diff --git a/d0/d01/smallest__circle_8cpp.html b/d0/d01/smallest__circle_8cpp.html index 800445c64..667afc445 100644 --- a/d0/d01/smallest__circle_8cpp.html +++ b/d0/d01/smallest__circle_8cpp.html @@ -463,7 +463,7 @@ Here is the call graph for this function:

Test case: result should be:
Circle with
radius 1.821078397711709
- centre at (2.142857142857143, 1.7857142857142856)

Todo:
This test fails
+ centre at (2.142857142857143, 1.7857142857142856)

Todo:
This test fails
188  {
189  std::vector<Point> Pv;
190  Pv.push_back(Point(0.5, 1));
diff --git a/d1/dbe/lu__decomposition_8h.html b/d1/dbe/lu__decomposition_8h.html new file mode 100644 index 000000000..b79f486c8 --- /dev/null +++ b/d1/dbe/lu__decomposition_8h.html @@ -0,0 +1,334 @@ + + + + + + + +Algorithms_in_C++: numerical_methods/lu_decomposition.h File Reference + + + + + + + + + + + + + + + +
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Algorithms_in_C++ +  1.0.0 +
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Set of algorithms implemented in C++.
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+Typedefs | +Functions
+
+
lu_decomposition.h File Reference
+
+
+ +

Functions associated with LU Decomposition of a square matrix. +More...

+
#include <iostream>
+#include <valarray>
+#include <vector>
+
+Include dependency graph for lu_decomposition.h:
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Go to the source code of this file.

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+Typedefs

template<typename T >
using matrix = std::vector< std::valarray< T > >
 
+ + + + + + + + +

+Functions

template<typename T >
int lu_decomposition (const matrix< T > &A, matrix< double > *L, matrix< double > *U)
 
template<typename T >
double determinant_lu (const matrix< T > &A)
 Compute determinant of an NxN square matrix using LU decomposition. Using LU decomposition, the determinant is given by the product of diagonal elements of matrices L and U. More...
 
+

Detailed Description

+

Functions associated with LU Decomposition of a square matrix.

+
Author
Krishna Vedala
+

Typedef Documentation

+ +

◆ matrix

+ +
+
+
+template<typename T >
+ + + + +
using matrix = std::vector<std::valarray<T> >
+
+

Define matrix type as a std::vector of std::valarray

+ +
+
+

Function Documentation

+ +

◆ determinant_lu()

+ +
+
+
+template<typename T >
+ + + + + + + + +
double determinant_lu (const matrix< T > & A)
+
+ +

Compute determinant of an NxN square matrix using LU decomposition. Using LU decomposition, the determinant is given by the product of diagonal elements of matrices L and U.

+
Template Parameters
+ + +
Tdatatype of input matrix - int, unsigned int, double, etc
+
+
+
Parameters
+ + +
Ainput square matrix
+
+
+
Returns
determinant of matrix A
+
90  {
+
91  matrix<double> L(A.size(), std::valarray<double>(A.size()));
+
92  matrix<double> U(A.size(), std::valarray<double>(A.size()));
+
93 
+
94  if (lu_decomposition(A, &L, &U) < 0)
+
95  return 0;
+
96 
+
97  double result = 1.f;
+
98  for (size_t i = 0; i < A.size(); i++) {
+
99  result *= L[i][i] * U[i][i];
+
100  }
+
101  return result;
+
102 }
+
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+
+
+
+ +
+
+ +

◆ lu_decomposition()

+ +
+
+
+template<typename T >
+ + + + + + + + + + + + + + + + + + + + + + + + +
int lu_decomposition (const matrix< T > & A,
matrix< double > * L,
matrix< double > * U 
)
+
+

