mirror of
https://github.com/TheAlgorithms/C
synced 2024-11-22 13:31:21 +03:00
added documentation and remove static matrix
This commit is contained in:
Krishna Vedala
parent
eea5188389
commit
5a4f592b87
@ -1,28 +1,20 @@
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/**
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* @file
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* Program to compute the QR decomposition of a
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* given matrix.
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*/
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#include <stdio.h>
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#include <math.h>
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#include <stdlib.h>
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#include <function_timer.h>
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#define ROWS 4
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#define COLUMNS 3
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double A[ROWS][COLUMNS] = {
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{-3.44827586, -1.62068966, -3.03448276},
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{-1.03448276, -0.5862069, -1.31034483},
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{-1.55172414, -0.37931034, 0.03448276}};
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void print_matrix(double A[][COLUMNS], int M, int N)
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{
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for (int row = 0; row < M; row++)
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{
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for (int col = 0; col < N; col++)
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printf("% 9.3g\t", A[row][col]);
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putchar('\n');
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}
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putchar('\n');
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}
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void print_2d(double **A, int M, int N)
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/**
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* function to display matrix on stdout
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*/
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void print_matrix(double **A, /**< matrix to print */
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int M, /**< number of rows of matrix */
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int N) /**< number of columns of matrix */
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{
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for (int row = 0; row < M; row++)
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{
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@ -33,6 +25,15 @@ void print_2d(double **A, int M, int N)
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putchar('\n');
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}
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/**
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* Compute dot product of two vectors of equal lengths
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*
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* If \f$\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\f$ and
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* \f$\vec{b}=\left[b_0,b_1,b_1,...,b_L\right]\f$ then
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* \f$\vec{a}\cdot\vec{b}=\displaystyle\sum_{i=0}^L a_i\times b_i\f$
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*
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* \returns \f$\vec{a}\cdot\vec{b}\f$
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**/
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double vector_dot(double *a, double *b, int L)
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{
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double mag = 0.f;
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@ -42,23 +43,52 @@ double vector_dot(double *a, double *b, int L)
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return mag;
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}
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/**
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* Compute magnitude of vector.
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*
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* If \f$\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\f$ then
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* \f$\left|\vec{a}\right|=\sqrt{\displaystyle\sum_{i=0}^L a_i^2}\f$
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*
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* \returns \f$\left|\vec{a}\right|\f$
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**/
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double vector_mag(double *vector, int L)
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{
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double dot = vector_dot(vector, vector, L);
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return sqrt(dot);
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}
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/**
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* Compute projection of vector \f$\vec{a}\f$ on \f$\vec{b}\f$ defined as
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* \f[\text{proj}_\vec{b}\vec{a}=\frac{\vec{a}\cdot\vec{b}}{\left|\vec{b}\right|^2}\vec{b}\f]
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*
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* \returns NULL if error, otherwise pointer to output
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**/
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double *vector_proj(double *a, double *b, double *out, int L)
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{
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double num = vector_dot(a, b, L);
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double deno = vector_dot(b, b, L);
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const double num = vector_dot(a, b, L);
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const double deno = vector_dot(b, b, L);
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if (deno == 0) /*! check for division by zero */
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return NULL;
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const double scalar = num / deno;
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for (int i = 0; i < L; i++)
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out[i] = num * b[i] / deno;
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out[i] = scalar * b[i];
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return out;
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}
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double *vector_sub(double *a, double *b, double *out, int L)
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/**
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* Compute vector subtraction
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*
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* \f$\vec{c}=\vec{a}-\vec{b}\f$
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*
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* \returns pointer to output vector
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**/
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double *vector_sub(double *a, /**< minuend */
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double *b, /**< subtrahend */
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double *out, /**< resultant vector */
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int L /**< length of vectors */
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)
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{
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for (int i = 0; i < L; i++)
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out[i] = a[i] - b[i];
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@ -66,7 +96,28 @@ double *vector_sub(double *a, double *b, double *out, int L)
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return out;
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}
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void qr_decompose(double A[][COLUMNS], double **Q, double **R, int M, int N)
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/**
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* Decompose matrix \f$A\f$ using [Gram-Schmidt process](https://en.wikipedia.org/wiki/QR_decomposition).
