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Corr.pas
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Corr.pas
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// ###################################################################
// #### This file is part of the mathematics library project, and is
// #### offered under the licence agreement described on
// #### http://www.mrsoft.org/
// ####
// #### Copyright:(c) 2017, Michael R. . All rights reserved.
// ####
// #### Unless required by applicable law or agreed to in writing, software
// #### distributed under the License is distributed on an "AS IS" BASIS,
// #### WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// #### See the License for the specific language governing permissions and
// #### limitations under the License.
// ###################################################################
unit Corr;
interface
uses SysUtils, Math, MatrixConst, Matrix, BaseMathPersistence, Types;
{$I 'mrMath_CPU.inc'}
// standard simple linear correlation method:
type
ECorrelateException = class(EBaseMatrixException);
type
TCorrelation = class(TMatrixClass)
protected
function InternalCorrelateArr( w1, w2 : PDouble; len : integer) : Double;
function InternalCorrelate(w1, w2: IMatrix; const VarianceRatioThreshold: double = 0): double;
function InternalWeightedCorrelate( w1, w2 : IMatrix; weights : IMatrix ) : double;
public
function Correlate(x, y : IMatrix; const VarianceRatioThreshold: double = 0) : double; overload; // correlation coefficient between t, r (must have the same length)
function Correlate(x, y : IMatrix; var prob, z : double) : double; overload; // pearson correlation with Fishers's z and probobality
function CorrelateWeighted(x, y, w : IMatrix) : double; overload; // weighted correlation
function CorrelateWeighted(x, y, w : IMatrix; var prob, z : double) : double; overload; // weighted correlation
// spearman correlation. X, Y need to be vectors
class function CorrelateSpearman( x, y : IMatrix; var zd, probd, rs, probrs : double ) : double;
class function Covariance(x, y : IMatrix; Unbiased : boolean = True) : IMatrix; overload; // covariance matrix
class function Covariance(A : IMatrix; Unbiased : boolean = True) : IMatrix; overload; // covariance matrix of matrix A
end;
// see: https://en.wikipedia.org/wiki/Dynamic_time_warping
// based on Timothy Felty's matlab script (google timothy felty dynamic time warping)
// -> enhanced with maximum search window
// -> enhanced with different distance methods
// Added the recursive fast dtw method based on
// FastDTW: Toward Accurate Dynamic Time Warping in Linear Time and Space
type
TDynamicTimeWarpDistMethod = (dtwSquared, dtwAbsolute, dtwSymKullbackLeibler);
TDynamicTimeWarepReduceFunc = procedure (X : PConstDoubleArr; inLen, inOffset : NativeInt; out newLen, newOffset : NativeInt) of object;
TDynamicTimeWarp = class(TCorrelation)
private
type
TCoordRec = record
i, j : integer;
end;
TDistRec = record
next : TCoordRec;
curr : TCoordRec;
dist : double;
end;
private
fd : TDoubleDynArray;
fAccDist : TDoubleDynArray;
fW1, fW2 : IMatrix;
fW1Arr, fW2Arr : TDoubleDynArray;
fNumW : integer;
fMaxSearchWin : integer;
fMethod : TDynamicTimeWarpDistMethod;
fMemX : IMatrix; // holds the aligned memory
fMemY : IMatrix;
fX : PConstDoubleArr; // fast access to fMemx and fMemY (sse aligned)
fY : PConstDoubleArr;
fWindow : Array of TCoordRec; // pairs of x and y indices. Used in dtw and fastdtw
fDistIdx : Array of TDistRec;
fPath : Array of TCoordRec; // i, j that build up the path
fNumPath : Integer;
fMaxPathLen : integer;
fMaxWinLen : integer;
fReduceByHalf : TDynamicTimeWarepReduceFunc;
// fastdtw implementation based on the python package on: https://pypi.python.org/pypi/fastdtw
// and: Stan Salvador, and Philip Chan. “FastDTW: Toward accurate dynamic time warping in linear time and space.” Intelligent Data Analysis 11.5 (2007): 561-580.
