Matrix. More...

#include <mat.h>

Data Structures
struct	Rect
	Rectangular area. More...

Public Member Functions
	Mat (int rows, int cols)
	Mat (float *data, int rows, int cols)
	Mat (float *data, int rows, int cols, int stride)
	Mat ()
virtual	~Mat ()
	Mat (const Mat &src)
	Make copy of matrix.
Mat	getROI (int startRow, int startCol, int roiRows, int roiCols)
	Create a subset of matrix as ROI (Region of Interest).
Mat	getROI (int startRow, int startCol, int roiRows, int roiCols, int stride)
	Create a subset of matrix as ROI (Region of Interest).
Mat	getROI (const Mat::Rect &rect)
	Create a subset of matrix as ROI (Region of Interest).
void	Copy (const Mat &src, int row_pos, int col_pos)
void	CopyHead (const Mat &src)
	copy header of matrix
void	PrintHead (void)
	print matrix header
Mat	Get (int row_start, int row_size, int col_start, int col_size)
Mat	Get (const Mat::Rect &rect)
Mat &	operator= (const Mat &src)
float &	operator() (int row, int col)
const float &	operator() (int row, int col) const
Mat &	operator+= (const Mat &A)
Mat &	operator+= (float C)
Mat &	operator-= (const Mat &A)
Mat &	operator-= (float C)
Mat &	operator*= (const Mat &A)
Mat &	operator*= (float C)
Mat &	operator/= (float C)
Mat &	operator/= (const Mat &B)
Mat	operator^ (int C)
void	swapRows (int row1, int row2)
Mat	t ()
Mat	block (int startRow, int startCol, int blockRows, int blockCols)
void	normalize (void)
float	norm (void)
void	clear (void)
Mat	gaussianEliminate ()
	Gaussian Elimination.
Mat	rowReduceFromGaussian ()
Mat	inverse ()
Mat	pinv ()
float	det (int n)

Static Public Member Functions
static Mat	eye (int size)
static Mat	ones (int size)
static Mat	ones (int rows, int cols)
static Mat	solve (Mat A, Mat b)
	Solve the matrix.
static Mat	bandSolve (Mat A, Mat b, int k)
	Band solve the matrix.
static Mat	roots (Mat A, Mat y)
	Solve the matrix.
static float	dotProduct (Mat A, Mat B)
	Dotproduct of two vectors.
static Mat	augment (Mat A, Mat B)
	Augmented matrices.

Data Fields
int	rows
int	cols
int	stride
int	padding
float *	data
int	length
bool	ext_buff
bool	sub_matrix

Static Public Attributes
static float	abs_tol = 1e-10

Private Member Functions
Mat	cofactor (int row, int col, int n)
Mat	adjoint ()
void	allocate ()
Mat	expHelper (const Mat &m, int num)

Detailed Description

Matrix.

The Mat class provides basic matrix operations on single-precision floating point values.

Definition at line 30 of file mat.h.

Constructor & Destructor Documentation

◆ Mat() [1/5]

dspm::Mat::Mat	(	int	rows,
		int	cols )

Constructor allocate internal buffer.

Parameters

[in]	rows	amount of matrix rows
[in]	cols	amount of matrix columns

Definition at line 69 of file mat.cpp.

{
    ESP_LOGD("Mat", "Mat(%i, %i)", rows, cols);
    this->rows = rows;
    this->cols = cols;
    this->sub_matrix = false;
    this->stride = cols;
    this->padding = 0;
    allocate();
    memset(this->data, 0, this->length * sizeof(float));
}

References allocate(), cols, data, ESP_LOGD, length, padding, rows, stride, and sub_matrix.

Referenced by adjoint(), augment(), bandSolve(), block(), cofactor(), Copy(), CopyHead(), det(), dotProduct(), expHelper(), eye(), gaussianEliminate(), Get(), Get(), getROI(), getROI(), getROI(), inverse(), Mat(), ones(), ones(), operator*=(), operator*=(), operator+=(), operator+=(), operator-=(), operator-=(), operator/=(), operator/=(), operator=(), operator^(), pinv(), roots(), rowReduceFromGaussian(), solve(), and t().

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◆ Mat() [2/5]

dspm::Mat::Mat	(	float *	data,
		int	rows,
		int	cols )

Constructor use external buffer.

Parameters

[in]	data	external buffer with row-major matrix data
[in]	rows	amount of matrix rows
[in]	cols	amount of matrix columns

Definition at line 81 of file mat.cpp.

{
    ESP_LOGD("Mat", "Mat(data, %i, %i)", rows, cols);
    this->rows = rows;
    this->cols = cols;
    this->sub_matrix = false;
    this->stride = cols;
    this->padding = 0;
    this->length = this->rows * this->cols;
    allocate();
    this->ext_buff = false;
    for (size_t i = 0; i < this->length; i++) {
        this->data[i] = data[i];
    }
}

References allocate(), cols, data, ESP_LOGD, ext_buff, length, padding, rows, stride, and sub_matrix.

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◆ Mat() [3/5]

dspm::Mat::Mat	(	float *	data,
		int	rows,
		int	cols,
		int	stride )

Constructor

Parameters

[in]	data	external buffer with row-major matrix data
[in]	rows	amount of matrix rows
[in]	cols	amount of matrix columns
[in]	stride	col stride

Definition at line 57 of file mat.cpp.

{
    this->rows = roi_rows;
    this->cols = roi_cols;
    this->stride = stride;
    this->padding = stride - roi_cols;
    this->length = this->rows * this->cols;
    this->sub_matrix = true;
    this->ext_buff = true;
    this->data = data;
}

References cols, data, ext_buff, length, padding, rows, stride, and sub_matrix.

◆ Mat() [4/5]

dspm::Mat::Mat ( )

Allocate matrix with undefined size.

Definition at line 98 of file mat.cpp.

{
    this->rows = 1;
    this->cols = 1;
    this->sub_matrix = false;
    this->stride = cols;
    this->padding = 0;
    ESP_LOGD("Mat", "Mat()");
 
    allocate();
    this->data[0] = 0;
}

References allocate(), cols, data, ESP_LOGD, padding, rows, stride, and sub_matrix.

Referenced by det().

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◆ ~Mat()

dspm::Mat::~Mat ( )

virtual

Definition at line 111 of file mat.cpp.

