43 #if defined(DEBUG) && !defined(NDEBUG) 113 const int n_iter = (k > n-
k) ? n-k : k;
114 for (
int j = 1; j <= n_iter; j++, n--) {
117 else if (ret % j == 0)
259 cs_math_3_distance(
const cs_real_t xa[3],
264 v[0] = xb[0] - xa[0];
265 v[1] = xb[1] - xa[1];
266 v[2] = xb[2] - xa[2];
268 return sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
284 cs_math_3_distance_dot_product(
const cs_real_t xa[3],
288 return ((xb[0] - xa[0])*xc[0]+(xb[1] - xa[1])*xc[1]+(xb[2] - xa[2])*xc[2]);
304 cs_math_3_square_distance(
const cs_real_t xa[3],
311 return (v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
347 cs_math_3_33_3_dot_product(
const cs_real_t n1[3],
352 = ( n1[0]*
t[0][0]*n2[0] + n1[1]*
t[1][0]*n2[0] + n1[2]*
t[2][0]*n2[0]
353 + n1[0]*
t[0][1]*n2[1] + n1[1]*
t[1][1]*n2[1] + n1[2]*
t[2][1]*n2[1]
354 + n1[0]*
t[0][2]*n2[2] + n1[1]*
t[1][2]*n2[2] + n1[2]*
t[2][2]*n2[2]);
375 cs_math_3_sym_33_3_dot_product(
const cs_real_t n1[3],
380 = ( n1[0]*
t[0]*n2[0] + n1[1]*
t[3]*n2[0] + n1[2]*
t[5]*n2[0]
381 + n1[0]*
t[3]*n2[1] + n1[1]*
t[1]*n2[1] + n1[2]*
t[4]*n2[1]
382 + n1[0]*
t[5]*n2[2] + n1[1]*
t[4]*n2[2] + n1[2]*
t[2]*n2[2]);
399 return sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
415 cs_real_t v2 = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
432 cs_math_3_normalise(
const cs_real_t vin[3],
439 vout[0] = inv_norm * vin[0];
440 vout[1] = inv_norm * vin[1];
441 vout[2] = inv_norm * vin[2];
456 cs_math_3_normalize(
const cs_real_t vin[3],
463 vout[0] = inv_norm * vin[0];
464 vout[1] = inv_norm * vin[1];
465 vout[2] = inv_norm * vin[2];
480 cs_math_3_orthogonal_projection(
const cs_real_t n[3],
484 vout[0] =
v[0]*(1.-n[0]*n[0])-
v[1]* n[1]*n[0] -
v[2]* n[2]*n[0];
485 vout[1] = -
v[0]* n[0]*n[1] +
v[1]*(1.-n[1]*n[1])-
v[2]* n[2]*n[1];
486 vout[2] = -
v[0]* n[0]*n[2] -
v[1]* n[1]*n[2] +
v[2]*(1.-n[2]*n[2]);
501 cs_math_3_normal_scaling(
const cs_real_t n[3],
505 cs_real_t v_dot_n = (factor -1.) * cs_math_3_dot_product(v, n);
506 for (
int i = 0; i < 3; i++)
507 v[i] += v_dot_n * n[i];
523 cs_math_33_normal_scaling_add(
const cs_real_t n[3],
528 ( n[0] * t[0][0] * n[0] + n[1] * t[1][0] * n[0] + n[2] * t[2][0] * n[0]
529 + n[0] * t[0][1] * n[1] + n[1] * t[1][1] * n[1] + n[2] * t[2][1] * n[1]
530 + n[0] * t[0][2] * n[2] + n[1] * t[1][2] * n[2] + n[2] * t[2][2] * n[2]);
531 for (
int i = 0; i < 3; i++) {
532 for (
int j = 0; j < 3; j++)
533 t[i][j] += n_t_n * n[i] * n[j];
548 cs_math_33_3_product(
const cs_real_t m[3][3],
552 mv[0] = m[0][0]*
v[0] + m[0][1]*