Perform LU decomposition on matrix

Parameters
+ + + + +
[in]Amatrix to decompose
[out]Loutput L matrix
[out]Uoutput U matrix
+
+
+
Returns
0 if no errors
+
+negative if error occurred
+
29  {
+
30  int row, col, j;
+
31  int mat_size = A.size();
+
32 
+
33  if (mat_size != A[0].size()) {
+
34  // check matrix is a square matrix
+
35  std::cerr << "Not a square matrix!\n";
+
36  return -1;
+
37  }
+
38 
+
39  // regularize each row
+
40  for (row = 0; row < mat_size; row++) {
+
41  // Upper triangular matrix
+
42 #ifdef _OPENMP
+
43 #pragma omp for
+
44 #endif
+
45  for (col = row; col < mat_size; col++) {
+
46  // Summation of L[i,j] * U[j,k]
+
47  double lu_sum = 0.;
+
48  for (j = 0; j < row; j++) {
+
49  lu_sum += L[0][row][j] * U[0][j][col];
+
50  }
+
51 
+
52  // Evaluate U[i,k]
+
53  U[0][row][col] = A[row][col] - lu_sum;
+
54  }
+
55 
+
56  // Lower triangular matrix
+
57 #ifdef _OPENMP
+
58 #pragma omp for
+
59 #endif
+
60  for (col = row; col < mat_size; col++) {
+
61  if (row == col) {
+
62  L[0][row][col] = 1.;
+
63  continue;
+
64  }
+
65 
+
66  // Summation of L[i,j] * U[j,k]
+
67  double lu_sum = 0.;
+
68  for (j = 0; j < row; j++) {
+
69  lu_sum += L[0][col][j] * U[0][j][row];
+
70  }
+
71 
+
72  // Evaluate U[i,k]
+
73  L[0][col][row] = (A[col][row] - lu_sum) / U[0][row][row];
+
74  }
+
75  }
+
76 
+
77  return 0;
+
78 }
+
+Here is the call graph for this function:
+
+
+
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+ +
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+
+
mat_size
ll mat_size
Definition: matrix_exponentiation.cpp:45
+
std::vector
STL class.
+
std::vector::size
T size(T... args)
+
std::cerr
+
std::valarray
STL class.
+
lu_decomposition
int lu_decomposition(const matrix< T > &A, matrix< double > *L, matrix< double > *U)
Definition: lu_decomposition.h:29
+ + + + diff --git a/d1/dbe/lu__decomposition_8h.js b/d1/dbe/lu__decomposition_8h.js new file mode 100644 index 000000000..e5734e378 --- /dev/null +++ b/d1/dbe/lu__decomposition_8h.js @@ -0,0 +1,6 @@ +var lu__decomposition_8h = +[ + [ "matrix", "d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5", null ], + [ "determinant_lu", "d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f", null ], + [ "lu_decomposition", "d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509", null ] +]; \ No newline at end of file diff --git a/d1/dbe/lu__decomposition_8h_a3108d43bd32c6fb3b3c158476c51ba7f_cgraph.map b/d1/dbe/lu__decomposition_8h_a3108d43bd32c6fb3b3c158476c51ba7f_cgraph.map new file mode 100644 index 000000000..376071840 --- /dev/null +++ b/d1/dbe/lu__decomposition_8h_a3108d43bd32c6fb3b3c158476c51ba7f_cgraph.map @@ -0,0 +1,5 @@ + + + + + diff --git a/d1/dbe/lu__decomposition_8h_a3108d43bd32c6fb3b3c158476c51ba7f_cgraph.md5 b/d1/dbe/lu__decomposition_8h_a3108d43bd32c6fb3b3c158476c51ba7f_cgraph.md5 new file mode 100644 index 000000000..470fcdea5 --- /dev/null +++ b/d1/dbe/lu__decomposition_8h_a3108d43bd32c6fb3b3c158476c51ba7f_cgraph.md5 @@ -0,0 +1 @@ +88a2ff7f08f53ee9aac3f59997d32991 \ No newline at end of file diff --git a/d1/dbe/lu__decomposition_8h_a3108d43bd32c6fb3b3c158476c51ba7f_cgraph.svg b/d1/dbe/lu__decomposition_8h_a3108d43bd32c6fb3b3c158476c51ba7f_cgraph.svg new file mode 100644 index 000000000..86202f5fa --- /dev/null +++ b/d1/dbe/lu__decomposition_8h_a3108d43bd32c6fb3b3c158476c51ba7f_cgraph.svg @@ -0,0 +1,58 @@ + + + + + + +determinant_lu + + + +Node1 + + +determinant_lu + + + + + +Node2 + + +lu_decomposition + + + + + +Node1->Node2 + + + + + +Node3 + + +std::vector::size + + + + + +Node1->Node3 + + + + + +Node2->Node3 + + + + + diff --git a/d1/dbe/lu__decomposition_8h_a75b8a228c6419ecda6077255d6d60509_cgraph.map b/d1/dbe/lu__decomposition_8h_a75b8a228c6419ecda6077255d6d60509_cgraph.map new file mode 100644 index 000000000..db3f16a64 --- /dev/null +++ b/d1/dbe/lu__decomposition_8h_a75b8a228c6419ecda6077255d6d60509_cgraph.map @@ -0,0 +1,4 @@ + + + + diff --git a/d1/dbe/lu__decomposition_8h_a75b8a228c6419ecda6077255d6d60509_cgraph.md5 b/d1/dbe/lu__decomposition_8h_a75b8a228c6419ecda6077255d6d60509_cgraph.md5 new file mode 100644 index 000000000..8057ce7fe --- /dev/null +++ b/d1/dbe/lu__decomposition_8h_a75b8a228c6419ecda6077255d6d60509_cgraph.md5 @@ -0,0 +1 @@ +2046e39037fadeac7e6958ecbc86a537 \ No newline at end of file diff --git a/d1/dbe/lu__decomposition_8h_a75b8a228c6419ecda6077255d6d60509_cgraph.svg b/d1/dbe/lu__decomposition_8h_a75b8a228c6419ecda6077255d6d60509_cgraph.svg new file mode 100644 index 000000000..e0f81b555 --- /dev/null +++ b/d1/dbe/lu__decomposition_8h_a75b8a228c6419ecda6077255d6d60509_cgraph.svg @@ -0,0 +1,37 @@ + + + + + + +lu_decomposition + + + +Node1 + + +lu_decomposition + + + + + +Node2 + + +std::vector::size + + + + + +Node1->Node2 + + + + + diff --git a/d1/dbe/lu__decomposition_8h_source.html b/d1/dbe/lu__decomposition_8h_source.html new file mode 100644 index 000000000..2b83f9d0b --- /dev/null +++ b/d1/dbe/lu__decomposition_8h_source.html @@ -0,0 +1,352 @@ + + + + + + + +Algorithms_in_C++: numerical_methods/lu_decomposition.h Source File + + + + + + + + + + + + + + + +
+
+ + + + + + +
+
Algorithms_in_C++ +  1.0.0 +
+
Set of algorithms implemented in C++.
+
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+
lu_decomposition.h
+
+
+Go to the documentation of this file.
1 /**
+
2  * @file lu_decomposition.h
+
3  * @author [Krishna Vedala](https://github.com/kvedala)
+
4  * @brief Functions associated with [LU
+
5  * Decomposition](https://en.wikipedia.org/wiki/LU_decomposition)
+
6  * of a square matrix.
+
7  */
+
8 #pragma once
+
9 
+
10 #include <iostream>
+
11 #include <valarray>
+
12 #include <vector>
+
13 #ifdef _OPENMP
+
14 #include <omp.h>
+
15 #endif
+
16 
+
17 /** Define matrix type as a `std::vector` of `std::valarray` */
+
18 template <typename T>
+
19 using matrix = std::vector<std::valarray<T>>;
+
20 
+
21 /** Perform LU decomposition on matrix
+
22  * \param[in] A matrix to decompose
+
23  * \param[out] L output L matrix
+
24  * \param[out] U output U matrix
+
25  * \returns 0 if no errors
+
26  * \returns negative if error occurred
+
27  */
+
28 template <typename T>
+
29 int lu_decomposition(const matrix<T> &A, matrix<double> *L, matrix<double> *U) {
+
30  int row, col, j;
+
31  int mat_size = A.size();
+
32 
+
33  if (mat_size != A[0].size()) {
+
34  // check matrix is a square matrix
+
35  std::cerr << "Not a square matrix!\n";
+
36  return -1;
+
37  }
+
38 
+
39  // regularize each row
+
40  for (row = 0; row < mat_size; row++) {
+
41  // Upper triangular matrix
+
42 #ifdef _OPENMP
+
43 #pragma omp for
+
44 #endif
+
45  for (col = row; col < mat_size; col++) {
+
46  // Summation of L[i,j] * U[j,k]
+
47  double lu_sum = 0.;
+
48  for (j = 0; j < row; j++) {
+
49  lu_sum += L[0][row][j] * U[0][j][col];
+
50  }
+
51 
+
52  // Evaluate U[i,k]
+
53  U[0][row][col] = A[row][col] - lu_sum;
+
54  }
+
55 
+
56  // Lower triangular matrix
+
57 #ifdef _OPENMP
+
58 #pragma omp for
+
59 #endif
+
60  for (col = row; col < mat_size; col++) {
+
61  if (row == col) {
+
62  L[0][row][col] = 1.;
+
63  continue;
+
64  }
+
65 
+
66  // Summation of L[i,j] * U[j,k]
+
67  double lu_sum = 0.;
+
68  for (j = 0; j < row; j++) {
+
69  lu_sum += L[0][col][j] * U[0][j][row];
+
70  }
+
71 
+
72  // Evaluate U[i,k]
+
73  L[0][col][row] = (A[col][row] - lu_sum) / U[0][row][row];
+
74  }
+
75  }
+
76 
+
77  return 0;
+
78 }
+
79 
+
80 /**
+
81  * @brief Compute determinant of an NxN square matrix using LU decomposition.
+
82  * Using LU decomposition, the determinant is given by the product of diagonal
+
83  * elements of matrices L and U.
+
84  *
+
85  * @tparam T datatype of input matrix - int, unsigned int, double, etc
+
86  * @param A input square matrix
+
87  * @return determinant of matrix A
+
88  */
+
89 template <typename T>
+
90 double determinant_lu(const matrix<T> &A) {
+
91  matrix<double> L(A.size(), std::valarray<double>(A.size()));
+
92  matrix<double> U(A.size(), std::valarray<double>(A.size()));
+
93 
+
94  if (lu_decomposition(A, &L, &U) < 0)
+
95  return 0;
+
96 
+
97  double result = 1.f;
+
98  for (size_t i = 0; i < A.size(); i++) {
+
99  result *= L[i][i] * U[i][i];
+
100  }
+
101  return result;
+
102 }
+
+
+
check_termination
bool check_termination(long double delta)
Definition: durand_kerner_roots.cpp:91
+
Sqrt
double Sqrt(double a)
Definition: sqrt_double.cpp:16
+
std::srand
T srand(T... args)
+
lcm
unsigned int lcm(unsigned int x, unsigned int y)
Definition: least_common_multiple.cpp:43
+
tests
void tests()
Definition: least_common_multiple.cpp:48
+
prime_numbers
std::vector< int > prime_numbers
Definition: prime_factorization.cpp:16
+
main
int main()
Definition: primes_up_to_billion.cpp:26
+
MAX_ITERATIONS
#define MAX_ITERATIONS
Maximum number of iterations to check.
Definition: false_position.cpp:24
+
statistics::stats_computer2::operator>>
friend std::istream & operator>>(std::istream &input, stats_computer2 &stat)
Definition: realtime_stats.cpp:97
+
mat_size
ll mat_size
Definition: matrix_exponentiation.cpp:45
+
EPSILON
#define EPSILON
solution accuracy limit
Definition: golden_search_extrema.cpp:17
+
test3
void test3()
Test function to find maxima for the function in the interval Expected result: .
Definition: brent_method_extrema.cpp:188
+
std::string
STL class.
+
std::uniform_int_distribution
+
primes
std::vector< int > primes(int max)
Definition: prime_numbers.cpp:12
+
miller_rabin_primality_test
bool miller_rabin_primality_test(T num, T repeats)
Definition: miller_rabin.cpp:125
+
std::clock_t
+
std::pair
+
main
int main()
Definition: brent_method_extrema.cpp:204
+
std::cos
T cos(T... args)
+
EPSILON
#define EPSILON
system accuracy limit
