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Eigendecomposition of a Fixed Size Matrix
[Fixed Size Matrices]


Defines

#define gel(M, i, j)   gan_mat_get_el(M,i,j)
#define sel(M, i, j, v)   gan_mat_set_el(M,i,j,v)
#define sgel(M, i, j)   gan_squmat_get_el(M,i,j)
#define ssel(M, i, j, v)   gan_squmat_set_el(M,i,j,v)
#define WORKSPACE_SIZE   100

Functions

Gan_Bool gan_symmat22_eigen (Gan_SquMatrix22 *A, Gan_Vector2 *W, Gan_Matrix22 *Z)
 Eigenvalues and maybe eigenvectors of symmetric 2x2 matrix.

Gan_Bool gan_symmat22f_eigen (Gan_SquMatrix22_f *A, Gan_Vector2_f *W, Gan_Matrix22_f *Z)
 Eigenvalues and maybe eigenvectors of symmetric 2x2 matrix.

Gan_Bool gan_mat33_eigen (Gan_Matrix33 *A, Gan_Complex W[3], Gan_Matrix33 *VL, Gan_Matrix33 *VR)
 Computes eigenvalues and eigenvectors of a 3x3 matrix.

Gan_Bool gan_mat33f_eigen (Gan_Matrix33_f *A, Gan_Complex_f W[3], Gan_Matrix33_f *VL, Gan_Matrix33_f *VR)
 Computes eigenvalues and eigenvectors of a 3x3 matrix.

Gan_Bool gan_symmat33f_eigen (Gan_SquMatrix33_f *A, Gan_Vector3_f *W, Gan_Matrix33_f *Z)
 Eigenvalues and maybe eigenvectors of symmetric 3x3 matrix.

Gan_Bool gan_symmat44_eigen (Gan_SquMatrix44 *A, Gan_Vector4 *W, Gan_Matrix44 *Z)
 Eigenvalues and maybe eigenvectors of symmetric 4x4 matrix.

Gan_Bool gan_symmat44f_eigsym (Gan_SquMatrix44_f *A, Gan_Vector4_f *W, Gan_Matrix44_f *Z)
 Eigenvalues and maybe eigenvectors of symmetric 4x4 matrix.


Function Documentation

Gan_Bool gan_mat33_eigen Gan_Matrix33   A,
Gan_Complex    W[3],
Gan_Matrix33   VL,
Gan_Matrix33   VR
 

Computes eigenvalues and eigenvectors of a 3x3 matrix.

Parameters:
A Pointer to the input 3x3 matrix
W 3-vector of complex eigenvalues
VL 3x3 matrix of left eigenvectors or NULL
VR 3x3 matrix of right eigenvectors or NULL
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Computes the eigenvalues and optionally the left and/or right eigenvectors of 3x3 matrix A. If either of the eigenvector matrices VL or VR are NULL, the corresponding eigenvectors are not computed.

See also:
gan_clapack_geev()

Gan_Bool gan_mat33f_eigen Gan_Matrix33_f   A,
Gan_Complex_f    W[3],
Gan_Matrix33_f   VL,
Gan_Matrix33_f   VR
 

Computes eigenvalues and eigenvectors of a 3x3 matrix.

Parameters:
A Pointer to the input 3x3 matrix
W 3-vector of complex eigenvalues
VL 3x3 matrix of left eigenvectors or NULL
VR 3x3 matrix of right eigenvectors or NULL
Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Computes the eigenvalues and optionally the left and/or right eigenvectors of 3x3 matrix A. If either of the eigenvector matrices VL or VR are NULL, the corresponding eigenvectors are not computed.

See also:
gan_clapackf_geev()

Gan_Bool gan_symmat22_eigen Gan_SquMatrix22   A,
Gan_Vector2   W,
Gan_Matrix22   Z
 

Eigenvalues and maybe eigenvectors of symmetric 2x2 matrix.

Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Computes the eigenvalues and, optionally, the eigenvectors of a symmetric 2x2 input matrix A, i.e. computing diagonal matrix W as the eigenvalues W, and orthogonal matrix of eigenvectors Z such that

If Z is passed as NULL then the eigenvectors are not computed.

NOTE: the contents of A are NOT destroyed.

The eigenvalues W are provided in ascending order.

Gan_Bool gan_symmat22f_eigen Gan_SquMatrix22_f   A,
Gan_Vector2_f   W,
Gan_Matrix22_f   Z
 

Eigenvalues and maybe eigenvectors of symmetric 2x2 matrix.

Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Computes the eigenvalues and, optionally, the eigenvectors of a symmetric 2x2 input matrix A, i.e. computing diagonal matrix W as the eigenvalues W, and orthogonal matrix of eigenvectors Z such that

If Z is passed as NULL then the eigenvectors are not computed.

NOTE: the contents of A are NOT destroyed.

The eigenvalues W are provided in ascending order.

Gan_Bool gan_symmat33f_eigen Gan_SquMatrix33_f   A,
Gan_Vector3_f   W,
Gan_Matrix33_f   Z
 

Eigenvalues and maybe eigenvectors of symmetric 3x3 matrix.

Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Computes the eigenvalues and, optionally, the eigenvectors of a symmetric 3x3 input matrix A, i.e. computing diagonal matrix W as the eigenvalues W, and orthogonal matrix of eigenvectors Z such that

If Z is passed as NULL then the eigenvectors are not computed.

NOTE: the contents of A are NOT destroyed.

The eigenvalues W are provided in ascending order.

Gan_Bool gan_symmat44_eigen Gan_SquMatrix44   A,
Gan_Vector4   W,
Gan_Matrix44   Z
 

Eigenvalues and maybe eigenvectors of symmetric 4x4 matrix.

Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Computes the eigenvalues and, optionally, the eigenvectors of a symmetric 4x4 input matrix A, i.e. computing diagonal matrix W as the eigenvalues W, and orthogonal matrix of eigenvectors Z such that

If Z is passed as NULL then the eigenvectors are not computed.

NOTE: the contents of A are NOT destroyed.

The eigenvalues W are provided in ascending order.

Gan_Bool gan_symmat44f_eigsym Gan_SquMatrix44_f   A,
Gan_Vector4_f   W,
Gan_Matrix44_f   Z
 

Eigenvalues and maybe eigenvectors of symmetric 4x4 matrix.

Returns:
GAN_TRUE on success, GAN_FALSE on failure.
Computes the eigenvalues and, optionally, the eigenvectors of a symmetric 4x4 input matrix A, i.e. computing diagonal matrix W as the eigenvalues W, and orthogonal matrix of eigenvectors Z such that

If Z is passed as NULL then the eigenvectors are not computed.

NOTE: the contents of A are NOT destroyed.

The eigenvalues W are provided in ascending order.


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