Hilbert Matrix 20x20 LDLT decomposition

 The following is LDLT decomposition of 20x20 Hilbert Matrix. The diagonal matrix contains very small number.

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$\mathrm{Hilbert\; Matrix\; H}=\left[\begin{array}{cccccccccccccccccccc}1& \frac{1}{2}& \frac{1}{3}& \frac{1}{4}& \frac{1}{5}& \frac{1}{6}& \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}\\ \frac{1}{2}& \frac{1}{3}& \frac{1}{4}& \frac{1}{5}& \frac{1}{6}& \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}\\ \frac{1}{3}& \frac{1}{4}& \frac{1}{5}& \frac{1}{6}& \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}\\ \frac{1}{4}& \frac{1}{5}& \frac{1}{6}& \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}\\ \frac{1}{5}& \frac{1}{6}& \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}\\ \frac{1}{6}& \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}\\ \frac{1}{7}& \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}\\ \frac{1}{8}& \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}\\ \frac{1}{9}& \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}\\ \frac{1}{10}& \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}\\ \frac{1}{11}& \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}\\ \frac{1}{12}& \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}\\ \frac{1}{13}& \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}\\ \frac{1}{14}& \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}\\ \frac{1}{15}& \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}& \frac{1}{34}\\ \frac{1}{16}& \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}& \frac{1}{34}& \frac{1}{35}\\ \frac{1}{17}& \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}& \frac{1}{34}& \frac{1}{35}& \frac{1}{36}\\ \frac{1}{18}& \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}& \frac{1}{34}& \frac{1}{35}& \frac{1}{36}& \frac{1}{37}\\ \frac{1}{19}& \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}& \frac{1}{34}& \frac{1}{35}& \frac{1}{36}& \frac{1}{37}& \frac{1}{38}\\ \frac{1}{20}& \frac{1}{21}& \frac{1}{22}& \frac{1}{23}& \frac{1}{24}& \frac{1}{25}& \frac{1}{26}& \frac{1}{27}& \frac{1}{28}& \frac{1}{29}& \frac{1}{30}& \frac{1}{31}& \frac{1}{32}& \frac{1}{33}& \frac{1}{34}& \frac{1}{35}& \frac{1}{36}& \frac{1}{37}& \frac{1}{38}& \frac{1}{39}\end{array}\right]$