Definition: brent_method_extrema.cpp:23
+
std::vector
STL class.
+
test2
void test2()
Test determinant computation using LU decomposition.
Definition: lu_decompose.cpp:66
+
std::vector::size
T size(T... args)
+
multiply
int multiply(int x, int res[], int res_size)
Definition: power_for_huge_numbers.cpp:25
+
ans
ll ans(ll n)
Definition: matrix_exponentiation.cpp:91
+
main
int main()
Definition: sieve_of_eratosthenes.cpp:59
+
print
void print(uint32_t N)
Definition: sieve_of_eratosthenes.cpp:40
+
complex_str
const char * complex_str(const std::complex< double > &x)
Definition: durand_kerner_roots.cpp:76
+
test3
void test3()
Test function to find maxima for the function in the interval Expected result: .
Definition: golden_search_extrema.cpp:123
+
get_minima
double get_minima(const std::function< double(double)> &f, double lim_a, double lim_b)
Get the real root of a function in the given interval.
Definition: brent_method_extrema.cpp:35
+
std::setfill
T setfill(T... args)
+
std::function
+
sgn
int sgn(T val)
Definition: bisection_method.cpp:32
+
statistics::stats_computer1::std
double std() const
Definition: realtime_stats.cpp:48
+
factors
std::vector< std::pair< int, int > > factors
Definition: prime_factorization.cpp:19
+
main
int main()
Definition: prime_factorization.cpp:62
+
reverse_binary
std::vector< T > reverse_binary(T num)
Definition: miller_rabin.cpp:19
+
std::sqrt
T sqrt(T... args)
+
power
void power(int x, int n)
Definition: power_for_huge_numbers.cpp:56
+
test1
void test1()
Test function to find minima for the function in the interval Expected result = 2.
Definition: golden_search_extrema.cpp:78
+
main
int main()
Definition: prime_numbers.cpp:26
+
std::mt19937
+
std::vector::push_back
T push_back(T... args)
+
main
int main()
Definition: modular_inverse_fermat_little_theorem.cpp:84
+
std::clock
T clock(T... args)
+
durand_kerner_algo
std::pair< uint32_t, double > durand_kerner_algo(const std::valarray< double > &coeffs, std::valarray< std::complex< double >> *roots, bool write_log=false)
Definition: durand_kerner_roots.cpp:109
+
test1
void test1()
Definition: lu_decompose.cpp:36
+
test
void test()
Definition: sum_of_digits.cpp:58
+
std::isnan
T isnan(T... args)
+
statistics
Statistical algorithms.
+
test2
void test2()
Definition: sum_of_digits.cpp:49
+
init
void init()
Definition: sieve_of_eratosthenes.cpp:52
+
std::snprintf
T snprintf(T... args)
+
std::random_device
+
std::numeric_limits::infinity
T infinity(T... args)
+
std::cout
+
std::ofstream
STL class.
+
main
int main()
Definition: false_position.cpp:39
+
std::isinf
T isinf(T... args)
+
statistics::stats_computer2::variance
double variance() const
Definition: realtime_stats.cpp:89
+
gcd
unsigned int gcd(unsigned int x, unsigned int y)
Definition: least_common_multiple.cpp:16
+
main
int main()
Definition: sqrt_double.cpp:42
+
sieve
void sieve(uint32_t N)
Definition: sieve_of_eratosthenes.cpp:25
+
modular_exponentiation
T modular_exponentiation(T base, const std::vector< T > &rev_binary_exponent, T mod)
Definition: miller_rabin.cpp:43
+
poly_function
std::complex< double > poly_function(const std::valarray< double > &coeffs, std::complex< double > x)
Definition: durand_kerner_roots.cpp:53
+
main
int main(int argc, char **argv)
Definition: lu_decompose.cpp:84
+
std::valarray
STL class.
+
std::complex::real
T real(T... args)
+
test1
void test1()
Definition: durand_kerner_roots.cpp:207
+
main
int main()
Definition: gaussian_elimination.cpp:9
+
std::ofstream::open
T open(T... args)
+
ACCURACY
#define ACCURACY
Definition: durand_kerner_roots.cpp:45
+
statistics::stats_computer1::mean
double mean() const
Definition: realtime_stats.cpp:42
+
statistics::stats_computer2
Definition: realtime_stats.cpp:72
+
main
int main(int argc, char **argv)
Definition: realtime_stats.cpp:158
+
sgn
int sgn(T val)
Definition: false_position.cpp:34
+
std::rand
T rand(T... args)
+
std::swap
T swap(T... args)
+
lu_decomposition.h
Functions associated with LU Decomposition of a square matrix.
+
test_function
void test_function(const float *test_data, const int number_of_samples)
Definition: realtime_stats.cpp:118
+
SieveOfEratosthenes
void SieveOfEratosthenes(int N)
Definition: prime_factorization.cpp:23
+
std::string::substr
T substr(T... args)
+
miller_test
bool miller_test(T d, T num)
Definition: miller_rabin.cpp:73
+
main
int main()
Definition: least_common_multiple.cpp:67
+
lu_decomposition
int lu_decomposition(const matrix< T > &A, matrix< double > *L, matrix< double > *U)
Definition: lu_decomposition.h:29
+
MAX
#define MAX
Definition: sieve_of_eratosthenes.cpp:16
+
binExpo
int64_t binExpo(int64_t a, int64_t b, int64_t m)
Definition: modular_inverse_fermat_little_theorem.cpp:52
+
std::endl
T endl(T... args)
+
statistics::stats_computer1::new_val
void new_val(T x)
Definition: realtime_stats.cpp:32
+
test2
void test2()
Test function to find root for the function in the interval Expected result: .
Definition: brent_method_extrema.cpp:165
+
std::left
T left(T... args)
+
statistics::stats_computer2::new_val
void new_val(T x)
Definition: realtime_stats.cpp:77
+
statistics::stats_computer1::variance
double variance() const
Definition: realtime_stats.cpp:45
+
sum_of_digits
int sum_of_digits(int num)
Definition: sum_of_digits.cpp:23
+
main
int main()
Definition: number_of_positive_divisors.cpp:62
+
std::vector::cbegin
T cbegin(T... args)
+
main
int main()
Definition: miller_rabin.cpp:183
+
std::strtod
T strtod(T... args)
+
main
int main()
Definition: power_for_huge_numbers.cpp:82
+
prime_factorization
void prime_factorization(int num)
Definition: prime_factorization.cpp:40
+
main
int main()
Definition: sum_of_digits.cpp:68
+
determinant_lu
double determinant_lu(const matrix< T > &A)
Compute determinant of an NxN square matrix using LU decomposition. Using LU decomposition,...
Definition: lu_decomposition.h:90
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std::fixed
T fixed(T... args)
+
statistics::stats_computer1
Definition: realtime_stats.cpp:27
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test2
void test2()
Test function to find maxima for the function in the interval Expected result: .
Definition: golden_search_extrema.cpp:100
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statistics::stats_computer2::std
double std() const
Definition: realtime_stats.cpp:92
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main
int main()
Definition: golden_search_extrema.cpp:139
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isprime
bool isprime[MAX]
Definition: sieve_of_eratosthenes.cpp:19
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test1
void test1()
Definition: sum_of_digits.cpp:40
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std::complex
STL class.
+
std::complex::imag
T imag(T... args)
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eq
static double eq(double i)
Definition: false_position.cpp:28
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test1
void test1()
Test function to find root for the function in the interval Expected result = 2.
Definition: brent_method_extrema.cpp:143
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add
std::string add(std::string a, std::string b)
Definition: string_fibonacci.cpp:24
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std::make_pair
T make_pair(T... args)
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std::time
T time(T... args)
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MAX_ITERATIONS
#define MAX_ITERATIONS
Maximum number of iterations to check.
Definition: bisection_method.cpp:22
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std::vector::cend
T cend(T... args)
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std::setw
T setw(T... args)
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std::max
T max(T... args)
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main
int main()
Definition: string_fibonacci.cpp:81
+
number_of_positive_divisors
int number_of_positive_divisors(int n)
Definition: number_of_positive_divisors.cpp:34
+
eq
static double eq(double i)
Definition: bisection_method.cpp:26
+
get_minima
double get_minima(const std::function< double(double)> &f, double lim_a, double lim_b)
Get the minima of a function in the given interval. To get the maxima, simply negate the function....
Definition: golden_search_extrema.cpp:29
+
fib_Accurate
void fib_Accurate(uint64_t n)
Definition: string_fibonacci.cpp:68
+
Sieve
void Sieve(int64_t n)
Definition: primes_up_to_billion.cpp:13
+
std::cin
+
operator<<
std::ostream & operator<<(std::ostream &out, matrix< T > const &v)
Definition: lu_decompose.cpp:18
+
statistics::stats_computer2::mean
double mean() const
Definition: realtime_stats.cpp:86
+
isPrime
bool isPrime(int64_t m)
Definition: modular_inverse_fermat_little_theorem.cpp:68
+
std::ofstream::is_open
T is_open(T... args)
+
test2
void test2()
Definition: durand_kerner_roots.cpp:242
+
main
int main()
Definition: bisection_method.cpp:37
+
std::exit
T exit(T... args)
+
MAX
#define MAX
Definition: power_for_huge_numbers.cpp:10
+
statistics::stats_computer1::operator>>
friend std::istream & operator>>(std::istream &input, stats_computer1 &stat)
Definition: realtime_stats.cpp:53
+
tests
void tests()
Definition: miller_rabin.cpp:157
+
prime
char prime[100000000]
Definition: primes_up_to_billion.cpp:10
+
std::pow
T pow(T... args)
+
isprime
bool isprime[1000006]
Definition: prime_factorization.cpp:13
+ + + + diff --git a/d1/df3/hash__search_8cpp.html b/d1/df3/hash__search_8cpp.html index 356548a49..df11fcde6 100644 --- a/d1/df3/hash__search_8cpp.html +++ b/d1/df3/hash__search_8cpp.html @@ -164,7 +164,7 @@ int 
Copyright
2020 Arctic2333