{
    ESP_LOGD("Mat", "~Mat(%i, %i), ext_buff=%i, data = %p", this->rows, this->cols, this->ext_buff, this->data);
    if (false == this->ext_buff) {
        delete[] data;
    }
}

References cols, data, ESP_LOGD, ext_buff, and rows.

◆ Mat() [5/5]

dspm::Mat::Mat ( const Mat & src )

Make copy of matrix.

if src matrix is sub matrix, only the header is copied if src matrix is matrix, header and data are copied

Parameters

[in] src source matrix

Definition at line 119 of file mat.cpp.

{
    this->rows = m.rows;
    this->cols = m.cols;
    this->padding = m.padding;
    this->stride = m.stride;
    this->data = m.data;
    this->sub_matrix = m.sub_matrix;
 
    if (m.sub_matrix) {
        this->length = m.length;
        this->data = m.data;
        this->ext_buff = true;
    } else {
        allocate();
        memcpy(this->data, m.data, this->length * sizeof(float));
    }
}

References allocate(), cols, data, ext_buff, length, m, Mat(), padding, rows, stride, and sub_matrix.

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Member Function Documentation

◆ adjoint()

Mat dspm::Mat::adjoint ( )

private

Definition at line 783 of file mat.cpp.

{
    Mat adj(this->rows, this->cols);
    if (this->rows == 1) {
        adj(0, 0) = 1;
        return adj;
    }
 
    // temp is used to store cofactors of A(,)
    int sign = 1;
    Mat temp(this->rows, this->cols);
 
    for (int i = 0; i < this->rows; i++) {
        for (int j = 0; j < this->cols; j++) {
            // Get cofactor of A(i,j)
            temp = this->cofactor( i, j, this->rows);
 
            // sign of adj(j,i) positive if sum of row
            // and column indexes is even.
            sign = ((i + j) % 2 == 0) ? 1 : -1;
 
            // Interchanging rows and columns to get the
            // transpose of the cofactor matrix
            adj(j, i) = (sign) * (temp.det(this->rows - 1));
        }
    }
    return adj;
}

References cofactor(), cols, det(), Mat(), and rows.

Referenced by inverse().

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◆ allocate()

void dspm::Mat::allocate ( )

private

Definition at line 834 of file mat.cpp.

{
    this->ext_buff = false;
    this->length = this->rows * this->cols;
    data = new float[this->length];
    ESP_LOGD("Mat", "allocate(%i) = %p", this->length, this->data);
}

References cols, data, ESP_LOGD, ext_buff, length, and rows.

Referenced by Mat(), Mat(), Mat(), Mat(), and operator=().

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◆ augment()

Mat dspm::Mat::augment	(	Mat	A,
		Mat	B )

static

Augmented matrices.

Augmented matrices

Parameters

[in]	A	Input vector A MxN
[in]	B	Input vector B MxK

Returns

Augmented matrix Mx(N+K)

Definition at line 585 of file mat.cpp.

{
    Mat AB(A.rows, A.cols + B.cols);
    for (int i = 0; i < AB.rows; ++i) {
        for (int j = 0; j < AB.cols; ++j) {
            if (j < A.cols) {
                AB(i, j) = A(i, j);
            } else {
                AB(i, j) = B(i, j - A.cols);
            }
        }
    }
    return AB;
}

References A, B, cols, Mat(), and rows.

Referenced by pinv(), and roots().

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◆ bandSolve()

Mat dspm::Mat::bandSolve	(	Mat	A,
		Mat	b,
		int	k )

static

Band solve the matrix.

Solve band matrix. Find roots for the matrix A*x = b with bandwidth k.

Parameters

[in]	A	matrix [N]x[N] with input coefficients
[in]	b	vector [N]x[1] with result values
[in]	k	upper bandwidth value

Returns

matrix [N]x[1] with roots

Definition at line 514 of file mat.cpp.

{
    // optimized Gaussian elimination
    int bandsBelow = (k - 1) / 2;
    for (int i = 0; i < A.rows; ++i) {
        if (A(i, i) == 0) {
            // pivot 0 - error
            ESP_LOGW("Mat", "Error: the coefficient matrix has 0 as a pivot. Please fix the input and try again.");
            Mat err_result(b.rows, 1);
            memset(err_result.data, 0, b.rows * sizeof(float));
            return err_result;
        }
        float a_ii = 1 / A(i, i);
        for (int j = i + 1; j < A.rows && j <= i + bandsBelow; ++j) {
            int k = i + 1;
            while ((k < A.cols) && (fabs(A(j, k)) > abs_tol)) {
                A(j, k) -= A(i, k) * (A(j, i) * a_ii);
                k++;
            }
            b(j, 0) -= b(i, 0) * (A(j, i) * a_ii);
            A(j, i) = 0;
        }
    }
 
    // Back substitution
    Mat x(b.rows, 1);
    x((x.rows - 1), 0) = b((x.rows - 1), 0) / A((x.rows - 1), (x.rows - 1));
    for (int i = x.rows - 2; i >= 0; --i) {
        float sum = 0;
        for (int j = i + 1; j < x.rows; ++j) {
            sum += A(i, j) * x(j, 0);
        }
        x(i, 0) = (b(i, 0) - sum) / A(i, i);
    }
 
    return x;
}

References A, abs_tol, data, k, Mat(), rows, and x.

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◆ block()

Mat dspm::Mat::block	(	int	startRow,
		int	startCol,
		int	blockRows,
		int	blockCols )

Return part of matrix from defined position (startRow, startCol) as a matrix[blockRows x blockCols].

Parameters

[in]	startRow	start row position
[in]	startCol	start column position
[in]	blockRows	amount of rows in result matrix
[in]	blockCols	amount of columns in the result matrix

Returns

matrix [blockRows]x[blockCols]

Definition at line 433 of file mat.cpp.

{
    Mat result(blockRows, blockCols);
    for (int i = 0; i < blockRows; ++i) {
        for (int j = 0; j < blockCols; ++j) {
            result(i, j) = (*this)(startRow + i, startCol + j);
        }
    }
    return result;
}

References Mat().

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◆ clear()

void dspm::Mat::clear ( void )

The method fill 0 to the matrix structure.

Definition at line 425 of file mat.cpp.