$L=\left[\begin{array}{cccccccccccccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{2}& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{3}& 1& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{4}& \frac{9}{10}& \frac{3}{2}& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{5}& \frac{4}{5}& \frac{12}{7}& 2& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{6}& \frac{5}{7}& \frac{25}{14}& \frac{25}{9}& \frac{5}{2}& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{7}& \frac{9}{14}& \frac{25}{14}& \frac{10}{3}& \frac{45}{11}& 3& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{8}& \frac{7}{12}& \frac{7}{4}& \frac{245}{66}& \frac{245}{44}& \frac{147}{26}& \frac{7}{2}& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{9}& \frac{8}{15}& \frac{56}{33}& \frac{392}{99}& \frac{980}{143}& \frac{112}{13}& \frac{112}{15}& 4& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{10}& \frac{27}{55}& \frac{18}{11}& \frac{588}{143}& \frac{1134}{143}& \frac{756}{65}& \frac{63}{5}& \frac{162}{17}& \frac{9}{2}& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{11}& \frac{5}{11}& \frac{225}{143}& \frac{600}{143}& \frac{1260}{143}& \frac{189}{13}& \frac{315}{17}& \frac{300}{17}& \frac{225}{19}& 5& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{12}& \frac{11}{26}& \frac{275}{182}& \frac{55}{13}& \frac{495}{52}& \frac{7623}{442}& \frac{847}{34}& \frac{9075}{323}& \frac{1815}{76}& \frac{605}{42}& \frac{11}{2}& 1& 0& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{13}& \frac{36}{91}& \frac{132}{91}& \frac{55}{13}& \frac{4455}{442}& \frac{4356}{221}& \frac{10164}{323}& \frac{13068}{323}& \frac{5445}{133}& \frac{220}{7}& \frac{396}{23}& 6& 1& 0& 0& 0& 0& 0& 0& 0\\ \frac{1}{14}& \frac{13}{35}& \frac{39}{28}& \frac{143}{34}& \frac{715}{68}& \frac{14157}{646}& \frac{61347}{1615}& \frac{122694}{2261}& \frac{16731}{266}& \frac{9295}{161}& \frac{1859}{46}& \frac{507}{25}& \frac{13}{2}& 1& 0& 0& 0& 0& 0& 0\\ \frac{1}{15}& \frac{7}{20}& \frac{91}{68}& \frac{637}{153}& \frac{7007}{646}& \frac{77077}{3230}& \frac{143143}{3230}& \frac{22308}{323}& \frac{39039}{437}& \frac{13013}{138}& \frac{91091}{1150}& \frac{1274}{25}& \frac{637}{27}& 7& 1& 0& 0& 0& 0& 0\\ \frac{1}{16}& \frac{45}{136}& \frac{175}{136}& \frac{15925}{3876}& \frac{28665}{2584}& \frac{33033}{1292}& \frac{65065}{1292}& \frac{1254825}{14858}& \frac{418275}{3496}& \frac{13013}{92}& \frac{63063}{460}& \frac{637}{6}& \frac{2275}{36}& \frac{1575}{58}& \frac{15}{2}& 1& 0& 0& 0& 0\\ \frac{1}{17}& \frac{16}{51}& \frac{400}{323}& \frac{3920}{969}& \frac{3640}{323}& \frac{8736}{323}& \frac{416416}{7429}& \frac{743600}{7429}& \frac{66924}{437}& \frac{4576}{23}& \frac{224224}{1035}& \frac{2912}{15}& \frac{36400}{261}& \frac{2240}{29}& \frac{960}{31}& 8& 1& 0& 0& 0\\ \frac{1}{18}& \frac{17}{57}& \frac{68}{57}& \frac{680}{171}& \frac{2380}{209}& \frac{12376}{437}& \frac{80444}{1311}& \frac{252824}{2185}& \frac{82654}{437}& \frac{165308}{621}& \frac{330616}{1035}& \frac{420784}{1305}& \frac{210392}{783}& \frac{161840}{899}& \frac{2890}{31}& \frac{1156}{33}& \frac{17}{2}& 1& 0& 0\\ \frac{1}{19}& \frac{27}{95}& \frac{153}{133}& \frac{816}{209}& \frac{55080}{4807}& \frac{12852}{437}& \frac{723996}{10925}& \frac{286416}{2185}& \frac{495924}{2185}& \frac{165308}{483}& \frac{1487772}{3335}& \frac{360672}{725}& \frac{420784}{899}& \frac{327726}{899}& \frac{78030}{341}& \frac{1224}{11}& \frac{1377}{35}& 9& 1& 0\\ \frac{1}{20}& \frac{19}{70}& \frac{171}{154}& \frac{969}{253}& \frac{2907}{253}& \frac{17442}{575}& \frac{40698}{575}& \frac{16796}{115}& \frac{214149}{805}& \frac{29838094}{70035}& \frac{29838094}{50025}& \frac{16275324}{22475}& \frac{1356277}{1798}& \frac{6572727}{9889}& \frac{165699}{341}& \frac{110466}{385}& \frac{18411}{140}& \frac{3249}{74}& \frac{19}{2}& 1\end{array}\right]$

$D=\left[\begin{array}{cccccccccccccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& \frac{1}{12}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& \frac{1}{180}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& \frac{1}{2800}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& \frac{1}{44100}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& \frac{1}{698544}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& \frac{1}{11099088}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& \frac{1}{176679360}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{2815827300}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{44914183600}& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{716830370256}& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{11445589052352}& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{182811491808400}& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{2920656969720000}& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{46670906271240000}& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{745904795339462400}& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{11922821963004219300}& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{190600129650794094000}& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{3047248986392325330000}& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& \frac{1}{48722219250572027160000}\end{array}\right]$

$\mathrm{Hilbert\; Matrix\; H}=LD{L}^{\mathrm{T}}$

Move constructor and emplace_back for std::vector performance improvement (Native C++)

Performance improvement with move constructor and emplace_back against copy constructor and push_back is very visible: See below program output.