In this algorithm, we use the method of division and reservation remainder to construct the hash function, and use the method of chain address to solve the conflict, that is, we link a chain list after the data, and store all the records whose keywords are synonyms in the same linear chain list.

Warning
This program is only for educational purposes. It has serious flaws in implementation with regards to memory management resulting in large amounts of memory leaks.
-
Todo:
fix the program for memory leaks and better structure in C++ and not C fashion
+
Todo:
fix the program for memory leaks and better structure in C++ and not C fashion

Typedef Documentation

◆ node

@@ -204,7 +204,7 @@ int 
Warning
dynamic memory allocated to n never gets freed.
-
Todo:
fix memory leak
+
Todo:
fix memory leak
55  { // Construct hash table
56  link p, n;
57  int index;
diff --git a/d4/d68/qr__decompose_8h_source.html b/d4/d68/qr__decompose_8h_source.html index c9cdc43fc..d5e14ed1b 100644 --- a/d4/d68/qr__decompose_8h_source.html +++ b/d4/d68/qr__decompose_8h_source.html @@ -306,189 +306,72 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
210 #endif // NUMERICAL_METHODS_QR_DECOMPOSE_H_
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check_termination
bool check_termination(long double delta)
Definition: durand_kerner_roots.cpp:91
save_exact_solution
void save_exact_solution(const double &X0, const double &X_MAX, const double &step_size, const std::valarray< double > &Y0)
Definition: ode_midpoint_euler.cpp:156
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Sqrt
double Sqrt(double a)
Definition: sqrt_double.cpp:16
std::srand
T srand(T... args)
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lcm
unsigned int lcm(unsigned int x, unsigned int y)
Definition: least_common_multiple.cpp:43
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tests
void tests()
Definition: least_common_multiple.cpp:48
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prime_numbers
std::vector< int > prime_numbers
Definition: prime_factorization.cpp:16
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main
int main()
Definition: primes_up_to_billion.cpp:26
semi_implicit_euler
double semi_implicit_euler(double dx, double x0, double x_max, std::valarray< double > *y, bool save_to_file=false)
Compute approximation using the semi-implicit-Euler method in the given limits.
Definition: ode_semi_implicit_euler.cpp:103
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operator<<
std::ostream & operator<<(std::ostream &out, std::vector< std::vector< T >> const &v)
Definition: lu_decompose.cpp:75
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MAX_ITERATIONS
#define MAX_ITERATIONS
Maximum number of iterations to check.
Definition: false_position.cpp:24
-
statistics::stats_computer2::operator>>
friend std::istream & operator>>(std::istream &input, stats_computer2 &stat)
Definition: realtime_stats.cpp:97
MAX_ITERATIONS
#define MAX_ITERATIONS
Maximum number of iterations to check.
Definition: newton_raphson_method.cpp:21
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mat_size
ll mat_size
Definition: matrix_exponentiation.cpp:45
-
EPSILON
#define EPSILON
solution accuracy limit
Definition: golden_search_extrema.cpp:17
-
test3
void test3()
Test function to find maxima for the function in the interval Expected result: .
Definition: brent_method_extrema.cpp:188
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std::string
STL class.
semi_implicit_euler_step
void semi_implicit_euler_step(const double dx, const double &x, std::valarray< double > *y, std::valarray< double > *dy)
Compute next step approximation using the semi-implicit-Euler method.
Definition: ode_semi_implicit_euler.cpp:82
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std::uniform_int_distribution
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primes
std::vector< int > primes(int max)
Definition: prime_numbers.cpp:12
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miller_rabin_primality_test
bool miller_rabin_primality_test(T num, T repeats)
Definition: miller_rabin.cpp:125
std::clock_t
operator+
std::vector< T > operator+(std::vector< T > const &A, std::vector< T > const &B)
Definition: ordinary_least_squares_regressor.cpp:196
eq
static double eq(double i)
Definition: newton_raphson_method.cpp:29
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std::pair
-
main
int main()
Definition: brent_method_extrema.cpp:204
std::cos
T cos(T... args)
-
EPSILON
#define EPSILON
system accuracy limit
Definition: brent_method_extrema.cpp:23
eq_der
static double eq_der(double i)
Definition: newton_raphson_method.cpp:39
exact_solution
void exact_solution(const double &x, std::valarray< double > *y)
Exact solution of the problem. Used for solution comparison.
Definition: ode_forward_euler.cpp:67
std::atof
T atof(T... args)
std::vector
STL class.
std::vector::size
T size(T... args)
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multiply
int multiply(int x, int res[], int res_size)
Definition: power_for_huge_numbers.cpp:25
main
int main(int argc, char *argv[])
Definition: ode_forward_euler.cpp:188
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ans
ll ans(ll n)
Definition: matrix_exponentiation.cpp:91
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main
int main()
Definition: sieve_of_eratosthenes.cpp:59
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print
void print(uint32_t N)
Definition: sieve_of_eratosthenes.cpp:40
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complex_str
const char * complex_str(const std::complex< double > &x)
Definition: durand_kerner_roots.cpp:76
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test3
void test3()
Test function to find maxima for the function in the interval Expected result: .
Definition: golden_search_extrema.cpp:123
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get_minima
double get_minima(const std::function< double(double)> &f, double lim_a, double lim_b)
Get the real root of a function in the given interval.
Definition: brent_method_extrema.cpp:35
std::setfill
T setfill(T... args)
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std::function
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sgn
int sgn(T val)
Definition: bisection_method.cpp:32
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statistics::stats_computer1::std
double std() const
Definition: realtime_stats.cpp:48
midpoint_euler_step
void midpoint_euler_step(const double dx, const double &x, std::valarray< double > *y, std::valarray< double > *dy)
Compute next step approximation using the midpoint-Euler method.
Definition: ode_midpoint_euler.cpp:85
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factors
std::vector< std::pair< int, int > > factors
Definition: prime_factorization.cpp:19
is_square
bool is_square(std::vector< std::vector< T >> const &A)
Definition: ordinary_least_squares_regressor.cpp:55
-
main
int main()
Definition: prime_factorization.cpp:62
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reverse_binary
std::vector< T > reverse_binary(T num)
Definition: miller_rabin.cpp:19
std::sqrt
T sqrt(T... args)
-
power
void power(int x, int n)
Definition: power_for_huge_numbers.cpp:56
qr_algorithm
Functions to compute QR decomposition of any rectangular matrix.
operator*
std::vector< std::vector< T > > operator*(std::vector< std::vector< T >> const &A, std::vector< std::vector< T >> const &B)
Definition: ordinary_least_squares_regressor.cpp:72
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test1
void test1()
Test function to find minima for the function in the interval Expected result = 2.
Definition: golden_search_extrema.cpp:78
-
main
int main()
Definition: prime_numbers.cpp:26
forward_euler_step
void forward_euler_step(const double dx, const double &x, std::valarray< double > *y, std::valarray< double > *dy)
Compute next step approximation using the forward-Euler method.
Definition: ode_forward_euler.cpp:86
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std::mt19937
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std::vector::push_back
T push_back(T... args)
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main
int main()
Definition: modular_inverse_fermat_little_theorem.cpp:84
std::clock
T clock(T... args)
-
durand_kerner_algo
std::pair< uint32_t, double > durand_kerner_algo(const std::valarray< double > &coeffs, std::valarray< std::complex< double >> *roots, bool write_log=false)
Definition: durand_kerner_roots.cpp:109
operator<<
std::ostream & operator<<(std::ostream &out, std::vector< std::vector< T >> const &v)
Definition: ordinary_least_squares_regressor.cpp:20
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test
void test()
Definition: sum_of_digits.cpp:58
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std::isnan
T isnan(T... args)
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statistics
Statistical algorithms.
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test2
void test2()
Definition: sum_of_digits.cpp:49
save_exact_solution
void save_exact_solution(const double &X0, const double &X_MAX, const double &step_size, const std::valarray< double > &Y0)
Definition: ode_forward_euler.cpp:152
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init
void init()
Definition: sieve_of_eratosthenes.cpp:52
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std::snprintf
T snprintf(T... args)
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std::random_device
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std::numeric_limits::infinity
T infinity(T... args)
qr_algorithm::vector_proj
std::valarray< T > vector_proj(const std::valarray< T > &a, const std::valarray< T > &b)
Definition: qr_decompose.h:104
std::cout
std::ofstream
STL class.
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main
int main()
Definition: false_position.cpp:39
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std::isinf
T isinf(T... args)
qr_algorithm::vector_mag
double vector_mag(const std::valarray< T > &a)
Definition: qr_decompose.h:92
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statistics::stats_computer2::variance
double variance() const
Definition: realtime_stats.cpp:89
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gcd
unsigned int gcd(unsigned int x, unsigned int y)
Definition: least_common_multiple.cpp:16
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main
int main()
Definition: sqrt_double.cpp:42
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sieve
void sieve(uint32_t N)
Definition: sieve_of_eratosthenes.cpp:25
std::ofstream::close
T close(T... args)
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modular_exponentiation
T modular_exponentiation(T base, const std::vector< T > &rev_binary_exponent, T mod)
Definition: miller_rabin.cpp:43
std::perror
T perror(T... args)
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poly_function
std::complex< double > poly_function(const std::valarray< double > &coeffs, std::complex< double > x)
Definition: durand_kerner_roots.cpp:53
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main
int main(int argc, char **argv)
Definition: lu_decompose.cpp:91
std::valarray
STL class.
main
int main()
Definition: ordinary_least_squares_regressor.cpp:358
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std::complex::real
T real(T... args)
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test1
void test1()