v[1] + m[0][2]*
v[2];
553 mv[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];
554 mv[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];
569 cs_math_33_3_product_add(
const cs_real_t m[3][3],
573 mv[0] += m[0][0]*
v[0] + m[0][1]*
v[1] + m[0][2]*
v[2];
574 mv[1] += m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];
575 mv[2] += m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];
590 cs_math_33t_3_product(
const cs_real_t m[3][3],
594 mv[0] = m[0][0]*
v[0] + m[1][0]*
v[1] + m[2][0]*
v[2];
595 mv[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
596 mv[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
612 cs_math_sym_33_3_product(
const cs_real_t m[6],
616 mv[0] = m[0] *
v[0] + m[3] *
v[1] + m[5] *
v[2];
617 mv[1] = m[3] * v[0] + m[1] * v[1] + m[4] * v[2];
618 mv[2] = m[5] * v[0] + m[4] * v[1] + m[2] * v[2];
634 cs_math_sym_33_3_product_add(
const cs_real_t m[6],
638 mv[0] += m[0] *
v[0] + m[3] *
v[1] + m[5] *
v[2];
639 mv[1] += m[3] * v[0] + m[1] * v[1] + m[4] * v[2];
640 mv[2] += m[5] * v[0] + m[4] * v[1] + m[2] * v[2];
656 return (t[0] + t[1] + t[2]);
671 cs_math_66_6_product(
const cs_real_t m[6][6],
675 for (
int i = 0; i < 6; i++) {
676 for (
int j = 0; j < 6; j++)
677 mv[i] = m[i][j] *
v[j];
693 cs_math_66_6_product_add(
const cs_real_t m[6][6],
697 for (
int i = 0; i < 6; i++) {
698 for (
int j = 0; j < 6; j++)
699 mv[i] += m[i][j] *
v[j];
714 cs_math_33_determinant(
const cs_real_t m[3][3])
716 const cs_real_t com0 = m[1][1]*m[2][2] - m[2][1]*m[1][2];
717 const cs_real_t com1 = m[2][1]*m[0][2] - m[0][1]*m[2][2];
718 const cs_real_t com2 = m[0][1]*m[1][2] - m[1][1]*m[0][2];
720 return m[0][0]*com0 + m[1][0]*com1 + m[2][0]*com2;
736 const cs_real_t com0 = m[1]*m[2] - m[4]*m[4];
737 const cs_real_t com1 = m[4]*m[5] - m[3]*m[2];
738 const cs_real_t com2 = m[3]*m[4] - m[1]*m[5];
740 return m[0]*com0 + m[3]*com1 + m[5]*com2;
753 #if defined(__INTEL_COMPILER) 754 #pragma optimization_level 0 762 uv[0] =
u[1]*
v[2] -
u[2]*
v[1];
763 uv[1] =
u[2]*v[0] -
u[0]*v[2];
764 uv[2] =
u[0]*v[1] -
u[1]*v[0];
779 #if defined(__INTEL_COMPILER) 780 #pragma optimization_level 0 784 cs_math_3_triple_product(
const cs_real_t u[3],
788 return (
u[1]*
v[2] -
u[2]*
v[1]) * w[0]
789 + (
u[2]*v[0] -
u[0]*v[2]) * w[1]
790 + (
u[0]*v[1] -
u[1]*v[0]) * w[2];
803 cs_math_33_inv_cramer(
const cs_real_t in[3][3],
806 out[0][0] = in[1][1]*in[2][2] - in[2][1]*in[1][2];
807 out[0][1] = in[2][1]*in[0][2] - in[0][1]*in[2][2];
808 out[0][2] = in[0][1]*in[1][2] - in[1][1]*in[0][2];