procedure ReduceByHalfPas(X : PConstDoubleArr; inLen, inOffset : NativeInt; out newLen, newOffset : NativeInt);
{$IFNDEF MRMATH_NOASM}
procedure ReduceByHalfSSE(X : PConstDoubleArr; inLen, inOffset : NativeInt; out newLen, newOffset : NativeInt);
{$ENDIF}
function ExpandWindow(inXLen, inYLen : integer; radius : integer) : Integer;
procedure InternalFastDTW(inXOffset, inXLen, inYOffset, inYLen : integer; radius : integer; var dist : double);
function InternalDTW(inXOffset, inXLen, inYOffset, inYLen : integer; window : integer) : double;
procedure DictNewCoords(var i, j, MaxDictIdx: integer); {$IFNDEF FPC} {$IF CompilerVersion >= 17.0} inline; {$IFEND} {$ENDIF}
function DictValue(i, j, MaxDictIdx: integer): double; {$IFNDEF FPC} {$IF CompilerVersion >= 17.0} inline; {$IFEND} {$ENDIF}
function GetPathByIndex(index: integer): TCoordRec;
procedure InitXY(x, y : IMatrix); overload;
procedure InitXY(x, y : TDoubleDynArray); overload;
public
// setup
class var UseSSE : boolean;
property W1 : IMatrix read fW1; // stores the last result (warped vector)
property W2 : IMatrix read fW2;
property W1Arr : TDoubleDynArray read fW1Arr;
property W2Arr : TDoubleDynArray read fW2Arr;
property Path[index : integer] : TCoordRec read GetPathByIndex;
property PathLen : integer read fNumPath;
property MaxPathLen : integer read fMaxPathLen;
property MaxWinLen : integer read fMaxWinLen;
function DTW(t, r : IMatrix; var dist : double; MaxSearchWin : integer = 0) : IMatrix; overload;
function DTWCorr(t, r : IMatrix; MaxSearchWin : integer = 0) : double; overload; // calculate the correlation coefficient between both warped vectors
function FastDTW(x, y : IMatrix; var dist : double; Radius : integer = 1) : IMatrix; overload; // applies fastdtw
function FastDTWCorr(t, r : IMatrix; Radius : integer = 1) : double; overload; // calculate the correlation coefficient between both warped vectors
function FastDTWCorr(t, r : IMatrix; var dist : double; Radius : integer = 1) : double; overload;
// same Methods but with dynamic arrays
function DTW(t, r : TDoubleDynArray; var dist : double; MaxSearchWin : integer = 0) : TDoubleDynArray; overload;
function DTWCorr(t, r : TDoubleDynArray; MaxSearchWin : integer = 0) : double; overload;
function FastDTW(x, y : TDoubleDynArray; var dist : double; Radius : integer = 1) : TDoubleDynArray; overload;
function FastDTWCorr(t, r : TDoubleDynArray; Radius : integer = 1) : double; overload;
function FastDTWCorr(t, r : TDoubleDynArray; var dist : double; Radius : integer = 1) : double; overload;
constructor Create(DistMethod : TDynamicTimeWarpDistMethod = dtwSquared); // -> 0 = infinity
destructor Destroy; override;
end;
// spearman rank-order correlation coefficient
// sum squared rank difference as D, number of standard deviations by which D deviates fro mits nullnypothesis as zd, two sided
// significance level of this deviation as probd, spearmans rank correlation as rs, and the two -sided significance level of its
// deviation from zero as probrs.
procedure spearmanCorr( data1, data2 : PConstDoubleArr; n : integer; var d, zd, probd, rs, probrs : double);
implementation
uses MatrixASMStubSwitch, MathUtilFunc, Statistics;
const cLocDivBy2 : Array[0..1] of double = (0.5, 0.5);
cTiny : double = 1e-20;
// ###########################################
// #### Correlation (base implementation)
// ###########################################
function TCorrelation.Correlate(x, y: IMatrix; var prob, z: double): double;
var df : integer;
t : double;
begin
Result := Correlate(x, y);
df := (x.Width*x.Height - 2);
t := Result * sqrt( df/( (1 - Result + cTiny)*(1 + Result + cTiny) ) );
z := 0.5*ln( (1 + (Result) + cTiny)/(1 - Result + cTiny)); // Fishers z transformation
prob := betaI( 0.5*df, 0.5, df/(df + sqr(t)) ); // probability
end;
// note: afterwards w1 and w2 are mean normalized and w2 width and height is changed!
