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Projective Normalisation of Fixed Size Matrices
[Fixed Size Matrices]


Defines

#define GAN_MAT_NORMALISE   gan_mat22_normalize
#define GAN_MAT_NORM_FNAME   "gan_mat22_normalize"
#define GAN_MATT_NORMALISE   gan_mat22T_normalize
#define GAN_MATT_NORM_FNAME   "gan_mat22T_normalize"
#define GAN_MATTYPE   Gan_Matrix22
#define GAN_SQUMATTYPE   Gan_SquMatrix22
#define GAN_SQUMATTYPEP   Gan_SquMatrix22
#define GAN_MAT_SCALE_S   gan_mat22_scale_s
#define GAN_MAT_DIVIDE_S   gan_mat22_divide_s
#define GAN_MAT_FNORM_S   gan_mat22_Fnorm_s
#define GAN_SYMMAT_IDENT_S   gan_symmat22_ident_s
#define GAN_SYMMAT_INVERT_Q   gan_symmat22_invert_q
#define GAN_SYMMAT_ZERO_Q   gan_symmat22_zero_q
#define GAN_SYMMAT_MULTV_Q   gan_symmat22_multv2_q
#define GAN_SYMMAT_DIVIDE_S   gan_symmat22_divide_s
#define GAN_SYMMAT_DIVIDE_I   gan_symmat22_divide_i
#define GAN_SYMMAT_INCREMENT   gan_symmat22_increment
#define GAN_SYMMAT_TRACE_S   gan_symmat22_trace_s
#define GAN_SYMMAT_SUB_Q   gan_symmat22_sub_q
#define GAN_SYMMAT_SUMSQR_Q   gan_symmat22_sumsqr_q
#define GAN_SYMMAT_CHOLESKY_Q   gan_symmat22_cholesky_q
#define GAN_SYMMAT_LRMULTM_Q   gan_symmat22_lrmultm22_q
#define GAN_SYMMATP_TRACE_S   gan_symmat22_trace_s
#define GAN_LTMATI_MULTV_S   gan_ltmat22I_multv2_s
#define GAN_MAT_RMULTLIT_S   gan_mat22_rmultl22IT_s
#define GAN_MAT_SLMULTT_Q   gan_mat22_slmultT_q
#define GAN_MAT_TPOSE_I   gan_mat22_tpose_i

Functions

Gan_Bool gan_mat22_normalize (Gan_Matrix22 *B, int n, double term_threshold, int max_iterations, Gan_SquMatrix22 *Lp)
 Normalize array of 2x2 matrices to identity inertia moment.

Gan_Bool gan_mat22T_normalize (Gan_Matrix22 *B, int n, double term_threshold, int max_iterations, Gan_SquMatrix22 *Lp)
 Normalize array of 2x2 matrices to identity inertia moment.

Gan_Bool gan_mat23_normalize (Gan_Matrix23 *B, int n, double term_threshold, int max_iterations, Gan_SquMatrix33 *Lp)
 Normalize array of 2x3 matrices to identity inertia moment.

Gan_Bool gan_mat24_normalize (Gan_Matrix24 *B, int n, double term_threshold, int max_iterations, Gan_SquMatrix44 *Lp)
 Normalize array of 2x4 matrices to identity inertia moment.

Gan_Bool gan_mat33_normalize (Gan_Matrix33 *B, int n, double term_threshold, int max_iterations, Gan_SquMatrix33 *Lp)
 Normalize array of 3x3 matrices to identity inertia moment.

Gan_Bool gan_mat33T_normalize (Gan_Matrix33 *B, int n, double term_threshold, int max_iterations, Gan_SquMatrix33 *Lp)
 Normalize array of 3x3 matrices to identity inertia moment.

Gan_Bool gan_mat34_normalize (Gan_Matrix34 *B, int n, double term_threshold, int max_iterations, Gan_SquMatrix44 *Lp)
 Normalize array of 3x4 matrices to identity inertia moment.