810 out[1][0] = in[2][0]*in[1][2] - in[1][0]*in[2][2];
811 out[1][1] = in[0][0]*in[2][2] - in[2][0]*in[0][2];
812 out[1][2] = in[1][0]*in[0][2] - in[0][0]*in[1][2];
814 out[2][0] = in[1][0]*in[2][1] - in[2][0]*in[1][1];
815 out[2][1] = in[2][0]*in[0][1] - in[0][0]*in[2][1];
816 out[2][2] = in[0][0]*in[1][1] - in[1][0]*in[0][1];
818 const double det = in[0][0]*out[0][0]+in[1][0]*out[0][1]+in[2][0]*out[0][2];
819 const double invdet = 1/det;
821 out[0][0] *= invdet, out[0][1] *= invdet, out[0][2] *= invdet;
822 out[1][0] *= invdet, out[1][1] *= invdet, out[1][2] *= invdet;
823 out[2][0] *= invdet, out[2][1] *= invdet, out[2][2] *= invdet;
835 cs_math_33_inv_cramer_in_place(
cs_real_t a[3][3])
837 cs_real_t a00 = a[1][1]*a[2][2] - a[2][1]*a[1][2];
838 cs_real_t a01 = a[2][1]*a[0][2] - a[0][1]*a[2][2];
839 cs_real_t a02 = a[0][1]*a[1][2] - a[1][1]*a[0][2];
840 cs_real_t a10 = a[2][0]*a[1][2] - a[1][0]*a[2][2];
841 cs_real_t a11 = a[0][0]*a[2][2] - a[2][0]*a[0][2];
842 cs_real_t a12 = a[1][0]*a[0][2] - a[0][0]*a[1][2];
843 cs_real_t a20 = a[1][0]*a[2][1] - a[2][0]*a[1][1];
844 cs_real_t a21 = a[2][0]*a[0][1] - a[0][0]*a[2][1];
845 cs_real_t a22 = a[0][0]*a[1][1] - a[1][0]*a[0][1];
847 double det_inv = 1. / (a[0][0]*a00 + a[1][0]*a01 + a[2][0]*a02);
849 a[0][0] = a00 * det_inv;
850 a[0][1] = a01 * det_inv;
851 a[0][2] = a02 * det_inv;
852 a[1][0] = a10 * det_inv;
853 a[1][1] = a11 * det_inv;
854 a[1][2] = a12 * det_inv;
855 a[2][0] = a20 * det_inv;
856 a[2][1] = a21 * det_inv;
857 a[2][2] = a22 * det_inv;
870 cs_math_33_inv_cramer_sym_in_place(
cs_real_t a[3][3])
872 cs_real_t a00 = a[1][1]*a[2][2] - a[2][1]*a[1][2];
873 cs_real_t a01 = a[2][1]*a[0][2] - a[0][1]*a[2][2];
874 cs_real_t a02 = a[0][1]*a[1][2] - a[1][1]*a[0][2];
875 cs_real_t a11 = a[0][0]*a[2][2] - a[2][0]*a[0][2];
876 cs_real_t a12 = a[1][0]*a[0][2] - a[0][0]*a[1][2];
877 cs_real_t a22 = a[0][0]*a[1][1] - a[1][0]*a[0][1];
879 double det_inv = 1. / (a[0][0]*a00 + a[1][0]*a01 + a[2][0]*a02);
881 a[0][0] = a00 * det_inv;
882 a[0][1] = a01 * det_inv;
883 a[0][2] = a02 * det_inv;
884 a[1][0] = a01 * det_inv;
885 a[1][1] = a11 * det_inv;
886 a[1][2] = a12 * det_inv;
887 a[2][0] = a02 * det_inv;
888 a[2][1] = a12 * det_inv;
889 a[2][2] = a22 * det_inv;
905 cs_math_sym_33_inv_cramer(
const cs_real_t s[6],
910 sout[0] = s[1]*s[2] - s[4]*s[4];
911 sout[1] = s[0]*s[2] - s[5]*s[5];
912 sout[2] = s[0]*s[1] - s[3]*s[3];
913 sout[3] = s[4]*s[5] - s[3]*s[2];
914 sout[4] = s[3]*s[5] - s[0]*s[4];