function TCorrelation.Correlate(x, y: IMatrix; const VarianceRatioThreshold: double = 0): double;
var w1, w2 : IMatrix;
begin
w1 := x;
if x.Height <> 1 then
w1 := x.Reshape(x.Width*x.Height, 1);
w2 := y;
if y.Height <> 1 then
w2 := y.Reshape(y.Width*y.Height, 1);
assert(w1.Width = w2.Width, 'Dimension error');
Result := InternalCorrelate(w1, w2, VarianceRatioThreshold);
end;
class function TCorrelation.Covariance(x, y: IMatrix; Unbiased : boolean = True): IMatrix;
var xc, tmp : IMatrix;
begin
if x.Width*x.Height <> y.Width*y.Height then
raise Exception.Create('Error length of x and y must be the same');
xc := TDoubleMatrixClass(x.GetObjRef.ClassType).Create(2, x.Width*x.Height);
// build matrix with 2 columns
if x.Width = 1
then
tmp := x
else
tmp := x.Reshape(1, x.Width*x.Height, True);
xc.SetColumn(0, tmp);
if y.Width = 1
then
tmp := y
else
tmp := y.Reshape(1, x.Width*x.Height, True);
xc.SetColumn(1, tmp);
Result := Covariance(xc, Unbiased);
end;
// each row is an observation, each column a variable
class function TCorrelation.Covariance(A: IMatrix; Unbiased: boolean): IMatrix;
var aMean : IMatrix;
ac : IMatrix;
tmp : IMatrix;
m : Integer;
begin
aMean := A.Mean(False);
ac := A.SubVec( aMean, True );
m := ac.Height;
tmp := ac.Transpose;
ac := tmp.Mult(ac);
if Unbiased then
dec(m);
if m > 0 then
ac.ScaleInPlace(1/m);
Result := ac;
end;
function TCorrelation.InternalCorrelate(w1, w2: IMatrix; const VarianceRatioThreshold: double = 0): double;
var meanVar1 : TMeanVarRec;
meanVar2 : TMeanVarRec;
begin
// note the routine avoids memory allocations thus it runs on the raw optimized functions:
// calc: 1/(n-1)/(var_w1*var_w2) sum_i=0_n (w1_i - mean_w1)*(w2_i - mean_w2)
MatrixMeanVar( @meanVar1, 2*sizeof(double), w1.StartElement, w1.LineWidth, w1.Width, 1, True, True);
MatrixMeanVar( @meanVar2, 2*sizeof(double), w2.StartElement, w2.LineWidth, w2.Width, 1, True, True);
// Optional: If signal has a MUCH smaller (eg: factor 3) variance
// than the reference signal -> don't scale it up
if (VarianceRatioThreshold <> 0) and (meanVar2.aVar*VarianceRatioThreshold < meanVar1.aVar) then
meanVar2.aVar := meanVar1.aVar;
// For norming the variance may not be zero
if SameValue(meanVar1.aVar, 0, cDefEpsilon) or SameValue(meanVar2.aVar, 0, cDefEpsilon) then
raise ECorrelateException.Create('Correlation Error: variance of an input vector is zero');
w1.AddInPlace( -meanVar1.aMean );
w2.AddInPlace( -meanVar2.aMean );
// dot product:
MatrixMult( @Result, sizeof(double), w1.StartElement, w2.StartElement, w1.Width, w1.Height, w2.Height, w2.Width, w1.LineWidth, sizeof(double) );
Result := Result/sqrt(meanVar1.aVar*meanVar2.aVar)/(w1.Width - 1);
end;
function TCorrelation.InternalCorrelateArr(w1, w2: PDouble;
len: integer): Double;
var meanVar1 : TMeanVarRec;
meanVar2 : TMeanVarRec;
begin
// calc: 1/(n-1)/(var_w1*var_w2) sum_i=0_n (w1_i - mean_w1)*(w2_i - mean_w2)
MatrixMeanVar( @meanVar1, 2*sizeof(double), w1, len*sizeof(double), len, 1, True, True);
MatrixMeanVar( @meanVar2, 2*sizeof(double), w2, len*sizeof(double), len, 1, True, True);
MatrixAddAndScale( w1, len*sizeof(double), len, 1, -meanVar1.aMean, 1 );
MatrixAddAndScale( w2, len*sizeof(double), len, 1, -meanVar2.aMean, 1 );
// dot product:
MatrixMult( @Result, sizeof(double), w1, w2, len, 1, 1, len, len*sizeof(double), sizeof(double));
Result := Result/sqrt(meanVar1.aVar*meanVar2.aVar)/(len - 1);
end;
function TCorrelation.InternalWeightedCorrelate(w1, w2,