Definition: durand_kerner_roots.cpp:207
predict_OLS_regressor
std::vector< float > predict_OLS_regressor(std::vector< std::vector< T >> const &X, std::vector< float > const &beta)
Definition: ordinary_least_squares_regressor.cpp:340
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main
int main()
Definition: gaussian_elimination.cpp:9
std::ofstream::open
T open(T... args)
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ACCURACY
#define ACCURACY
Definition: durand_kerner_roots.cpp:45
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statistics::stats_computer1::mean
double mean() const
Definition: realtime_stats.cpp:42
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statistics::stats_computer2
Definition: realtime_stats.cpp:72
qr_algorithm::operator<<
std::ostream & operator<<(std::ostream &out, std::valarray< std::valarray< T >> const &v)
Definition: qr_decompose.h:33
forward_euler
double forward_euler(double dx, double x0, double x_max, std::valarray< double > *y, bool save_to_file=false)
Compute approximation using the forward-Euler method in the given limits.
Definition: ode_forward_euler.cpp:102
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main
int main(int argc, char **argv)
Definition: realtime_stats.cpp:158
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sgn
int sgn(T val)
Definition: false_position.cpp:34
std::rand
T rand(T... args)
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std::swap
T swap(T... args)
problem
void problem(const double &x, std::valarray< double > *y, std::valarray< double > *dy)
Problem statement for a system with first-order differential equations. Updates the system differenti...
Definition: ode_semi_implicit_euler.cpp:53
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test_function
void test_function(const float *test_data, const int number_of_samples)
Definition: realtime_stats.cpp:118
std::sin
T sin(T... args)
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SieveOfEratosthenes
void SieveOfEratosthenes(int N)
Definition: prime_factorization.cpp:23
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std::string::substr
T substr(T... args)
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miller_test
bool miller_test(T d, T num)
Definition: miller_rabin.cpp:73
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main
int main()
Definition: least_common_multiple.cpp:67
EPSILON
#define EPSILON
system accuracy limit
Definition: newton_raphson_method.cpp:20
problem
void problem(const double &x, std::valarray< double > *y, std::valarray< double > *dy)
Problem statement for a system with first-order differential equations. Updates the system differenti...
Definition: ode_forward_euler.cpp:54
data
int data[MAX]
test data
Definition: hash_search.cpp:24
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MAX
#define MAX
Definition: sieve_of_eratosthenes.cpp:16
fit_OLS_regressor
std::vector< float > fit_OLS_regressor(std::vector< std::vector< T >> const &X, std::vector< T > const &Y)
Definition: ordinary_least_squares_regressor.cpp:310
operator-
std::vector< T > operator-(std::vector< T > const &A, std::vector< T > const &B)
Definition: ordinary_least_squares_regressor.cpp:175
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binExpo
int64_t binExpo(int64_t a, int64_t b, int64_t m)
Definition: modular_inverse_fermat_little_theorem.cpp:52
std::endl
T endl(T... args)
get_inverse
std::vector< std::vector< float > > get_inverse(std::vector< std::vector< T >> const &A)
Definition: ordinary_least_squares_regressor.cpp:218
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statistics::stats_computer1::new_val
void new_val(T x)
Definition: realtime_stats.cpp:32
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test2
void test2()
Test function to find root for the function in the interval Expected result: .
Definition: brent_method_extrema.cpp:165
qr_algorithm::vector_dot
double vector_dot(const std::valarray< T > &a, const std::valarray< T > &b)
Definition: qr_decompose.h:76
std::left
T left(T... args)
problem
void problem(const double &x, std::valarray< double > *y, std::valarray< double > *dy)
Problem statement for a system with first-order differential equations. Updates the system differenti...
Definition: ode_midpoint_euler.cpp:53
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statistics::stats_computer2::new_val
void new_val(T x)
Definition: realtime_stats.cpp:77
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statistics::stats_computer1::variance
double variance() const
Definition: realtime_stats.cpp:45
main
int main()
Definition: newton_raphson_method.cpp:44
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sum_of_digits
int sum_of_digits(int num)
Definition: sum_of_digits.cpp:23
midpoint_euler
double midpoint_euler(double dx, double x0, double x_max, std::valarray< double > *y, bool save_to_file=false)
Compute approximation using the midpoint-Euler method in the given limits.
Definition: ode_midpoint_euler.cpp:107
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main
int main()
Definition: number_of_positive_divisors.cpp:62
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std::vector::cbegin
T cbegin(T... args)
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main
int main()
Definition: miller_rabin.cpp:183
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std::strtod
T strtod(T... args)
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main
int main()
Definition: power_for_huge_numbers.cpp:82
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prime_factorization
void prime_factorization(int num)
Definition: prime_factorization.cpp:40
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main
int main()
Definition: sum_of_digits.cpp:68
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std::fixed
T fixed(T... args)
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statistics::stats_computer1
Definition: realtime_stats.cpp:27
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test2
void test2()
Test function to find maxima for the function in the interval Expected result: .
Definition: golden_search_extrema.cpp:100
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statistics::stats_computer2::std
double std() const
Definition: realtime_stats.cpp:92
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main
int main()
Definition: golden_search_extrema.cpp:139
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isprime
bool isprime[MAX]
Definition: sieve_of_eratosthenes.cpp:19
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test1
void test1()
Definition: sum_of_digits.cpp:40
qr_algorithm::qr_decompose
void qr_decompose(const std::valarray< std::valarray< T >> &A, std::valarray< std::valarray< T >> *Q, std::valarray< std::valarray< T >> *R)
Definition: qr_decompose.h:146
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std::complex
STL class.
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std::complex::imag
T imag(T... args)
main
int main(int argc, char *argv[])
Definition: ode_semi_implicit_euler.cpp:189
std::size_t
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eq
static double eq(double i)
Definition: false_position.cpp:28
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test1
void test1()
Test function to find root for the function in the interval Expected result = 2.
Definition: brent_method_extrema.cpp:143
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add
std::string add(std::string a, std::string b)
Definition: string_fibonacci.cpp:24
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std::make_pair
T make_pair(T... args)
std::time
T time(T... args)
save_exact_solution
void save_exact_solution(const double &X0, const double &X_MAX, const double &step_size, const std::valarray< double > &Y0)
Definition: ode_semi_implicit_euler.cpp:153
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MAX_ITERATIONS
#define MAX_ITERATIONS
Maximum number of iterations to check.
Definition: bisection_method.cpp:22
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std::vector::cend
T cend(T... args)
exact_solution
void exact_solution(const double &x, std::valarray< double > *y)
Exact solution of the problem. Used for solution comparison.
Definition: ode_semi_implicit_euler.cpp:66
std::setw
T setw(T... args)
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std::max
T max(T... args)
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main
int main()
Definition: string_fibonacci.cpp:81
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number_of_positive_divisors
int number_of_positive_divisors(int n)
Definition: number_of_positive_divisors.cpp:34
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eq
static double eq(double i)
Definition: bisection_method.cpp:26
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get_minima
double get_minima(const std::function< double(double)> &f, double lim_a, double lim_b)
Get the minima of a function in the given interval. To get the maxima, simply negate the function....
Definition: golden_search_extrema.cpp:29
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fib_Accurate
void fib_Accurate(uint64_t n)
Definition: string_fibonacci.cpp:68
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Sieve
void Sieve(int64_t n)
Definition: primes_up_to_billion.cpp:13
std::cin
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statistics::stats_computer2::mean
double mean() const
Definition: realtime_stats.cpp:86
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isPrime
bool isPrime(int64_t m)
Definition: modular_inverse_fermat_little_theorem.cpp:68
std::numeric_limits
std::ofstream::is_open
T is_open(T... args)
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test2
void test2()
Definition: durand_kerner_roots.cpp:242
exact_solution
void exact_solution(const double &x, std::valarray< double > *y)
Exact solution of the problem. Used for solution comparison.
Definition: ode_midpoint_euler.cpp:66
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lu_decomposition
int lu_decomposition(const std::vector< std::vector< double >> &A, std::vector< std::vector< double >> *L, std::vector< std::vector< double >> *U)
Definition: lu_decompose.cpp:22
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main
int main()
Definition: bisection_method.cpp:37
operator/
std::vector< float > operator/(std::vector< T > const &A, float const scalar)
Definition: ordinary_least_squares_regressor.cpp:166
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std::exit
T exit(T... args)
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MAX
#define MAX
Definition: power_for_huge_numbers.cpp:10
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statistics::stats_computer1::operator>>
friend std::istream & operator>>(std::istream &input, stats_computer1 &stat)
Definition: realtime_stats.cpp:53
main
int main(int argc, char *argv[])
Definition: ode_midpoint_euler.cpp:192
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tests
void tests()
Definition: miller_rabin.cpp:157
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prime
char prime[100000000]
Definition: primes_up_to_billion.cpp:10
std::pow
T pow(T... args)
-
isprime
bool isprime[1000006]
Definition: prime_factorization.cpp:13
get_transpose
std::vector< std::vector< T > > get_transpose(std::vector< std::vector< T >> const &A)
Definition: ordinary_least_squares_regressor.cpp:289
-

global vector variables used in the ans function.

