Hilbert Matrix 20x20 LDLT decomposition

 The following is LDLT decomposition of 20x20 Hilbert Matrix A.

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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

Setup ssh on Ubuntu

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

check ip address of your Ubuntu computer using ifconfig

in my case, it is 192.168.11.103

Connect Ubuntu from Windows computer using Tera term via SSH

http://www.teraterm.org/

install Teraeterm Menu, and 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 and choose your Ubuntu connection profile and connect to Ubuntu.

Determine your Windows computer IP address

run cmd and type ipconfig. my Windows computer IP is 192.168.11.199

Install Cygwin/X on Windows

 

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

Additionally install xterm and xhost from Cygwin setup

Open C:\cygwin64\bin\startxwin with text editor and modify

serverargs="" with

serverargs="+iglx -wgl -listen tcp"

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

With Cygwin/X icon on system tray,  choose System tools → XTerm to run xterm

Disable authentication

On XTerm window, run

xhost +

Connect Ubuntu from Windows computer using Teraterm via SSH

left click Teraterm menu and connect to Ubuntu.

Type on Ubuntu console

export DISPLAY="192.168.11.199:0"

gnome-session

to run gnome desktop session onto your Cygwin/X X server. Ubuntu desktop is shown on your Windows computer. Remote Ubuntu computer can be used as a local native Ubuntu computer from Windows

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