weights: IMatrix): double;
var sumweights : double;
wMean1, wMean2 : double;
weightedW1, weightedW2 : IMatrix;
t : IMatrix;
ww : IMatrix;
sxx, syy : double;
begin
// calculated correlation according to
// r = S_xy/sqrt(S_xx*S_yy)
// where S_xy = sum_i=0_n weights[i]*( x[i] - M(x, w) )*( y[i] - M(y, w))
// S_xx = sum_i=0_n weights[i]*( x[i] - M(x, w) )^2
// S_yy = sum_i=0_n weights[i]*( y[i] - M(y, w) )^2
// M(x, w) = sum_i=0_n w[i]*x[i] / sum w
// M(y, w) = sum_i=0_n w[i]*y[i] / sum w
// normalize weighted mean
MatrixSum( @sumweights, sizeof(double), weights.StartElement, weights.LineWidth, weights.Width, 1, True );
if SameValue(sumweights, 0, eps(1)) then
raise ECorrelateException.Create('Weighting vector sums to zero');
ww := weights;
if not sameValue(sumweights, 1, eps( 1 ) ) then
ww := weights.Scale( 1/sumweights );
if sumweights > cDefEpsilon then
begin
MatrixMtxVecMult( @wMean1, sizeof(double), w1.StartElement, ww.StartElement, w1.LineWidth, sizeof(double), w1.Width, 1, 1, 0 );
MatrixMtxVecMult( @wMean2, sizeof(double), w2.StartElement, ww.StartElement, w2.LineWidth, sizeof(double), w2.Width, 1, 1, 0 );
weightedW1 := w1.ScaleAndAdd(-wMean1, 1);
weightedW2 := w2.ScaleAndAdd(-wMean2, 1);
t := weightedW1.ElementWiseMult(weightedw2);
MatrixMtxVecMult( @Result, sizeof(double), t.StartElement, ww.StartElement, t.LineWidth, sizeof(double), t.Width, 1, 1, 0);
weightedw1.ElementWiseMultInPlace(weightedw1);
weightedw2.ElementWiseMultInPlace(weightedw2);
MatrixMtxVecMult( @sxx, sizeof(double), weightedW1.StartElement, ww.StartElement, weightedW1.LineWidth, sizeof(double), weightedW1.Width, 1, 1, 0);
MatrixMtxVecMult( @syy, sizeof(double), weightedW2.StartElement, ww.StartElement, weightedW2.LineWidth, sizeof(double), weightedW2.Width, 1, 1, 0);
sxx := sqrt(sxx*syy);
if sxx < eps(Result) then
raise ECorrelateException.Create('Variances close too machine precission - out of bounds');
Result := Result/sxx;
end
else
raise ECorrelateException.Create('Sum of weights <= 0');
end;
// ###########################################
// #### Dynamic time warping
// ###########################################
{ TDynamicTimeWarp }
constructor TDynamicTimeWarp.Create(DistMethod : TDynamicTimeWarpDistMethod = dtwSquared);
begin
fMethod := DistMethod;
{$IFNDEF MRMATH_NOASM}
if UseSSE
then
fReduceByHalf := {$IFDEF FPC}@{$ENDIF}ReduceByHalfSSE
else
{$ENDIF}
fReduceByHalf := {$IFDEF FPC}@{$ENDIF}ReduceByHalfPas;
inherited Create;
end;
// ###########################################
// #### Base DTW algorithm
// ###########################################
function TDynamicTimeWarp.DTW(t, r: IMatrix; var dist: double; MaxSearchWin : integer = 0): IMatrix;
begin
DTW( t.SubMatrix, r.SubMatrix, dist, MaxSearchWin);
fW1 := TDoubleMatrix.Create( Copy( fW1Arr, 0, fNumW ), fNumW, 1);
fW2 := TDoubleMatrix.Create( Copy( fW2Arr, 0, fNumW ), fNumW, 1);
Result := fw1;
end;
function TDynamicTimeWarp.DTWCorr(t, r: IMatrix; MaxSearchWin : integer = 0): double;
var dist : double;
begin
// ###########################################
// #### Create time warping vectors -> stored in fw1, fw2
DTW(t, r, dist, MaxSearchWin);
// ###########################################
// #### Calculate correlation
Result := InternalCorrelate(fw1, fw2);
end;
// ###########################################
// #### Fast DTW
// ###########################################
function TDynamicTimeWarp.FastDTW(x, y: IMatrix; var dist: double; Radius : integer = 1): IMatrix;