There are many pitfalls in move constructors. Please read the textbook before utilizing it.

BTW, this is just demonstration purpose for the pointer member to contain only one int value. In this particular case, replacing int *p with int  v improves the performance much more,

C++ Program

#include <iostream>
#include <vector>
#include <stdio.h>
#include <map>
using namespace std;

static int PtrToId(const void* p) {
    static int id = 400;
    static map<const void*, int> ptrIdMap;
    auto found = ptrIdMap.find(p);
    if (found != ptrIdMap.end()) {
        return found->second;
    }
    
    ptrIdMap[p] = id;
    id += 8;

    return ptrIdMap[p];
}

class A {
public:
    int *p = nullptr;
    static int newCounter;

    A(void) {
        p = new int;
        ++newCounter;
        *p = 0;
        cout << "Ctor  new this=" << PtrToId(this) << ", p=" << PtrToId(p) << endl;
    }

    A(int d) {
        p = new int;
        ++newCounter;
        *p = d;
        cout << "Ctor(int) this=" << PtrToId(this) << ", p=" << PtrToId(p) << ", *p=" << *p << endl;
    }

    A(const A& rhs) {
        p = new int;
        ++newCounter;
        *p = *(rhs.p);
        cout << "Copy ctor this=" << PtrToId(this) << ", p=" << PtrToId(p) << ", *p=" << *p << endl;
    }

    ~A(void) {
        cout << "Dtor  del this=" << PtrToId(this) << ", p=" << PtrToId(p) << ", *p=" << *p << endl;
        delete p;
        p = nullptr;
    }
};
int A::newCounter = 0;

class B {
public:
    int *p = nullptr;
    static int newCounter;

    B(void) {
        p = new int;
        ++newCounter;
        *p = 0;
        cout << "Ctor  new this=" << PtrToId(this) << ", p=" << PtrToId(p) << endl;
    }

    B(int d) {
        p = new int;
        ++newCounter;
        *p = d;
        cout << "Ctor(int) this=" << PtrToId(this) << ", p=" << PtrToId(p) << ", *p=" << *p << endl;
    };

    B(const B& rhs) {
        p = new int;
        ++newCounter;
        *p = *(rhs.p);
        cout << "Copy ctor this=" << PtrToId(this) << ", p=" << PtrToId(p) << ", *p=" << *p << ", &rhs=" << PtrToId(&rhs) << endl;
    }

    B(B&& rhs) noexcept {
        p = rhs.p;
        rhs.p = nullptr;

        cout << "Move ctor this=" << PtrToId(this) << ", p=" << PtrToId(p) << ", *p=" << *p << ", &rhs=" << PtrToId(&rhs) << endl;
    }

    ~B(void) {
        if (p) {
            cout << "Dtor  del this=" << PtrToId(this) << ", p=" << PtrToId(p) << ", *p=" << *p << endl;
            delete p;
            p = nullptr;
        } else {
            cout << "Dtor      this=" << PtrToId(this) << ", p=nullptr" << endl;
        }
    }
};
int B::newCounter = 0;

template <typename T>
static void Print(vector<T> &v, const char* name)
{
    for (int i = 0; i < v.size(); ++i) {
        printf(" &(%s[%d])=%d, p=%d, *p=%d\n", name, i, PtrToId(&(v[i])), PtrToId(v[i].p), *(v[i].p));
    }
}

int main(void)
{
    {
        printf("vA/push_back Begin\n");
        vector<A> vA;

        printf("push_back(10)\n");
        vA.push_back(10);
        Print(vA, "vA");

        printf("\npush_back(20)\n");
        vA.push_back(20);
        Print(vA, "vA");

        printf("\npush_back(30)\n");
        vA.push_back(30);
        Print(vA, "vA");

        printf("\nvA/push_back end\n");
    }
    printf("new int is called %d times.\n", A::newCounter);
    A::newCounter = 0;