915 sout[5] = s[3]*s[4] - s[1]*s[5];
917 detinv = 1. / (s[0]*sout[0] + s[3]*sout[3] + s[5]*sout[5]);
938 cs_math_33_product(
const cs_real_t m1[3][3],
942 mout[0][0] = m1[0][0]*m2[0][0] + m1[0][1]*m2[1][0] + m1[0][2]*m2[2][0];
943 mout[0][1] = m1[0][0]*m2[0][1] + m1[0][1]*m2[1][1] + m1[0][2]*m2[2][1];
944 mout[0][2] = m1[0][0]*m2[0][2] + m1[0][1]*m2[1][2] + m1[0][2]*m2[2][2];
946 mout[1][0] = m1[1][0]*m2[0][0] + m1[1][1]*m2[1][0] + m1[1][2]*m2[2][0];
947 mout[1][1] = m1[1][0]*m2[0][1] + m1[1][1]*m2[1][1] + m1[1][2]*m2[2][1];
948 mout[1][2] = m1[1][0]*m2[0][2] + m1[1][1]*m2[1][2] + m1[1][2]*m2[2][2];
950 mout[2][0] = m1[2][0]*m2[0][0] + m1[2][1]*m2[1][0] + m1[2][2]*m2[2][0];
951 mout[2][1] = m1[2][0]*m2[0][1] + m1[2][1]*m2[1][1] + m1[2][2]*m2[2][1];
952 mout[2][2] = m1[2][0]*m2[0][2] + m1[2][1]*m2[1][2] + m1[2][2]*m2[2][2];
967 cs_math_33_transform_r_to_a(
const cs_real_t m[3][3],
973 _m[0][0] = m[0][0]*q[0][0] + m[0][1]*q[1][0] + m[0][2]*q[2][0];
974 _m[0][1] = m[0][0]*q[0][1] + m[0][1]*q[1][1] + m[0][2]*q[2][1];
975 _m[0][2] = m[0][0]*q[0][2] + m[0][1]*q[1][2] + m[0][2]*q[2][2];
977 _m[1][0] = m[1][0]*q[0][0] + m[1][1]*q[1][0] + m[1][2]*q[2][0];
978 _m[1][1] = m[1][0]*q[0][1] + m[1][1]*q[1][1] + m[1][2]*q[2][1];
979 _m[1][2] = m[1][0]*q[0][2] + m[1][1]*q[1][2] + m[1][2]*q[2][2];
981 _m[2][0] = m[2][0]*q[0][0] + m[2][1]*q[1][0] + m[2][2]*q[2][0];
982 _m[2][1] = m[2][0]*q[0][1] + m[2][1]*q[1][1] + m[2][2]*q[2][1];
983 _m[2][2] = m[2][0]*q[0][2] + m[2][1]*q[1][2] + m[2][2]*q[2][2];
986 mout[0][0] = q[0][0]*_m[0][0] + q[1][0]*_m[1][0] + q[2][0]*_m[2][0];
987 mout[0][1] = q[0][0]*_m[0][1] + q[1][0]*_m[1][1] + q[2][0]*_m[2][1];
988 mout[0][2] = q[0][0]*_m[0][2] + q[1][0]*_m[1][2] + q[2][0]*_m[2][2];
990 mout[1][0] = q[0][1]*_m[0][0] + q[1][1]*_m[1][0] + q[2][1]*_m[2][0];
991 mout[1][1] = q[0][1]*_m[0][1] + q[1][1]*_m[1][1] + q[2][1]*_m[2][1];
992 mout[1][2] = q[0][1]*_m[0][2] + q[1][1]*_m[1][2] + q[2][1]*_m[2][2];
994 mout[2][0] = q[0][2]*_m[0][0] + q[1][2]*_m[1][0] + q[2][2]*_m[2][0];
995 mout[2][1] = q[0][2]*_m[0][1] + q[1][2]*_m[1][1] + q[2][2]*_m[2][1];
996 mout[2][2] = q[0][2]*_m[0][2] + q[1][2]*_m[1][2] + q[2][2]*_m[2][2];
1011 cs_math_33_transform_a_to_r(
const cs_real_t m[3][3],
1017 _m[0][0] = m[0][0]*q[0][0] + m[0][1]*q[0][1] + m[0][2]*q[0][2];
1018 _m[0][1] = m[0][0]*q[1][0] + m[0][1]*q[1][1] + m[0][2]*q[1][2];
1019 _m[0][2] = m[0][0]*q[2][0] + m[0][1]*q[2][1] + m[0][2]*q[2][2];
1021 _m[1][0] = m[1][0]*q[0][0] + m[1][1]*q[0][1] + m[1][2]*q[0][2];