var counter: Integer;
begin
dist := 0;
radius := Max(1, radius);
// ###########################################
// #### Preparation
fMaxPathLen := 0;
fMaxWinLen := 0;
InitXY(x, y);
// prepare memory
if Length(fWindow) < Max(x.Width, y.Width)*2 then
begin
SetLength(fWindow, (radius*4 + 4)*Max(x.Width, y.Width));
SetLength(fPath, 3*Max(x.Width, y.Width));
SetLength(fDistIdx, Length(fWindow));
end;
// ###########################################
// #### Find optimal path
fNumPath := 0;
InternalFastDTW(0, x.Width, 0, y.Width, Max(1, Radius), dist);
// ###########################################
// #### Build result
if not Assigned(fW1) then
begin
fW1 := MatrixClass.Create(fNumPath, 1);
fW2 := MatrixClass.Create(fNumPath, 1);
end;
fW1.UseFullMatrix;
fW2.UseFullMatrix;
if fW1.Width < fNumPath then
begin
fW1.SetWidthHeight(fNumPath, 1);
fW2.SetWidthHeight(fNumPath, 1);
end;
fW1.SetSubMatrix(0, 0, fNumPath, 1);
fW2.SetSubMatrix(0, 0, fNumPath, 1);
for counter := 0 to fNumPath - 1 do
begin
fW1.Vec[counter] := fX^[fPath[counter].i];
fW2.Vec[counter] := fY^[fPath[counter].j];
end;
Result := FW1;
end;
function TDynamicTimeWarp.FastDTW(x, y: TDoubleDynArray; var dist: double;
Radius: integer): TDoubleDynArray;
var counter: Integer;
begin
dist := 0;
radius := Max(1, radius);
// ###########################################
// #### Preparation
fMaxPathLen := 0;
fMaxWinLen := 0;
InitXY(x, y);
// prepare memory
if Length(fWindow) < Max(Length(x), Length(y))*2 then
begin
SetLength(fWindow, (radius*4 + 4)*Max(Length(x), Length(y)));
SetLength(fPath, 3*Max(Length(x), Length(y)));
SetLength(fDistIdx, Length(fWindow));
end;
// ###########################################
// #### Find optimal path
fNumPath := 0;
InternalFastDTW(0, Length(x), 0, Length(y), Max(1, Radius), dist);
// ###########################################
// #### Build result
if not Assigned(fW1) then
begin
fW1 := TDoubleMatrix.Create(fNumPath, 1);
fW2 := TDoubleMatrix.Create(fNumPath, 1);
end;
fW1.UseFullMatrix;
fW2.UseFullMatrix;
if fW1.Width < fNumPath then
begin
fW1.SetWidthHeight(fNumPath, 1);
fW2.SetWidthHeight(fNumPath, 1);
end;
fW1.SetSubMatrix(0, 0, fNumPath, 1);
fW2.SetSubMatrix(0, 0, fNumPath, 1);
for counter := 0 to fNumPath - 1 do
begin
fW1.Vec[counter] := fX^[fPath[counter].i];
fW2.Vec[counter] := fY^[fPath[counter].j];
end;
Result := FW1.SubMatrix;
end;
function TDynamicTimeWarp.FastDTWCorr(t, r: IMatrix; var dist: double;
Radius: integer): double;
begin
// ###########################################
// #### Create time warping vectors -> stored in fw1, fw2
FastDTW(t, r, dist, radius);
// ###########################################
// #### Calculate correlation
Result := InternalCorrelate(fw1, fw2);
end;
function TDynamicTimeWarp.FastDTWCorr(t, r: TDoubleDynArray;
Radius: integer): double;
var dist : double;
begin
Result := FastDTWCorr(t, r, dist, radius);
end;
function TDynamicTimeWarp.FastDTWCorr(t, r: TDoubleDynArray; var dist: double;
Radius: integer): double;
begin
// ###########################################
// #### Create time warping vectors -> stored in fw1, fw2
FastDTW(t, r, dist, radius);
// ###########################################
// #### Calculate correlation
Result := InternalCorrelate(fw1, fw2);
end;
function TDynamicTimeWarp.GetPathByIndex(index: integer): TCoordRec;
begin
Result := fPath[index];
end;
function TDynamicTimeWarp.FastDTWCorr(t, r: IMatrix; Radius : integer = 1): double;
var dist : double;
begin
