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muhammadalhroobmuhammadalhroob
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[Math] Optimize the TMatrix multplication function
Rewrite the matrix multplication function. Rearrange the loops and use blocking to enhance the speed (a factor of 6 for very large matrices).
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‎math/matrix/src/TMatrixT.cxx‎

Lines changed: 126 additions & 81 deletions
Original file line numberDiff line numberDiff line change
@@ -31,7 +31,6 @@ See the \ref Matrix page for the documentation of the linear algebra package
3131
#include "TMatrixDEigen.h"
3232
#include "TMath.h"
3333

34-
3534
////////////////////////////////////////////////////////////////////////////////
3635
/// Constructor for (nrows x ncols) matrix
3736

@@ -3077,22 +3076,68 @@ TMatrixT<Element> &TMatrixTAutoloadOps::ElementDiv(TMatrixT<Element> &target, co
30773076
/// Elementary routine to calculate matrix multiplication A*B
30783077

30793078
template <class Element>
3080-
void TMatrixTAutoloadOps::AMultB(const Element *const ap, Int_t na, Int_t ncolsa, const Element *const bp, Int_t nb,
3079+
void TMatrixTAutoloadOps::AMultB(const Element *const ap, Int_t na, Int_t ncolsa, const Element *const bp, Int_t /*nb*/,
30813080
Int_t ncolsb, Element *cp)
30823081
{
3083-
const Element *arp0 = ap; // Pointer to A[i,0];
3084-
while (arp0 < ap + na) {
3085-
for (const Element *bcp = bp; bcp < bp + ncolsb;) { // Pointer to the j-th column of B, Start bcp = B[0,0]
3086-
const Element *arp = arp0; // Pointer to the i-th row of A, reset to A[i,0]
3087-
Element cij = 0;
3088-
while (bcp < bp + nb) { // Scan the i-th row of A and
3089-
cij += *arp++ * *bcp; // the j-th col of B
3090-
bcp += ncolsb;
3082+
const Int_t M = na / ncolsa;
3083+
const Int_t N = ncolsa;
3084+
const Int_t P = ncolsb;
3085+
3086+
if (M <= 12 && N <= 12 && P <= 12) {
3087+
for (Int_t i = 0; i < M; ++i) {
3088+
for (Int_t j = 0; j < P; ++j) {
3089+
Element sum = Element(0);
3090+
for (Int_t k = 0; k < N; ++k) {
3091+
sum += ap[i * N + k] * bp[k * P + j];
3092+
}
3093+
cp[i * P + j] = sum;
3094+
}
3095+
}
3096+
return;
3097+
}
3098+
const Int_t BLOCK = (M >= 192 && N >= 192 && P >= 192) ? 48 : 32;
3099+
#ifdef _OPENMP
3100+
#pragma omp parallel for collapse(2) if (M * P > 10000)
3101+
#endif
3102+
for (Int_t i0 = 0; i0 < M; i0 += BLOCK) {
3103+
for (Int_t j0 = 0; j0 < P; j0 += BLOCK) {
3104+
const Int_t i1 = (i0 + BLOCK < M) ? i0 + BLOCK : M;
3105+
const Int_t j1 = (j0 + BLOCK < P) ? j0 + BLOCK : P;
3106+
for (Int_t i = i0; i < i1; ++i) {
3107+
Int_t j = j0;
3108+
for (; j <= j1 - 4; j += 4) {
3109+
cp[i * P + j + 0] = Element(0);
3110+
cp[i * P + j + 1] = Element(0);
3111+
cp[i * P + j + 2] = Element(0);
3112+
cp[i * P + j + 3] = Element(0);
3113+
}
3114+
for (; j < j1; ++j)
3115+
cp[i * P + j] = Element(0);
3116+
}
3117+
3118+
// ────────────────────── Accumulate over k blocks ──────────────────────
3119+
for (Int_t k0 = 0; k0 < N; k0 += BLOCK) {
3120+
const Int_t k1 = (k0 + BLOCK < N) ? k0 + BLOCK : N;
3121+
3122+
for (Int_t i = i0; i < i1; ++i) {
3123+
for (Int_t k = k0; k < k1; ++k) {
3124+
const Element aik = ap[i * N + k];
3125+
3126+
Int_t j = j0;
3127+
// Main 4-wide accumulation
3128+
for (; j <= j1 - 4; j += 4) {
3129+
cp[i * P + j + 0] += aik * bp[k * P + j + 0];
3130+
cp[i * P + j + 1] += aik * bp[k * P + j + 1];
3131+
cp[i * P + j + 2] += aik * bp[k * P + j + 2];
3132+
cp[i * P + j + 3] += aik * bp[k * P + j + 3];
3133+
}
3134+
// Remainder
3135+
for (; j < j1; ++j)
3136+
cp[i * P + j] += aik * bp[k * P + j];
3137+
}
3138+
}
30913139
}
3092-
*cp++ = cij;
3093-
bcp -= nb - 1; // Set bcp to the (j+1)-th col
30943140
}
3095-
arp0 += ncolsa; // Set ap to the (i+1)-th row
30963141
}
30973142
}
30983143