1022 _m[1][1] = m[1][0]*q[1][0] + m[1][1]*q[1][1] + m[1][2]*q[1][2];
1023 _m[1][2] = m[1][0]*q[2][0] + m[1][1]*q[2][1] + m[1][2]*q[2][2];
1025 _m[2][0] = m[2][0]*q[0][0] + m[2][1]*q[0][1] + m[2][2]*q[0][2];
1026 _m[2][1] = m[2][0]*q[1][0] + m[2][1]*q[1][1] + m[2][2]*q[1][2];
1027 _m[2][2] = m[2][0]*q[2][0] + m[2][1]*q[2][1] + m[2][2]*q[2][2];
1030 mout[0][0] = q[0][0]*_m[0][0] + q[0][1]*_m[1][0] + q[0][2]*_m[2][0];
1031 mout[0][1] = q[0][0]*_m[0][1] + q[0][1]*_m[1][1] + q[0][2]*_m[2][1];
1032 mout[0][2] = q[0][0]*_m[0][2] + q[0][1]*_m[1][2] + q[0][2]*_m[2][2];
1034 mout[1][0] = q[1][0]*_m[0][0] + q[1][1]*_m[1][0] + q[1][2]*_m[2][0];
1035 mout[1][1] = q[1][0]*_m[0][1] + q[1][1]*_m[1][1] + q[1][2]*_m[2][1];
1036 mout[1][2] = q[1][0]*_m[0][2] + q[1][1]*_m[1][2] + q[1][2]*_m[2][2];
1038 mout[2][0] = q[2][0]*_m[0][0] + q[2][1]*_m[1][0] + q[2][2]*_m[2][0];
1039 mout[2][1] = q[2][0]*_m[0][1] + q[2][1]*_m[1][1] + q[2][2]*_m[2][1];
1040 mout[2][2] = q[2][0]*_m[0][2] + q[2][1]*_m[1][2] + q[2][2]*_m[2][2];
1055 cs_math_33_extract_sym_ant(
const cs_real_t m[3][3],
1060 m_sym[0][0] = 0.5 * (m[0][0] + m[0][0]);
1061 m_sym[0][1] = 0.5 * (m[0][1] + m[1][0]);
1062 m_sym[0][2] = 0.5 * (m[0][2] + m[2][0]);
1063 m_sym[1][0] = 0.5 * (m[1][0] + m[0][1]);
1064 m_sym[1][1] = 0.5 * (m[1][1] + m[1][1]);
1065 m_sym[1][2] = 0.5 * (m[1][2] + m[2][1]);
1066 m_sym[2][0] = 0.5 * (m[2][0] + m[0][2]);
1067 m_sym[2][1] = 0.5 * (m[2][1] + m[1][2]);
1068 m_sym[2][2] = 0.5 * (m[2][2] + m[2][2]);
1071 m_ant[0][0] = 0.5 * (m[0][0] - m[0][0]);
1072 m_ant[0][1] = 0.5 * (m[0][1] - m[1][0]);
1073 m_ant[0][2] = 0.5 * (m[0][2] - m[2][0]);
1074 m_ant[1][0] = 0.5 * (m[1][0] - m[0][1]);
1075 m_ant[1][1] = 0.5 * (m[1][1] - m[1][1]);
1076 m_ant[1][2] = 0.5 * (m[1][2] - m[2][1]);
1077 m_ant[2][0] = 0.5 * (m[2][0] - m[0][2]);
1078 m_ant[2][1] = 0.5 * (m[2][1] - m[1][2]);
1079 m_ant[2][2] = 0.5 * (m[2][2] - m[2][2]);
1093 cs_math_33_product_add(
const cs_real_t m1[3][3],
1097 mout[0][0] += m1[0][0]*m2[0][0] + m1[0][1]*m2[1][0] + m1[0][2]*m2[2][0];
1098 mout[0][1] += m1[0][0]*m2[0][1] + m1[0][1]*m2[1][1] + m1[0][2]*m2[2][1];
1099 mout[0][2] += m1[0][0]*m2[0][2] + m1[0][1]*m2[1][2] + m1[0][2]*m2[2][2];
1101 mout[1][0] += m1[1][0]*m2[0][0] + m1[1][1]*m2[1][0] + m1[1][2]*m2[2][0];
1102 mout[1][1] += m1[1][0]*m2[0][1] + m1[1][1]*m2[1][1] + m1[1][2]*m2[2][1];
1103 mout[1][2] += m1[1][0]*m2[0][2] + m1[1][1]*m2[1][2] + m1[1][2]*m2[2][2];
1105 mout[2][0] += m1[2][0]*m2[0][0] + m1[2][1]*m2[1][0] + m1[2][2]*m2[2][0];
