2x3matrix.h File Reference

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <gandalf/common/misc_defs.h>
#include <gandalf/linalg/2vector.h>
#include <gandalf/linalg/3vector.h>
#include <gandalf/linalg/2x2matrix.h>
#include <gandalf/linalg/3x3matrix.h>
#include <gandalf/linalg/mat_gen.h>

Go to the source code of this file.

Classes

struct Gan_Matrix23

Structure definition for double precision 2x3 matrix. More...

Defines

#define GAN_REP3_AS(a, b, p1, p2, p3)   (a p1 b, a p2 b, a p3 b)

#define GAN_REP3_AS_C(a, b)   GAN_REP3_AS(a,b,x,y,z)

#define GAN_REP3_A(a, p1, p2, p3)   (a p1, a p2, a p3)

#define GAN_REP3_A_C(a)   GAN_REP3_A(a,x,y,z)

#define GAN_FREP3_A(a, b, p1, p2, p3, q1, q2, q3)   (a p1 b q1, a p2 b q2, a p3 b q3)

#define GAN_FREP3_A_C(a, b, p1, p2, p3)   GAN_FREP3_A(a,b,x,y,z,p1,p2,p3)

#define GAN_REP3_ABS(a, b, c, p1, p2, p3, q1, q2, q3)   (a p1 b q1 c, a p2 b q2 c, a p3 b q3 c)

#define GAN_REP3_AAS(a, b, c, p1, p2, p3)   GAN_REP3_ABS(a,b,c,p1,p2,p3,p1,p2,p3)

#define GAN_REP3_AAS_C(a, b, c)   GAN_REP3_AAS(a,b,c,x,y,z)

#define GAN_REP3_AB(a, b, p1, p2, p3, q1, q2, q3)   (a p1 b q1, a p2 b q2, a p3 b q3)

#define GAN_REP3_AA(a, b, p1, p2, p3)   GAN_REP3_AB(a,b,p1,p2,p3,p1,p2,p3)

#define GAN_REP3_AA_C(a, b)   GAN_REP3_AA(a,b,x,y,z)

#define GAN_REP3_ABCS(a, b, c, d, p1, p2, p3, q1, q2, q3, r1, r2, r3)   (a p1 b q1 c r1 d, a p2 b q2 c r2 d, a p3 b q3 c r3 d)

#define GAN_REP3_ABC(a, b, c, p1, p2, p3, q1, q2, q3, r1, r2, r3)   (a p1 b q1 c r1, a p2 b q2 c r2, a p3 b q3 c r3)

#define GAN_REP3_AAA(a, b, c, p1, p2, p3)   GAN_REP3_ABC(a,b,c,p1,p2,p3,p1,p2,p3,p1,p2,p3)

#define GAN_REP3_AAA_C(a, b, c)   GAN_REP3_AAA(a,b,c,x,y,z)

#define GAN_REP3_OP_AB(a, b, p1, p2, p3, q1, q2, q3, op)   (a p1 b q1 op a p2 b q2 op a p3 b q3)

#define GAN_REP3_OP_AA(a, b, p1, p2, p3, op)   GAN_REP3_OP_AB(a,b,p1,p2,p3,p1,p2,p3,op)

#define GAN_REP3_OP_AA_C(a, b, op)   GAN_REP3_OP_AA(a,b,x,y,z,op)

#define GAN_FREP23_A(a, b, p1, p2, q1, q2, q3, r11, r12, r13, r21, r22, r23)

#define GAN_FREP23_A_C(a, b, r11, r12, r13, r21, r22, r23)   GAN_FREP23_A(a,b,x,y,x,y,z,r11,r12,r13,r21,r22,r23)

#define GAN_REP23_ABCS(a, b, c, d, p1, p2, q1, q2, q3, r1, r2, s1, s2, s3, t1, t2, u1, u2, u3)

#define GAN_REP23_ABC(a, b, c, p1, p2, q1, q2, q3, r1, r2, s1, s2, s3, t1, t2, u1, u2, u3)

#define GAN_REP23_AAAS(a, b, c, d, p1, p2, q1, q2, q3)   GAN_REP23_ABCS(a,b,c,d,p1,p2,q1,q2,q3,p1,p2,q1,q2,q3,p1,p2,q1,q2,q3)

#define GAN_REP23_AAA(a, b, c, p1, p2, q1, q2, q3)   GAN_REP23_ABC(a,b,c,p1,p2,q1,q2,q3,p1,p2,q1,q2,q3,p1,p2,q1,q2,q3)

#define GAN_REP23_ABS(a, b, c, p1, p2, q1, q2, q3, r1, r2, s1, s2, s3)

#define GAN_REP23_AB(a, b, p1, p2, q1, q2, q3, r1, r2, s1, s2, s3)

#define GAN_REP23_AAS(a, b, c, p1, p2, q1, q2, q3)   GAN_REP23_ABS(a,b,c,p1,p2,q1,q2,q3,p1,p2,q1,q2,q3)

#define GAN_REP23_AA(a, b, p1, p2, q1, q2, q3)   GAN_REP23_AB(a,b,p1,p2,q1,q2,q3,p1,p2,q1,q2,q3)

#define GAN_REP23_AS(a, b, p1, p2, q1, q2, q3)

#define GAN_REP23_A(a, p1, p2, q1, q2, q3)

#define GAN_REP23_AS_C(a, b)   GAN_REP23_AS(a,b,x,y,x,y,z)

#define GAN_REP23_AAS_C(a, b, c)   GAN_REP23_AAS(a,b,c,x,y,x,y,z)

#define GAN_REP23_AAAS_C(a, b, c, d)   GAN_REP23_AAAS(a,b,c,d,x,y,x,y,z)

#define GAN_REP23_A_C(a)   GAN_REP23_A(a,x,y,x,y,z)

#define GAN_REP23_AA_C(a, b)   GAN_REP23_AA(a,b,x,y,x,y,z)

#define GAN_REP23_AAA_C(a, b, c)   GAN_REP23_AAA(a,b,c,x,y,x,y,z)

#define GAN_MAT23_MULT1D(a, b, c, p1, p2, q1, q2, q3)

#define GAN_MAT23T_MULT1D(a, b, c, p1, p2, p3, q1, q2)