@@ -3214,43 +3259,43 @@ template class TMatrixT<Float_t>;
32143259
#include "TMatrixFfwd.h"
32153260
#include "TMatrixFSymfwd.h"
32163261

3217-
template TMatrixF TMatrixTAutoloadOps::operator+<Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3218-
template TMatrixF TMatrixTAutoloadOps::operator+<Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3219-
template TMatrixF TMatrixTAutoloadOps::operator+<Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3220-
template TMatrixF TMatrixTAutoloadOps::operator+<Float_t>(const TMatrixF &source, Float_t val);
3221-
template TMatrixF TMatrixTAutoloadOps::operator+<Float_t>(Float_t val, const TMatrixF &source);
3222-
template TMatrixF TMatrixTAutoloadOps::operator-<Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3223-
template TMatrixF TMatrixTAutoloadOps::operator-<Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3224-
template TMatrixF TMatrixTAutoloadOps::operator-<Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3225-
template TMatrixF TMatrixTAutoloadOps::operator-<Float_t>(const TMatrixF &source, Float_t val);
3226-
template TMatrixF TMatrixTAutoloadOps::operator-<Float_t>(Float_t val, const TMatrixF &source);
3227-
template TMatrixF TMatrixTAutoloadOps::operator*<Float_t>(Float_t val, const TMatrixF &source);
3228-
template TMatrixF TMatrixTAutoloadOps::operator*<Float_t>(const TMatrixF &source, Float_t val);
3229-
template TMatrixF TMatrixTAutoloadOps::operator*<Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3230-
template TMatrixF TMatrixTAutoloadOps::operator*<Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3231-
template TMatrixF TMatrixTAutoloadOps::operator*<Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3232-
template TMatrixF TMatrixTAutoloadOps::operator*<Float_t>(const TMatrixFSym &source1, const TMatrixFSym &source2);
3233-
template TMatrixF TMatrixTAutoloadOps::operator&&<Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3234-
template TMatrixF TMatrixTAutoloadOps::operator&&<Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3235-
template TMatrixF TMatrixTAutoloadOps::operator&&<Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3236-
template TMatrixF TMatrixTAutoloadOps::operator||<Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3237-
template TMatrixF TMatrixTAutoloadOps::operator||<Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3238-
template TMatrixF TMatrixTAutoloadOps::operator||<Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3239-
template TMatrixF TMatrixTAutoloadOps::operator><Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3240-
template TMatrixF TMatrixTAutoloadOps::operator><Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3241-
template TMatrixF TMatrixTAutoloadOps::operator><Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3242-
template TMatrixF TMatrixTAutoloadOps::operator>=<Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3243-
template TMatrixF TMatrixTAutoloadOps::operator>=<Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3244-
template TMatrixF TMatrixTAutoloadOps::operator>=<Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3245-
template TMatrixF TMatrixTAutoloadOps::operator<=<Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3246-
template TMatrixF TMatrixTAutoloadOps::operator<=<Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3247-
template TMatrixF TMatrixTAutoloadOps::operator<=<Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3262+
template TMatrixF TMatrixTAutoloadOps::operator+ <Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3263+
template TMatrixF TMatrixTAutoloadOps::operator+ <Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3264+
template TMatrixF TMatrixTAutoloadOps::operator+ <Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3265+
template TMatrixF TMatrixTAutoloadOps::operator+ <Float_t>(const TMatrixF &source, Float_t val);
3266+