1106 mout[2][1] += m1[2][0]*m2[0][1] + m1[2][1]*m2[1][1] + m1[2][2]*m2[2][1];
1107 mout[2][2] += m1[2][0]*m2[0][2] + m1[2][1]*m2[1][2] + m1[2][2]*m2[2][2];
1127 cs_math_sym_33_product(
const cs_real_t s1[6],
1132 sout[0] = s1[0]*s2[0] + s1[3]*s2[3] + s1[5]*s2[5];
1134 sout[1] = s1[3]*s2[3] + s1[1]*s2[1] + s1[4]*s2[4];
1136 sout[2] = s1[5]*s2[5] + s1[4]*s2[4] + s1[2]*s2[2];
1138 sout[3] = s1[0]*s2[3] + s1[3]*s2[1] + s1[5]*s2[4];
1140 sout[4] = s1[3]*s2[5] + s1[1]*s2[4] + s1[4]*s2[2];
1142 sout[5] = s1[0]*s2[5] + s1[3]*s2[4] + s1[5]*s2[2];
1156 cs_math_reduce_sym_prod_33_to_66(
const cs_real_t s[3][3],
1159 int tens2vect[3][3];
1160 int iindex[6], jindex[6];
1162 tens2vect[0][0] = 0; tens2vect[0][1] = 3; tens2vect[0][2] = 5;
1163 tens2vect[1][0] = 3; tens2vect[1][1] = 1; tens2vect[1][2] = 4;
1164 tens2vect[2][0] = 5; tens2vect[2][1] = 4; tens2vect[2][2] = 2;
1166 iindex[0] = 0; iindex[1] = 1; iindex[2] = 2;
1167 iindex[3] = 0; iindex[4] = 1; iindex[5] = 0;
1169 jindex[0] = 0; jindex[1] = 1; jindex[2] = 2;
1170 jindex[3] = 1; jindex[4] = 2; jindex[5] = 2;
1176 for (
int i = 0; i < 6; i++) {
1179 for (
int k = 0;
k < 3;
k++) {
1180 int ik = tens2vect[
k][ii];
1181 int jk = tens2vect[
k][jj];
1183 sout[
ik][i] += s[
k][jj];
1185 sout[jk][i] += s[
k][ii];
1205 cs_math_sym_33_double_product(
const cs_real_t s1[6],
1213 _sout[0][0] = s1[0]*s2[0] + s1[3]*s2[3] + s1[5]*s2[5];
1215 _sout[1][1] = s1[3]*s2[3] + s1[1]*s2[1] + s1[4]*s2[4];
1217 _sout[2][2] = s1[5]*s2[5] + s1[4]*s2[4] + s1[2]*s2[2];
1219 _sout[0][1] = s1[0]*s2[3] + s1[3]*s2[1] + s1[5]*s2[4];
1221 _sout[1][0] = s2[0]*s1[3] + s2[3]*s1[1] + s2[5]*s1[4];
1223 _sout[1][2] = s1[3]*s2[5] + s1[1]*s2[4] + s1[4]*s2[2];
1225 _sout[2][1] = s2[3]*s1[5] + s2[1]*s1[4] + s2[4]*s1[2];
1227 _sout[0][2] = s1[0]*s2[5] + s1[3]*s2[4] + s1[5]*s2[2];
1229 _sout[2][0] = s2[0]*s1[5] + s2[3]*s1[4] + s2[5]*s1[2];
1231 sout[0][0] = _sout[0][0]*s3[0] + _sout[0][1]*s3[3] + _sout[0][2]*s3[5];
1233 sout[1][1] = _sout[1][0]*s3[3] + _sout[1][1]*s3[1] + _sout[1][2]*s3[4];
1235 sout[2][2] = _sout[2][0]*s3[5] + _sout[2][1]*s3[4] + _sout[2][2]*s3[2];
1237 sout[0][1] = _sout[0][0]*s3[3] + _sout[0][1]*s3[1] + _sout[0][2]*s3[4];
1239 sout[1][0] = s3[0]*_sout[1][0] + s3[3]*_sout[1][1] + s3[5]*_sout[1][2];
1241 sout[1][2] = _sout[1][0]*s3[5] + _sout[1][1]*s3[4] + _sout[1][2]*s3[2];
1243 sout[2][1] = s3[3]*_sout[2][0] + s3[1]*_sout[2][1] + s3[4]*_sout[2][2];
1245 sout[0][2] = _sout[0][0]*s3[5] + _sout[0][1]*s3[4] + _sout[0][2]*s3[2];
1247 sout[2][0] = s3[0]*_sout[2][0] + s3[3]*_sout[2][1] + s3[5]*_sout[2][2];