{
    for (int row = 0; row < this->rows; row++) {
        memset(this->data + (row * this->stride), 0, this->cols * sizeof(float));
    }
}

References cols, data, rows, and stride.

◆ cofactor()

Mat dspm::Mat::cofactor	(	int	row,
		int	col,
		int	n )

private

Definition at line 722 of file mat.cpp.

{
    int i = 0, j = 0;
    Mat result(n, n);
    // Looping for each element of the matrix
    for (int r = 0; r < n; r++) {
        for (int c = 0; c < n; c++) {
            //  Copying into temporary matrix only those element
            //  which are not in given row and column
            if (r != row && c != col) {
                result(i, j++) = (*this)(r, c);
 
                // Row is filled, so increase row index and
                // reset col index
                if (j == this->rows - 1) {
                    j = 0;
                    i++;
                }
            }
        }
    }
    return result;
}

References Mat(), n, and rows.

Referenced by adjoint().

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◆ Copy()

void dspm::Mat::Copy	(	const Mat &	src,
		int	row_pos,
		int	col_pos )

Make copy of matrix.

Parameters

[in]	src	source matrix
[in]	row_pos	start row position of destination matrix
[in]	col_pos	start col position of destination matrix

Definition at line 168 of file mat.cpp.

{
    if ((row_pos + src.rows) > this->rows) {
        return;
    }
    if ((col_pos + src.cols) > this->cols) {
        return;
    }
 
    for (size_t r = 0; r < src.rows; r++) {
        memcpy(&this->data[(r + row_pos) * this->stride + col_pos], &src.data[r * src.cols], src.cols * sizeof(float));
    }
}

References cols, data, Mat(), rows, and stride.

Referenced by ekf_imu13states::StateXdot(), ekf_imu13states::UpdateRefMeasurement(), ekf_imu13states::UpdateRefMeasurement(), and ekf_imu13states::UpdateRefMeasurementMagn().

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◆ CopyHead()

void dspm::Mat::CopyHead ( const Mat & src )

copy header of matrix

Make a shallow copy of matrix (no data copy)

Parameters

[in] src source matrix

Definition at line 182 of file mat.cpp.

{
    if (!this->ext_buff) {
        delete[] this->data;
    }
    this->rows = src.rows;
    this->cols = src.cols;
    this->length = src.length;
    this->padding = src.padding;
    this->stride = src.stride;
    this->data = src.data;
    this->ext_buff = src.ext_buff;
    this->sub_matrix = src.sub_matrix;
}

References cols, data, ext_buff, length, Mat(), padding, rows, stride, and sub_matrix.

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◆ det()

float dspm::Mat::det ( int n )

Find determinant

Parameters

[in] n element number in first row

Returns

determinant value

Definition at line 746 of file mat.cpp.

{
    //  Base case : if matrix contains single element
    if (n == 1) {
        return (*this)(0, 0);
    }
 
    float det = 1.0;
    Mat *temp = new Mat(n, n);
    *temp = *this;
 
    for (int i = 0; i < n; i++) {
        int pivot = i;
        for (int j = i + 1; j < n; j++) {
            if (std::abs((*temp)(j, i)) > std::abs((*temp)(pivot, i))) {
                pivot = j;
            }
        }
        if (pivot != i) {
            temp->swapRows(i, pivot);
            det *= -1;
        }
        if ((*temp)(i, i) == 0) {
            return 0;
        }
        det *= (*temp)(i, i);
        for (int j = i + 1; j < n; j++) {
            float factor = (*temp)(j, i) / (*temp)(i, i);
            for (int k = i + 1; k < n; k++) {
                (*temp)(j, k) -= factor * (*temp)(i, k);
            }
        }
    }
    delete temp;
    return det;
}

References det(), k, Mat(), Mat(), n, and swapRows().

Referenced by adjoint(), det(), and inverse().

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◆ dotProduct()

float dspm::Mat::dotProduct	(	Mat	A,
		Mat	B )

static

Dotproduct of two vectors.

The method returns dotproduct of two vectors

Parameters

[in]	A	Input vector A Nx1
[in]	B	Input vector B Nx1

Returns

dotproduct value

Definition at line 576 of file mat.cpp.

{
    float sum = 0;
    for (int i = 0; i < a.rows; ++i) {
        sum += (a(i, 0) * b(i, 0));
    }
    return sum;
}

References Mat(), and rows.

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◆ expHelper()

Mat dspm::Mat::expHelper	(	const Mat &	m,
		int	num )

private

Definition at line 842 of file mat.cpp.

{
    if (num == 0) {
        return Mat::eye(m.rows);
    } else if (num == 1) {
        return m;
    } else if (num % 2 == 0) {  // num is even
        return expHelper(m * m, num / 2);
    } else {                    // num is odd
        return m * expHelper(m * m, (num - 1) / 2);
    }
}

References expHelper(), eye(), m, and Mat().

Referenced by expHelper(), and operator^().

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◆ eye()

Mat dspm::Mat::eye ( int size )

static

Create identity matrix. Create a square matrix and fill diagonal with 1.

Parameters

[in] size matrix size

Returns

matrix [N]x[N] with 1 in diagonal

Definition at line 394 of file mat.cpp.

{
    Mat temp(size, size);
    for (int i = 0; i < temp.rows; ++i) {
        for (int j = 0; j < temp.cols; ++j) {
            if (i == j) {
                temp(i, j) = 1;
            } else {
                temp(i, j) = 0;
            }
        }
    }
    return temp;
}

References cols, Mat(), and rows.

Referenced by ekf::CovariancePrediction(), dispaly_esp_text(), dispaly_esp_text(), dispaly_esp_text(), dispaly_esp_text(), draw_3d_image(), draw_3d_image(), draw_3d_image(), draw_3d_image(), draw_3d_image_task(), draw_3d_image_task(), draw_3d_image_task(), draw_3d_image_task(), draw_3d_image_task(), draw_3d_image_task(), draw_3d_image_task(), draw_3d_image_task(), expHelper(), ekf_imu13states::Init(), ekf_imu13states::LinearizeFG(), pinv(), ekf_imu13states::TestFull(), ekf::UpdateRef(), ekf_imu13states::UpdateRefMeasurement(), and ekf_imu13states::UpdateRefMeasurementMagn().

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◆ gaussianEliminate()

Mat dspm::Mat::gaussianEliminate ( )

Gaussian Elimination.