Todo:
@stepfencurryxiao add documetnation
+

global vector variables used in the ans function.

Todo:
@stepfencurryxiao add documetnation
@@ -435,7 +435,7 @@ Here is the call graph for this function:
-

global variable mat_size

Todo:
@stepfencurryxiao add documetnation
+

global variable mat_size

Todo:
@stepfencurryxiao add documetnation
diff --git a/d7/d39/lu__decomposition_8h__dep__incl.map b/d7/d39/lu__decomposition_8h__dep__incl.map new file mode 100644 index 000000000..90498cf4f --- /dev/null +++ b/d7/d39/lu__decomposition_8h__dep__incl.map @@ -0,0 +1,4 @@ + + + + diff --git a/d7/d39/lu__decomposition_8h__dep__incl.md5 b/d7/d39/lu__decomposition_8h__dep__incl.md5 new file mode 100644 index 000000000..c707d3416 --- /dev/null +++ b/d7/d39/lu__decomposition_8h__dep__incl.md5 @@ -0,0 +1 @@ +2313f24130ed2a5ca7a822b076b6579c \ No newline at end of file diff --git a/d7/d39/lu__decomposition_8h__dep__incl.svg b/d7/d39/lu__decomposition_8h__dep__incl.svg new file mode 100644 index 000000000..35438520f --- /dev/null +++ b/d7/d39/lu__decomposition_8h__dep__incl.svg @@ -0,0 +1,39 @@ + + + + + + +numerical_methods/lu_decomposition.h + + + +Node1 + + +numerical_methods/lu +_decomposition.h + + + + + +Node2 + + +numerical_methods/lu +_decompose.cpp + + + + + +Node1->Node2 + + + + + diff --git a/d9/d69/median__search_8cpp.html b/d9/d69/median__search_8cpp.html index 3249d423e..182e81db3 100644 --- a/d9/d69/median__search_8cpp.html +++ b/d9/d69/median__search_8cpp.html @@ -160,7 +160,7 @@ template<class X >
-
Todo:
add documentation
+
Todo:
add documentation
18  {
19  if (s1->size() >= x && s1->size() + s2->size() < x) {
20  std::cout << (*s2)[0] << " is the " << x + 1 << "th element from front";
diff --git a/dc/d37/lu__decompose_8cpp__incl.map b/dc/d37/lu__decompose_8cpp__incl.map index 2544e7c25..63ef084ac 100644 --- a/dc/d37/lu__decompose_8cpp__incl.map +++ b/dc/d37/lu__decompose_8cpp__incl.map @@ -1,7 +1,10 @@ - - - - - + + + + + + + + diff --git a/dc/d37/lu__decompose_8cpp__incl.md5 b/dc/d37/lu__decompose_8cpp__incl.md5 index d14f77b15..23df4099d 100644 --- a/dc/d37/lu__decompose_8cpp__incl.md5 +++ b/dc/d37/lu__decompose_8cpp__incl.md5 @@ -1 +1 @@ -0aaf50ef77094991d705b3bba1630939 \ No newline at end of file +c49d4414684dfa5c0216b861a7d3fdd1 \ No newline at end of file diff --git a/dc/d37/lu__decompose_8cpp__incl.svg b/dc/d37/lu__decompose_8cpp__incl.svg index 2f08e9c80..20eed1693 100644 --- a/dc/d37/lu__decompose_8cpp__incl.svg +++ b/dc/d37/lu__decompose_8cpp__incl.svg @@ -4,18 +4,18 @@ - - + + numerical_methods/lu_decompose.cpp - + Node1 - -numerical_methods/lu -_decompose.cpp + +numerical_methods/lu +_decompose.cpp @@ -23,61 +23,112 @@ Node2 - -ctime + +cassert Node1->Node2 - - + + Node3 - -iomanip + +ctime Node1->Node3 - - + + Node4 - -iostream + +iomanip Node1->Node4 - - + + Node5 - -vector + +iostream Node1->Node5 - - + + + + + +Node6 + + +./lu_decomposition.h + + + + + +Node1->Node6 + + + + + +Node6->Node5 + + + + + +Node7 + + +valarray + + + + + +Node6->Node7 + + + + + +Node8 + + +vector + + + + + +Node6->Node8 + + diff --git a/dc/dc5/paranthesis__matching_8cpp.html b/dc/dc5/paranthesis__matching_8cpp.html index 4250e23fb..cd33aacf0 100644 --- a/dc/dc5/paranthesis__matching_8cpp.html +++ b/dc/dc5/paranthesis__matching_8cpp.html @@ -141,7 +141,7 @@ char 
Note
Do not know the application of this, however.
Implementation is C-type and does not utilize the C++ constructs
-
Todo:
implement as a C++ class
+
Todo:
implement as a C++ class

Macro Definition Documentation

◆ MAX

diff --git a/dc/dfe/ternary__search_8cpp.html b/dc/dfe/ternary__search_8cpp.html index bf8812bae..a9db39aab 100644 --- a/dc/dfe/ternary__search_8cpp.html +++ b/dc/dfe/ternary__search_8cpp.html @@ -185,7 +185,7 @@ Functions
-

get_input function is to receive input from standard IO

Todo:
@christianbender Get input from STDIO or write input to memory as done above.
+

get_input function is to receive input from standard IO

Todo:
@christianbender Get input from STDIO or write input to memory as done above.
36 {}
diff --git a/dd/d65/lu__decompose_8cpp.html b/dd/d65/lu__decompose_8cpp.html index 9eeccb828..f8705a3c1 100644 --- a/dd/d65/lu__decompose_8cpp.html +++ b/dd/d65/lu__decompose_8cpp.html @@ -99,24 +99,29 @@ $(document).ready(function(){initNavTree('dd/d65/lu__decompose_8cpp.html','../..

LU decomposition of a square matrix More...

-
#include <ctime>
+
#include <cassert>
+#include <ctime>
#include <iomanip>
#include <iostream>
-#include <vector>
+#include "./lu_decomposition.h"
Include dependency graph for lu_decompose.cpp:
-
+
- - - - - + + + + + + + +

Functions

int lu_decomposition (const std::vector< std::vector< double >> &A, std::vector< std::vector< double >> *L, std::vector< std::vector< double >> *U)
 
template<typename T >
std::ostream & operator<< (std::ostream &out, std::vector< std::vector< T >> const &v)
 
template<typename T >
std::ostream & operator<< (std::ostream &out, matrix< T > const &v)
 
void test1 ()
 
+void test2 ()
 Test determinant computation using LU decomposition.
 
int main (int argc, char **argv)
 
@@ -124,97 +129,6 @@ Functions

LU decomposition of a square matrix

Author
Krishna Vedala

Function Documentation

- -

◆ lu_decomposition()

- -
-
- - - - - - - - - - - - - - - - - - - - - - - - -
int lu_decomposition (const std::vector< std::vector< double >> & A,
std::vector< std::vector< double >> * L,
std::vector< std::vector< double >> * U 
)
-
-

Perform LU decomposition on matrix

Parameters
- - - - -
[in]Amatrix to decompose
[out]Loutput L matrix
[out]Uoutput U matrix
-
-
-
Returns
0 if no errors
-
-negative if error occurred
-
24  {
-
25  int row, col, j;
-
26  int mat_size = A.size();
-
27 
-
28  if (mat_size != A[0].size()) {
-
29  // check matrix is a square matrix
-
30  std::cerr << "Not a square matrix!\n";
-
31  return -1;
-
32  }
-
33 
-
34  // regularize each row
-
35  for (row = 0; row < mat_size; row++) {
-
36  // Upper triangular matrix
-
37 #ifdef _OPENMP
-
38 #pragma omp for
-
39 #endif
-
40  for (col = row; col < mat_size; col++) {
-
41  // Summation of L[i,j] * U[j,k]
-
42  double lu_sum = 0.;
-
43  for (j = 0; j < row; j++) lu_sum += L[0][row][j] * U[0][j][col];
-
44 
-
45  // Evaluate U[i,k]
-
46  U[0][row][col] = A[row][col] - lu_sum;
-
47  }
-
48 
-
49  // Lower triangular matrix
-
50 #ifdef _OPENMP
-
51 #pragma omp for
-
52 #endif
-
53  for (col = row; col < mat_size; col++) {
-
54  if (row == col) {
-
55  L[0][row][col] = 1.;
-
56  continue;
-
57  }
-
58 
-
59  // Summation of L[i,j] * U[j,k]
-
60  double lu_sum = 0.;
-
61  for (j = 0; j < row; j++) lu_sum += L[0][col][j] * U[0][j][row];
-
62 
-
63  // Evaluate U[i,k]
-
64  L[0][col][row] = (A[col][row] - lu_sum) / U[0][row][row];
-
65  }
-
66  }
-
67 
-
68  return 0;
-
69 }
-
-
-

