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37 #ifndef GMX_MATH_VEC_H
38 #define GMX_MATH_VEC_H
41 collection of in-line ready operations:
43 lookup-table optimized scalar operations:
44 real gmx_invsqrt(real x)
49 void rvec_add(const rvec a,const rvec b,rvec c) c = a + b
50 void dvec_add(const dvec a,const dvec b,dvec c) c = a + b
51 void ivec_add(const ivec a,const ivec b,ivec c) c = a + b
52 void rvec_inc(rvec a,const rvec b) a += b
53 void dvec_inc(dvec a,const dvec b) a += b
54 void ivec_inc(ivec a,const ivec b) a += b
55 void rvec_sub(const rvec a,const rvec b,rvec c) c = a - b
56 void dvec_sub(const dvec a,const dvec b,dvec c) c = a - b
57 void rvec_dec(rvec a,rvec b) a -= b
58 void copy_rvec(const rvec a,rvec b) b = a (reals)
59 void copy_dvec(const dvec a,dvec b) b = a (reals)
60 void copy_ivec(const ivec a,ivec b) b = a (integers)
61 void ivec_sub(const ivec a,const ivec b,ivec c) c = a - b
62 void svmul(real a,rvec v1,rvec v2) v2 = a * v1
63 void dsvmul(double a,dvec v1,dvec v2) v2 = a * v1
64 void clear_rvec(rvec a) a = 0
65 void clear_dvec(dvec a) a = 0
66 void clear_ivec(rvec a) a = 0
67 void clear_rvecs(int n,rvec v[])
68 real iprod(rvec a,rvec b) = a . b (inner product)
69 double diprod(dvec a,dvec b) = a . b (inner product)
70 real iiprod(ivec a,ivec b) = a . b (integers)
71 real norm2(rvec a) = | a |^2 ( = x*y*z )
72 double dnorm2(dvec a) = | a |^2 ( = x*y*z )
73 real norm(rvec a) = | a |
74 double dnorm(dvec a) = | a |
75 void cprod(rvec a,rvec b,rvec c) c = a x b (cross product)
76 void dprod(rvec a,rvec b,rvec c) c = a x b (cross product)
77 void dprod(rvec a,rvec b,rvec c) c = a * b (direct product)
78 real cos_angle(rvec a,rvec b)
79 real cos_angle_no_table(rvec a,rvec b)
80 real distance2(rvec v1, rvec v2) = | v2 - v1 |^2
81 void unitv(rvec src,rvec dest) dest = src / |src|
82 void unitv_no_table(rvec src,rvec dest) dest = src / |src|
84 matrix (3x3) operations:
85 ! indicates that dest should not be the same as a, b or src
86 the _ur0 varieties work on matrices that have only zeros
87 in the upper right part, such as box matrices, these varieties
88 could produce less rounding errors, not due to the operations themselves,
89 but because the compiler can easier recombine the operations
90 void copy_mat(matrix a,matrix b) b = a
91 void clear_mat(matrix a) a = 0
92 void mmul(matrix a,matrix b,matrix dest) ! dest = a . b
93 void mmul_ur0(matrix a,matrix b,matrix dest) dest = a . b
94 void transpose(matrix src,matrix dest) ! dest = src*
95 void tmmul(matrix a,matrix b,matrix dest) ! dest = a* . b
96 void mtmul(matrix a,matrix b,matrix dest) ! dest = a . b*
97 real det(matrix a) = det(a)
98 void m_add(matrix a,matrix b,matrix dest) dest = a + b
99 void m_sub(matrix a,matrix b,matrix dest) dest = a - b
100 void msmul(matrix m1,real r1,matrix dest) dest = r1 * m1
101 void m_inv_ur0(matrix src,matrix dest) dest = src^-1
102 void m_inv(matrix src,matrix dest) ! dest = src^-1
103 void mvmul(matrix a,rvec src,rvec dest) ! dest = a . src
104 void mvmul_ur0(matrix a,rvec src,rvec dest) dest = a . src
105 void tmvmul_ur0(matrix a,rvec src,rvec dest) dest = a* . src
106 real trace(matrix m) = trace(m)