Gaussian Elimination of matrix

Returns

result matrix

Definition at line 600 of file mat.cpp.

{
    Mat Ab(*this);
    int rows = Ab.rows;
    int cols = Ab.cols;
    int Acols = cols - 1;
 
    int i = 0; // row tracker
    int j = 0; // column tracker
 
    // iterate through the rows
    while (i < rows) {
        // find a pivot for the row
        bool pivot_found = false;
        while (j < Acols && !pivot_found) {
            if (Ab(i, j) != 0) { // pivot not equal to 0
                pivot_found = true;
            } else { // check for a possible swap
                int max_row = i;
                float max_val = 0;
                for (int k = i + 1; k < rows; ++k) {
                    float cur_abs = Ab(k, j) >= 0 ? Ab(k, j) : -1 * Ab(k, j);
                    if (cur_abs > max_val) {
                        max_row = k;
                        max_val = cur_abs;
                    }
                }
                if (max_row != i) {
                    Ab.swapRows(max_row, i);
                    pivot_found = true;
                } else {
                    j++;
                }
            }
        }
 
        // perform elimination as normal if pivot was found
        if (pivot_found) {
            for (int t = i + 1; t < rows; ++t) {
                for (int s = j + 1; s < cols; ++s) {
                    Ab(t, s) = Ab(t, s) - Ab(i, s) * (Ab(t, j) / Ab(i, j));
                    if (Ab(t, s) < abs_tol && Ab(t, s) > -1 * abs_tol) {
                        Ab(t, s) = 0;
                    }
                }
                Ab(t, j) = 0;
            }
        }
 
        i++;
        j++;
    }
 
    return Ab;
}

References abs_tol, cols, k, Mat(), rows, swapRows(), and t().

Referenced by pinv().

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◆ Get() [1/2]

Mat dspm::Mat::Get ( const Mat::Rect & rect )

Make copy of matrix.

Parameters

[in] rect rectangular area of interest

Returns

result matrix size row_size x col_size

Definition at line 226 of file mat.cpp.

{
    return (Get(rect.y, rect.height, rect.x, rect.width));
}

References Get(), dspm::Mat::Rect::height, Mat(), dspm::Mat::Rect::width, dspm::Mat::Rect::x, and dspm::Mat::Rect::y.

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◆ Get() [2/2]

Mat dspm::Mat::Get	(	int	row_start,
		int	row_size,
		int	col_start,
		int	col_size )

Make copy of matrix.

Parameters

[in]	row_start	start row position of source matrix to copy
[in]	row_size	size of wor elements of source matrix to copy
[in]	col_start	start col position of source matrix to copy
[in]	col_size	size of wor elements of source matrix to copy

Returns

result matrix size row_size x col_size

Definition at line 209 of file mat.cpp.

{
    Mat result(row_size, col_size);
 
    if ((row_start + row_size) > this->rows) {
        return result;
    }
    if ((col_start + col_size) > this->cols) {
        return result;
    }
 
    for (size_t r = 0; r < result.rows; r++) {
        memcpy(&result.data[r * result.cols], &this->data[(r + row_start) * this->stride + col_start], result.cols * sizeof(float));
    }
    return result;
}

References cols, data, Mat(), and rows.

Referenced by Get(), ekf_imu13states::LinearizeFG(), and operator*=().

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◆ getROI() [1/3]

Mat dspm::Mat::getROI ( const Mat::Rect & rect )

Create a subset of matrix as ROI (Region of Interest).

Parameters

[in] rect rectangular area of interest

Returns

result matrix size rect.rectRows x rect.rectCols

Definition at line 158 of file mat.cpp.

{
    return (getROI(rect.y, rect.x, rect.height, rect.width, this->cols));
}

References getROI(), dspm::Mat::Rect::height, Mat(), dspm::Mat::Rect::width, dspm::Mat::Rect::x, and dspm::Mat::Rect::y.

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◆ getROI() [2/3]

Mat dspm::Mat::getROI	(	int	startRow,
		int	startCol,
		int	roiRows,
		int	roiCols )

Create a subset of matrix as ROI (Region of Interest).

Parameters

[in]	startRow	start row position of source matrix to get the subset matrix from
[in]	startCol	start col position of source matrix to get the subset matrix from
[in]	roiRows	size of row elements of source matrix to get the subset matrix from
[in]	roiCols	size of col elements of source matrix to get the subset matrix from

Returns

result matrix size roiRows x roiCols

Definition at line 163 of file mat.cpp.

{
    return (getROI(startRow, startCol, roiRows, roiCols, this->cols));
}

References cols, getROI(), and Mat().

Referenced by getROI(), and getROI().

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◆ getROI() [3/3]

Mat dspm::Mat::getROI	(	int	startRow,
		int	startCol,
		int	roiRows,
		int	roiCols,
		int	stride )

Create a subset of matrix as ROI (Region of Interest).

Parameters

[in]	startRow	start row position of source matrix to get the subset matrix from
[in]	startCol	start col position of source matrix to get the subset matrix from
[in]	roiRows	size of row elements of source matrix to get the subset matrix from
[in]	roiCols	size of col elements of source matrix to get the subset matrix from
[in]	stride	number of cols + padding between 2 rows

Returns

result matrix size roiRows x roiCols

Definition at line 138 of file mat.cpp.

{
    Mat result(this->data, roiRows, roiCols, 0);
 
    if ((startRow + roiRows) > this->rows) {
        return result;
    }
    if ((startCol + roiCols) > this->cols) {
        return result;
    }
 
    const int ptr_move = startRow * this->cols + startCol;
    float *new_data_ptr = this->data + ptr_move;
 
    result.data = new_data_ptr;
    result.stride = stride;
    result.padding = result.stride - result.cols;
    return result;
}

References cols, data, Mat(), padding, rows, and stride.

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◆ inverse()

Mat dspm::Mat::inverse ( )

Find the inverse matrix

Returns

inverse matrix

Definition at line 812 of file mat.cpp.

{
    Mat result(this->rows, this->cols);
    // Find determinant of matrix
    float det = this->det(this->rows);
    if (det == 0) {
        //std::cout << "Singular matrix, can't find its inverse";
        return result;
    }
 
    // Find adjoint
    Mat adj = this->adjoint();
 
    // Find Inverse using formula "inverse(A) = adj(A)/det(A)"
    for (int i = 0; i < this->rows; i++)
        for (int j = 0; j < this->cols; j++) {
            result(i, j) = adj(i, j) / float(det);
        }
 
    return result;
}

References adjoint(), cols, det(), Mat(), and rows.