#define GAN_MATTYPE   Gan_Matrix23

#define GAN_MATRIX_TYPE   Gan_Matrix

#define GAN_SQUMATRIX_TYPE   Gan_SquMatrix

#define GAN_VECTOR_TYPE   Gan_Vector

#define GAN_MAT_ELEMENT_TYPE   GAN_DOUBLE

#define GAN_REALTYPE   double

#define GAN_FWRITE_LENDIAN   gan_fwrite_lendian_f64

#define GAN_FREAD_LENDIAN   gan_fread_lendian_f64

#define GAN_VECTYPE1   Gan_Vector2

#define GAN_VECTYPE2   Gan_Vector3

#define GAN_MATTYPEL   Gan_Matrix22

#define GAN_MATTYPER   Gan_Matrix33

#define GAN_SQUMATTYPEL   Gan_SquMatrix22

#define GAN_SQUMATTYPER   Gan_SquMatrix33

#define GAN_MAT_FPRINT   gan_mat23_fprint

#define GAN_MAT_PRINT   gan_mat23_print

#define GAN_MAT_FSCANF   gan_mat23_fscanf

#define GAN_MAT_FWRITE   gan_mat23_fwrite

#define GAN_MAT_FREAD   gan_mat23_fread

#define GAN_MAT_ZERO_Q   gan_mat23_zero_q

#define GAN_MAT_ZERO_S   gan_mat23_zero_s

#define GAN_MAT_COPY_Q   gan_mat23_copy_q

#define GAN_MAT_COPY_S   gan_mat23_copy_s

#define GAN_MAT_SCALE_Q   gan_mat23_scale_q

#define GAN_MAT_SCALE_I   gan_mat23_scale_i

#define GAN_MAT_SCALE_S   gan_mat23_scale_s

#define GAN_MAT_DIVIDE_Q   gan_mat23_divide_q

#define GAN_MAT_DIVIDE_I   gan_mat23_divide_i

#define GAN_MAT_DIVIDE_S   gan_mat23_divide_s

#define GAN_MAT_NEGATE_Q   gan_mat23_negate_q

#define GAN_MAT_NEGATE_I   gan_mat23_negate_i

#define GAN_MAT_NEGATE_S   gan_mat23_negate_s

#define GAN_MAT_UNIT_Q   gan_mat23_unit_q

#define GAN_MAT_UNIT_I   gan_mat23_unit_i

#define GAN_MAT_UNIT_S   gan_mat23_unit_s

#define GAN_MAT_ADD_Q   gan_mat23_add_q

#define GAN_MAT_ADD_I1   gan_mat23_add_i1

#define GAN_MAT_ADD_I2   gan_mat23_add_i2

#define GAN_MAT_INCREMENT   gan_mat23_increment

#define GAN_MAT_ADD_S   gan_mat23_add_s

#define GAN_MAT_SUB_Q   gan_mat23_sub_q

#define GAN_MAT_SUB_I1   gan_mat23_sub_i1

#define GAN_MAT_SUB_I2   gan_mat23_sub_i2

#define GAN_MAT_DECREMENT   gan_mat23_decrement

#define GAN_MAT_SUB_S   gan_mat23_sub_s

#define GAN_VEC_OUTER_Q   gan_vec23_outer_q

#define GAN_VEC_OUTER_S   gan_vec23_outer_s

#define GAN_MAT_MULTV_Q   gan_mat23_multv3_q

#define GAN_MAT_MULTV_S   gan_mat23_multv3_s

#define GAN_MATT_MULTV_Q   gan_mat23T_multv2_q

#define GAN_MATT_MULTV_S   gan_mat23T_multv2_s

#define GAN_MAT_LMULTM_Q   gan_mat23_lmultm22_q

#define GAN_MAT_LMULTM_S   gan_mat23_lmultm22_s

#define GAN_MAT_LMULTMT_Q   gan_mat23_lmultm22T_q

#define GAN_MAT_LMULTMT_S   gan_mat23_lmultm22T_s

#define GAN_MAT_RMULTM_Q   gan_mat23_rmultm33_q

#define GAN_MAT_RMULTM_S   gan_mat23_rmultm33_s

#define GAN_MAT_RMULTMT_Q   gan_mat23_rmultm33T_q

#define GAN_MAT_RMULTMT_S   gan_mat23_rmultm33T_s

#define GAN_MAT_LMULTMT_SYM_Q   gan_mat23_lmultm23T_sym_q

#define GAN_MAT_LMULTMT_SYM_S   gan_mat23_lmultm23T_sym_s

#define GAN_MAT_RMULTMT_SYM_Q   gan_mat23_rmultm23T_sym_q

#define GAN_MAT_RMULTMT_SYM_S   gan_mat23_rmultm23T_sym_s

#define GAN_MAT_SLMULTT_Q   gan_mat23_slmultT_q

#define GAN_MAT_SLMULTT_S   gan_mat23_slmultT_s

#define GAN_MAT_SRMULTT_Q   gan_mat23_srmultT_q

#define GAN_MAT_SRMULTT_S   gan_mat23_srmultT_s

#define GAN_MAT_LMULTS_Q   gan_mat23_lmults22_q

#define GAN_MAT_LMULTS_S   gan_mat23_lmults22_s

#define GAN_MAT_RMULTS_Q   gan_mat23_rmults33_q

#define GAN_MAT_RMULTS_S   gan_mat23_rmults33_s

#define GAN_SYMMATL_LRMULT_Q   gan_symmat22_lrmultm23T_q

#define GAN_SYMMATL_LRMULT_S   gan_symmat22_lrmultm23T_s

#define GAN_SYMMATR_LRMULT_Q   gan_symmat33_lrmultm23_q

#define GAN_SYMMATR_LRMULT_S   gan_symmat33_lrmultm23_s

#define GAN_MAT_LMULTL_Q   gan_mat23_lmultl22_q

#define GAN_MAT_LMULTL_S   gan_mat23_lmultl22_s

#define GAN_MAT_LMULTL_I   gan_mat23_lmultl22_i

#define GAN_MAT_LMULTLI_Q   gan_mat23_lmultl22I_q

#define GAN_MAT_LMULTLI_S   gan_mat23_lmultl22I_s

#define GAN_MAT_LMULTLI_I   gan_mat23_lmultl22I_i

#define GAN_MAT_LMULTLT_Q   gan_mat23_lmultl22T_q

#define GAN_MAT_LMULTLT_S   gan_mat23_lmultl22T_s

#define GAN_MAT_LMULTLT_I   gan_mat23_lmultl22T_i

#define GAN_MAT_LMULTLIT_Q   gan_mat23_lmultl22IT_q

#define GAN_MAT_LMULTLIT_S   gan_mat23_lmultl22IT_s

#define GAN_MAT_LMULTLIT_I   gan_mat23_lmultl22IT_i

#define GAN_MAT_RMULTL_Q   gan_mat23_rmultl33_q

#define GAN_MAT_RMULTL_S   gan_mat23_rmultl33_s

#define GAN_MAT_RMULTL_I   gan_mat23_rmultl33_i

#define GAN_MAT_RMULTLI_Q   gan_mat23_rmultl33I_q

#define GAN_MAT_RMULTLI_S   gan_mat23_rmultl33I_s

#define GAN_MAT_RMULTLI_I   gan_mat23_rmultl33I_i

#define GAN_MAT_RMULTLT_Q   gan_mat23_rmultl33T_q

#define GAN_MAT_RMULTLT_S   gan_mat23_rmultl33T_s

#define GAN_MAT_RMULTLT_I   gan_mat23_rmultl33T_i

#define GAN_MAT_RMULTLIT_Q   gan_mat23_rmultl33IT_q

#define GAN_MAT_RMULTLIT_S   gan_mat23_rmultl33IT_s

#define GAN_MAT_RMULTLIT_I   gan_mat23_rmultl33IT_i

#define GAN_MAT_SUMSQR_Q   gan_mat23_sumsqr_q

#define GAN_MAT_SUMSQR_S   gan_mat23_sumsqr_s

#define GAN_MAT_FNORM_Q   gan_mat23_Fnorm_q

#define GAN_MAT_FNORM_S   gan_mat23_Fnorm_s

#define GAN_MAT_FROM_MAT_Q   gan_mat23_from_mat_q

#define GAN_MAT_FROM_MAT_S   gan_mat23_from_mat_s

Typedefs

typedef Gan_Matrix23 Gan_Matrix23

Structure definition for double precision 2x3 matrix.