    {
        printf("\nvA/emplace_back Begin\n");
        vector<A> vA;

        printf("emplace_back(10)\n");
        vA.emplace_back(10);
        Print(vA, "vA");

        printf("\nemplace_back(20)\n");
        vA.emplace_back(20);
        Print(vA, "vA");

        printf("\nemplace_back(30)\n");
        vA.emplace_back(30);
        Print(vA, "vA");

        printf("\nvA/emplace_back end\n");
    }
    printf("new int is called %d times.\n", A::newCounter);

    {
        printf("\nvB/push_back begin\n");
        vector<B> vB;

        printf("push_back(10)\n");
        vB.push_back(10);
        Print(vB, "vB");

        printf("\npush_back(20)\n");
        vB.push_back(20);
        Print(vB, "vB");

        printf("\npush_back(30)\n");
        vB.push_back(30);
        Print(vB, "vB");

        printf("\nvB/push_back end\n");
    }
    printf("new int is called %d times.\n", B::newCounter);

    B::newCounter = 0;
    {
        printf("\nvB/emplace_back begin\n");
        vector<B> vB;

        printf("emplace_back(10)\n");
        vB.emplace_back(10);
        Print(vB, "vB");

        printf("\emplace_back(20)\n");
        vB.emplace_back(20);
        Print(vB, "vB");

        printf("\emplace_back(30)\n");
        vB.emplace_back(30);
        Print(vB, "vB");

        printf("\nvB/emplace_back end\n");
    }
    printf("new int is called %d times.\n", B::newCounter);

    return 0;
}

 

Program Output

vA/push_back Begin
push_back(10)
Ctor(int) this=408, p=400, *p=10
Copy ctor this=424, p=416, *p=10
Dtor  del this=408, p=400, *p=10
 &(vA[0])=424, p=416, *p=10

push_back(20)
Ctor(int) this=440, p=432, *p=20
Copy ctor this=456, p=448, *p=20
Copy ctor this=472, p=464, *p=10
Dtor  del this=424, p=416, *p=10
Dtor  del this=440, p=432, *p=20
 &(vA[0])=472, p=464, *p=10
 &(vA[1])=456, p=448, *p=20

push_back(30)
Ctor(int) this=488, p=480, *p=30
Copy ctor this=496, p=416, *p=30
Copy ctor this=512, p=504, *p=10
Copy ctor this=528, p=520, *p=20
Dtor  del this=472, p=464, *p=10
Dtor  del this=456, p=448, *p=20
Dtor  del this=488, p=480, *p=30
 &(vA[0])=512, p=504, *p=10
 &(vA[1])=528, p=520, *p=20
 &(vA[2])=496, p=416, *p=30

vA/push_back end
Dtor  del this=512, p=504, *p=10
Dtor  del this=528, p=520, *p=20
Dtor  del this=496, p=416, *p=30
new int is called 9 times.

vA/emplace_back Begin
emplace_back(10)
Ctor(int) this=472, p=480, *p=10
 &(vA[0])=472, p=480, *p=10

emplace_back(20)
Ctor(int) this=544, p=536, *p=20
Copy ctor this=560, p=552, *p=10
Dtor  del this=472, p=480, *p=10
 &(vA[0])=560, p=552, *p=10
 &(vA[1])=544, p=536, *p=20

emplace_back(30)
Ctor(int) this=576, p=568, *p=30
Copy ctor this=592, p=584, *p=10
Copy ctor this=608, p=600, *p=20
Dtor  del this=560, p=552, *p=10
Dtor  del this=544, p=536, *p=20
 &(vA[0])=592, p=584, *p=10
 &(vA[1])=608, p=600, *p=20
 &(vA[2])=576, p=568, *p=30

vA/emplace_back end
Dtor  del this=592, p=584, *p=10
Dtor  del this=608, p=600, *p=20
Dtor  del this=576, p=568, *p=30
new int is called 6 times.