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◆ norm()

float dspm::Mat::norm ( void )

Return norm of the vector. If it's matrix, calculate matrix norm

Returns

matrix norm

Definition at line 456 of file mat.cpp.

{
    float sqr_norm = 0;
    for (int i = 0; i < this->rows; ++i) {
        for (int j = 0; j < this->cols; ++j) {
            sqr_norm += (*this)(i, j) * (*this)(i, j);
        }
    }
    sqr_norm = sqrtf(sqr_norm);
    return sqr_norm;
}

References cols, and rows.

Referenced by draw_3d_image_task(), draw_3d_image_task(), kalman_filter_task(), kalman_filter_task(), kalman_filter_task(), kalman_filter_task(), ekf::rotm2quat(), ekf_imu13states::TestFull(), ekf_imu13states::UpdateRefMeasurement(), ekf_imu13states::UpdateRefMeasurement(), and ekf_imu13states::UpdateRefMeasurementMagn().

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◆ normalize()

void dspm::Mat::normalize ( void )

Normalizes the vector, i.e. divides it by its own norm. If it's matrix, calculate matrix norm

Definition at line 444 of file mat.cpp.

{
    float sqr_norm = 0;
    for (int i = 0; i < this->rows; ++i) {
        for (int j = 0; j < this->cols; ++j) {
            sqr_norm += (*this)(i, j) * (*this)(i, j);
        }
    }
    sqr_norm = 1 / sqrtf(sqr_norm);
    *this *= sqr_norm;
}

References cols, and rows.

◆ ones() [1/2]

Mat dspm::Mat::ones	(	int	rows,
		int	cols )

static

Create matrix with all elements 1. Create a matrix and fill all elements with 1.

Parameters

[in]	rows	matrix rows
[in]	cols	matrix cols

Returns

matrix [N]x[N] with 1 in all elements

Definition at line 414 of file mat.cpp.

{
    Mat temp(rows, cols);
    for (int row = 0; row < temp.rows; ++row) {
        for (int col = 0; col < temp.cols; ++col) {
            temp(row, col) = 1;
        }
    }
    return temp;
}

References cols, Mat(), and rows.

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◆ ones() [2/2]

Mat dspm::Mat::ones ( int size )

static

Create matrix with all elements 1. Create a square matrix and fill all elements with 1.

Parameters

[in] size matrix size

Returns

matrix [N]x[N] with 1 in all elements

Definition at line 409 of file mat.cpp.

{
    return (ones(size, size));
}

References Mat(), and ones().

Referenced by ones().

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◆ operator()() [1/2]

float & dspm::Mat::operator()	(	int	row,
		int	col )

inline

Access to the matrix elements.

Parameters

[in]	row	row position
[in]	col	column position

Returns

element of matrix M[row][col]

Definition at line 218 of file mat.h.

    {
        return data[row * this->stride + col];
    }

References data.

◆ operator()() [2/2]

const float & dspm::Mat::operator()	(	int	row,
		int	col ) const

inline

Access to the matrix elements.

Parameters

[in]	row	row position
[in]	col	column position

Returns

element of matrix M[row][col]

Definition at line 230 of file mat.h.

    {
        return data[row * this->stride + col];
    }

References data.

◆ operator*=() [1/2]

Mat & dspm::Mat::operator*= ( const Mat & A )

*= operator The operator use DSP optimized implementation of multiplication.

Parameters

[in] A source matrix

Returns

result matrix: result -= A

Definition at line 312 of file mat.cpp.

{
    if (this->cols != m.rows) {
        ESP_LOGW("Mat", "operator *= Error: matrices do not have equal dimensions");
        return *this;
    }
 
    if (this->sub_matrix || m.sub_matrix) {
        Mat temp = this->Get(0, this->rows, 0, this->cols);
        dspm_mult_ex_f32(temp.data, m.data, this->data, temp.rows, temp.cols, m.cols, temp.padding, m.padding, this->padding);
    } else {
        Mat temp = *this;
        dspm_mult_f32(temp.data, m.data, this->data, temp.rows, temp.cols, m.cols);
    }
    return (*this);
}

References cols, data, dspm_mult_ex_f32, dspm_mult_f32, Get(), m, Mat(), padding, rows, and sub_matrix.

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◆ operator*=() [2/2]

Mat & dspm::Mat::operator*= ( float C )

+= with constant operator The operator use DSP optimized implementation of multiplication.

Parameters

[in] C constant value

Returns

result matrix: result *= C

Definition at line 329 of file mat.cpp.

{
    if (this->sub_matrix) {
        dspm_mulc_f32(this->data, this->data, num, this->rows, this->cols, this->padding, this->padding, 1, 1);
    } else {
        dsps_mulc_f32_ansi(this->data, this->data, this->length, num, 1, 1);
    }
    return *this;
}

References cols, data, dspm_mulc_f32, dsps_mulc_f32_ansi(), length, Mat(), padding, rows, and sub_matrix.

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◆ operator+=() [1/2]

Mat & dspm::Mat::operator+= ( const Mat & A )

+= operator The operator use DSP optimized implementation of multiplication.

Parameters

[in] A source matrix

Returns

result matrix: result += A

Definition at line 262 of file mat.cpp.

{
    if ((this->rows != m.rows) || (this->cols != m.cols)) {
        ESP_LOGW("Mat", "operator += Error: matrices do not have equal dimensions");
        return *this;
    }
 
    if (this->sub_matrix || m.sub_matrix) {
        dspm_add_f32(this->data, m.data, this->data, this->rows, this->cols, this->padding, m.padding, this->padding, 1, 1, 1);
    } else {
        dsps_add_f32(this->data, m.data, this->data, this->length, 1, 1, 1);
    }
    return *this;
}

References data, dspm_add_f32, dsps_add_f32, m, Mat(), rows, and sub_matrix.

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◆ operator+=() [2/2]

Mat & dspm::Mat::operator+= ( float C )

+= operator The operator use DSP optimized implementation of multiplication.

Parameters

[in] C constant

Returns

result matrix: result += C

Definition at line 277 of file mat.cpp.