1265 qv->
meas = magnitude;
1269 qv->
unitv[0] = inv * v[0];
1270 qv->
unitv[1] = inv * v[1];
1271 qv->
unitv[2] = inv * v[2];
Definition: cs_field_pointer.h:70
integer, save ik
Definition: numvar.f90:75
#define restrict
Definition: cs_defs.h:142
cs_real_t cs_real_6_t[6]
vector of 6 floating-point values
Definition: cs_defs.h:337
const cs_real_t cs_math_big_r
cs_math_sym_tensor_component_t
Definition: cs_math.h:61
const cs_real_t cs_math_pi
const cs_real_t cs_math_1ov6
#define BEGIN_C_DECLS
Definition: cs_defs.h:510
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:715
const cs_real_t cs_math_epzero
const cs_real_t cs_math_1ov24
const cs_real_t cs_math_1ov12
const cs_real_t cs_math_2ov3
const cs_real_t cs_math_4ov3
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:351
double cs_real_t
Floating-point value.
Definition: cs_defs.h:322
Definition: cs_defs.h:368
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:471
double precision, dimension(:,:,:), allocatable v
Definition: atimbr.f90:114
const cs_real_t cs_math_1ov3
double cs_math_get_machine_epsilon(void)
Get the value related to the machine precision.
Definition: cs_math.c:245
void cs_math_set_machine_epsilon(void)
Compute the value related to the machine precision.
Definition: cs_math.c:224
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:501
double meas
Definition: cs_defs.h:370
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:265
const cs_real_t cs_math_5ov3
double precision, dimension(:,:,:), allocatable u
Definition: atimbr.f90:113
void cs_math_33_eig_val_vec(const cs_real_t m_in[3][3], const cs_real_t tol_err, cs_real_t eig_val[restrict 3], cs_real_t eig_vec[restrict 3][3])
Evaluate eigenvalues and eigenvectors of a real symmetric matrix m1[3,3]: m1*m2 = lambda*m2...
Definition: cs_math.c:533
cs_real_t cs_real_3_t[3]
vector of 3 floating-point values
Definition: cs_defs.h:335
const cs_real_t cs_math_zero_threshold
double unitv[3]
Definition: cs_defs.h:371
int cs_lnum_t
local mesh entity id
Definition: cs_defs.h:316
#define END_C_DECLS
Definition: cs_defs.h:511
cs_real_t cs_real_33_t[3][3]
3x3 matrix of floating-point values
Definition: cs_defs.h:342
Definition: cs_field_pointer.h:92
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 (Euclidean norm) between two points xa and xb in a Cartesian coordinate system of ...
Definition: cs_math.c:438
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:657
double precision, save b
Definition: cs_fuel_incl.f90:146