Functions

Gan_Matrix23 * gan_mat23_fill_q (Gan_Matrix23 *A, double XX, double XY, double XZ, double YX, double YY, double YZ)

Macro: Fill 2x3 matrix with values.

Gan_Matrix22 * gan_mat23_rmultm23T_q (const Gan_Matrix23 *A, const Gan_Matrix23 *B, Gan_Matrix22 *C)

Macro: Multiply 2x3 matrix by the transpose of 2x3 matrix.

Gan_Vector2 * gan_mat23_multv2h_q (const Gan_Matrix23 *A, const Gan_Vector2 *p, double h, Gan_Vector2 *q)

Macro: Multiply 2x3 matrix by homogeneous 2-vector.

void gan_mat23_get_rows_q (const Gan_Matrix23 *A, Gan_Vector3 *p, Gan_Vector3 *q)

Macro: Extract rows of 2x3 matrix.

void gan_mat23_get_cols_q (const Gan_Matrix23 *A, Gan_Vector2 *p, Gan_Vector2 *q, Gan_Vector2 *r)

Macro: Extract columns of 2x3 matrix.

Gan_Matrix22 * gan_mat23_get_m22l_q (const Gan_Matrix23 *A, Gan_Matrix22 *B)

Macro: Extract left-hand 2x2 part of 2x3 matrix.

Gan_Vector2 * gan_mat23_get_v2r_q (const Gan_Matrix23 *A, Gan_Vector2 *p)

Macro: Extract right-hand column of 2x3 matrix.

Gan_Matrix23 * gan_mat23_set_parts_q (Gan_Matrix23 *A, const Gan_Matrix22 *B, const Gan_Vector2 *p)

Macro: Build 2x3 matrix from 2x2 matrix and column 2-vector.

Gan_Matrix23 * gan_mat23_zero_q (const Gan_Matrix23 *A)

Macro: Fill fixed size matrix with zero.

Gan_Matrix23 * gan_mat23_copy_q (Gan_Matrix23 *A, Gan_Matrix23 *B)

Macro: Copy fixed size matrix.

Gan_Matrix23 * gan_mat23_scale_q (Gan_Matrix23 *A, double a, Gan_Matrix23 *B)

Macro: Scale fixed size matrix.

Gan_Matrix23 * gan_mat23_scale_i (Gan_Matrix23 *A, double a)

Macro: Scale fixed size matrix.

Gan_Matrix23 * gan_mat23_divide_q (Gan_Matrix23 *A, double a, Gan_Matrix23 *B)

Macro: Divide fixed size matrix by scalar.

Gan_Matrix23 * gan_mat23_divide_i (Gan_Matrix23 *A, double a)

Macro: Divide fixed size matrix by scalar.

Gan_Matrix23 * gan_mat23_negate_q (Gan_Matrix23 *A, Gan_Matrix23 *B)

Macro: Negate fixed size matrix.

Gan_Matrix23 * gan_mat23_negate_i (Gan_Matrix23 *A)

Macro: Negate fixed size matrix.

Gan_Matrix23 * gan_mat23_unit_i (Gan_Matrix23 *A)

Macro: Scale matrix to unit norm.

Gan_Matrix23 * gan_mat23_add_q (Gan_Matrix23 *A, Gan_Matrix23 *B, Gan_Matrix23 *C)

Macro: Add two fixed size matrices.

Gan_Matrix23 * gan_mat23_add_i1 (Gan_Matrix23 *A, Gan_Matrix23 *B)

Macro: Add two fixed size matrices.

Gan_Matrix23 * gan_mat23_add_i2 (Gan_Matrix23 *A, Gan_Matrix23 *B)

Macro: Add two fixed size matrices.

Gan_Matrix23 * gan_mat23_increment (Gan_Matrix23 *A, Gan_Matrix23 *B)

Macro: Increment a fixed size vector by another.

Gan_Matrix23 * gan_mat23_sub_q (Gan_Matrix23 *A, Gan_Matrix23 *B, Gan_Matrix23 *C)

Macro: Subtract two fixed size matrices.

Gan_Matrix23 * gan_mat23_sub_i1 (Gan_Matrix23 *A, Gan_Matrix23 *B)

Macro: Subtract two fixed size matrices.

Gan_Matrix23 * gan_mat23_sub_i2 (Gan_Matrix23 *A, Gan_Matrix23 *B)

Macro: Subtract two fixed size matrices.

Gan_Matrix23 * gan_mat23_decrement (Gan_Matrix23 *A, Gan_Matrix23 *B)

Macro: Decrement a fixed size vector by another.

Gan_Matrix23 * gan_vec23_outer_q (const Gan_Vector2 *p, const Gan_Vector3 *q, Gan_Matrix23 *A)

Macro: Compute the outer product of two fixed size vectors.

Gan_Vector2 * gan_mat23_multv3_q (const Gan_Matrix23 *A, Gan_Vector3 *p, Gan_Vector2 *q)

Macro: Matrix/vector product.

Gan_Vector3 * gan_mat23T_multv2_q (const Gan_Matrix23 *A, Gan_Vector2 *p, Gan_Vector3 *q)

Macro: Matrix/vector product with the matrix transposed.

Gan_Matrix23 * gan_mat23_lmultm22_q (Gan_Matrix23 *A, const Gan_Matrix22 *B, Gan_Matrix23 *C)

Macro: Left-multiply a matrix by another matrix.

Gan_Matrix23 * gan_mat23_lmultm22T_q (Gan_Matrix23 *A, const Gan_Matrix22 *B, Gan_Matrix23 *C)

Macro: Left-multiply a matrix by the transpose of another matrix.

Gan_Matrix23 * gan_mat23_rmultm33_q (Gan_Matrix23 *A, const Gan_Matrix33 *B, Gan_Matrix23 *C)

Macro: Right-multiply a matrix by another matrix.

Gan_Matrix23 * gan_mat23_rmultm33T_q (Gan_Matrix23 *A, const Gan_Matrix33 *B, Gan_Matrix23 *C)

Macro: Right-multiply a matrix by the transpose of another matrix.