109 /* The file only depends on config.h for GMX_SOFTWARE_INVSQRT and
110 HAVE_*SQRT*. This is no problem with public headers because
111 it is OK if user code uses a different rsqrt implementation */
119 #include "utilities.h"
120 #include "vectypes.h"
122 #include "../utility/basedefinitions.h"
123 #include "../utility/fatalerror.h"
124 #include "../utility/real.h"
129 } /* avoid screwing up indentation */
132 #ifdef GMX_SOFTWARE_INVSQRT
133 #define EXP_LSB 0x00800000
134 #define EXP_MASK 0x7f800000
136 #define FRACT_MASK 0x007fffff
137 #define FRACT_SIZE 11 /* significant part of fraction */
138 #define FRACT_SHIFT (EXP_SHIFT-FRACT_SIZE)
139 #define EXP_ADDR(val) (((val)&EXP_MASK)>>EXP_SHIFT)
140 #define FRACT_ADDR(val) (((val)&(FRACT_MASK|EXP_LSB))>>FRACT_SHIFT)
142 extern const unsigned int gmx_invsqrt_exptab[];
143 extern const unsigned int gmx_invsqrt_fracttab[];
151 static gmx_inline real gmx_software_invsqrt(real x)
153 const real half = 0.5;
154 const real three = 3.0;
155 t_convert result, bit_pattern;
156 unsigned int exp, fract;
163 bit_pattern.fval = x;
164 exp = EXP_ADDR(bit_pattern.bval);
165 fract = FRACT_ADDR(bit_pattern.bval);
166 result.bval = gmx_invsqrt_exptab[exp] | gmx_invsqrt_fracttab[fract];
169 y = (half*lu*(three-((x*lu)*lu)));
171 y2 = (half*y*(three-((x*y)*y)));
173 return y2; /* 10 Flops */
175 return y; /* 5 Flops */
178 #define gmx_invsqrt(x) gmx_software_invsqrt(x)
180 #endif /* gmx_invsqrt */
185 # define gmx_invsqrt(x) rsqrt(x)
187 # define gmx_invsqrt(x) (1.0/sqrt(x))
191 # define gmx_invsqrt(x) rsqrtf(x)
192 # elif defined HAVE_RSQRT
193 # define gmx_invsqrt(x) rsqrt(x)
194 # elif defined HAVE_SQRTF
195 # define gmx_invsqrt(x) (1.0/sqrtf(x))
197 # define gmx_invsqrt(x) (1.0/sqrt(x))
203 static gmx_inline real sqr(real x)
208 static gmx_inline double dsqr(double x)
213 /* Maclaurin series for sinh(x)/x, useful for NH chains and MTTK pressure control
214 Here, we compute it to 10th order, which might be overkill, 8th is probably enough,
215 but it's not very much more expensive. */
217 static gmx_inline real series_sinhx(real x)
220 return (1 + (x2/6.0)*(1 + (x2/20.0)*(1 + (x2/42.0)*(1 + (x2/72.0)*(1 + (x2/110.0))))));
223 static gmx_inline void rvec_add(const rvec a, const rvec b, rvec c)
236 static gmx_inline void dvec_add(const dvec a, const dvec b, dvec c)
249 static gmx_inline void ivec_add(const ivec a, const ivec b, ivec c)
262 static gmx_inline void rvec_inc(rvec a, const rvec b)
275 static gmx_inline void dvec_inc(dvec a, const dvec b)
288 static gmx_inline void rvec_sub(const rvec a, const rvec b, rvec c)
301 static gmx_inline void dvec_sub(const dvec a, const dvec b, dvec c)
314 static gmx_inline void rvec_dec(rvec a, const rvec b)
327 static gmx_inline void copy_rvec(const rvec a, rvec b)
334 static gmx_inline void copy_rvecn(gmx_cxx_const rvec *a, rvec *b, int startn, int endn)
337 for (i = startn; i < endn; i++)
345 static gmx_inline void copy_dvec(const dvec a, dvec b)
352 static gmx_inline void copy_ivec(const ivec a, ivec b)
359 static gmx_inline void ivec_sub(const ivec a, const ivec b, ivec c)
372 static gmx_inline void copy_mat(gmx_cxx_const matrix a, matrix b)
374 copy_rvec(a[XX], b[XX]);
375 copy_rvec(a[YY], b[YY]);