// ###########################################
// #### Create time warping vectors -> stored in fw1, fw2
FastDTW(t, r, dist, radius);
// ###########################################
// #### Calculate correlation
Result := InternalCorrelate(fw1, fw2);
end;
// ###########################################
// #### path functions
// ###########################################
function TDynamicTimeWarp.DictValue(i, j : integer; MaxDictIdx : integer) : double;
var cnt : integer;
begin
Result := MaxDouble;
for cnt := MaxDictIDx - 1 downto 0 do
begin
if (i = fDistIdx[cnt].curr.i) and (j = fDistIdx[cnt].curr.j) then
begin
Result := fDistIdx[cnt].dist;
break;
end;
end;
end;
destructor TDynamicTimeWarp.Destroy;
begin
fW1 := nil;
fW2 := nil;
fAccDist := nil;
fW1Arr := nil;
fW2Arr := nil;
inherited;
end;
procedure TDynamicTimeWarp.DictNewCoords(var i, j : integer; var MaxDictIdx : integer);
begin
dec(MaxDictIdx);
while (MaxDictIdx >= 0) and ((fDistIdx[MaxDictIdx].curr.i <> i) or (fDistIdx[maxDictIdx].curr.j <> j)) do
dec(MaxDictIdx);
if MaxDictIdx >= 0 then
begin
i := fDistIdx[MaxDictIdx].next.i;
j := fDistIdx[MaxDictIdx].next.j;
end;
end;
// ###########################################
// #### private fast dtw functions
// ###########################################
function TDynamicTimeWarp.InternalDTW(inXOffset, inXLen, inYOffset, inYLen : integer; window : integer) : double;
var i, j : Integer;
cnt : integer;
dt : double;
dIdx : integer;
dist0, dist1, dist2 : double;
tmp : TCoordRec;
begin
// perform a full inXLen*inYLen coordinate space
if window = 0 then
begin
if Length(fWindow) < inXLen*inYLen then
SetLength(fWindow, inXLen*inYLen);
for i := 1 to inXLen do
begin
for j := 1 to inYLen do
begin
fWindow[window].i := i;
fWindow[window].j := j;
inc(window);
end;
end;
end;
fMaxWinLen := Max(fMaxWinLen, window);
if Length( fDistIdx ) < (inXLen*inYLen) then
SetLength( fDistIdx, inXLen*inYLen );
// ###########################################
// #### Prepare a path list through the given coordinate list
// first we take a forward step through a given set of coordinates
// and then search back for the shortest path
fDistIdx[0].dist := 0;
fDistIdx[0].next.i := 0;
fDistIdx[0].next.j := 0;
fDistIdx[0].curr.i := 0;
fDistIdx[0].curr.j := 0;
dIdx := 1;
for cnt := 0 to window - 1 do
begin
i := fWindow[cnt].i;
j := fWindow[cnt].j;
case fMethod of
dtwSquared: dt := sqr( fX^[inXOffset + i - 1] - fY^[inYOffset + j - 1]);
dtwAbsolute: dt := abs( fX^[inXOffset + i - 1] - fY^[inYOffset + j - 1] );
dtwSymKullbackLeibler: dt := fX^[inXOffset + i - 1] - fY^[inYOffset + j - 1]*(ln(fX^[inXOffset + i - 1]) - ln(fY^[inYOffset + j - 1]));
else
dt := abs( fX^[inXOffset + i - 1] - fY^[inYOffset + j - 1] );
end;
dist0 := DictValue(i - 1, j, dIdx);
dist1 := DictValue(i, j - 1, dIdx);
dist2 := DictValue(i - 1, j - 1, dIdx);
if (dist0 = cMaxDouble) and (dist1 = cMaxDouble) and (dist2 = cMaxDouble) then
continue;
fDistIdx[dIdx].curr.i := i;
fDistIdx[dIdx].curr.j := j;
// according to the distance measure store the path coordinates for the next step
if dist2 <= Min(dist1, dist0) then
begin
fDistIdx[dIdx].dist := dist2 + dt;
fDistIdx[dIdx].next.i := i - 1;
fDistIdx[dIdx].next.j := j - 1;
end
else if dist0 < Min(dist1, dist2) then
begin
fDistIdx[dIdx].dist := dist0 + dt;
fDistIdx[dIdx].next.i := i - 1;
fDistIdx[dIdx].next.j := j;
end
else
begin
fDistIdx[dIdx].dist := dist1 + dt;
fDistIdx[dIdx].next.i := i;
fDistIdx[dIdx].next.j := j - 1;
end;
inc(dIdx);
end;