Gan_SquMatrix33 * gan_mat23_lmultm23T_sym_q (const Gan_Matrix23 *A, const Gan_Matrix23 *B, Gan_SquMatrix33 *C)

Macro: Matrix product producing a symmetric matrix.

Gan_SquMatrix22 * gan_mat23_rmultm23T_sym_q (const Gan_Matrix23 *A, const Gan_Matrix23 *B, Gan_SquMatrix22 *C)

Macro: Matrix product producing a symmetric matrix.

Gan_Matrix23 * gan_mat23_lmults22_q (Gan_Matrix23 *A, const Gan_SquMatrix22 *B, Gan_Matrix23 *C)

Macro: Left-multiply a matrix by a symmetric matrix.

Gan_Matrix23 * gan_mat23_rmults33_q (Gan_Matrix23 *A, const Gan_SquMatrix33 *B, Gan_Matrix23 *C)

Macro: Right-multiply a matrix by a symmetric matrix.

Gan_SquMatrix33 * gan_symmat22_lrmultm23T_q (const Gan_SquMatrix22 *A, const Gan_Matrix23 *B, const Gan_Matrix23 *C, Gan_SquMatrix33 *D)

Macro: Matrix triple product involving symmetric matrices.

Gan_SquMatrix22 * gan_symmat33_lrmultm23_q (const Gan_SquMatrix33 *A, const Gan_Matrix23 *B, const Gan_Matrix23 *C, Gan_SquMatrix22 *D)

Macro: Matrix triple product involving symmetric matrices.

Gan_Matrix23 * gan_mat23_lmultl22_q (Gan_Matrix23 *A, const Gan_SquMatrix22 *B, Gan_Matrix23 *C)

Macro: Left-multiply a matrix by a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_lmultl22I_q (Gan_Matrix23 *A, const Gan_SquMatrix22 *B, Gan_Matrix23 *C)

Macro: Left-multiply a matrix by the inverse of a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_lmultl22T_q (Gan_Matrix23 *A, const Gan_SquMatrix22 *B, Gan_Matrix23 *C)

Macro: Left-multiply a matrix by the transpose of a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_lmultl22IT_q (Gan_Matrix23 *A, const Gan_SquMatrix22 *B, Gan_Matrix23 *C)

Macro: Left-multiply a matrix by the inverse transpose of a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_rmultl33_q (Gan_Matrix23 *A, const Gan_SquMatrix33 *B, Gan_Matrix23 *C)

Macro: Right-multiply a matrix by a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_rmultl33I_q (Gan_Matrix23 *A, const Gan_SquMatrix33 *B, Gan_Matrix23 *C)

Macro: Right-multiply a matrix by the inverse of a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_rmultl33T_q (Gan_Matrix23 *A, const Gan_SquMatrix33 *B, Gan_Matrix23 *C)

Macro: Right-multiply a matrix by the transpose of a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_rmultl33IT_q (Gan_Matrix23 *A, const Gan_SquMatrix33 *B, Gan_Matrix23 *C)

Macro: Right-multiply a matrix by the inverse transpose of a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_lmultl22_i (Gan_Matrix23 *A, const Gan_SquMatrix22 *B)

Macro: Left-multiply a matrix by a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_lmultl22I_i (Gan_Matrix23 *A, const Gan_SquMatrix22 *B)

Macro: Left-multiply a matrix by the inverse of a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_lmultl22T_i (Gan_Matrix23 *A, const Gan_SquMatrix22 *B)

Macro: Left-multiply a matrix by the transpose of a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_lmultl22IT_i (Gan_Matrix23 *A, const Gan_SquMatrix22 *B)

Macro: Left-multiply a matrix by the inverse transpose of a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_rmultl33_i (Gan_Matrix23 *A, const Gan_SquMatrix33 *B)

Macro: Right-multiply a matrix by a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_rmultl33I_i (Gan_Matrix23 *A, const Gan_SquMatrix33 *B)

Macro: Right-multiply a matrix by the inverse of a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_rmultl33T_i (Gan_Matrix23 *A, const Gan_SquMatrix33 *B)

Macro: Right-multiply a matrix by the transpose of a lower-triangular matrix.

Gan_Matrix23 * gan_mat23_rmultl33IT_i (Gan_Matrix23 *A, const Gan_SquMatrix33 *B)

Macro: Right-multiply a matrix by the inverse transpose of a lower-triangular matrix.

Gan_SquMatrix33 * gan_mat23_slmultT_q (Gan_Matrix23 *A, const Gan_SquMatrix33 *B)

Macro: Left-multiply a matrix by its own transpose, producing a symmetric matrix.

Gan_SquMatrix22 * gan_mat23_srmultT_q (const Gan_Matrix23 *A, Gan_SquMatrix22 *B)

Macro: Right-multiply a matrix by its own transpose, producing a symmetric matrix.

double gan_mat23_sumsqr_q (const Gan_Matrix23 *A)

Macro: Returns sum of squares of matrix elements.

double gan_mat23_Fnorm_q (const Gan_Matrix23 *A)

Macro: Frobenius norm of matrix.

Detailed Description

Module: 2x3 matrices (double precision)

Part of: Gandalf Library

Version:: 1.10

Date:: 2002/12/06 17:48:53

Author:: pm

Define Documentation

#define GAN_FREP23_A ( a,
b,
p1,
p2,
q1,
q2,
q3,
r11,
r12,
r13,
r21,
r22,
r23 )

Value:
(GAN_FREP3_A(a,b,p1##q1,p1##q2,p1##q3,r11,r12,r13),\ GAN_FREP3_A(a,b,p2##q1,p2##q2,p2##q3,r21,r22,r23))

#define GAN_REP23_A ( a,
p1,
p2,
q1,
q2,
q3 )

Value:
(GAN_REP3_A(a,p1##q1,p1##q2,p1##q3),\ GAN_REP3_A(a,p2##q1,p2##q2,p2##q3))

#define GAN_REP23_AB ( a,
b,
p1,
p2,
q1,
q2,
q3,
r1,
r2,
s1,
s2,
s3 )

Value:
(GAN_REP3_AB(a,b,p1##q1,p1##q2,p1##q3,r1##s1,r1##s2,r1##s3),\ GAN_REP3_AB(a,b,p2##q1,p2##q2,p2##q3,r2##s1,r2##s2,r2##s3))

#define GAN_REP23_ABC ( a,
b,
c,
p1,
p2,
q1,
q2,
q3,
r1,
r2,
s1,
s2,
s3,
t1,
t2,
u1,
u2,
u3 )

Value:
(GAN_REP3_ABC(a,b,c,p1##q1,p1##q2,p1##q3,r1##s1,r1##s2,r1##s3,t1##u1,t1##u2,t1##u3),\ GAN_REP3_ABC(a,b,c,p2##q1,p2##q2,p2##q3,r2##s1,r2##s2,r2##s3,t2##u1,t2##u2,t2##u3))