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*
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* \f{eqnarray*}{
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* \text{given that}\quad A &=& \left[\mathbf{a}_1,\mathbf{a}_2,\ldots,\mathbf{a}_{N-1},\right]\\
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* \text{where}\quad\mathbf{a}_i &=& \left[a_{0i},a_{1i},a_{2i},\ldots,a_{(M-1)i}\right]^T\quad\ldots\mbox{(column vectors)}\\
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* \text{then}\quad\mathbf{u}_i &=& \mathbf{a}_i -\sum_{j=0}^{i-1}\text{proj}_{\mathbf{u}_j}\mathbf{a}_i\\
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* \mathbf{e}_i &=&\frac{\mathbf{u}_i}{\left|\mathbf{u}_i\right|}\\
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* Q &=& \begin{bmatrix}\mathbf{e}_0 & \mathbf{e}_1 & \mathbf{e}_2 & \dots & \mathbf{e}_{N-1}\end{bmatrix}\\
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* R &=& \begin{bmatrix}\langle\mathbf{e}_0\,,\mathbf{a}_0\rangle & \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle & \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle & \dots \\
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* 0 & \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle & \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle & \dots\\
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* 0 & 0 & \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle & \dots\\
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* \vdots & \vdots & \vdots & \ddots
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* \end{bmatrix}\\
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* \f}
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**/
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void qr_decompose(double **A, /**< input matrix to decompose */
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double **Q, /**< output decomposed matrix */
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double **R, /**< output decomposed matrix */
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int M, /**< number of rows of matrix A */
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int N /**< number of columns of matrix A */
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)
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{
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double *col_vector = (double *)malloc(M * sizeof(double));
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double *col_vector2 = (double *)malloc(M * sizeof(double));
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@ -111,16 +162,31 @@ void qr_decompose(double A[][COLUMNS], double **Q, double **R, int M, int N)
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int main(void)
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{
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// double A[][COLUMNS] = {
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// {1, -1, 4},
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// {1, 4, -2},
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// {1, 4, 2},
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// {1, -1, 0}};
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double **A;
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unsigned int ROWS, COLUMNS;
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printf("Enter the number of rows and columns: ");
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scanf("%u %u", &ROWS, &COLUMNS);
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if (ROWS < COLUMNS)
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{
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fprintf(stderr, "Number of rows must be greater than or equal to number of columns.\n");
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return -1;
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}
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printf("Enter matrix elements row-wise:\n");
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A = (double **)malloc(ROWS * sizeof(double *));
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for (int i = 0; i < ROWS; i++)
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A[i] = (double *)malloc(COLUMNS * sizeof(double));
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for (int i = 0; i < ROWS; i++)
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for (int j = 0; j < COLUMNS; j++)
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scanf("%lf", &A[i][j]);
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print_matrix(A, ROWS, COLUMNS);
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double **R = (double **)malloc(sizeof(double) * COLUMNS * COLUMNS);
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double **Q = (double **)malloc(sizeof(double) * ROWS * COLUMNS);
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double **R = (double **)malloc(sizeof(double *) * ROWS);
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double **Q = (double **)malloc(sizeof(double *) * ROWS);
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if (!Q || !R)
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{
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perror("Unable to allocate memory for Q & R!");
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@ -129,7 +195,7 @@ int main(void)
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for (int i = 0; i < ROWS; i++)
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{
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R[i] = (double *)malloc(sizeof(double) * COLUMNS);
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Q[i] = (double *)malloc(sizeof(double) * COLUMNS);
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Q[i] = (double *)malloc(sizeof(double) * ROWS);
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if (!Q[i] || !R[i])
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{
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perror("Unable to allocate memory for Q & R.");
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@ -142,15 +208,17 @@ int main(void)
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qr_decompose(A, Q, R, ROWS, COLUMNS);
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double dtime = end_timer_delete(t1);
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print_2d(R, ROWS, COLUMNS);
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print_2d(Q, ROWS, COLUMNS);
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print_matrix(R, ROWS, COLUMNS);
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print_matrix(Q, ROWS, COLUMNS);
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printf("Time taken to compute: %.4g sec\n", dtime);
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for (int i = 0; i < ROWS; i++)
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{
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free(A[i]);
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free(R[i]);
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free(Q[i]);
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}
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free(A);
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free(R);
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free(Q);
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return 0;
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