376 copy_rvec(a[ZZ], b[ZZ]);
379 static gmx_inline void svmul(real a, const rvec v1, rvec v2)
386 static gmx_inline void dsvmul(double a, const dvec v1, dvec v2)
393 static gmx_inline real distance2(const rvec v1, const rvec v2)
395 return sqr(v2[XX]-v1[XX]) + sqr(v2[YY]-v1[YY]) + sqr(v2[ZZ]-v1[ZZ]);
398 static gmx_inline void clear_rvec(rvec a)
400 /* The ibm compiler has problems with inlining this
401 * when we use a const real variable
408 static gmx_inline void clear_dvec(dvec a)
410 /* The ibm compiler has problems with inlining this
411 * when we use a const real variable
418 static gmx_inline void clear_ivec(ivec a)
425 static gmx_inline void clear_rvecs(int n, rvec v[])
429 for (i = 0; (i < n); i++)
435 static gmx_inline void clear_mat(matrix a)
437 const real nul = 0.0;
439 a[XX][XX] = a[XX][YY] = a[XX][ZZ] = nul;
440 a[YY][XX] = a[YY][YY] = a[YY][ZZ] = nul;
441 a[ZZ][XX] = a[ZZ][YY] = a[ZZ][ZZ] = nul;
444 static gmx_inline real iprod(const rvec a, const rvec b)
446 return (a[XX]*b[XX]+a[YY]*b[YY]+a[ZZ]*b[ZZ]);
449 static gmx_inline double diprod(const dvec a, const dvec b)
451 return (a[XX]*b[XX]+a[YY]*b[YY]+a[ZZ]*b[ZZ]);
454 static gmx_inline int iiprod(const ivec a, const ivec b)
456 return (a[XX]*b[XX]+a[YY]*b[YY]+a[ZZ]*b[ZZ]);
459 static gmx_inline real norm2(const rvec a)
461 return a[XX]*a[XX]+a[YY]*a[YY]+a[ZZ]*a[ZZ];
464 static gmx_inline double dnorm2(const dvec a)
466 return a[XX]*a[XX]+a[YY]*a[YY]+a[ZZ]*a[ZZ];
470 * As dnorm() uses sqrt() (which is slow) _only_ use it if you are sure you
471 * don't need 1/dnorm(), otherwise use dnorm2()*dinvnorm(). */
472 static gmx_inline double dnorm(const dvec a)
474 return sqrt(diprod(a, a));
478 * As norm() uses sqrtf() (which is slow) _only_ use it if you are sure you
479 * don't need 1/norm(), otherwise use norm2()*invnorm(). */
480 static gmx_inline real norm(const rvec a)
482 /* This is ugly, but we deliberately do not define gmx_sqrt() and handle the
483 * float/double case here instead to avoid gmx_sqrt() being accidentally used. */
486 #elif defined HAVE_SQRTF
487 return sqrtf(iprod(a, a));
489 return sqrt(iprod(a, a));
493 static gmx_inline real invnorm(const rvec a)
495 return gmx_invsqrt(norm2(a));
498 static gmx_inline real dinvnorm(const dvec a)
500 return gmx_invsqrt(dnorm2(a));
504 * Do _not_ use these routines to calculate the angle between two vectors
505 * as acos(cos_angle(u,v)). While it might seem obvious, the acos function
506 * is very flat close to -1 and 1, which will lead to accuracy-loss.
507 * Instead, use the new gmx_angle() function directly.
509 static gmx_inline real
510 cos_angle(const rvec a, const rvec b)
513 * ax*bx + ay*by + az*bz
514 * cos-vec (a,b) = ---------------------
519 double aa, bb, ip, ipa, ipb, ipab; /* For accuracy these must be double! */
521 ip = ipa = ipb = 0.0;
522 for (m = 0; (m < DIM); m++) /* 18 */
533 cosval = ip*gmx_invsqrt(ipab); /* 7 */
553 * Do _not_ use these routines to calculate the angle between two vectors
554 * as acos(cos_angle(u,v)). While it might seem obvious, the acos function
555 * is very flat close to -1 and 1, which will lead to accuracy-loss.
556 * Instead, use the new gmx_angle() function directly.
