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 IMatrixSparse <MatrixByArr> GetMatrixSparse()
{
if (this is HessMatrixSparse)
{
return((this as HessMatrixSparse).GetMatrixSparse());
}
if (this is HessMatrixDense)
{
return(HessMatrixSparse.FromMatrix(this).GetMatrixSparse());
}
if (this is HessMatrixLayeredArray)
{
return(this as IMatrixSparse <MatrixByArr>);
}
throw new NotImplementedException();
}
private static HessMatrix Get_BInvDC
(HessMatrix A
, HessMatrix C
, HessMatrix D
, bool process_disp_console
, string[] options
, 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 }
});
}
}
HessMatrixSparse 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 (process_disp_console)
{
System.Console.Write("Y");
}
//Matlab.Execute("[i,j,s] = find(sparse(BinvDC));");
//int[] listi = Matlab.GetVectorInt("i");
//int[] listj = Matlab.GetVectorInt("j");
//double[] lists = Matlab.GetVector("s");
//int colsize = Matlab.GetValueInt("size(BinvDC,1)");
//int rowsize = Matlab.GetValueInt("size(BinvDC,2)");
//Matrix BBinvDDCC = Matrix.Zeros(colsize, rowsize);
//for(int i=0; i<listi.Length; i++)
// BBinvDDCC[listi[i], listj[i]] = lists[i];
//GC.Collect(0);
BB_invDD_CC = HessMatrixSparse.FromMatrix(BBinvDDCC, parallel); if (process_disp_console)
{
System.Console.Write("Z), ");
}
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);
}
static HessMatrix GetMulImpl(HessMatrix left, HessMatrix right, ILinAlg ila, bool warning)
{
if (HDebug.Selftest())
{
Matrix h1 = 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 h2 = HessMatrixSparse.FromMatrix(h1);
Matrix h11 = Matrix.GetMul(h1, h1);
HessMatrix h22 = HessMatrix.GetMulImpl(h2, h2, null, false);
Matrix hdiff = h11 - h22;
HDebug.AssertToleranceMatrix(0, hdiff);
}
if ((left is HessMatrixDense) && (right is HessMatrixDense))
{
if (ila != null)
{
return(new HessMatrixDense {
hess = ila.Mul(left, right)
});
}
if (warning)
{
HDebug.ToDo("Check (HessMatrixDense * HessMatrixDense) !!!");
}
}
Dictionary <int, Dictionary <int, Tuple <int, int, MatrixByArr> > > left_ic_rows = new Dictionary <int, Dictionary <int, Tuple <int, int, MatrixByArr> > >();
foreach (var ic_row in left.EnumRowBlocksAll())
{
left_ic_rows.Add(ic_row.Item1, ic_row.Item2.HToDictionaryWithKeyItem2());
}
Dictionary <int, Dictionary <int, Tuple <int, int, MatrixByArr> > > right_ir_cols = new Dictionary <int, Dictionary <int, Tuple <int, int, MatrixByArr> > >();
foreach (var ir_col in right.EnumColBlocksAll())
{
right_ir_cols.Add(ir_col.Item1, ir_col.Item2.HToDictionaryWithKeyItem1());
}
HessMatrix mul = null;
if ((left is HessMatrixDense) && (right is HessMatrixDense))
{
mul = HessMatrixDense.ZerosDense(left.ColSize, right.RowSize);
}
else
{
mul = HessMatrixSparse.ZerosSparse(left.ColSize, right.RowSize);
}
for (int ic = 0; ic < left.ColBlockSize; ic++)
{
var left_row = left_ic_rows[ic];
if (left_row.Count == 0)
{
continue;
}
for (int ir = 0; ir < right.RowBlockSize; ir++)
{
var right_col = right_ir_cols[ir];
if (right_col.Count == 0)
{
continue;
}
foreach (var left_ck in left_row)
{
int ik = left_ck.Key;
HDebug.Assert(ic == left_ck.Value.Item1);
HDebug.Assert(ik == left_ck.Value.Item2);
if (right_col.ContainsKey(ik))
{
var right_kr = right_col[ik];
HDebug.Assert(ik == right_kr.Item1);
HDebug.Assert(ir == right_kr.Item2);
MatrixByArr mul_ckr = mul.GetBlock(ic, ir) + left_ck.Value.Item3 * right_kr.Item3;
mul.SetBlock(ic, ir, mul_ckr);
}
}
}
}
return(mul);
}