{
    if (this->sub_matrix) {
        dspm_addc_f32(this->data, this->data, C, this->rows, this->cols, this->padding, this->padding, 1, 1);
    } else {
        dsps_addc_f32_ansi(this->data, this->data, this->length, C, 1, 1);
    }
    return *this;
}

References C, cols, data, dspm_addc_f32, dsps_addc_f32_ansi(), length, Mat(), padding, rows, and sub_matrix.

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◆ operator-=() [1/2]

Mat & dspm::Mat::operator-= ( const Mat & A )

-= operator The operator use DSP optimized implementation of multiplication.

Parameters

[in] A source matrix

Returns

result matrix: result -= A

Definition at line 287 of file mat.cpp.

{
    if ((this->rows != m.rows) || (this->cols != m.cols)) {
        ESP_LOGW("Mat", "operator -= Error: matrices do not have equal dimensions");
        return *this;
    }
 
    if (this->sub_matrix || m.sub_matrix) {
        dspm_sub_f32(this->data, m.data, this->data, this->rows, this->cols, this->padding, m.padding, this->padding, 1, 1, 1);
    } else {
        dsps_sub_f32(this->data, m.data, this->data, this->length, 1, 1, 1);
    }
    return *this;
}

References data, dspm_sub_f32, dsps_sub_f32, m, Mat(), rows, and sub_matrix.

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◆ operator-=() [2/2]

Mat & dspm::Mat::operator-= ( float C )

-= operator The operator use DSP optimized implementation of multiplication.

Parameters

[in] C constant

Returns

result matrix: result -= C

Definition at line 302 of file mat.cpp.

{
    if (this->sub_matrix) {
        dspm_addc_f32(this->data, this->data, -C, this->rows, this->cols, this->padding, this->padding, 1, 1);
    } else {
        dsps_addc_f32_ansi(this->data, this->data, this->length, -C, 1, 1);
    }
    return *this;
}

References C, cols, data, dspm_addc_f32, dsps_addc_f32_ansi(), length, Mat(), padding, rows, and sub_matrix.

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◆ operator/=() [1/2]

Mat & dspm::Mat::operator/= ( const Mat & B )

/= operator

Parameters

[in] B source matrix

Returns

result matrix: result[i,j] = result[i,j]/B[i,j]

Definition at line 339 of file mat.cpp.

{
    if ((this->rows != B.rows) || (this->cols != B.cols)) {
        ESP_LOGW("Mat", "operator /= Error: matrices do not have equal dimensions");
        return *this;
    }
 
    for (int row = 0; row < this->rows; row++) {
        for (int col = 0; col < this->cols; col++) {
            (*this)(row, col) = (*this)(row, col) / B(row, col);
        }
    }
    return (*this);
}

References B, cols, Mat(), and rows.

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◆ operator/=() [2/2]

Mat & dspm::Mat::operator/= ( float C )

/= with constant operator The operator use DSP optimized implementation of multiplication.

Parameters

[in] C constant value

Returns

result matrix: result /= C

Definition at line 354 of file mat.cpp.

{
    if (this->sub_matrix) {
        dspm_mulc_f32(this->data, this->data, 1 / num, this->rows, this->cols, this->padding, this->padding, 1, 1);
    } else {
        dsps_mulc_f32_ansi(this->data, this->data, this->length, 1 / num, 1, 1);
    }
    return *this;
}

References cols, data, dspm_mulc_f32, dsps_mulc_f32_ansi(), length, Mat(), padding, rows, and sub_matrix.

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◆ operator=()

Mat & dspm::Mat::operator= ( const Mat & src )

Copy operator

Parameters

[in] src source matrix

Returns

matrix copy

Definition at line 231 of file mat.cpp.

{
    if (this == &m) {
        return *this;
    }
 
    // matrix dimensions not equal
    if (this->rows != m.rows || this->cols != m.cols) {
        // left operand is a sub-matrix - error
        if (this->sub_matrix) {
            ESP_LOGE("Mat", "operator = Error for sub-matrices: operands matrices dimensions %dx%d and %dx%d do not match", this->rows, this->cols, m.rows, m.cols);
            return *this;
        }
        if (!this->ext_buff) {
            delete[] this->data;
        }
        this->ext_buff = false;
        this->rows = m.rows;
        this->cols = m.cols;
        this->stride = this->cols;
        this->padding = 0;
        this->sub_matrix = false;
        allocate();
    }
 
    for (int row = 0; row < this->rows; row++) {
        memcpy(this->data + (row * this->stride), m.data + (row * m.stride), this->cols * sizeof(float));
    }
    return *this;
}

References allocate(), cols, data, ext_buff, m, Mat(), padding, rows, stride, and sub_matrix.

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◆ operator^()

Mat dspm::Mat::operator^ ( int C )

^= xor with constant operator The operator use DSP optimized implementation of multiplication.

Parameters

[in] C constant value

Returns

result matrix: result ^= C

Definition at line 364 of file mat.cpp.

{
    Mat temp(*this);
    return expHelper(temp, num);
}

References expHelper(), and Mat().

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◆ pinv()

Mat dspm::Mat::pinv ( )

Find pseudo inverse matrix

Returns

inverse matrix

Definition at line 707 of file mat.cpp.

{
    Mat I = Mat::eye(this->rows);
    Mat AI = Mat::augment(*this, I);
    Mat U = AI.gaussianEliminate();
    Mat IAInverse = U.rowReduceFromGaussian();
    Mat AInverse(this->rows, this->cols);
    for (int i = 0; i < this->rows; ++i) {
        for (int j = 0; j < this->cols; ++j) {
            AInverse(i, j) = IAInverse(i, j + this->cols);
        }
    }
    return AInverse;
}

References augment(), cols, eye(), gaussianEliminate(), Mat(), rowReduceFromGaussian(), and rows.

Referenced by ekf::UpdateRef().

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◆ PrintHead()

void dspm::Mat::PrintHead ( void )

print matrix header

Print all information about matrix to the terminal

Parameters

[in] src source matrix

Definition at line 197 of file mat.cpp.