#define GAN_REP23_ABCS ( a,
b,
c,
d,
p1,
p2,
q1,
q2,
q3,
r1,
r2,
s1,
s2,
s3,
t1,
t2,
u1,
u2,
u3 )

Value:
(GAN_REP3_ABCS(a,b,c,d,p1##q1,p1##q2,p1##q3,r1##s1,r1##s2,r1##s3,t1##u1,t1##u2,t1##u3),\ GAN_REP3_ABCS(a,b,c,d,p2##q1,p2##q2,p2##q3,r2##s1,r2##s2,r2##s3,t2##u1,t2##u2,t2##u3))

#define GAN_REP23_ABS ( a,
b,
c,
p1,
p2,
q1,
q2,
q3,
r1,
r2,
s1,
s2,
s3 )

Value:
(GAN_REP3_ABS(a,b,c,p1##q1,p1##q2,p1##q3,r1##s1,r1##s2,r1##s3),\ GAN_REP3_ABS(a,b,c,p2##q1,p2##q2,p2##q3,r2##s1,r2##s2,r2##s3))

#define GAN_REP23_AS ( a,
b,
p1,
p2,
q1,
q2,
q3 )

Value:
(GAN_REP3_AS(a,b,p1##q1,p1##q2,p1##q3),\ GAN_REP3_AS(a,b,p2##q1,p2##q2,p2##q3))

#define GAN_REP3_AS ( a,
b,
p1,
p2,
p3 ) (a p1 b, a p2 b, a p3 b)

File:
RCSfile
repeat3_noc.h,v
Module: Macros for 3-fold repetition of vector/matrix operations Part of: Gandalf Library
Revision:
Revision
1.5
Last edited:
Date
2002/04/18 14:56:25
Author:
Author
pm
Copyright: (c) 2000 Imagineer Software Limited
Notes: Not to be compiled separately

