43 #if defined(DEBUG) && !defined(NDEBUG) 97 const short int n_iter = (k > n-
k) ? n-k : k;
98 for (
short int j = 1; j <= n_iter; j++, n--) {
101 else if (ret % j == 0)
192 v[0] = xb[0] - xa[0];
193 v[1] = xb[1] - xa[1];
194 v[2] = xb[2] - xa[2];
196 return sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
216 return ((xb[0] - xa[0])*xc[0]+(xb[1] - xa[1])*xc[1]+(xb[2] - xa[2])*xc[2]);
239 return (v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
257 cs_real_t uv = u[0]*v[0] + u[1]*v[1] + u[2]*v[2];
275 return sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
291 cs_real_t v2 = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
313 vout[0] = inv_norm * vin[0];
314 vout[1] = inv_norm * vin[1];
315 vout[2] = inv_norm * vin[2];
334 vout[0] = v[0]*(1.-n[0]*n[0])- v[1]* n[1]*n[0] - v[2]* n[2]*n[0];
335 vout[1] = -v[0]* n[0]*n[1] + v[1]*(1.-n[1]*n[1])- v[2]* n[2]*n[1];
336 vout[2] = -v[0]* n[0]*n[2] - v[1]* n[1]*n[2] + v[2]*(1.-n[2]*n[2]);
355 mv[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2];
356 mv[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];
357 mv[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];
376 mv[0] += m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2];
377 mv[1] += m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];
378 mv[2] += m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];
397 mv[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
398 mv[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
399 mv[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
419 mv[0] = m[0] * v[0] + m[3] * v[1] + m[5] * v[2];
420 mv[1] = m[3] * v[0] + m[1] * v[1] + m[4] * v[2];
421 mv[2] = m[5] * v[0] + m[4] * v[1] + m[2] * v[2];
441 mv[0] += m[0] * v[0] + m[3] * v[1] + m[5] * v[2];
442 mv[1] += m[3] * v[0] + m[1] * v[1] + m[4] * v[2];
443 mv[2] += m[5] * v[0] + m[4] * v[1] + m[2] * v[2];
462 for (
int i = 0; i < 6; i++) {
463 for (
int j = 0; j < 6; j++)
464 mv[i] = m[i][j] * v[j];
484 for (
int i = 0; i < 6; i++) {
485 for (
int j = 0; j < 6; j++)
486 mv[i] += m[i][j] * v[j];
503 const cs_real_t com0 = m[1][1]*m[2][2] - m[2][1]*m[1][2];
504 const cs_real_t com1 = m[2][1]*m[0][2] - m[0][1]*m[2][2];
505 const cs_real_t com2 = m[0][1]*m[1][2] - m[1][1]*m[0][2];
507 return m[0][0]*com0 + m[1][0]*com1 + m[2][0]*com2;
523 const cs_real_t com0 = m[1]*m[2] - m[4]*m[4];
524 const cs_real_t com1 = m[4]*m[5] - m[3]*m[2];
525 const cs_real_t com2 = m[3]*m[4] - m[1]*m[5];
527 return m[0]*com0 + m[3]*com1 + m[5]*com2;
541 #if defined(__INTEL_COMPILER) 542 #pragma optimization_level 0 550 uv[0] = u[1]*v[2] - u[2]*v[1];
551 uv[1] = u[2]*v[0] - u[0]*v[2];
552 uv[2] = u[0]*v[1] - u[1]*v[0];
568 out[0][0] = in[1][1]*in[2][2] - in[2][1]*in[1][2];
569 out[0][1] = in[2][1]*in[0][2] - in[0][1]*in[2][2];
570 out[0][2] = in[0][1]*in[1][2] - in[1][1]*in[0][2];