{
    std::cout << "rows     " << this->rows << std::endl;
    std::cout << "cols     " << this->cols << std::endl;
    std::cout << "lenght   " << this->length << std::endl;
    std::cout << "data     " << this->data << std::endl;
    std::cout << "ext_buff " << this->ext_buff << std::endl;
    std::cout << "sub_mat  " << this->sub_matrix << std::endl;
    std::cout << "stride   " << this->stride << std::endl;
    std::cout << "padding  " << this->padding << std::endl << std::endl;
}

References cols, data, ext_buff, length, padding, rows, stride, and sub_matrix.

◆ roots()

Mat dspm::Mat::roots	(	Mat	A,
		Mat	y )

static

Solve the matrix.

Different way to solve the matrix. Find roots for the matrix A*x = y

Parameters

[in]	A	matrix [N]x[N] with input coefficients
[in]	y	vector [N]x[1] with result values

Returns

matrix [N]x[1] with roots

Definition at line 552 of file mat.cpp.

{
    int n = A.cols + 1;
 
    Mat result(y.rows, 1);
 
    Mat g_m = Mat::augment(A, y);
    for (int j = 0; j < A.cols; j++) {
        float g_jj = 1 / g_m(j, j);
        for (int i = 0; i < A.cols; i++) {
            if (i != j) {
                float c = g_m(i, j) * g_jj;
                for (int k = 0; k < n; k++) {
                    g_m(i, k) = g_m(i, k) - c * g_m(j, k);
                }
            }
        }
    }
    for (int i = 0; i < A.rows; i++) {
        result(i, 0) = g_m(i, A.cols) / g_m(i, i);
    }
    return result;
}

References A, augment(), k, Mat(), n, and y.

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◆ rowReduceFromGaussian()

Mat dspm::Mat::rowReduceFromGaussian ( )

Row reduction for Gaussian elimination

Returns

result matrix

Definition at line 656 of file mat.cpp.

{
    Mat R(*this);
    int rows = R.rows;
    int cols = R.cols;
 
    int i = rows - 1; // row tracker
    int j = cols - 2; // column tracker
 
    // iterate through every row
    while (i >= 0) {
        // find the pivot column
        int k = j - 1;
        while (k >= 0) {
            if (R(i, k) != 0) {
                j = k;
            }
            k--;
        }
 
        // zero out elements above pivots if pivot not 0
        if (R(i, j) != 0) {
            for (int t = i - 1; t >= 0; --t) {
                for (int s = 0; s < cols; ++s) {
                    if (s != j) {
                        R(t, s) = R(t, s) - R(i, s) * (R(t, j) / R(i, j));
                        if (R(t, s) < abs_tol && R(t, s) > -1 * abs_tol) {
                            R(t, s) = 0;
                        }
                    }
                }
                R(t, j) = 0;
            }
 
            // divide row by pivot
            for (int k = j + 1; k < cols; ++k) {
                R(i, k) = R(i, k) / R(i, j);
                if (R(i, k) < abs_tol && R(i, k) > -1 * abs_tol) {
                    R(i, k) = 0;
                }
            }
            R(i, j) = 1;
        }
 
        i--;
        j--;
    }
 
    return R;
}

References abs_tol, cols, k, Mat(), rows, and t().

Referenced by pinv().

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◆ solve()

Mat dspm::Mat::solve	(	Mat	A,
		Mat	b )

static

Solve the matrix.

Solve matrix. Find roots for the matrix A*x = b

Parameters

[in]	A	matrix [N]x[N] with input coefficients
[in]	b	vector [N]x[1] with result values

Returns

matrix [N]x[1] with roots

Definition at line 468 of file mat.cpp.

{
    // Gaussian elimination
    for (int i = 0; i < A.rows; ++i) {
        if (A(i, i) == 0) {
            // pivot 0 - error
            ESP_LOGW("Mat", "Error: the coefficient matrix has 0 as a pivot. Please fix the input and try again.");
            Mat err_result(0, 0);
            return err_result;
        }
        float a_ii = 1 / A(i, i);
        for (int j = i + 1; j < A.rows; ++j) {
            float a_ji = A(j, i) * a_ii;
            for (int k = i + 1; k < A.cols; ++k) {
                A(j, k) -= A(i, k) * a_ji;
                if ((A(j, k) < abs_tol) && (A(j, k) > -1 * abs_tol)) {
                    A(j, k) = 0;
                }
            }
            b(j, 0) -= b(i, 0) * a_ji;
            if (A(j, 0) < abs_tol && A(j, 0) > -1 * abs_tol) {
                A(j, 0) = 0;
            }
            A(j, i) = 0;
        }
    }
 
    // Back substitution
    Mat x(b.rows, 1);
    x((x.rows - 1), 0) = b((x.rows - 1), 0) / A((x.rows - 1), (x.rows - 1));
    if (x((x.rows - 1), 0) < abs_tol && x((x.rows - 1), 0) > -1 * abs_tol) {
        x((x.rows - 1), 0) = 0;
    }
    for (int i = x.rows - 2; i >= 0; --i) {
        float sum = 0;
        for (int j = i + 1; j < x.rows; ++j) {
            sum += A(i, j) * x(j, 0);
        }
        x(i, 0) = (b(i, 0) - sum) / A(i, i);
        if (x(i, 0) < abs_tol && x(i, 0) > -1 * abs_tol) {
            x(i, 0) = 0;
        }
    }
    return x;
}

References A, abs_tol, k, Mat(), rows, and x.

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◆ swapRows()

void dspm::Mat::swapRows	(	int	row1,
		int	row2 )

Swap two rows between each other.

Parameters

[in]	row1	position of first row
[in]	row2	position of second row

Definition at line 370 of file mat.cpp.

{
    if ((this->rows <= r1) || (this->rows <= r2)) {
        ESP_LOGW("Mat", "swapRows Error: row %d or %d out of matrix row %d range", r1, r2, this->rows);
    } else {
        for (int i = 0; i < this->cols; i++) {
            float temp = this->data[r1 * this->stride + i];
            this->data[r1 * this->stride + i] = this->data[r2 * this->stride + i];
            this->data[r2 * this->stride + i] = temp;
        }
    }
}

References cols, data, rows, and stride.

Referenced by det(), and gaussianEliminate().

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◆ t()

Mat dspm::Mat::t ( )

Matrix transpose. Change rows and columns between each other.

Returns

transposed matrix

Definition at line 383 of file mat.cpp.