Generated on Fri Mar 17 12:44:48 2006 by

1.3.9.1


Classes
struct	Gan_Matrix23
	Structure definition for double precision 2x3 matrix. More...
Defines
#define	GAN_REP3_AS(a, b, p1, p2, p3) (a p1 b, a p2 b, a p3 b)
#define	GAN_REP3_AS_C(a, b) GAN_REP3_AS(a,b,x,y,z)
#define	GAN_REP3_A(a, p1, p2, p3) (a p1, a p2, a p3)
#define	GAN_REP3_A_C(a) GAN_REP3_A(a,x,y,z)
#define	GAN_FREP3_A(a, b, p1, p2, p3, q1, q2, q3) (a p1 b q1, a p2 b q2, a p3 b q3)
#define	GAN_FREP3_A_C(a, b, p1, p2, p3) GAN_FREP3_A(a,b,x,y,z,p1,p2,p3)
#define	GAN_REP3_ABS(a, b, c, p1, p2, p3, q1, q2, q3) (a p1 b q1 c, a p2 b q2 c, a p3 b q3 c)
#define	GAN_REP3_AAS(a, b, c, p1, p2, p3) GAN_REP3_ABS(a,b,c,p1,p2,p3,p1,p2,p3)
#define	GAN_REP3_AAS_C(a, b, c) GAN_REP3_AAS(a,b,c,x,y,z)
#define	GAN_REP3_AB(a, b, p1, p2, p3, q1, q2, q3) (a p1 b q1, a p2 b q2, a p3 b q3)
#define	GAN_REP3_AA(a, b, p1, p2, p3) GAN_REP3_AB(a,b,p1,p2,p3,p1,p2,p3)
#define	GAN_REP3_AA_C(a, b) GAN_REP3_AA(a,b,x,y,z)
#define	GAN_REP3_ABCS(a, b, c, d, p1, p2, p3, q1, q2, q3, r1, r2, r3) (a p1 b q1 c r1 d, a p2 b q2 c r2 d, a p3 b q3 c r3 d)
#define	GAN_REP3_ABC(a, b, c, p1, p2, p3, q1, q2, q3, r1, r2, r3) (a p1 b q1 c r1, a p2 b q2 c r2, a p3 b q3 c r3)
#define	GAN_REP3_AAA(a, b, c, p1, p2, p3) GAN_REP3_ABC(a,b,c,p1,p2,p3,p1,p2,p3,p1,p2,p3)
#define	GAN_REP3_AAA_C(a, b, c) GAN_REP3_AAA(a,b,c,x,y,z)
#define	GAN_REP3_OP_AB(a, b, p1, p2, p3, q1, q2, q3, op) (a p1 b q1 op a p2 b q2 op a p3 b q3)
#define	GAN_REP3_OP_AA(a, b, p1, p2, p3, op) GAN_REP3_OP_AB(a,b,p1,p2,p3,p1,p2,p3,op)
#define	GAN_REP3_OP_AA_C(a, b, op) GAN_REP3_OP_AA(a,b,x,y,z,op)
#define	GAN_FREP23_A(a, b, p1, p2, q1, q2, q3, r11, r12, r13, r21, r22, r23)
#define	GAN_FREP23_A_C(a, b, r11, r12, r13, r21, r22, r23) GAN_FREP23_A(a,b,x,y,x,y,z,r11,r12,r13,r21,r22,r23)
#define	GAN_REP23_ABCS(a, b, c, d, p1, p2, q1, q2, q3, r1, r2, s1, s2, s3, t1, t2, u1, u2, u3)
#define	GAN_REP23_ABC(a, b, c, p1, p2, q1, q2, q3, r1, r2, s1, s2, s3, t1, t2, u1, u2, u3)
#define	GAN_REP23_AAAS(a, b, c, d, p1, p2, q1, q2, q3) GAN_REP23_ABCS(a,b,c,d,p1,p2,q1,q2,q3,p1,p2,q1,q2,q3,p1,p2,q1,q2,q3)
#define	GAN_REP23_AAA(a, b, c, p1, p2, q1, q2, q3) GAN_REP23_ABC(a,b,c,p1,p2,q1,q2,q3,p1,p2,q1,q2,q3,p1,p2,q1,q2,q3)
#define	GAN_REP23_ABS(a, b, c, p1, p2, q1, q2, q3, r1, r2, s1, s2, s3)
#define	GAN_REP23_AB(a, b, p1, p2, q1, q2, q3, r1, r2, s1, s2, s3)
#define	GAN_REP23_AAS(a, b, c, p1, p2, q1, q2, q3) GAN_REP23_ABS(a,b,c,p1,p2,q1,q2,q3,p1,p2,q1,q2,q3)
#define	GAN_REP23_AA(a, b, p1, p2, q1, q2, q3) GAN_REP23_AB(a,b,p1,p2,q1,q2,q3,p1,p2,q1,q2,q3)
#define	GAN_REP23_AS(a, b, p1, p2, q1, q2, q3)
#define	GAN_REP23_A(a, p1, p2, q1, q2, q3)
#define	GAN_REP23_AS_C(a, b) GAN_REP23_AS(a,b,x,y,x,y,z)
#define	GAN_REP23_AAS_C(a, b, c) GAN_REP23_AAS(a,b,c,x,y,x,y,z)
#define	GAN_REP23_AAAS_C(a, b, c, d) GAN_REP23_AAAS(a,b,c,d,x,y,x,y,z)
#define	GAN_REP23_A_C(a) GAN_REP23_A(a,x,y,x,y,z)
#define	GAN_REP23_AA_C(a, b) GAN_REP23_AA(a,b,x,y,x,y,z)
#define	GAN_REP23_AAA_C(a, b, c) GAN_REP23_AAA(a,b,c,x,y,x,y,z)
#define	GAN_MAT23_MULT1D(a, b, c, p1, p2, q1, q2, q3)
#define	GAN_MAT23T_MULT1D(a, b, c, p1, p2, p3, q1, q2)
#define	GAN_MATTYPE Gan_Matrix23
#define	GAN_MATRIX_TYPE Gan_Matrix
#define	GAN_SQUMATRIX_TYPE Gan_SquMatrix
#define	GAN_VECTOR_TYPE Gan_Vector
#define	GAN_MAT_ELEMENT_TYPE GAN_DOUBLE
#define	GAN_REALTYPE double
#define	GAN_FWRITE_LENDIAN gan_fwrite_lendian_f64
#define	GAN_FREAD_LENDIAN gan_fread_lendian_f64
#define	GAN_VECTYPE1 Gan_Vector2
#define	GAN_VECTYPE2 Gan_Vector3
#define	GAN_MATTYPEL Gan_Matrix22
#define	GAN_MATTYPER Gan_Matrix33
#define	GAN_SQUMATTYPEL Gan_SquMatrix22
#define	GAN_SQUMATTYPER Gan_SquMatrix33
#define	GAN_MAT_FPRINT gan_mat23_fprint
#define	GAN_MAT_PRINT gan_mat23_print
#define	GAN_MAT_FSCANF gan_mat23_fscanf
#define	GAN_MAT_FWRITE gan_mat23_fwrite
#define	GAN_MAT_FREAD gan_mat23_fread
#define	GAN_MAT_ZERO_Q gan_mat23_zero_q
#define	GAN_MAT_ZERO_S gan_mat23_zero_s
#define	GAN_MAT_COPY_Q gan_mat23_copy_q
#define	GAN_MAT_COPY_S gan_mat23_copy_s
#define	GAN_MAT_SCALE_Q gan_mat23_scale_q
#define	GAN_MAT_SCALE_I gan_mat23_scale_i
#define	GAN_MAT_SCALE_S gan_mat23_scale_s
#define	GAN_MAT_DIVIDE_Q gan_mat23_divide_q
#define	GAN_MAT_DIVIDE_I gan_mat23_divide_i
#define	GAN_MAT_DIVIDE_S gan_mat23_divide_s
#define	GAN_MAT_NEGATE_Q gan_mat23_negate_q
#define	GAN_MAT_NEGATE_I gan_mat23_negate_i
#define	GAN_MAT_NEGATE_S gan_mat23_negate_s
#define	GAN_MAT_UNIT_Q gan_mat23_unit_q
#define	GAN_MAT_UNIT_I gan_mat23_unit_i
#define	GAN_MAT_UNIT_S gan_mat23_unit_s
#define	GAN_MAT_ADD_Q gan_mat23_add_q
#define	GAN_MAT_ADD_I1 gan_mat23_add_i1
#define	GAN_MAT_ADD_I2 gan_mat23_add_i2
#define	GAN_MAT_INCREMENT gan_mat23_increment
#define	GAN_MAT_ADD_S gan_mat23_add_s
#define	GAN_MAT_SUB_Q gan_mat23_sub_q
#define	GAN_MAT_SUB_I1 gan_mat23_sub_i1
#define	GAN_MAT_SUB_I2 gan_mat23_sub_i2
#define	GAN_MAT_DECREMENT gan_mat23_decrement
#define	GAN_MAT_SUB_S gan_mat23_sub_s
#define	GAN_VEC_OUTER_Q gan_vec23_outer_q
#define	GAN_VEC_OUTER_S gan_vec23_outer_s
#define	GAN_MAT_MULTV_Q gan_mat23_multv3_q
#define	GAN_MAT_MULTV_S gan_mat23_multv3_s
#define	GAN_MATT_MULTV_Q gan_mat23T_multv2_q
#define	GAN_MATT_MULTV_S gan_mat23T_multv2_s
#define	GAN_MAT_LMULTM_Q gan_mat23_lmultm22_q
#define	GAN_MAT_LMULTM_S gan_mat23_lmultm22_s
#define	GAN_MAT_LMULTMT_Q gan_mat23_lmultm22T_q
#define	GAN_MAT_LMULTMT_S gan_mat23_lmultm22T_s
