Linear algebra and matrix operations.

Functions
int DSPL_API	matrix_eig_cmplx (complex_t *a, int n, complex_t *v, int *info)
	Eigenvalues calculation of the complex square matrix a. More...
int DSPL_API	matrix_eye (double *a, int n, int m)
	The real identity matrix size n x m generation. More...
int DSPL_API	matrix_eye_cmplx (complex_t *a, int n, int m)
	The complex identity matrix size n x m generation. More...
int DSPL_API	matrix_mul (double *a, int na, int ma, double *b, int nb, int mb, double *c)
	Matrix multiplication. More...

Detailed Description

This group describes the linear algebra algorithms and matrix operations. DSPL-2.0 using internal interface for BLAS and LAPACK packages.

Function Documentation

matrix_eig_cmplx()

int matrix_eig_cmplx	(	complex_t *	a,
		int	n,
		complex_t *	v,
		int *	info
	)

Eigenvalues calculation of the complex square matrix a.

---

Function calculates n eigenvalues of the matrix a size n x n.

Parameters

[in]	a	Pointer to the complex matrix a size n x n. Matrix is stored in the memory as column-major array.
[in]	n	Size of matrix n x n.
[out]	v	Pointer to the eigenvalues vector. Vector size is ]n x 1]. Memory must be allocated.
[out]	info	Pointer to the zgees LAPACK subroutine output parameter. If an error occurs while calculating the vector of eigenvalues, the LAPACK subroutine returns an error code that can be read from this pointer.

Returns

RES_OK — function is calculated successfully.
Else code error.
If an ERROR_LAPACK error occurs, the LAPACK package error code will be written to the info address.

Eigenvalues calculation example:

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "dspl.h"
 
#define N  3
 
int main()
{
    void* handle;           /* DSPL handle         */
    handle = dspl_load();   /* Load DSPL function  */
 
    complex_t a[N*N] = {{1.0, 0.0}, {1.0, 0.0}, {0.0, 0.0},
                        {2.0, 0.0}, {0.0, 0.0}, {1.0, 0.0},
                        {3.0, 0.0}, {0.0, 0.0}, {0.0, 0.0}};
 
    complex_t v[N];
    int err, info;
    matrix_print_cmplx(a, N, N, "A", "%8.2f%+8.2fi");
 
    err = matrix_eig_cmplx(a, N, v, &info);
    if(err!=RES_OK)
    {
        printf("ERROR CODE: 0x%.8x, info = %d\n", err, info);
    }
 
    matrix_print_cmplx(v, N, 1, "v", "%10.6f%+10.6fi");
 
    dspl_free(handle);      /* free dspl handle  */
    return 0;
}
 

This program calculates eigenvalues of the matrix size 3 x 3 and print its to display.
Result:

A = [ % size [3 x 3] type: complex
1.00   +0.00i,     2.00   +0.00i,     3.00   +0.00i;
1.00   +0.00i,     0.00   +0.00i,     0.00   +0.00i;
0.00   +0.00i,     1.00   +0.00i,     0.00   +0.00i;];

v = [ % size [3 x 1] type: complex
 2.374424 -0.000000i;    
-0.687212 +0.889497i;
-0.687212 -0.889497i;];

Author

Sergey Bakhurin www.dsplib.org

Definition at line 143 of file matrix_eig_cmplx.c.

Referenced by polyroots().

matrix_eye()

int matrix_eye	(	double *	a,
		int	n,
		int	m
	)

The real identity matrix size n x m generation.

---

Function fills matrix a by zeros and sets main diagonal as ones.

Parameters

[in]	a	Pointer to the real matrix size n x m. Matrix is stored in the memory as column-major array.
[in]	n	Matrix a rows number.
[in]	m	Matrix a columns number..

Returns

RES_OK — function is calculated successfully.
Else code error.

Author

Sergey Bakhurin www.dsplib.org

Definition at line 80 of file matrix_eye.c.

matrix_eye_cmplx()

int matrix_eye_cmplx	(	complex_t *	a,
		int	n,
		int	m
	)

The complex identity matrix size n x m generation.

---

Function fills matrix a by zeros and sets main diagonal as ones.

Parameters

[in]	a	Pointer to the complex matrix size n x m. Matrix is stored in the memory as column-major array.
[in]	n	Matrix a rows number.
[in]	m	Matrix a columns number..

Returns

RES_OK — function is calculated successfully.
Else code error.

Author

Sergey Bakhurin www.dsplib.org

Definition at line 81 of file matrix_eye_cmplx.c.

matrix_mul()

int matrix_mul	(	double *	a,
		int	na,
		int	ma,
		double *	b,
		int	nb,
		int	mb,
		double *	c
	)

Matrix multiplication.

---

The function calculates the product of matrices \(\mathbf{C} = \mathbf{AB}\), here \(\mathbf{A}\) – matrix contains \(N_A\) rows and \(M_A\) columns, \(\mathbf{B}\) – matrix contains \(N_B\) rows and \(M_B\) columns, product matrix \(\mathbf{C} = \mathbf{AB}\) contains \(N_A\) rows and \(M_B\) columns.

Note

Matrix multiplication requires the equality \(M_A = N_B\).
Function uses BLAS subroutine dgemm.

Parameters

[in]	a	Pointer to the input matrix \(\mathbf{A}\) size na x ma. Matrix must be located in memory as column-major array.
[in]	na	Matrix a rows number.
[in]	ma	Matrix a columns number.
[in]	b	Pointer to the input matrix \(\mathbf{B}\) size nb x mb. Matrix must be located in memory as column-major array.
[in]	nb	Matrix b rows number. Necessary equality ma = nb.
[in]	mb	Matrix a columns number.
[out]	c	Pointer to the output matrix \(\mathbf{С} = \mathbf{AB}\). Matrix size is na x mb. Memory must be allocated.

Returns

RES_OK — function is calculated successfully.
Else error code.
Example:

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "dspl.h"
 
#define N 4
#define M 3
#define K 5
 
int main()
{
    void* handle;           /* DSPL handle         */
    handle = dspl_load();   /* Load DSPL function  */
 
    double a[N*K], b[K*M], c[N*M];
 
    linspace(0, N*K, N*K, DSPL_PERIODIC, a);
    matrix_print(a, N, K, "A", "%8.2f");
 
    linspace(0, K*M, K*M, DSPL_PERIODIC, b);
    matrix_print(b, K, M, "B", "%8.2f");
    
    matrix_mul(a, N, K, b, K, M, c);
    matrix_print(c, N, M, "C", "%8.2f");
 
    dspl_free(handle);      /* free dspl handle  */
    return 0; 
}
 

The program forms and multiplies two matrices. The original matrices and their product are printed.

The result of the program:

A = [ % size [4 x 5] type: real
0.00,     4.00,     8.00,    12.00,    16.00;
1.00,     5.00,     9.00,    13.00,    17.00;
2.00,     6.00,    10.00,    14.00,    18.00;
3.00,     7.00,    11.00,    15.00,    19.00;];

B = [ % size [5 x 3] type: real
0.00,     5.00,    10.00;
1.00,     6.00,    11.00;
2.00,     7.00,    12.00;
3.00,     8.00,    13.00;
4.00,     9.00,    14.00;];

C = [ % size [4 x 3] type: real
120.00,   320.00,   520.00;
130.00,   355.00,   580.00;
140.00,   390.00,   640.00;
150.00,   425.00,   700.00;]; 

Author

Sergey Bakhurin www.dsplib.org

Definition at line 191 of file matrix_mul.c.