template TMatrixF TMatrixTAutoloadOps::operator+ <Float_t>(Float_t val, const TMatrixF &source);
3267+
template TMatrixF TMatrixTAutoloadOps::operator- <Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3268+
template TMatrixF TMatrixTAutoloadOps::operator- <Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3269+
template TMatrixF TMatrixTAutoloadOps::operator- <Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3270+
template TMatrixF TMatrixTAutoloadOps::operator- <Float_t>(const TMatrixF &source, Float_t val);
3271+
template TMatrixF TMatrixTAutoloadOps::operator- <Float_t>(Float_t val, const TMatrixF &source);
3272+
template TMatrixF TMatrixTAutoloadOps::operator* <Float_t>(Float_t val, const TMatrixF &source);
3273+
template TMatrixF TMatrixTAutoloadOps::operator* <Float_t>(const TMatrixF &source, Float_t val);
3274+
template TMatrixF TMatrixTAutoloadOps::operator* <Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3275+
template TMatrixF TMatrixTAutoloadOps::operator* <Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3276+
template TMatrixF TMatrixTAutoloadOps::operator* <Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3277+
template TMatrixF TMatrixTAutoloadOps::operator* <Float_t>(const TMatrixFSym &source1, const TMatrixFSym &source2);
3278+
template TMatrixF TMatrixTAutoloadOps::operator&& <Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3279+
template TMatrixF TMatrixTAutoloadOps::operator&& <Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3280+
template TMatrixF TMatrixTAutoloadOps::operator&& <Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3281+
template TMatrixF TMatrixTAutoloadOps::operator|| <Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3282+
template TMatrixF TMatrixTAutoloadOps::operator|| <Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3283+
template TMatrixF TMatrixTAutoloadOps::operator|| <Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3284+
template TMatrixF TMatrixTAutoloadOps::operator><Float_t>(const TMatrixF & source1, const TMatrixF & source2);
3285+
template TMatrixF TMatrixTAutoloadOps::operator><Float_t>(const TMatrixF & source1, const TMatrixFSym & source2);
3286+
template TMatrixF TMatrixTAutoloadOps::operator><Float_t>(const TMatrixFSym & source1, const TMatrixF & source2);
3287+
template TMatrixF TMatrixTAutoloadOps::operator>= <Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3288+
template TMatrixF TMatrixTAutoloadOps::operator>= <Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3289+
template TMatrixF TMatrixTAutoloadOps::operator>= <Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3290+
template TMatrixF TMatrixTAutoloadOps::operator<= <Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3291+
template TMatrixF TMatrixTAutoloadOps::operator<= <Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3292+
template TMatrixF TMatrixTAutoloadOps::operator<= <Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
32483293
template TMatrixF TMatrixTAutoloadOps::operator< <Float_t>(const TMatrixF &source1, const TMatrixF &source2);
32493294
template TMatrixF TMatrixTAutoloadOps::operator< <Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
32503295
template TMatrixF TMatrixTAutoloadOps::operator< <Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3251-
template TMatrixF TMatrixTAutoloadOps::operator!=<Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3252-
template TMatrixF TMatrixTAutoloadOps::operator!=<Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3253-
template TMatrixF TMatrixTAutoloadOps::operator!=<Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
3296+
template TMatrixF TMatrixTAutoloadOps::operator!= <Float_t>(const TMatrixF &source1, const TMatrixF &source2);
3297+
template TMatrixF TMatrixTAutoloadOps::operator!= <Float_t>(const TMatrixF &source1, const TMatrixFSym &source2);
3298+
template TMatrixF TMatrixTAutoloadOps::operator!= <Float_t>(const TMatrixFSym &source1, const TMatrixF &source2);
32543299