#define	GAN_MAT_RMULTM_Q gan_mat23_rmultm33_q
#define	GAN_MAT_RMULTM_S gan_mat23_rmultm33_s
#define	GAN_MAT_RMULTMT_Q gan_mat23_rmultm33T_q
#define	GAN_MAT_RMULTMT_S gan_mat23_rmultm33T_s
#define	GAN_MAT_LMULTMT_SYM_Q gan_mat23_lmultm23T_sym_q
#define	GAN_MAT_LMULTMT_SYM_S gan_mat23_lmultm23T_sym_s
#define	GAN_MAT_RMULTMT_SYM_Q gan_mat23_rmultm23T_sym_q
#define	GAN_MAT_RMULTMT_SYM_S gan_mat23_rmultm23T_sym_s
#define	GAN_MAT_SLMULTT_Q gan_mat23_slmultT_q
#define	GAN_MAT_SLMULTT_S gan_mat23_slmultT_s
#define	GAN_MAT_SRMULTT_Q gan_mat23_srmultT_q
#define	GAN_MAT_SRMULTT_S gan_mat23_srmultT_s
#define	GAN_MAT_LMULTS_Q gan_mat23_lmults22_q
#define	GAN_MAT_LMULTS_S gan_mat23_lmults22_s
#define	GAN_MAT_RMULTS_Q gan_mat23_rmults33_q
#define	GAN_MAT_RMULTS_S gan_mat23_rmults33_s
#define	GAN_SYMMATL_LRMULT_Q gan_symmat22_lrmultm23T_q
#define	GAN_SYMMATL_LRMULT_S gan_symmat22_lrmultm23T_s
#define	GAN_SYMMATR_LRMULT_Q gan_symmat33_lrmultm23_q
#define	GAN_SYMMATR_LRMULT_S gan_symmat33_lrmultm23_s
#define	GAN_MAT_LMULTL_Q gan_mat23_lmultl22_q
#define	GAN_MAT_LMULTL_S gan_mat23_lmultl22_s
#define	GAN_MAT_LMULTL_I gan_mat23_lmultl22_i
#define	GAN_MAT_LMULTLI_Q gan_mat23_lmultl22I_q
#define	GAN_MAT_LMULTLI_S gan_mat23_lmultl22I_s
#define	GAN_MAT_LMULTLI_I gan_mat23_lmultl22I_i
#define	GAN_MAT_LMULTLT_Q gan_mat23_lmultl22T_q
#define	GAN_MAT_LMULTLT_S gan_mat23_lmultl22T_s
#define	GAN_MAT_LMULTLT_I gan_mat23_lmultl22T_i
#define	GAN_MAT_LMULTLIT_Q gan_mat23_lmultl22IT_q
#define	GAN_MAT_LMULTLIT_S gan_mat23_lmultl22IT_s
#define	GAN_MAT_LMULTLIT_I gan_mat23_lmultl22IT_i
#define	GAN_MAT_RMULTL_Q gan_mat23_rmultl33_q
#define	GAN_MAT_RMULTL_S gan_mat23_rmultl33_s
#define	GAN_MAT_RMULTL_I gan_mat23_rmultl33_i
#define	GAN_MAT_RMULTLI_Q gan_mat23_rmultl33I_q
#define	GAN_MAT_RMULTLI_S gan_mat23_rmultl33I_s
#define	GAN_MAT_RMULTLI_I gan_mat23_rmultl33I_i
#define	GAN_MAT_RMULTLT_Q gan_mat23_rmultl33T_q
#define	GAN_MAT_RMULTLT_S gan_mat23_rmultl33T_s
#define	GAN_MAT_RMULTLT_I gan_mat23_rmultl33T_i
#define	GAN_MAT_RMULTLIT_Q gan_mat23_rmultl33IT_q
#define	GAN_MAT_RMULTLIT_S gan_mat23_rmultl33IT_s
#define	GAN_MAT_RMULTLIT_I gan_mat23_rmultl33IT_i
#define	GAN_MAT_SUMSQR_Q gan_mat23_sumsqr_q
#define	GAN_MAT_SUMSQR_S gan_mat23_sumsqr_s
#define	GAN_MAT_FNORM_Q gan_mat23_Fnorm_q
#define	GAN_MAT_FNORM_S gan_mat23_Fnorm_s
#define	GAN_MAT_FROM_MAT_Q gan_mat23_from_mat_q
#define	GAN_MAT_FROM_MAT_S gan_mat23_from_mat_s
Typedefs
typedef Gan_Matrix23	Gan_Matrix23
	Structure definition for double precision 2x3 matrix.
Functions
Gan_Matrix23 *	gan_mat23_fill_q (Gan_Matrix23 *A, double XX, double XY, double XZ, double YX, double YY, double YZ)
	Macro: Fill 2x3 matrix with values.
Gan_Matrix22 *	gan_mat23_rmultm23T_q (const Gan_Matrix23 A, const Gan_Matrix23 B, Gan_Matrix22 *C)
	Macro: Multiply 2x3 matrix by the transpose of 2x3 matrix.
Gan_Vector2 *	gan_mat23_multv2h_q (const Gan_Matrix23 A, const Gan_Vector2 p, double h, Gan_Vector2 *q)
	Macro: Multiply 2x3 matrix by homogeneous 2-vector.
void	gan_mat23_get_rows_q (const Gan_Matrix23 A, Gan_Vector3 p, Gan_Vector3 *q)
	Macro: Extract rows of 2x3 matrix.
void	gan_mat23_get_cols_q (const Gan_Matrix23 A, Gan_Vector2 p, Gan_Vector2 q, Gan_Vector2 r)
	Macro: Extract columns of 2x3 matrix.
Gan_Matrix22 *	gan_mat23_get_m22l_q (const Gan_Matrix23 A, Gan_Matrix22 B)
	Macro: Extract left-hand 2x2 part of 2x3 matrix.
Gan_Vector2 *	gan_mat23_get_v2r_q (const Gan_Matrix23 A, Gan_Vector2 p)
	Macro: Extract right-hand column of 2x3 matrix.
Gan_Matrix23 *	gan_mat23_set_parts_q (Gan_Matrix23 A, const Gan_Matrix22 B, const Gan_Vector2 *p)
	Macro: Build 2x3 matrix from 2x2 matrix and column 2-vector.
Gan_Matrix23 *	gan_mat23_zero_q (const Gan_Matrix23 *A)
	Macro: Fill fixed size matrix with zero.
Gan_Matrix23 *	gan_mat23_copy_q (Gan_Matrix23 A, Gan_Matrix23 B)
	Macro: Copy fixed size matrix.
Gan_Matrix23 *	gan_mat23_scale_q (Gan_Matrix23 A, double a, Gan_Matrix23 B)
	Macro: Scale fixed size matrix.
Gan_Matrix23 *	gan_mat23_scale_i (Gan_Matrix23 *A, double a)
	Macro: Scale fixed size matrix.
Gan_Matrix23 *	gan_mat23_divide_q (Gan_Matrix23 A, double a, Gan_Matrix23 B)
	Macro: Divide fixed size matrix by scalar.
Gan_Matrix23 *	gan_mat23_divide_i (Gan_Matrix23 *A, double a)
	Macro: Divide fixed size matrix by scalar.
Gan_Matrix23 *	gan_mat23_negate_q (Gan_Matrix23 A, Gan_Matrix23 B)
	Macro: Negate fixed size matrix.
Gan_Matrix23 *	gan_mat23_negate_i (Gan_Matrix23 *A)
	Macro: Negate fixed size matrix.
Gan_Matrix23 *	gan_mat23_unit_i (Gan_Matrix23 *A)
	Macro: Scale matrix to unit norm.
Gan_Matrix23 *	gan_mat23_add_q (Gan_Matrix23 A, Gan_Matrix23 B, Gan_Matrix23 *C)
	Macro: Add two fixed size matrices.
Gan_Matrix23 *	gan_mat23_add_i1 (Gan_Matrix23 A, Gan_Matrix23 B)
	Macro: Add two fixed size matrices.
Gan_Matrix23 *	gan_mat23_add_i2 (Gan_Matrix23 A, Gan_Matrix23 B)
	Macro: Add two fixed size matrices.
Gan_Matrix23 *	gan_mat23_increment (Gan_Matrix23 A, Gan_Matrix23 B)
	Macro: Increment a fixed size vector by another.
Gan_Matrix23 *	gan_mat23_sub_q (Gan_Matrix23 A, Gan_Matrix23 B, Gan_Matrix23 *C)
	Macro: Subtract two fixed size matrices.
Gan_Matrix23 *	gan_mat23_sub_i1 (Gan_Matrix23 A, Gan_Matrix23 B)
	Macro: Subtract two fixed size matrices.
Gan_Matrix23 *	gan_mat23_sub_i2 (Gan_Matrix23 A, Gan_Matrix23 B)
	Macro: Subtract two fixed size matrices.