vB/push_back begin
push_back(10)
Ctor(int) this=624, p=616, *p=10
Move ctor this=632, p=616, *p=10, &rhs=624
Dtor      this=624, p=nullptr
 &(vB[0])=632, p=616, *p=10

push_back(20)
Ctor(int) this=648, p=640, *p=20
Move ctor this=656, p=640, *p=20, &rhs=648
Move ctor this=664, p=616, *p=10, &rhs=632
Dtor      this=632, p=nullptr
Dtor      this=648, p=nullptr
 &(vB[0])=664, p=616, *p=10
 &(vB[1])=656, p=640, *p=20

push_back(30)
Ctor(int) this=680, p=672, *p=30
Move ctor this=688, p=672, *p=30, &rhs=680
Move ctor this=696, p=616, *p=10, &rhs=664
Move ctor this=704, p=640, *p=20, &rhs=656
Dtor      this=664, p=nullptr
Dtor      this=656, p=nullptr
Dtor      this=680, p=nullptr
 &(vB[0])=696, p=616, *p=10
 &(vB[1])=704, p=640, *p=20
 &(vB[2])=688, p=672, *p=30

vB/push_back end
Dtor  del this=696, p=616, *p=10
Dtor  del this=704, p=640, *p=20
Dtor  del this=688, p=672, *p=30
new int is called 3 times.

vB/emplace_back begin
emplace_back(10)
Ctor(int) this=712, p=552, *p=10
 &(vB[0])=712, p=552, *p=10
emplace_back(20)
Ctor(int) this=728, p=720, *p=20
Move ctor this=632, p=552, *p=10, &rhs=712
Dtor      this=712, p=nullptr
 &(vB[0])=632, p=552, *p=10
 &(vB[1])=728, p=720, *p=20
emplace_back(30)
Ctor(int) this=576, p=448, *p=30
Move ctor this=592, p=552, *p=10, &rhs=632
Move ctor this=608, p=720, *p=20, &rhs=728
Dtor      this=632, p=nullptr
Dtor      this=728, p=nullptr
 &(vB[0])=592, p=552, *p=10
 &(vB[1])=608, p=720, *p=20
 &(vB[2])=576, p=448, *p=30

vB/emplace_back end
Dtor  del this=592, p=552, *p=10
Dtor  del this=608, p=720, *p=20
Dtor  del this=576, p=448, *p=30
new int is called 3 times.

How to Show Remote Ubuntu Desktop screen from Windows computer

Terminology

• X server: it runs on Windows, wait connection from Ubuntu and provides display, mouse, keyboard to X client that connected onto windows computer. Cygwin/X is used.
  
• X client: it runs on Ubuntu and connect to Windows and show GUI onto X Server on Windows. gnome-session, gnome-terminal,  firefox, xclock, xeyes, ...
• SSH server: it runs on Ubuntu and wait connection from Windows computer. openssh-server is used.
• SSH client: it runs on Windows and connect to SSH server. Teraterm is used.

There are two physical computers, Windows computer and Ubuntu computer. I'm going to do the following things: On Windows, start Cygwin/X to wait to accept remote X client connection, then run Teraterm  to connect Ubuntu and run some X client on Ubuntu to connect to Cygwin/X of Windows to show Ubuntu GUI on Windows computer screen.

Setup ssh on Ubuntu computer

On Ubuntu computer, apt install ssh to install/enable sshd. 

sudo apt install openssh-server

 

And allow ssh connection to firewall by

sudo ufw allow ssh

Determine your Ubuntu computer IP address

Check ip address of your Ubuntu computer. On Ubuntu computer, open Terminal and type

ifconfig

 

In my case, it is 192.168.11.103

Connect Ubuntu from Windows computer using Tera term via SSH

 

On Windows computer, visit 

    https://teratermproject.github.io/index-en.html

 and download Teraterm installer.

On installation, make sure to choose to install "Teraeterm Menu" feature and set it runs on Windows startup. 