◆ main()

@@ -241,53 +155,24 @@ negative if error occurred

Main function

-
91  {
-
92  int mat_size = 3; // default matrix size
-
93  const int range = 50;
-
94  const int range2 = range >> 1;
-
95 
-
96  if (argc == 2)
-
97  mat_size = atoi(argv[1]);
-
98 
-
99  std::srand(std::time(NULL)); // random number initializer
-
100 
-
101  /* Create a square matrix with random values */
-
102  std::vector<std::vector<double>> A(mat_size);
-
103  std::vector<std::vector<double>> L(mat_size); // output
-
104  std::vector<std::vector<double>> U(mat_size); // output
-
105  for (int i = 0; i < mat_size; i++) {
-
106  // calloc so that all valeus are '0' by default
-
107  A[i] = std::vector<double>(mat_size);
-
108  L[i] = std::vector<double>(mat_size);
-
109  U[i] = std::vector<double>(mat_size);
-
110  for (int j = 0; j < mat_size; j++)
-
111  /* create random values in the limits [-range2, range-1] */
-
112  A[i][j] = static_cast<double>(std::rand() % range - range2);
-
113  }
-
114 
-
115  std::clock_t start_t = std::clock();
-
116  lu_decomposition(A, &L, &U);
-
117  std::clock_t end_t = std::clock();
-
118  std::cout << "Time taken: "
-
119  << static_cast<double>(end_t - start_t) / CLOCKS_PER_SEC << "\n";
-
120 
-
121  std::cout << "A = \n" << A << "\n";
-
122  std::cout << "L = \n" << L << "\n";
-
123  std::cout << "U = \n" << U << "\n";
-
124 
-
125  return 0;
-
126 }
+
84  {
+
85  std::srand(std::time(NULL)); // random number initializer
+
86 
+
87  test1();
+
88  test2();
+
89  return 0;
+
90 }
Here is the call graph for this function:
-
+
- -

◆ operator<<()

+ +

◆ operator<<()

@@ -303,7 +188,7 @@ template<typename T >
- std::vector< std::vector< T >> const &  + matrix< T > const &  v  @@ -314,23 +199,73 @@ template<typename T >

operator to print a matrix

-
76  {
-
77  const int width = 10;
-
78  const char separator = ' ';
-
79 
-
80  for (size_t row = 0; row < v.size(); row++) {
-
81  for (size_t col = 0; col < v[row].size(); col++)
-
82  out << std::left << std::setw(width) << std::setfill(separator)
-
83  << v[row][col];
-
84  out << std::endl;
-
85  }
-
86 
-
87  return out;
-
88 }
+
18  {
+
19  const int width = 10;
+
20  const char separator = ' ';
+
21 
+
22  for (size_t row = 0; row < v.size(); row++) {
+
23  for (size_t col = 0; col < v[row].size(); col++)
+
24  out << std::left << std::setw(width) << std::setfill(separator)
+
25  << v[row][col];
+
26  out << std::endl;
+
27  }
+
28 
+
29  return out;
+
30 }
Here is the call graph for this function:
-
+
+
+
+ +
+
+ +

◆ test1()