Gan_Matrix23 *	gan_mat23_decrement (Gan_Matrix23 A, Gan_Matrix23 B)
	Macro: Decrement a fixed size vector by another.
Gan_Matrix23 *	gan_vec23_outer_q (const Gan_Vector2 p, const Gan_Vector3 q, Gan_Matrix23 *A)
	Macro: Compute the outer product of two fixed size vectors.
Gan_Vector2 *	gan_mat23_multv3_q (const Gan_Matrix23 A, Gan_Vector3 p, Gan_Vector2 *q)
	Macro: Matrix/vector product.
Gan_Vector3 *	gan_mat23T_multv2_q (const Gan_Matrix23 A, Gan_Vector2 p, Gan_Vector3 *q)
	Macro: Matrix/vector product with the matrix transposed.
Gan_Matrix23 *	gan_mat23_lmultm22_q (Gan_Matrix23 A, const Gan_Matrix22 B, Gan_Matrix23 *C)
	Macro: Left-multiply a matrix by another matrix.
Gan_Matrix23 *	gan_mat23_lmultm22T_q (Gan_Matrix23 A, const Gan_Matrix22 B, Gan_Matrix23 *C)
	Macro: Left-multiply a matrix by the transpose of another matrix.
Gan_Matrix23 *	gan_mat23_rmultm33_q (Gan_Matrix23 A, const Gan_Matrix33 B, Gan_Matrix23 *C)
	Macro: Right-multiply a matrix by another matrix.
Gan_Matrix23 *	gan_mat23_rmultm33T_q (Gan_Matrix23 A, const Gan_Matrix33 B, Gan_Matrix23 *C)
	Macro: Right-multiply a matrix by the transpose of another matrix.
Gan_SquMatrix33 *	gan_mat23_lmultm23T_sym_q (const Gan_Matrix23 A, const Gan_Matrix23 B, Gan_SquMatrix33 *C)
	Macro: Matrix product producing a symmetric matrix.
Gan_SquMatrix22 *	gan_mat23_rmultm23T_sym_q (const Gan_Matrix23 A, const Gan_Matrix23 B, Gan_SquMatrix22 *C)
	Macro: Matrix product producing a symmetric matrix.
Gan_Matrix23 *	gan_mat23_lmults22_q (Gan_Matrix23 A, const Gan_SquMatrix22 B, Gan_Matrix23 *C)
	Macro: Left-multiply a matrix by a symmetric matrix.
Gan_Matrix23 *	gan_mat23_rmults33_q (Gan_Matrix23 A, const Gan_SquMatrix33 B, Gan_Matrix23 *C)
	Macro: Right-multiply a matrix by a symmetric matrix.
Gan_SquMatrix33 *	gan_symmat22_lrmultm23T_q (const Gan_SquMatrix22 A, const Gan_Matrix23 B, const Gan_Matrix23 C, Gan_SquMatrix33 D)
	Macro: Matrix triple product involving symmetric matrices.
Gan_SquMatrix22 *	gan_symmat33_lrmultm23_q (const Gan_SquMatrix33 A, const Gan_Matrix23 B, const Gan_Matrix23 C, Gan_SquMatrix22 D)
	Macro: Matrix triple product involving symmetric matrices.
Gan_Matrix23 *	gan_mat23_lmultl22_q (Gan_Matrix23 A, const Gan_SquMatrix22 B, Gan_Matrix23 *C)
	Macro: Left-multiply a matrix by a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_lmultl22I_q (Gan_Matrix23 A, const Gan_SquMatrix22 B, Gan_Matrix23 *C)
	Macro: Left-multiply a matrix by the inverse of a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_lmultl22T_q (Gan_Matrix23 A, const Gan_SquMatrix22 B, Gan_Matrix23 *C)
	Macro: Left-multiply a matrix by the transpose of a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_lmultl22IT_q (Gan_Matrix23 A, const Gan_SquMatrix22 B, Gan_Matrix23 *C)
	Macro: Left-multiply a matrix by the inverse transpose of a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_rmultl33_q (Gan_Matrix23 A, const Gan_SquMatrix33 B, Gan_Matrix23 *C)
	Macro: Right-multiply a matrix by a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_rmultl33I_q (Gan_Matrix23 A, const Gan_SquMatrix33 B, Gan_Matrix23 *C)
	Macro: Right-multiply a matrix by the inverse of a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_rmultl33T_q (Gan_Matrix23 A, const Gan_SquMatrix33 B, Gan_Matrix23 *C)
	Macro: Right-multiply a matrix by the transpose of a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_rmultl33IT_q (Gan_Matrix23 A, const Gan_SquMatrix33 B, Gan_Matrix23 *C)
	Macro: Right-multiply a matrix by the inverse transpose of a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_lmultl22_i (Gan_Matrix23 A, const Gan_SquMatrix22 B)
	Macro: Left-multiply a matrix by a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_lmultl22I_i (Gan_Matrix23 A, const Gan_SquMatrix22 B)
	Macro: Left-multiply a matrix by the inverse of a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_lmultl22T_i (Gan_Matrix23 A, const Gan_SquMatrix22 B)
	Macro: Left-multiply a matrix by the transpose of a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_lmultl22IT_i (Gan_Matrix23 A, const Gan_SquMatrix22 B)
	Macro: Left-multiply a matrix by the inverse transpose of a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_rmultl33_i (Gan_Matrix23 A, const Gan_SquMatrix33 B)
	Macro: Right-multiply a matrix by a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_rmultl33I_i (Gan_Matrix23 A, const Gan_SquMatrix33 B)
	Macro: Right-multiply a matrix by the inverse of a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_rmultl33T_i (Gan_Matrix23 A, const Gan_SquMatrix33 B)
	Macro: Right-multiply a matrix by the transpose of a lower-triangular matrix.
Gan_Matrix23 *	gan_mat23_rmultl33IT_i (Gan_Matrix23 A, const Gan_SquMatrix33 B)
	Macro: Right-multiply a matrix by the inverse transpose of a lower-triangular matrix.
Gan_SquMatrix33 *	gan_mat23_slmultT_q (Gan_Matrix23 A, const Gan_SquMatrix33 B)
	Macro: Left-multiply a matrix by its own transpose, producing a symmetric matrix.
Gan_SquMatrix22 *	gan_mat23_srmultT_q (const Gan_Matrix23 A, Gan_SquMatrix22 B)
	Macro: Right-multiply a matrix by its own transpose, producing a symmetric matrix.
double	gan_mat23_sumsqr_q (const Gan_Matrix23 *A)
	Macro: Returns sum of squares of matrix elements.
double	gan_mat23_Fnorm_q (const Gan_Matrix23 *A)
	Macro: Frobenius norm of matrix.