbr, bval.CloneT());
}
}
}
else
{
foreach (int nbc in col_idx2nidx[bc])
{
foreach (int nbr in row_idx2nidx[br])
{
lock (nhess)
nhess.SetBlock(nbc, nbr, bval);
}
}
}
};
if (parallel)
{
Parallel.ForEach(EnumBlocksInCols(col_idxs.ToArray()), func);
}
else
{
foreach (var bc_br_bval in EnumBlocksInCols(col_idxs.ToArray()))
{
func(bc_br_bval);
}
}
}
if (SubMatrixByAtomsImpl_selftest2)
{
SubMatrixByAtomsImpl_selftest2 = false;
HessMatrix tnhess = SubMatrixByAtomsImpl0(idxColAtoms, idxRowAtoms);
HDebug.Assert(HessMatrix.HessMatrixSparseEqual(nhess, tnhess));
//////////////////////////////////////////
Matrix thess1 = new double[, ] {
{ 0, 1, 2, 3, 4, 5 }
, { 1, 2, 3, 4, 5, 6 }
, { 2, 3, 4, 5, 6, 7 }
, { 3, 4, 5, 6, 7, 8 }
, { 4, 5, 6, 7, 8, 9 }
, { 5, 6, 7, 8, 9, 0 }
};
HessMatrix thess2 = HessMatrixDense.FromMatrix(thess1);
HessMatrix thess3 = thess2.SubMatrixByAtomsImpl(false, new int[] { 0 }, new int[] { 1 }, true);
Matrix thess4 = new double[, ] {
{ 3, 4, 5 }
, { 4, 5, 6 }
, { 5, 6, 7 }
};
HDebug.AssertToleranceMatrix(0, thess3 - thess4);
}
return(nhess);
}