558 static gmx_inline real
559 cos_angle_no_table(const rvec a, const rvec b)
561 /* This version does not need the invsqrt lookup table */
564 double aa, bb, ip, ipa, ipb; /* For accuracy these must be double! */
566 ip = ipa = ipb = 0.0;
567 for (m = 0; (m < DIM); m++) /* 18 */
575 cosval = ip/sqrt(ipa*ipb); /* 12 */
590 static gmx_inline void cprod(const rvec a, const rvec b, rvec c)
592 c[XX] = a[YY]*b[ZZ]-a[ZZ]*b[YY];
593 c[YY] = a[ZZ]*b[XX]-a[XX]*b[ZZ];
594 c[ZZ] = a[XX]*b[YY]-a[YY]*b[XX];
597 static gmx_inline void dcprod(const dvec a, const dvec b, dvec c)
599 c[XX] = a[YY]*b[ZZ]-a[ZZ]*b[YY];
600 c[YY] = a[ZZ]*b[XX]-a[XX]*b[ZZ];
601 c[ZZ] = a[XX]*b[YY]-a[YY]*b[XX];
604 /* This routine calculates the angle between a & b without any loss of accuracy close to 0/PI.
605 * If you only need cos(theta), use the cos_angle() routines to save a few cycles.
606 * This routine is faster than it might appear, since atan2 is accelerated on many CPUs (e.g. x86).
608 static gmx_inline real
609 gmx_angle(const rvec a, const rvec b)
619 return atan2(wlen, s);
622 static gmx_inline void mmul_ur0(gmx_cxx_const matrix a, gmx_cxx_const matrix b, matrix dest)
624 dest[XX][XX] = a[XX][XX]*b[XX][XX];
627 dest[YY][XX] = a[YY][XX]*b[XX][XX]+a[YY][YY]*b[YY][XX];
628 dest[YY][YY] = a[YY][YY]*b[YY][YY];
630 dest[ZZ][XX] = a[ZZ][XX]*b[XX][XX]+a[ZZ][YY]*b[YY][XX]+a[ZZ][ZZ]*b[ZZ][XX];
631 dest[ZZ][YY] = a[ZZ][YY]*b[YY][YY]+a[ZZ][ZZ]*b[ZZ][YY];
632 dest[ZZ][ZZ] = a[ZZ][ZZ]*b[ZZ][ZZ];
635 static gmx_inline void mmul(gmx_cxx_const matrix a, gmx_cxx_const matrix b, matrix dest)
637 dest[XX][XX] = a[XX][XX]*b[XX][XX]+a[XX][YY]*b[YY][XX]+a[XX][ZZ]*b[ZZ][XX];
638 dest[YY][XX] = a[YY][XX]*b[XX][XX]+a[YY][YY]*b[YY][XX]+a[YY][ZZ]*b[ZZ][XX];
639 dest[ZZ][XX] = a[ZZ][XX]*b[XX][XX]+a[ZZ][YY]*b[YY][XX]+a[ZZ][ZZ]*b[ZZ][XX];
640 dest[XX][YY] = a[XX][XX]*b[XX][YY]+a[XX][YY]*b[YY][YY]+a[XX][ZZ]*b[ZZ][YY];
641 dest[YY][YY] = a[YY][XX]*b[XX][YY]+a[YY][YY]*b[YY][YY]+a[YY][ZZ]*b[ZZ][YY];
642 dest[ZZ][YY] = a[ZZ][XX]*b[XX][YY]+a[ZZ][YY]*b[YY][YY]+a[ZZ][ZZ]*b[ZZ][YY];
643 dest[XX][ZZ] = a[XX][XX]*b[XX][ZZ]+a[XX][YY]*b[YY][ZZ]+a[XX][ZZ]*b[ZZ][ZZ];
644 dest[YY][ZZ] = a[YY][XX]*b[XX][ZZ]+a[YY][YY]*b[YY][ZZ]+a[YY][ZZ]*b[ZZ][ZZ];
645 dest[ZZ][ZZ] = a[ZZ][XX]*b[XX][ZZ]+a[ZZ][YY]*b[YY][ZZ]+a[ZZ][ZZ]*b[ZZ][ZZ];