Gan_Bool gan_mat44_normalize (Gan_Matrix44 *B, int n, double term_threshold, int max_iterations, Gan_SquMatrix44 *Lp)
 Normalize array of 4x4 matrices to identity inertia moment.

Gan_Bool gan_mat44T_normalize (Gan_Matrix44 *B, int n, double term_threshold, int max_iterations, Gan_SquMatrix44 *Lp)
 Normalize array of 4x4 matrices to identity inertia moment.


Function Documentation

Gan_Bool gan_mat22_normalize Gan_Matrix22   B,
int    n,
double    term_threshold,
int    max_iterations,
Gan_SquMatrix22   Lp
 

Normalize array of 2x2 matrices to identity inertia moment.

Parameters:
B array of matrices to normalise
n number of vectors in array
term_threshold termination threshold
max_iterations maximum number of iterations
Lp pointer to solution for triangular normalising matrix
Returns:
GAN_TRUE on success, or GAN_FALSE if the algorithm failed.
This function applies projective normalization to the array of n 2x2 matrices B. After the normalization, the matrices B are transformed by a lower triangular matrix , and scaled to unit length, so that the transformed vectors

satisfy the equation

where is the 2x2 identity matrix.

term_threshold specifies a threshold on the smallness of an adjustment to , below which the algorithm terminates successfully.

max_iterations specifies the maximum number of iterations to perform. If this is reached without the above threshold being reached, the algorithm terminates with failure, returning GAN_FALSE.

Lp is a pointer set to the final solution for the triangular matrix . If it is passed as NULL then Lp is ignored.

Upon successful termination, the matrices B are transformed to as shown above, and GAN_TRUE is returned.

See also:
gan_mat22T_normalize, gan_vec2_normalize(), gan_mat22_normalize().

Gan_Bool gan_mat22T_normalize Gan_Matrix22   B,
int    n,
double    term_threshold,
int    max_iterations,
Gan_SquMatrix22   Lp
 

Normalize array of 2x2 matrices to identity inertia moment.

Parameters:
B array of matrices to normalise
n number of vectors in array
term_threshold termination threshold
max_iterations maximum number of iterations
Lp pointer to solution for triangular normalising matrix
Returns:
GAN_TRUE on success, or GAN_FALSE on failure.
This function applies projective normalization to the array of n 2x2 matrices B. After the normalization, the matrices B are transformed by a lower triangular matrix , and scaled to unit length, so that the transformed vectors

satisfy the equation

where is the 2x2 identity matrix.

term_threshold specifies a threshold on the smallness of an adjustment to , below which the algorithm terminates successfully.

max_iterations specifies the maximum number of iterations to perform. If this is reached without the above threshold being reached, the algorithm terminates with failure, returning GAN_FALSE.

Lp is a pointer set to the final solution for the triangular matrix . If it is passed as NULL then Lp is ignored.

Upon successful termination, the matrices B are transformed to as shown above, and GAN_TRUE is returned.

See also:
gan_mat22_normalize(), gan_vec2_normalize(), gan_mat22_normalize().

Gan_Bool gan_mat23_normalize Gan_Matrix23   B,
int    n,
double    term_threshold,
int    max_iterations,
Gan_SquMatrix33   Lp
 

Normalize array of 2x3 matrices to identity inertia moment.

Parameters:
B array of matrices to normalise
n number of vectors in array
term_threshold termination threshold
max_iterations maximum number of iterations
Lp pointer to solution for triangular normalising matrix
Returns:
GAN_TRUE on success, or GAN_FALSE if the algorithm failed.
This function applies projective normalization to the array of n 2x3 matrices B. After the normalization, the matrices B are transformed by a lower triangular matrix , and scaled to unit length, so that the transformed vectors

satisfy the equation

where is the 3x3 identity matrix.

term_threshold specifies a threshold on the smallness of an adjustment to , below which the algorithm terminates successfully.

max_iterations specifies the maximum number of iterations to perform. If this is reached without the above threshold being reached, the algorithm terminates with failure, returning GAN_FALSE.