// ###########################################
// #### Build path (backwards)
Result := fDistIdx[dIdx - 1].dist;
i := inXLen;
j := inYLen;
fNumPath := 0;
while ( (i > 0) and (j > 0) ) and (dIdx >= 0) do
begin
fPath[fNumPath].i := i - 1;
fPath[fNumPath].j := j - 1;
inc(fNumPath);
DictNewCoords(i, j, dIdx);
end;
// reverse path
i := 0;
j := fNumPath - 1;
while i < j do
begin
tmp := fPath[i];
fPath[i] := fPath[j];
fPath[j] := tmp;
inc(i);
dec(j);
end;
fMaxPathLen := Max(fMaxPathLen, fNumPath);
end;
procedure TDynamicTimeWarp.InitXY(x, y: IMatrix);
begin
if not Assigned(fMemX) or (fMemX.Width < 2* (x.Width + x.Width and 1)) then
begin
fMemx := MatrixClass.Create( 2* (x.Width + x.Width and 1), 1);
fX := PConstDoubleArr(fMemX.StartElement);
end;
Move(x.StartElement^, fx^[0], sizeof(double)*x.Width);
if not Assigned(fMemY) or (fMemY.Width < 2* (y.Width + y.Width and 1)) then
begin
fMemY := MatrixClass.Create( 2* (y.Width + y.Width and 1), 1);
fY := PConstDoubleArr(fMemY.StartElement);
end;
Move(y.StartElement^, fy^[0], sizeof(double)*y.Width);
end;
procedure TDynamicTimeWarp.InitXY(x, y: TDoubleDynArray);
var lenX, lenY : integer;
begin
lenX := Length(x);
lenY := Length(y);
if not Assigned(fMemX) or (fMemX.Width < 2* (lenX + lenX and 1)) then
begin
fMemx := MatrixClass.Create( 2* (lenX + lenX and 1), 1);
fX := PConstDoubleArr(fMemX.StartElement);
end;
Move(x[0], fx^[0], sizeof(double)*lenX);
if not Assigned(fMemY) or (fMemY.Width < 2* (lenY + lenY and 1)) then
begin
fMemY := MatrixClass.Create( 2* (lenY + lenY and 1), 1);
fY := PConstDoubleArr(fMemY.StartElement);
end;
Move(y[0], fy^[0], sizeof(double)*lenY);
end;
procedure TDynamicTimeWarp.InternalFastDTW(inXOffset, inXLen, inYOffset, inYLen : integer; radius : integer; var dist : double);
var minTimeSize : Integer;
newXOffset, newXLen : NativeInt;
newYOffset, newYLen : NativeInt;
windowCnt : integer;
begin
minTimeSize := radius + 2;
// check for break condition
if (inXLen < minTimeSize) or (inYLen < minTimeSize) then
begin
dist := InternalDTW(inXOffset, inXLen, inYOffset, inYLen, 0);
exit;
end;
// reduce by half recursively
fReduceByHalf(fX, inXLen, inXOffset, newXLen, newXOffset);
fReduceByHalf(fY, inYLen, inYOffset, newYLen, newYOffset);
InternalFastDTW(newXOffset, newXLen, newYOffset, newYLen, radius, dist);
// rebuild
windowCnt := ExpandWindow(inXLen, inYLen, radius);
dist := InternalDTW(inXOffset, inXLen, inYOffset, inYLen, windowCnt);
end;
procedure TDynamicTimeWarp.ReduceByHalfPas(X : PConstDoubleArr; inLen, inOffset : NativeInt; out newLen, newOffset : NativeInt);
var counter: NativeInt;
idx : NativeInt;
begin
newOffset := inOffset + inLen;
newLen := inLen div 2;
idx := inOffset;
for counter := newOffset to newOffset + newLen - 1 do
begin
X^[counter] := 0.5*(x^[idx] + X^[idx + 1]);
inc(idx, 2);
end;
end;
{$IFNDEF MRMATH_NOASM}
{$IFDEF x64}
// 64bit version
procedure TDynamicTimeWarp.ReduceByHalfSSE(X : PConstDoubleArr; inLen,
inOffset: NativeInt; out newLen, newOffset: NativeInt);
{$IFDEF FPC}
begin
{$ENDIF}
asm
{$IFDEF UNIX}
// Linux uses a diffrent ABI -> copy over the registers so they meet with winABI
// (note that the 5th and 6th parameter are are on the stack)
// The parameters are passed in the following order:
// RDI, RSI, RDX, RCX -> mov to RCX, RDX, R8, R9
mov r8, rdx;
mov r9, rcx;
mov rcx, rdi;
mov rdx, rsi;
{$ENDIF}
// rcx self, rdx X, r8 inLen, r9 = inOffset
// newOffset := inOffset + inLen;
// newOffset := newOffset + newOffset and 1;