{
    Mat ret(this->cols, this->rows);
    for (int i = 0; i < this->rows; ++i) {
        for (int j = 0; j < this->cols; ++j) {
            ret(j, i) = this->data[i * this->stride + j];
        }
    }
    return ret;
}

References cols, data, Mat(), rows, and stride.

Referenced by ekf::CovariancePrediction(), draw_3d_image_task(), draw_3d_image_task(), gaussianEliminate(), rowReduceFromGaussian(), ekf_imu13states::TestFull(), update_rotation_matrix(), ekf::UpdateRef(), ekf_imu13states::UpdateRefMeasurement(), ekf_imu13states::UpdateRefMeasurement(), and ekf_imu13states::UpdateRefMeasurementMagn().

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Field Documentation

◆ abs_tol

float dspm::Mat::abs_tol = 1e-10

static

Max acceptable absolute tolerance

Definition at line 39 of file mat.h.

Referenced by bandSolve(), gaussianEliminate(), rowReduceFromGaussian(), and solve().

◆ cols

int dspm::Mat::cols

Amount of columns

Definition at line 34 of file mat.h.

Referenced by adjoint(), allocate(), augment(), clear(), Copy(), CopyHead(), draw_3d_image(), draw_3d_image(), draw_3d_image(), draw_3d_image(), eye(), gaussianEliminate(), Get(), getROI(), getROI(), init_perspective_matrix(), inverse(), Mat(), Mat(), Mat(), Mat(), Mat(), norm(), normalize(), ones(), dspm::operator*(), operator*=(), operator*=(), dspm::operator+(), operator+=(), dspm::operator-(), operator-=(), operator/=(), operator/=(), operator=(), dspm::operator==(), pinv(), print_matrix(), PrintHead(), rowReduceFromGaussian(), swapRows(), t(), update_perspective_matrix(), update_rotation_matrix(), and ~Mat().

◆ data

float* dspm::Mat::data

Buffer with matrix data

Definition at line 37 of file mat.h.

Referenced by allocate(), bandSolve(), clear(), Copy(), CopyHead(), ekf::dFdq(), ekf::dFdq_inv(), draw_3d_image(), draw_3d_image(), draw_3d_image(), draw_3d_image(), draw_3d_image_task(), draw_3d_image_task(), Get(), getROI(), kalman_filter_calibration(), kalman_filter_calibration(), kalman_filter_calibration(), kalman_filter_calibration(), kalman_filter_task(), kalman_filter_task(), kalman_filter_task(), kalman_filter_task(), ekf_imu13states::LinearizeFG(), Mat(), Mat(), Mat(), Mat(), Mat(), operator()(), operator()(), dspm::operator*(), dspm::operator*(), operator*=(), operator*=(), dspm::operator+(), dspm::operator+(), operator+=(), operator+=(), dspm::operator-(), dspm::operator-(), operator-=(), operator-=(), dspm::operator/(), operator/=(), operator=(), PrintHead(), ekf::qProduct(), ekf::quat2eul(), ekf::SkewSym4x4(), swapRows(), t(), ekf_imu13states::TestFull(), update_rotation_matrix(), ekf_imu13states::UpdateRefMeasurement(), ekf_imu13states::UpdateRefMeasurement(), ekf_imu13states::UpdateRefMeasurementMagn(), and ~Mat().

◆ ext_buff

bool dspm::Mat::ext_buff

Flag indicates that matrix use external buffer

Definition at line 40 of file mat.h.

Referenced by allocate(), CopyHead(), Mat(), Mat(), Mat(), operator=(), PrintHead(), and ~Mat().

◆ length

int dspm::Mat::length

Total amount of data in data array

Definition at line 38 of file mat.h.

Referenced by allocate(), CopyHead(), Mat(), Mat(), Mat(), Mat(), operator*=(), operator+=(), operator-=(), operator/=(), and PrintHead().

◆ padding

int dspm::Mat::padding

Padding between 2 rows

Definition at line 36 of file mat.h.

Referenced by CopyHead(), getROI(), Mat(), Mat(), Mat(), Mat(), Mat(), dspm::operator*(), dspm::operator*(), operator*=(), operator*=(), dspm::operator+(), dspm::operator+(), operator+=(), dspm::operator-(), dspm::operator-(), operator-=(), dspm::operator/(), operator/=(), operator=(), and PrintHead().

◆ rows

int dspm::Mat::rows

Amount of rows

Definition at line 33 of file mat.h.

◆ stride

int dspm::Mat::stride

Stride = (number of elements in a row) + padding

Definition at line 35 of file mat.h.

Referenced by clear(), Copy(), CopyHead(), getROI(), Mat(), Mat(), Mat(), Mat(), Mat(), operator=(), PrintHead(), swapRows(), and t().

◆ sub_matrix

bool dspm::Mat::sub_matrix

Flag indicates that matrix is a subset of another matrix

Definition at line 41 of file mat.h.

Referenced by CopyHead(), Mat(), Mat(), Mat(), Mat(), Mat(), dspm::operator*(), operator*=(), operator*=(), dspm::operator+(), operator+=(), operator+=(), dspm::operator-(), operator-=(), operator-=(), operator/=(), operator=(), and PrintHead().

The documentation for this class was generated from the following files:

Data Structures

Public Member Functions

Static Public Member Functions

Data Fields

Static Public Attributes

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Mat() [1/5]

◆ Mat() [2/5]

◆ Mat() [3/5]

◆ Mat() [4/5]

◆ ~Mat()

◆ Mat() [5/5]

Member Function Documentation

◆ adjoint()

◆ allocate()

◆ augment()

◆ bandSolve()

◆ block()

◆ clear()

◆ cofactor()

◆ Copy()

◆ CopyHead()

◆ det()

◆ dotProduct()

◆ expHelper()

◆ eye()

◆ gaussianEliminate()

◆ Get() [1/2]

◆ Get() [2/2]

◆ getROI() [1/3]

◆ getROI() [2/3]

◆ getROI() [3/3]

◆ inverse()

◆ norm()

◆ normalize()

◆ ones() [1/2]

◆ ones() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator=()

◆ operator^()

◆ pinv()

◆ PrintHead()

◆ roots()

◆ rowReduceFromGaussian()

◆ solve()

◆ swapRows()

◆ t()

Field Documentation

◆ abs_tol

◆ cols

◆ data

◆ ext_buff

◆ length

◆ padding

◆ rows

◆ stride

◆ sub_matrix