Lp is a pointer set to the final solution for the triangular matrix . If it is passed as NULL then Lp is ignored.

Upon successful termination, the matrices B are transformed to as shown above, and GAN_TRUE is returned.

See also:
gan_vec3_normalize(), gan_mat33_normalize().

Gan_Bool gan_mat24_normalize Gan_Matrix24   B,
int    n,
double    term_threshold,
int    max_iterations,
Gan_SquMatrix44   Lp
 

Normalize array of 2x4 matrices to identity inertia moment.

Parameters:
B array of matrices to normalise
n number of vectors in array
term_threshold termination threshold
max_iterations maximum number of iterations
Lp pointer to solution for triangular normalising matrix
Returns:
GAN_TRUE on success, or GAN_FALSE if the algorithm failed.
This function applies projective normalization to the array of n 2x4 matrices B. After the normalization, the matrices B are transformed by a lower triangular matrix , and scaled to unit length, so that the transformed vectors

satisfy the equation

where is the 4x4 identity matrix.

term_threshold specifies a threshold on the smallness of an adjustment to , below which the algorithm terminates successfully.

max_iterations specifies the maximum number of iterations to perform. If this is reached without the above threshold being reached, the algorithm terminates with failure, returning GAN_FALSE.

Lp is a pointer set to the final solution for the triangular matrix . If it is passed as NULL then Lp is ignored.

Upon successful termination, the matrices B are transformed to as shown above, and GAN_TRUE is returned.

See also:
gan_vec4_normalize(), gan_mat44_normalize().

Gan_Bool gan_mat33_normalize Gan_Matrix33   B,
int    n,
double    term_threshold,
int    max_iterations,
Gan_SquMatrix33   Lp
 

Normalize array of 3x3 matrices to identity inertia moment.

Parameters:
B array of matrices to normalise
n number of vectors in array
term_threshold termination threshold
max_iterations maximum number of iterations
Lp pointer to solution for triangular normalising matrix
Returns:
GAN_TRUE on success, or GAN_FALSE if the algorithm failed.
This function applies projective normalization to the array of n 3x3 matrices B. After the normalization, the matrices B are transformed by a lower triangular matrix , and scaled to unit length, so that the transformed vectors

satisfy the equation

where is the 3x3 identity matrix.

term_threshold specifies a threshold on the smallness of an adjustment to , below which the algorithm terminates successfully.

max_iterations specifies the maximum number of iterations to perform. If this is reached without the above threshold being reached, the algorithm terminates with failure, returning GAN_FALSE.

Lp is a pointer set to the final solution for the triangular matrix . If it is passed as NULL then Lp is ignored.

Upon successful termination, the matrices B are transformed to as shown above, and GAN_TRUE is returned.

See also:
gan_mat33T_normalize, gan_vec3_normalize(), gan_mat33_normalize().

Gan_Bool gan_mat33T_normalize Gan_Matrix33   B,
int    n,
double    term_threshold,
int    max_iterations,
Gan_SquMatrix33   Lp
 

Normalize array of 3x3 matrices to identity inertia moment.

Parameters:
B array of matrices to normalise
n number of vectors in array
term_threshold termination threshold
max_iterations maximum number of iterations
Lp pointer to solution for triangular normalising matrix
Returns:
GAN_TRUE on success, or GAN_FALSE on failure.
This function applies projective normalization to the array of n 3x3 matrices B. After the normalization, the matrices B are transformed by a lower triangular matrix , and scaled to unit length, so that the transformed vectors

satisfy the equation

where is the 3x3 identity matrix.

term_threshold specifies a threshold on the smallness of an adjustment to , below which the algorithm terminates successfully.

max_iterations specifies the maximum number of iterations to perform. If this is reached without the above threshold being reached, the algorithm terminates with failure, returning GAN_FALSE.

Lp is a pointer set to the final solution for the triangular matrix . If it is passed as NULL then Lp is ignored.