mov r10, newOffset;
mov r11, r8;
add r11, r9;
inc r11; // make sure the last bit is 0
and r11, $FFFFFFFFFFFFFFFE; // clear the lowest bit (ensure SSE alignment)
mov [r10], r11;
// newLen := inLen div 2;
shr r8, 1;
mov r10, newLen;
mov [r10], r8;
movupd xmm3, [rip + cLocDivBy2];
// test if we have enough elements to handle 2 elements at once
cmp r8, 2;
jl @lastElem;
@loop1:
// loop handles two elements in one step
movapd xmm0, [rdx + 8*r9];
movapd xmm1, [rdx + 8*r9 + 16];
// perform xmm0 = 0.5( [rcx + 8] + [rcx + 16]), 0.5*([rcx + 16] + [rcx + 32])
haddpd xmm0, xmm1;
mulpd xmm0, xmm3;
// write back two element
movapd [rdx + 8*r11], xmm0;
add r11, 2;
add r9, 4;
sub r8, 2;
jg @loop1;
test r8, r8;
je @exit;
@lastElem:
// last element
movsd xmm0, [rcx + 8*r9];
movsd xmm1, [rcx + 8*r9 + 8];
addsd xmm0, xmm1;
mulsd xmm0, xmm3;
movsd [rdx + 8*r11], xmm0;
@exit:
end;
{$IFDEF FPC}
end;
{$ENDIF}
{$ELSE}
// 32 bit version
procedure TDynamicTimeWarp.ReduceByHalfSSE(X : PConstDoubleArr; inLen,
inOffset: NativeInt; out newLen, newOffset: NativeInt);
{$IFDEF FPC}
begin
{$ENDIF}
asm
// edx: X, ecx : inlen
push ebx;
// newOffset := inOffset + inLen;
mov ebx, newOffset;
mov eax, inOffset;
//add eax, inLen;
add eax, ecx;
inc eax; // make sure the last bit is 0
and eax, $FFFFFFFE; // clear the lowest bit (ensure SSE alignment)
mov [ebx], eax;
// newLen := inLen div 2;
//mov ecx, inLen;
shr ecx, 1;
mov ebx, newLen;
mov [ebx], ecx;
movupd xmm3, cLocDivBy2;
// eax := counter for x[idx]
// edx := counter for x[counter];
//mov edx, X;
mov ebx, inOffset;
// test if we have enough elements to handle 2 elements at once
cmp ecx, 2;
jl @lastElem;
@loop1:
// loop handles two elements in one step
movapd xmm0, [edx + 8*ebx];
movapd xmm1, [edx + 8*ebx + 16];
// perform xmm0 = 0.5( [edx + 8] + [edx + 16]), 0.5*([edx + 16] + [edx + 32])
haddpd xmm0, xmm1;
mulpd xmm0, xmm3;
// write back two element
movapd [edx + 8*eax], xmm0;
add eax, 2;
add ebx, 4;
sub ecx, 2;
jg @loop1;
test ecx, ecx;
je @exit;
@lastElem:
// last element
movsd xmm0, [edx + 8*ebx];
movsd xmm1, [edx + 8*ebx + 8];
addsd xmm0, xmm1;
mulsd xmm0, xmm3;
movsd [edx + 8*eax], xmm0;
@exit:
pop ebx;
end;
{$IFDEF FPC}
end;
{$ENDIF}
{$ENDIF}
{$ENDIF}
function TDynamicTimeWarp.ExpandWindow(inXLen, inYLen, radius: integer): Integer;
var cnt : integer;
baseI, baseJ : integer;
minJ, maxJ : integer;
pathCnt : integer;
prevRadiusPathIdx : integer;
nextRadiusPathIdx : integer;
i, j : integer;
base : integer;
numItems : integer;
begin
Result := 0;
prevRadiusPathIdx := 0;
nextRadiusPathIdx := 0;
base := fNumPath - 1;
// handle last element
for cnt := 1 to radius do
begin
fPath[fNumPath].i := fPath[base].i + cnt;
fPath[fNumPath].j := fPath[base].j;
inc(fNumPath);
end;
baseI := -1;
// build up new window from the previous path
for cnt := 0 to fNumPath - 1 do
begin
// check if we already caught that particular i
if fPath[cnt].i = baseI then
continue;
baseI := fPath[cnt].i;
baseJ := fPath[cnt].j;
// find the min max in the given radius
minJ := Max(0, baseJ - radius);
maxJ := baseJ + radius;
// find previous
while (fPath[prevRadiusPathIdx].i < baseI - radius) do
inc(prevRadiusPathIdx);
// find next
while (nextRadiusPathIdx < fNumPath - 1) and (fPath[nextRadiusPathIdx].i <= baseI + radius) do
inc(nextRadiusPathIdx);
// find boundaries
for pathCnt := prevRadiusPathIdx to nextRadiusPathIdx do
begin
minj := Max(0, Min( fPath[pathCnt].j - radius, minJ) );
maxj := Max( fPath[pathCnt].j + radius, maxJ);