572 out[1][0] = in[2][0]*in[1][2] - in[1][0]*in[2][2];
573 out[1][1] = in[0][0]*in[2][2] - in[2][0]*in[0][2];
574 out[1][2] = in[1][0]*in[0][2] - in[0][0]*in[1][2];
576 out[2][0] = in[1][0]*in[2][1] - in[2][0]*in[1][1];
577 out[2][1] = in[2][0]*in[0][1] - in[0][0]*in[2][1];
578 out[2][2] = in[0][0]*in[1][1] - in[1][0]*in[0][1];
580 const double det = in[0][0]*out[0][0]+in[1][0]*out[0][1]+in[2][0]*out[0][2];
581 const double invdet = 1/det;
583 out[0][0] *= invdet, out[0][1] *= invdet, out[0][2] *= invdet;
584 out[1][0] *= invdet, out[1][1] *= invdet, out[1][2] *= invdet;
585 out[2][0] *= invdet, out[2][1] *= invdet, out[2][2] *= invdet;
599 cs_real_t a00 = a[1][1]*a[2][2] - a[2][1]*a[1][2];
600 cs_real_t a01 = a[2][1]*a[0][2] - a[0][1]*a[2][2];
601 cs_real_t a02 = a[0][1]*a[1][2] - a[1][1]*a[0][2];
602 cs_real_t a10 = a[2][0]*a[1][2] - a[1][0]*a[2][2];
603 cs_real_t a11 = a[0][0]*a[2][2] - a[2][0]*a[0][2];
604 cs_real_t a12 = a[1][0]*a[0][2] - a[0][0]*a[1][2];
605 cs_real_t a20 = a[1][0]*a[2][1] - a[2][0]*a[1][1];
606 cs_real_t a21 = a[2][0]*a[0][1] - a[0][0]*a[2][1];
607 cs_real_t a22 = a[0][0]*a[1][1] - a[1][0]*a[0][1];
609 double det_inv = 1. / (a[0][0]*a00 + a[1][0]*a01 + a[2][0]*a02);
611 a[0][0] = a00 * det_inv;
612 a[0][1] = a01 * det_inv;
613 a[0][2] = a02 * det_inv;
614 a[1][0] = a10 * det_inv;
615 a[1][1] = a11 * det_inv;
616 a[1][2] = a12 * det_inv;
617 a[2][0] = a20 * det_inv;
618 a[2][1] = a21 * det_inv;
619 a[2][2] = a22 * det_inv;
634 cs_real_t a00 = a[1][1]*a[2][2] - a[2][1]*a[1][2];
635 cs_real_t a01 = a[2][1]*a[0][2] - a[0][1]*a[2][2];
636 cs_real_t a02 = a[0][1]*a[1][2] - a[1][1]*a[0][2];
637 cs_real_t a11 = a[0][0]*a[2][2] - a[2][0]*a[0][2];
638 cs_real_t a12 = a[1][0]*a[0][2] - a[0][0]*a[1][2];
639 cs_real_t a22 = a[0][0]*a[1][1] - a[1][0]*a[0][1];
641 double det_inv = 1. / (a[0][0]*a00 + a[1][0]*a01 + a[2][0]*a02);
643 a[0][0] = a00 * det_inv;
644 a[0][1] = a01 * det_inv;
645 a[0][2] = a02 * det_inv;
646 a[1][0] = a01 * det_inv;
647 a[1][1] = a11 * det_inv;
648 a[1][2] = a12 * det_inv;
649 a[2][0] = a02 * det_inv;
650 a[2][1] = a12 * det_inv;
651 a[2][2] = a22 * det_inv;
672 sout[0] = s[1]*s[2] - s[4]*s[4];
673 sout[1] = s[0]*s[2] - s[5]*s[5];
674 sout[2] = s[0]*s[1] - s[3]*s[3];
675 sout[3] = s[4]*s[5] - s[3]*s[2];
676 sout[4] = s[3]*s[5] - s[0]*s[4];
677 sout[5] = s[3]*s[4] - s[1]*s[5];
679 detinv = 1. / (s[0]*sout[0] + s[3]*sout[3] + s[5]*sout[5]);
710 sout[0] = s1[0]*s2[0] + s1[3]*s2[3] + s1[5]*s2[5];
712 sout[1] = s1[3]*s2[3] + s1[1]*s2[1] + s1[4]*s2[4];
714 sout[2] = s1[5]*s2[5] + s1[4]*s2[4] + s1[2]*s2[2];
716 sout[3] = s1[0]*s2[3] + s1[3]*s2[1] + s1[5]*s2[4];
718 sout[4] = s1[3]*s2[5] + s1[1]*s2[4] + s1[4]*s2[2];
720 sout[5] = s1[0]*s2[5] + s1[3]*s2[4] + s1[5]*s2[2];
738 int iindex[6], jindex[6];
740 tens2vect[0][0] = 0; tens2vect[0][1] = 3; tens2vect[0][2] = 5;