32553300
template TMatrixF &TMatrixTAutoloadOps::Add<Float_t>(TMatrixF &target, Float_t scalar, const TMatrixF &source);
32563301
template TMatrixF &TMatrixTAutoloadOps::Add<Float_t>(TMatrixF &target, Float_t scalar, const TMatrixFSym &source);
@@ -3271,43 +3316,43 @@ template void TMatrixTAutoloadOps::AMultBt<Float_t>(const Float_t *const ap, Int
32713316

32723317
template class TMatrixT<Double_t>;
32733318

3274-
template TMatrixD TMatrixTAutoloadOps::operator+<Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3275-
template TMatrixD TMatrixTAutoloadOps::operator+<Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3276-
template TMatrixD TMatrixTAutoloadOps::operator+<Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3277-
template TMatrixD TMatrixTAutoloadOps::operator+<Double_t>(const TMatrixD &source, Double_t val);
3278-
template TMatrixD TMatrixTAutoloadOps::operator+<Double_t>(Double_t val, const TMatrixD &source);
3279-
template TMatrixD TMatrixTAutoloadOps::operator-<Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3280-
template TMatrixD TMatrixTAutoloadOps::operator-<Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3281-
template TMatrixD TMatrixTAutoloadOps::operator-<Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3282-
template TMatrixD TMatrixTAutoloadOps::operator-<Double_t>(const TMatrixD &source, Double_t val);
3283-
template TMatrixD TMatrixTAutoloadOps::operator-<Double_t>(Double_t val, const TMatrixD &source);
3284-
template TMatrixD TMatrixTAutoloadOps::operator*<Double_t>(Double_t val, const TMatrixD &source);
3285-
template TMatrixD TMatrixTAutoloadOps::operator*<Double_t>(const TMatrixD &source, Double_t val);
3286-
template TMatrixD TMatrixTAutoloadOps::operator*<Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3287-
template TMatrixD TMatrixTAutoloadOps::operator*<Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3288-
template TMatrixD TMatrixTAutoloadOps::operator*<Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3289-
template TMatrixD TMatrixTAutoloadOps::operator*<Double_t>(const TMatrixDSym &source1, const TMatrixDSym &source2);
3290-
template TMatrixD TMatrixTAutoloadOps::operator&&<Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3291-
template TMatrixD TMatrixTAutoloadOps::operator&&<Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3292-
template TMatrixD TMatrixTAutoloadOps::operator&&<Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3293-
template TMatrixD TMatrixTAutoloadOps::operator||<Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3294-
template TMatrixD TMatrixTAutoloadOps::operator||<Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3295-
template TMatrixD TMatrixTAutoloadOps::operator||<Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3296-
template TMatrixD TMatrixTAutoloadOps::operator><Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3297-
template TMatrixD TMatrixTAutoloadOps::operator><Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3298-
template TMatrixD TMatrixTAutoloadOps::operator><Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3299-
template TMatrixD TMatrixTAutoloadOps::operator>=<Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3300-
template TMatrixD TMatrixTAutoloadOps::operator>=<Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3301-
template TMatrixD TMatrixTAutoloadOps::operator>=<Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3302-
template TMatrixD TMatrixTAutoloadOps::operator<=<Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3303-
template TMatrixD TMatrixTAutoloadOps::operator<=<Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3304-
template TMatrixD TMatrixTAutoloadOps::operator<=<Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3319+
template TMatrixD TMatrixTAutoloadOps::operator+ <Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3320+
template TMatrixD TMatrixTAutoloadOps::operator+ <Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3321+
template TMatrixD TMatrixTAutoloadOps::operator+ <Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3322+
template TMatrixD TMatrixTAutoloadOps::operator+ <Double_t>(const TMatrixD &source, Double_t val);
3323+
template TMatrixD TMatrixTAutoloadOps::operator+ <Double_t>(Double_t val, const TMatrixD &source);