Upon successful termination, the matrices B are transformed to as shown above, and GAN_TRUE is returned.

See also:
gan_mat33_normalize(), gan_vec3_normalize(), gan_mat33_normalize().

Gan_Bool gan_mat34_normalize Gan_Matrix34   B,
int    n,
double    term_threshold,
int    max_iterations,
Gan_SquMatrix44   Lp
 

Normalize array of 3x4 matrices to identity inertia moment.

Parameters:
B array of matrices to normalise
n number of vectors in array
term_threshold termination threshold
max_iterations maximum number of iterations
Lp pointer to solution for triangular normalising matrix
Returns:
GAN_TRUE on success, or GAN_FALSE if the algorithm failed.
This function applies projective normalization to the array of n 3x4 matrices B. After the normalization, the matrices B are transformed by a lower triangular matrix , and scaled to unit length, so that the transformed vectors

satisfy the equation

where is the 4x4 identity matrix.

term_threshold specifies a threshold on the smallness of an adjustment to , below which the algorithm terminates successfully.

max_iterations specifies the maximum number of iterations to perform. If this is reached without the above threshold being reached, the algorithm terminates with failure, returning GAN_FALSE.

Lp is a pointer set to the final solution for the triangular matrix . If it is passed as NULL then Lp is ignored.

Upon successful termination, the matrices B are transformed to as shown above, and GAN_TRUE is returned.

See also:
gan_vec4_normalize(), gan_mat44_normalize().

Gan_Bool gan_mat44_normalize Gan_Matrix44   B,
int    n,
double    term_threshold,
int    max_iterations,
Gan_SquMatrix44   Lp
 

Normalize array of 4x4 matrices to identity inertia moment.

Parameters:
B array of matrices to normalise
n number of vectors in array
term_threshold termination threshold
max_iterations maximum number of iterations
Lp pointer to solution for triangular normalising matrix
Returns:
GAN_TRUE on success, or GAN_FALSE if the algorithm failed.
This function applies projective normalization to the array of n 4x4 matrices B. After the normalization, the matrices B are transformed by a lower triangular matrix , and scaled to unit length, so that the transformed vectors

satisfy the equation

where is the 4x4 identity matrix.

term_threshold specifies a threshold on the smallness of an adjustment to , below which the algorithm terminates successfully.

max_iterations specifies the maximum number of iterations to perform. If this is reached without the above threshold being reached, the algorithm terminates with failure, returning GAN_FALSE.

Lp is a pointer set to the final solution for the triangular matrix . If it is passed as NULL then Lp is ignored.

Upon successful termination, the matrices B are transformed to as shown above, and GAN_TRUE is returned.

See also:
gan_mat44T_normalize, gan_vec4_normalize(), gan_mat44_normalize().

Gan_Bool gan_mat44T_normalize Gan_Matrix44   B,
int    n,
double    term_threshold,
int    max_iterations,
Gan_SquMatrix44   Lp
 

Normalize array of 4x4 matrices to identity inertia moment.

Parameters:
B array of matrices to normalise
n number of vectors in array
term_threshold termination threshold
max_iterations maximum number of iterations
Lp pointer to solution for triangular normalising matrix
Returns:
GAN_TRUE on success, or GAN_FALSE on failure.
This function applies projective normalization to the array of n 4x4 matrices B. After the normalization, the matrices B are transformed by a lower triangular matrix , and scaled to unit length, so that the transformed vectors

satisfy the equation

where is the 4x4 identity matrix.

term_threshold specifies a threshold on the smallness of an adjustment to , below which the algorithm terminates successfully.

max_iterations specifies the maximum number of iterations to perform. If this is reached without the above threshold being reached, the algorithm terminates with failure, returning GAN_FALSE.

Lp is a pointer set to the final solution for the triangular matrix . If it is passed as NULL then Lp is ignored.

Upon successful termination, the matrices B are transformed to as shown above, and GAN_TRUE is returned.

See also:
gan_mat44_normalize(), gan_vec4_normalize(), gan_mat44_normalize().


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