741 tens2vect[1][0] = 3; tens2vect[1][1] = 1; tens2vect[1][2] = 4;
742 tens2vect[2][0] = 5; tens2vect[2][1] = 4; tens2vect[2][2] = 2;
744 iindex[0] = 0; iindex[1] = 1; iindex[2] = 2;
745 iindex[3] = 0; iindex[4] = 1; iindex[5] = 0;
747 jindex[0] = 0; jindex[1] = 1; jindex[2] = 2;
748 jindex[3] = 1; jindex[4] = 2; jindex[5] = 2;
754 for (
int i = 0; i < 6; i++) {
757 for (
int k = 0;
k < 3;
k++) {
758 int ik = tens2vect[
k][ii];
759 int jk = tens2vect[
k][jj];
761 sout[
ik][i] += s[
k][jj];
763 sout[jk][i] += s[
k][ii];
791 _sout[0][0] = s1[0]*s2[0] + s1[3]*s2[3] + s1[5]*s2[5];
793 _sout[1][1] = s1[3]*s2[3] + s1[1]*s2[1] + s1[4]*s2[4];
795 _sout[2][2] = s1[5]*s2[5] + s1[4]*s2[4] + s1[2]*s2[2];
797 _sout[0][1] = s1[0]*s2[3] + s1[3]*s2[1] + s1[5]*s2[4];
799 _sout[1][0] = s2[0]*s1[3] + s2[3]*s1[1] + s2[5]*s1[4];
801 _sout[1][2] = s1[3]*s2[5] + s1[1]*s2[4] + s1[4]*s2[2];
803 _sout[2][1] = s2[3]*s1[5] + s2[1]*s1[4] + s2[4]*s1[2];
805 _sout[0][2] = s1[0]*s2[5] + s1[3]*s2[4] + s1[5]*s2[2];
807 _sout[2][0] = s2[0]*s1[5] + s2[3]*s1[4] + s2[5]*s1[2];
809 sout[0][0] = _sout[0][0]*s3[0] + _sout[0][1]*s3[3] + _sout[0][2]*s3[5];
811 sout[1][1] = _sout[1][0]*s3[3] + _sout[1][1]*s3[1] + _sout[1][2]*s3[4];
813 sout[2][2] = _sout[2][0]*s3[5] + _sout[2][1]*s3[4] + _sout[2][2]*s3[2];
815 sout[0][1] = _sout[0][0]*s3[3] + _sout[0][1]*s3[1] + _sout[0][2]*s3[4];
817 sout[1][0] = s3[0]*_sout[1][0] + s3[3]*_sout[1][1] + s3[5]*_sout[1][2];
819 sout[1][2] = _sout[1][0]*s3[5] + _sout[1][1]*s3[4] + _sout[1][2]*s3[2];
821 sout[2][1] = s3[3]*_sout[2][0] + s3[1]*_sout[2][1] + s3[4]*_sout[2][2];
823 sout[0][2] = _sout[0][0]*s3[5] + _sout[0][1]*s3[4] + _sout[0][2]*s3[2];
825 sout[2][0] = s3[0]*_sout[2][0] + s3[3]*_sout[2][1] + s3[5]*_sout[2][2];
841 cs_real_t magnitude = sqrt(v[0]*v[0]+v[1]*v[1]+v[2]*v[2]);
843 qv->
meas = magnitude;
847 qv->
unitv[0] = inv * v[0];
848 qv->
unitv[1] = inv * v[1];
849 qv->
unitv[2] = inv * v[2];
static void cs_math_sym_33_inv_cramer(const cs_real_t s[6], cs_real_t sout[restrict 6])
Compute the inverse of a symmetric matrix using Cramer's rule.
Definition: cs_math.h:667
Definition: cs_field_pointer.h:70
integer, save ik
Definition: numvar.f90:75
static cs_real_t cs_math_3_distance_dot_product(const cs_real_t xa[3], const cs_real_t xb[3], const cs_real_t xc[3])
Compute .
Definition: cs_math.h:212
#define restrict
Definition: cs_defs.h:122
static cs_real_t cs_math_3_dot_product(const cs_real_t u[3], const cs_real_t v[3])
Compute the dot product of two vectors of 3 real values.
Definition: cs_math.h:254
const cs_real_t cs_math_onesix
cs_real_t cs_real_6_t[6]
vector of 6 floating-point values
Definition: cs_defs.h:311
size_t len
Definition: mei_scanner.c:569
static void cs_math_3_normalise(const cs_real_t vin[3], cs_real_t vout[restrict 3])
Normalize a vector of 3 real values.