3324+
template TMatrixD TMatrixTAutoloadOps::operator- <Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3325+
template TMatrixD TMatrixTAutoloadOps::operator- <Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3326+
template TMatrixD TMatrixTAutoloadOps::operator- <Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3327+
template TMatrixD TMatrixTAutoloadOps::operator- <Double_t>(const TMatrixD &source, Double_t val);
3328+
template TMatrixD TMatrixTAutoloadOps::operator- <Double_t>(Double_t val, const TMatrixD &source);
3329+
template TMatrixD TMatrixTAutoloadOps::operator* <Double_t>(Double_t val, const TMatrixD &source);
3330+
template TMatrixD TMatrixTAutoloadOps::operator* <Double_t>(const TMatrixD &source, Double_t val);
3331+
template TMatrixD TMatrixTAutoloadOps::operator* <Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3332+
template TMatrixD TMatrixTAutoloadOps::operator* <Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3333+
template TMatrixD TMatrixTAutoloadOps::operator* <Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3334+
template TMatrixD TMatrixTAutoloadOps::operator* <Double_t>(const TMatrixDSym &source1, const TMatrixDSym &source2);
3335+
template TMatrixD TMatrixTAutoloadOps::operator&& <Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3336+
template TMatrixD TMatrixTAutoloadOps::operator&& <Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3337+
template TMatrixD TMatrixTAutoloadOps::operator&& <Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3338+
template TMatrixD TMatrixTAutoloadOps::operator|| <Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3339+
template TMatrixD TMatrixTAutoloadOps::operator|| <Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3340+
template TMatrixD TMatrixTAutoloadOps::operator|| <Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3341+
template TMatrixD TMatrixTAutoloadOps::operator><Double_t>(const TMatrixD & source1, const TMatrixD & source2);
3342+
template TMatrixD TMatrixTAutoloadOps::operator><Double_t>(const TMatrixD & source1, const TMatrixDSym & source2);
3343+
template TMatrixD TMatrixTAutoloadOps::operator><Double_t>(const TMatrixDSym & source1, const TMatrixD & source2);
3344+
template TMatrixD TMatrixTAutoloadOps::operator>= <Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3345+
template TMatrixD TMatrixTAutoloadOps::operator>= <Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3346+
template TMatrixD TMatrixTAutoloadOps::operator>= <Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3347+
template TMatrixD TMatrixTAutoloadOps::operator<= <Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3348+
template TMatrixD TMatrixTAutoloadOps::operator<= <Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3349+
template TMatrixD TMatrixTAutoloadOps::operator<= <Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
33053350
template TMatrixD TMatrixTAutoloadOps::operator< <Double_t>(const TMatrixD &source1, const TMatrixD &source2);
33063351
template TMatrixD TMatrixTAutoloadOps::operator< <Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
33073352
template TMatrixD TMatrixTAutoloadOps::operator< <Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3308-
template TMatrixD TMatrixTAutoloadOps::operator!=<Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3309-
template TMatrixD TMatrixTAutoloadOps::operator!=<Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3310-
template TMatrixD TMatrixTAutoloadOps::operator!=<Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
3353+
template TMatrixD TMatrixTAutoloadOps::operator!= <Double_t>(const TMatrixD &source1, const TMatrixD &source2);
3354+
template TMatrixD TMatrixTAutoloadOps::operator!= <Double_t>(const TMatrixD &source1, const TMatrixDSym &source2);
3355+
template TMatrixD TMatrixTAutoloadOps::operator!= <Double_t>(const TMatrixDSym &source1, const TMatrixD &source2);
33113356

33123357
template TMatrixD &TMatrixTAutoloadOps::Add<Double_t>(TMatrixD &target, Double_t scalar, const TMatrixD &source);
33133358
template TMatrixD &TMatrixTAutoloadOps::Add<Double_t>(TMatrixD &target, Double_t scalar, const TMatrixDSym &source);

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