 

After install, right click Teraterm Menu icon on system tray and add your Ubuntu computer IP address, username, password and enable ssh. 

 

Left click Teraterm menu icon on the system tray, choose your Ubuntu connection profile to connect to Ubuntu.

Determine your Windows computer IP address

 

On Windows, run cmd and type 

ipconfig

 

It shows IP address of your computer. My Windows computer IP is 192.168.11.199

Install Cygwin/X on Windows

 

Install Cygwin/X onto Windows computer https://x.cygwin.com/

 

My Cygwin installation directory is C:\cygwin64

On Cygwin installation, check xterm and xhost from package selection

Open C:\cygwin64\bin\startxwin with your text editor (I use Sakura editor) and modify

serverargs="" with

serverargs="+iglx -wgl -listen tcp"

On windows start menu, choose Cygwin-X → Xwin server to run Cygwin X server.

Disable X server authentication of Windows Cygwin/X server to allow connection from Ubuntu

On Windows, left click Cygwin/X icon on system tray, choose System tools → XTerm to run xterm
On XTerm window, type

 

xhost +

Connect Ubuntu from Windows computer using Teraterm via SSH

On Windows, left click Teraterm menu and connect to Ubuntu computer.

Type the following commands on Teraterm command prompt to run gnome desktop session onto your Cygwin/X X server.

export DISPLAY="192.168.11.199:0"

export WAYLAND_DISPLAY="192.168.11.199:0"

export XDG_SESSION_TYPE=x11

gnome-session

Where 192.168.11.199 is IP address of my Windows, that is determined by ipconfig on the earlier step. 

 Ubuntu desktop is shown on your Windows computer. Remote Ubuntu computer can be used as a local native Ubuntu computer from Windows

If it is not necessary to run whole Ubuntu desktop on your Windows desktop, just run gnome-terminal or xterm instead of gnome-session

MobaXterm

There is relatively new X server program called MobaXterm. I don't tested it but maybe it is easier to use

How to add language input method to offline Windows 11 22H2 computer

For this topic, Internet information seems a bit unreliable because language feature installation process is completely changed on Windows 11. 

Follow these steps.

Step 1

Download Windows 11 Languages and Optional Features, version 22H2 iso file from your Visual Studio Subscription page.

 

 

Step 2

Mount downloaded iso using Windows Explorer, double-click download iso to mount it.

In my case, iso image is mounted as H:\

 

Step 3

Run cmd as administrator  and type those commands to install language packs. "ja-JP" means Japanese. Change it to your language code. H:\ should be replaced your mounted iso image drive letter.

dism /online /add-capability /capabilityname:Language.Basic~~~ja-JP~0.0.1.0 /source:H:\LanguagesAndOptionalFeatures /LimitAccess

dism /online /add-capability /capabilityname:Language.Handwriting~~~ja-JP~0.0.1.0 /source:H:\LanguagesAndOptionalFeatures /LimitAccess
dism /online /add-capability /capabilityname:Language.OCR~~~ja-JP~0.0.1.0 /source:H:\LanguagesAndOptionalFeatures /LimitAccess
dism /online /add-capability /capabilityname:Language.Speech~~~ja-JP~0.0.1.0 /source:H:\LanguagesAndOptionalFeatures /LimitAccess
dism /online /add-capability /capabilityname:Language.TextToSpeech~~~ja-JP~0.0.1.0 /source:H:\LanguagesAndOptionalFeatures /LimitAccess
dism /online /add-capability /capabilityname:Language.Fonts.Jpan~~~und-JPAN~0.0.1.0 /source:H:\LanguagesAndOptionalFeatures /LimitAccess

 

Step 4

 

Open settings (right click start icon and choose Settings) → Time ＆ Language → Lauguage ＆ region, push "Add a language" button to add language. Some caution message such as your computer is offline may be shown but adding language should work.

Some thoughts

The dism command argument /online does not mean internet connection, it means language pack will be installed onto currently running OS.

Without /LimitAccess option, dism try to connect internet.

It seems /add-package option is deprecated and replaced to /add-capability