Definition: cs_math.h:306
const cs_real_t cs_math_big_r
static void cs_math_sym_33_3_product_add(const cs_real_t m[6], const cs_real_t v[3], cs_real_t mv[restrict 3])
Compute the product of a symmetric matrix of 3x3 real values by a vector of 3 real values and add it ...
Definition: cs_math.h:437
static void cs_math_66_6_product(const cs_real_t m[6][6], const cs_real_t v[6], cs_real_t mv[restrict 6])
Compute the product of a matrix of 6x6 real values by a vector of 6 real values.
Definition: cs_math.h:458
static cs_real_t cs_math_pow3(cs_real_t x)
Compute the cube of a real value.
Definition: cs_math.h:153
static void cs_math_33_inv_cramer_in_place(cs_real_t a[3][3])
Inverse a 3x3 matrix in place, using Cramer's rule.
Definition: cs_math.h:597
static void cs_math_33_3_product(const cs_real_t m[3][3], const cs_real_t v[3], cs_real_3_t mv)
Compute the product of a matrix of 3x3 real values by a vector of 3 real values.
Definition: cs_math.h:351
const cs_real_t cs_math_pi
#define BEGIN_C_DECLS
Definition: cs_defs.h:461
void cs_math_fw_and_bw_lu(const cs_real_t a_lu[], const int n, cs_real_t x[], const cs_real_t b[])
Block Jacobi utilities. Compute forward and backward to solve an LU P*P system.
Definition: cs_math.c:537
const cs_real_t cs_math_epzero
static cs_real_t cs_math_sym_33_determinant(const cs_real_6_t m)
Compute the determinant of a 3x3 symmetric matrix.
Definition: cs_math.h:521
static cs_real_t cs_math_3_distance(const cs_real_t xa[3], const cs_real_t xb[3])
Compute the (euclidean) distance between two points xa and xb in a cartesian coordinate system of dim...
Definition: cs_math.h:187
void cs_math_33_eigen(const cs_real_t m[3][3], cs_real_t *eig_ratio, cs_real_t *eig_max)
Compute max/min eigenvalues ratio and max. eigenvalue of a 3x3 symmetric matrix with non-symmetric st...
Definition: cs_math.c:300
static void cs_math_sym_33_double_product(const cs_real_t s1[6], const cs_real_t s2[6], const cs_real_t s3[6], cs_real_t sout[restrict 3][3])
Compute the product of three symmetric matrices.
Definition: cs_math.h:783
double cs_real_t
Floating-point value.
Definition: cs_defs.h:297
Definition: cs_defs.h:337
Definition: cs_field_pointer.h:68
const cs_real_t cs_math_one24
static cs_real_t cs_math_3_square_norm(const cs_real_t v[3])
Compute the square norm of a vector of 3 real values.
Definition: cs_math.h:289
static cs_real_t cs_math_sq(cs_real_t x)
Compute the square of a real value.
Definition: cs_math.h:121
double cs_math_surftri(const cs_real_t xv[3], const cs_real_t xe[3], const cs_real_t xf[3])
Compute the area of the convex_hull generated by 3 points. This corresponds to the computation of the...
Definition: cs_math.c:420
double precision, dimension(:,:,:), allocatable v
Definition: atimbr.f90:114
static void cs_math_sym_33_product(const cs_real_t s1[6], const cs_real_t s2[6], cs_real_t sout[restrict 6])
Compute the product of two symmetric matrices. Warning: this is valid if and only if s1 and s2 commut...
Definition: cs_math.h:705
static void cs_math_66_6_product_add(const cs_real_t m[6][6], const cs_real_t v[6], cs_real_t mv[restrict 6])
Compute the product of a matrix of 6x6 real values by a vector of 6 real values and add it to the vec...
Definition: cs_math.h:480
double cs_math_get_machine_epsilon(void)
Get the value related to the machine precision.
Definition: cs_math.c:195
const cs_real_t cs_math_onetwelve
static void cs_math_33_inv_cramer_sym_in_place(cs_real_t a[3][3])
Inverse a 3x3 symmetric matrix (with non-symmetric storage) in place, using Cramer's rule...
Definition: cs_math.h:632
void cs_math_set_machine_epsilon(void)
Compute the value related to the machine precision.
Definition: cs_math.c:174
static cs_real_t cs_math_pow2(cs_real_t x)
Compute the square of a real value.