+ +
+
+ + + + + + + +
void test1 ()
+
+

Test LU decomposition

Todo:
better ways to self-check a matrix output?
+
36  {
+
37  int mat_size = 3; // default matrix size
+
38  const int range = 50;
+
39  const int range2 = range >> 1;
+
40 
+
41  /* Create a square matrix with random values */
+
42  matrix<double> A(mat_size, std::valarray<double>(mat_size));
+
43  matrix<double> L(mat_size, std::valarray<double>(mat_size)); // output
+
44  matrix<double> U(mat_size, std::valarray<double>(mat_size)); // output
+
45  for (int i = 0; i < mat_size; i++) {
+
46  // calloc so that all valeus are '0' by default
+
47  for (int j = 0; j < mat_size; j++)
+
48  /* create random values in the limits [-range2, range-1] */
+
49  A[i][j] = static_cast<double>(std::rand() % range - range2);
+
50  }
+
51 
+
52  std::clock_t start_t = std::clock();
+
53  lu_decomposition(A, &L, &U);
+
54  std::clock_t end_t = std::clock();
+
55  std::cout << "Time taken: "
+
56  << static_cast<double>(end_t - start_t) / CLOCKS_PER_SEC << "\n";
+
57 
+
58  std::cout << "A = \n" << A << "\n";
+
59  std::cout << "L = \n" << L << "\n";
+
60  std::cout << "U = \n" << U << "\n";
+
61 }
+
+Here is the call graph for this function:
+
+
@@ -342,17 +277,18 @@ Here is the call graph for this function:
mat_size
ll mat_size
Definition: matrix_exponentiation.cpp:45
std::vector
STL class.
-
std::vector::size
T size(T... args)
+
test2
void test2()
Test determinant computation using LU decomposition.
Definition: lu_decompose.cpp:66
std::setfill
T setfill(T... args)
std::clock
T clock(T... args)
- -
std::atoi
T atoi(T... args)
+
test1
void test1()
Definition: lu_decompose.cpp:36
+ +
std::valarray
STL class.
std::rand
T rand(T... args)
+
lu_decomposition
int lu_decomposition(const matrix< T > &A, matrix< double > *L, matrix< double > *U)
Definition: lu_decomposition.h:29
std::endl
T endl(T... args)
std::left
T left(T... args)
std::time
T time(T... args)
std::setw
T setw(T... args)
-
lu_decomposition
int lu_decomposition(const std::vector< std::vector< double >> &A, std::vector< std::vector< double >> *L, std::vector< std::vector< double >> *U)
Definition: lu_decompose.cpp:22
diff --git a/dir_9c6faab82c22511b50177aa2e38e2780.html b/dir_9c6faab82c22511b50177aa2e38e2780.html index a16c94ae4..ab49586e2 100644 --- a/dir_9c6faab82c22511b50177aa2e38e2780.html +++ b/dir_9c6faab82c22511b50177aa2e38e2780.html @@ -118,6 +118,9 @@ Files file  lu_decompose.cpp  LU decomposition of a square matrix
  +file  lu_decomposition.h [code] + Functions associated with LU Decomposition of a square matrix.
+  file  newton_raphson_method.cpp  Solve the equation \(f(x)=0\) using Newton-Raphson method for both real and complex solutions.
  diff --git a/dir_9c6faab82c22511b50177aa2e38e2780.js b/dir_9c6faab82c22511b50177aa2e38e2780.js index 9446dd72f..619a46663 100644 --- a/dir_9c6faab82c22511b50177aa2e38e2780.js +++ b/dir_9c6faab82c22511b50177aa2e38e2780.js @@ -7,6 +7,7 @@ var dir_9c6faab82c22511b50177aa2e38e2780 = [ "gaussian_elimination.cpp", "d0/de2/gaussian__elimination_8cpp.html", "d0/de2/gaussian__elimination_8cpp" ], [ "golden_search_extrema.cpp", "d6/d7a/golden__search__extrema_8cpp.html", "d6/d7a/golden__search__extrema_8cpp" ], [ "lu_decompose.cpp", "dd/d65/lu__decompose_8cpp.html", "dd/d65/lu__decompose_8cpp" ], + [ "lu_decomposition.h", "d1/dbe/lu__decomposition_8h.html", "d1/dbe/lu__decomposition_8h" ], [ "newton_raphson_method.cpp", "de/dd3/newton__raphson__method_8cpp.html", "de/dd3/newton__raphson__method_8cpp" ], [ "ode_forward_euler.cpp", "db/dd3/ode__forward__euler_8cpp.html", "db/dd3/ode__forward__euler_8cpp" ], [ "ode_midpoint_euler.cpp", "d6/dd3/ode__midpoint__euler_8cpp.html", "d6/dd3/ode__midpoint__euler_8cpp" ], diff --git a/files.html b/files.html index dc4cf1c4e..70c4468bf 100644 --- a/files.html +++ b/files.html @@ -156,15 +156,16 @@ $(document).ready(function(){initNavTree('files.html',''); initResizable(); });  gaussian_elimination.cppGaussian elimination method  golden_search_extrema.cppFind extrema of a univariate real function in a given interval using golden section search algorithm  lu_decompose.cppLU decomposition of a square matrix - newton_raphson_method.cppSolve the equation \(f(x)=0\) using Newton-Raphson method for both real and complex solutions - ode_forward_euler.cppSolve a multivariable first order ordinary differential equation (ODEs) using forward Euler method - ode_midpoint_euler.cppSolve a multivariable first order ordinary differential equation (ODEs) using midpoint Euler method - ode_semi_implicit_euler.cppSolve a multivariable first order ordinary differential equation (ODEs) using semi implicit Euler method - ordinary_least_squares_regressor.cppLinear regression example using Ordinary least squares - qr_decompose.hLibrary functions to compute QR decomposition of a given matrix - qr_decomposition.cppProgram to compute the QR decomposition of a given matrix - qr_eigen_values.cppCompute real eigen values and eigen vectors of a symmetric matrix using QR decomposition method - successive_approximation.cppMethod of successive approximations using fixed-point iteration method + lu_decomposition.hFunctions associated with LU Decomposition of a square matrix + newton_raphson_method.cppSolve the equation \(f(x)=0\) using Newton-Raphson method for both real and complex solutions + ode_forward_euler.cppSolve a multivariable first order ordinary differential equation (ODEs) using forward Euler method + ode_midpoint_euler.cppSolve a multivariable first order ordinary differential equation (ODEs) using midpoint Euler method + ode_semi_implicit_euler.cppSolve a multivariable first order ordinary differential equation (ODEs) using semi implicit Euler method + ordinary_least_squares_regressor.cppLinear regression example using Ordinary least squares + qr_decompose.hLibrary functions to compute QR decomposition of a given matrix + qr_decomposition.cppProgram to compute the QR decomposition of a given matrix + qr_eigen_values.cppCompute real eigen values and eigen vectors of a symmetric matrix using QR decomposition method + successive_approximation.cppMethod of successive approximations using fixed-point iteration method  ► others  buzz_number.cppA buzz number is a number that is either divisible by 7 or has last digit as 7  decimal_to_binary.cppFunction to convert decimal number to binary representation diff --git a/globals_d.html b/globals_d.html index e123c7b46..fba1aa608 100644 --- a/globals_d.html +++ b/globals_d.html @@ -99,6 +99,9 @@ $(document).ready(function(){initNavTree('globals_d.html',''); initResizable();
  • deleteNode() : avltree.cpp
    • +
  • determinant_lu() +: lu_decomposition.h +
  • double_factorial_iterative() : double_factorial.cpp
    • diff --git a/globals_func_d.html b/globals_func_d.html index e9ac8c320..ca164ae21 100644 --- a/globals_func_d.html +++ b/globals_func_d.html @@ -96,6 +96,9 @@ $(document).ready(function(){initNavTree('globals_func_d.html',''); initResizabl
  • deleteNode() : avltree.cpp
    • +
  • determinant_lu() +: lu_decomposition.h +
  • double_factorial_iterative() : double_factorial.cpp
    • diff --git a/globals_func_i.html b/globals_func_i.html index f2f884875..e655cc54b 100644 --- a/globals_func_i.html +++ b/globals_func_i.html @@ -123,12 +123,12 @@ $(document).ready(function(){initNavTree('globals_func_i.html',''); initResizabl
  • is_square() : ordinary_least_squares_regressor.cpp
    • -
  • isPrime() -: modular_inverse_fermat_little_theorem.cpp -
  • IsPrime() : primality_test.cpp
    • +
  • isPrime() +: modular_inverse_fermat_little_theorem.cpp +
  • it_ternary_search() : ternary_search.cpp
    • diff --git a/globals_func_l.html b/globals_func_l.html index 560b679f2..2104ee05e 100644 --- a/globals_func_l.html +++ b/globals_func_l.html @@ -109,7 +109,7 @@ $(document).ready(function(){initNavTree('globals_func_l.html',''); initResizabl : linear_search.cpp
  • lu_decomposition() -: lu_decompose.cpp +: lu_decomposition.h
    • diff --git a/globals_func_o.html b/globals_func_o.html index 6d737914d..cc337254b 100644 --- a/globals_func_o.html +++ b/globals_func_o.html @@ -111,7 +111,7 @@ $(document).ready(function(){initNavTree('globals_func_o.html',''); initResizabl
  • operator<<() : complex_numbers.cpp , ordinary_least_squares_regressor.cpp -, lu_decompose.cpp +, lu_decompose.cpp
  • operator==() : complex_numbers.cpp diff --git a/globals_func_t.html b/globals_func_t.html index 39d69b392..b14566ce5 100644 --- a/globals_func_t.html +++ b/globals_func_t.html @@ -106,6 +106,7 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
  • test1() : adaline_learning.cpp +, lu_decompose.cpp , qr_eigen_values.cpp , kohonen_som_topology.cpp , kohonen_som_trace.cpp @@ -124,16 +125,17 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl , brent_method_extrema.cpp , durand_kerner_roots.cpp , golden_search_extrema.cpp +, lu_decompose.cpp , qr_eigen_values.cpp , smallest_circle.cpp
  • test3() -: smallest_circle.cpp +: kohonen_som_trace.cpp +, brent_method_extrema.cpp , golden_search_extrema.cpp +, smallest_circle.cpp , adaline_learning.cpp , kohonen_som_topology.cpp -, kohonen_som_trace.cpp -, brent_method_extrema.cpp
  • test_2d_classes() : kohonen_som_topology.cpp @@ -163,9 +165,9 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl : kohonen_som_trace.cpp
  • tests() -: double_factorial.cpp +: comb_sort.cpp +, double_factorial.cpp , complex_numbers.cpp -, comb_sort.cpp , least_common_multiple.cpp , miller_rabin.cpp
    • diff --git a/globals_i.html b/globals_i.html index d94fa9949..874e9f42f 100644 --- a/globals_i.html +++ b/globals_i.html @@ -123,16 +123,18 @@ $(document).ready(function(){initNavTree('globals_i.html',''); initResizable();
  • is_square() : ordinary_least_squares_regressor.cpp
    • +
  • isprime +: sieve_of_eratosthenes.cpp +
  • IsPrime() : primality_test.cpp
    • -
  • isprime -: prime_factorization.cpp -, sieve_of_eratosthenes.cpp -
  • isPrime() : modular_inverse_fermat_little_theorem.cpp
    • +
  • isprime +: prime_factorization.cpp +
  • it_ternary_search() : ternary_search.cpp
    • diff --git a/globals_l.html b/globals_l.html index c36b96383..13d9c2272 100644 --- a/globals_l.html +++ b/globals_l.html @@ -118,7 +118,7 @@ $(document).ready(function(){initNavTree('globals_l.html',''); initResizable(); : matrix_exponentiation.cpp
  • lu_decomposition() -: lu_decompose.cpp +: lu_decomposition.h
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  • mat_mul() : qr_eigen_values.cpp @@ -190,17 +190,20 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
  • mat_size : matrix_exponentiation.cpp
    • +
  • matrix +: lu_decomposition.h +
  • MAX : sieve_of_eratosthenes.cpp -, paranthesis_matching.cpp +, power_for_huge_numbers.cpp , hash_search.cpp , ternary_search.cpp +, paranthesis_matching.cpp , fibonacci_fast.cpp -, power_for_huge_numbers.cpp
  • MAX_ITERATIONS -: newton_raphson_method.cpp -, false_position.cpp +: false_position.cpp +, newton_raphson_method.cpp , bisection_method.cpp
  • MAX_NUM @@ -243,8 +246,8 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable(); : tower_of_hanoi.cpp
  • multiply() -: power_for_huge_numbers.cpp -, matrix_exponentiation.cpp +: matrix_exponentiation.cpp +, power_for_huge_numbers.cpp
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  • operator<<() : complex_numbers.cpp , ordinary_least_squares_regressor.cpp -, lu_decompose.cpp +, lu_decompose.cpp
  • operator==() : complex_numbers.cpp diff --git a/globals_p.html b/globals_p.html index 04a415f1a..f8d03aa9e 100644 --- a/globals_p.html +++ b/globals_p.html @@ -130,12 +130,12 @@ $(document).ready(function(){initNavTree('globals_p.html',''); initResizable();
  • predict_OLS_regressor() : ordinary_least_squares_regressor.cpp
    • -
  • PRIME -: rabin_karp.cpp -
  • prime : primes_up_to_billion.cpp
    • +
  • PRIME +: rabin_karp.cpp +
  • prime_factorization() : prime_factorization.cpp
    • diff --git a/globals_t.html b/globals_t.html index 03a34787a..878149bde 100644 --- a/globals_t.html +++ b/globals_t.html @@ -106,6 +106,7 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
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  • test3() -: smallest_circle.cpp +: brent_method_extrema.cpp , golden_search_extrema.cpp +, smallest_circle.cpp +, kohonen_som_trace.cpp , adaline_learning.cpp , kohonen_som_topology.cpp -, kohonen_som_trace.cpp -, brent_method_extrema.cpp
  • test_2d_classes() : kohonen_som_topology.cpp @@ -167,10 +169,10 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
  • tests() : complex_numbers.cpp -, least_common_multiple.cpp -, miller_rabin.cpp , double_factorial.cpp , comb_sort.cpp +, least_common_multiple.cpp +, miller_rabin.cpp
  • TH() : tower_of_hanoi.cpp diff --git a/globals_type.html b/globals_type.html index 571238874..327358212 100644 --- a/globals_type.html +++ b/globals_type.html @@ -94,6 +94,9 @@ $(document).ready(function(){initNavTree('globals_type.html',''); initResizable(
  • link : hash_search.cpp
    • +
  • matrix +: lu_decomposition.h +
  • node : hash_search.cpp
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