Definition: cs_math.h:137
double precision, save a
Definition: cs_fuel_incl.f90:146
double cs_math_voltet(const cs_real_t xv[3], const cs_real_t xe[3], const cs_real_t xf[3], const cs_real_t xc[3])
Compute the volume of the convex_hull generated by 4 points. This is equivalent to the computation of...
Definition: cs_math.c:450
double meas
Definition: cs_defs.h:339
void cs_math_sym_33_eigen(const cs_real_t m[6], cs_real_t eig_vals[3])
Compute all eigenvalues of a 3x3 symmetric matrix with symmetric storage.
Definition: cs_math.c:215
static cs_real_t cs_math_33_determinant(const cs_real_t m[3][3])
Compute the determinant of a 3x3 matrix.
Definition: cs_math.h:501
static cs_real_t cs_math_3_norm(const cs_real_t v[3])
Compute the euclidean norm of a vector of dimension 3.
Definition: cs_math.h:273
static void cs_math_33_inv_cramer(const cs_real_t in[3][3], cs_real_t out[3][3])
Inverse a 3x3 matrix.
Definition: cs_math.h:565
cs_real_t cs_real_3_t[3]
vector of 3 floating-point values
Definition: cs_defs.h:309
static void cs_math_3_orthogonal_projection(const cs_real_t n[3], const cs_real_t v[3], cs_real_t vout[restrict 3])
Orthogonal projection of a vector with respect to a normalised vector.
Definition: cs_math.h:330
static void cs_math_3_cross_product(const cs_real_t u[3], const cs_real_t v[3], cs_real_t uv[restrict 3])
Compute the cross product of two vectors of 3 real values.
Definition: cs_math.h:546
static void cs_math_33_3_product_add(const cs_real_t m[3][3], const cs_real_t v[3], cs_real_3_t mv)
Compute the product of a matrix of 3x3 real values by a vector of 3 real values add.
Definition: cs_math.h:372
const cs_real_t cs_math_zero_threshold
double unitv[3]
Definition: cs_defs.h:340
const cs_real_t cs_math_onethird
int cs_lnum_t
local mesh entity id
Definition: cs_defs.h:293
static cs_real_t cs_math_pow4(cs_real_t x)
Compute the 4-th power of a real value.
Definition: cs_math.h:169
static int cs_math_binom(short int n, short int k)
Computes the binomial coefficient of n and k.
Definition: cs_math.h:91
static cs_real_t cs_math_3_square_distance(const cs_real_t xa[3], const cs_real_t xb[3])
Compute the squared distance between two points xa and xb in a cartesian coordinate system of dimensi...
Definition: cs_math.h:232
static void cs_nvec3(const cs_real_3_t v, cs_nvec3_t *qv)
Define a cs_nvec3_t structure from a cs_real_3_t.
Definition: cs_math.h:838
#define END_C_DECLS
Definition: cs_defs.h:462
static void cs_math_33t_3_product(const cs_real_t m[3][3], const cs_real_t v[3], cs_real_3_t mv)
Compute the product of the transpose of a matrix of 3x3 real values by a vector of 3 real values...
Definition: cs_math.h:393
cs_real_t cs_real_33_t[3][3]
3x3 matrix of floating-point values
Definition: cs_defs.h:315
static void cs_math_sym_33_3_product(const cs_real_t m[6], const cs_real_t v[3], cs_real_t mv[restrict 3])
Compute the product of a symmetric matrix of 3x3 real values by a vector of 3 real values...
Definition: cs_math.h:415
void cs_math_3_length_unitv(const cs_real_t xa[3], const cs_real_t xb[3], cs_real_t *len, cs_real_3_t unitv)
Compute the length (euclidien norm) between two points xa and xb in a cartesian coordinate system of ...
Definition: cs_math.c:387
const cs_real_t cs_math_infinite_r
void cs_math_fact_lu(cs_lnum_t n_blocks, const int b_size, const cs_real_t *a, cs_real_t *a_lu)
Compute LU factorization of an array of dense matrices of identical size.
Definition: cs_math.c:479
static void cs_math_reduce_sym_prod_33_to_66(const cs_real_t s[3][3], cs_real_t sout[restrict 6][6])
Compute a 6x6 matrix A, equivalent to a 3x3 matrix s, such as: A*R_6 = R*s^t + s*R.
Definition: cs_math.h:734
double precision, save b
Definition: cs_fuel_incl.f90:146