648 static gmx_inline void transpose(gmx_cxx_const matrix src, matrix dest)
650 dest[XX][XX] = src[XX][XX];
651 dest[YY][XX] = src[XX][YY];
652 dest[ZZ][XX] = src[XX][ZZ];
653 dest[XX][YY] = src[YY][XX];
654 dest[YY][YY] = src[YY][YY];
655 dest[ZZ][YY] = src[YY][ZZ];
656 dest[XX][ZZ] = src[ZZ][XX];
657 dest[YY][ZZ] = src[ZZ][YY];
658 dest[ZZ][ZZ] = src[ZZ][ZZ];
661 static gmx_inline void tmmul(gmx_cxx_const matrix a, gmx_cxx_const matrix b, matrix dest)
663 /* Computes dest=mmul(transpose(a),b,dest) - used in do_pr_pcoupl */
664 dest[XX][XX] = a[XX][XX]*b[XX][XX]+a[YY][XX]*b[YY][XX]+a[ZZ][XX]*b[ZZ][XX];
665 dest[XX][YY] = a[XX][XX]*b[XX][YY]+a[YY][XX]*b[YY][YY]+a[ZZ][XX]*b[ZZ][YY];
666 dest[XX][ZZ] = a[XX][XX]*b[XX][ZZ]+a[YY][XX]*b[YY][ZZ]+a[ZZ][XX]*b[ZZ][ZZ];
667 dest[YY][XX] = a[XX][YY]*b[XX][XX]+a[YY][YY]*b[YY][XX]+a[ZZ][YY]*b[ZZ][XX];
668 dest[YY][YY] = a[XX][YY]*b[XX][YY]+a[YY][YY]*b[YY][YY]+a[ZZ][YY]*b[ZZ][YY];
669 dest[YY][ZZ] = a[XX][YY]*b[XX][ZZ]+a[YY][YY]*b[YY][ZZ]+a[ZZ][YY]*b[ZZ][ZZ];
670 dest[ZZ][XX] = a[XX][ZZ]*b[XX][XX]+a[YY][ZZ]*b[YY][XX]+a[ZZ][ZZ]*b[ZZ][XX];
671 dest[ZZ][YY] = a[XX][ZZ]*b[XX][YY]+a[YY][ZZ]*b[YY][YY]+a[ZZ][ZZ]*b[ZZ][YY];
672 dest[ZZ][ZZ] = a[XX][ZZ]*b[XX][ZZ]+a[YY][ZZ]*b[YY][ZZ]+a[ZZ][ZZ]*b[ZZ][ZZ];
675 static gmx_inline void mtmul(gmx_cxx_const matrix a, gmx_cxx_const matrix b, matrix dest)
677 /* Computes dest=mmul(a,transpose(b),dest) - used in do_pr_pcoupl */
678 dest[XX][XX] = a[XX][XX]*b[XX][XX]+a[XX][YY]*b[XX][YY]+a[XX][ZZ]*b[XX][ZZ];
679 dest[XX][YY] = a[XX][XX]*b[YY][XX]+a[XX][YY]*b[YY][YY]+a[XX][ZZ]*b[YY][ZZ];
680 dest[XX][ZZ] = a[XX][XX]*b[ZZ][XX]+a[XX][YY]*b[ZZ][YY]+a[XX][ZZ]*b[ZZ][ZZ];
681 dest[YY][XX] = a[YY][XX]*b[XX][XX]+a[YY][YY]*b[XX][YY]+a[YY][ZZ]*b[XX][ZZ];
682 dest[YY][YY] = a[YY][XX]*b[YY][XX]+a[YY][YY]*b[YY][YY]+a[YY][ZZ]*b[YY][ZZ];
683 dest[YY][ZZ] = a[YY][XX]*b[ZZ][XX]+a[YY][YY]*b[ZZ][YY]+a[YY][ZZ]*b[ZZ][ZZ];
684 dest[ZZ][XX] = a[ZZ][XX]*b[XX][XX]+a[ZZ][YY]*b[XX][YY]+a[ZZ][ZZ]*b[XX][ZZ];
685 dest[ZZ][YY] = a[ZZ][XX]*b[YY][XX]+a[ZZ][YY]*b[YY][YY]+a[ZZ][ZZ]*b[YY][ZZ];
686 dest[ZZ][ZZ] = a[ZZ][XX]*b[ZZ][XX]+a[ZZ][YY]*b[ZZ][YY]+a[ZZ][ZZ]*b[ZZ][ZZ];
689 static gmx_inline real det(gmx_cxx_const matrix a)
691 return ( a[XX][XX]*(a[YY][YY]*a[ZZ][ZZ]-a[ZZ][YY]*a[YY][ZZ])
692 -a[YY][XX]*(a[XX][YY]*a[ZZ][ZZ]-a[ZZ][YY]*a[XX][ZZ])
693 +a[ZZ][XX]*(a[XX][YY]*a[YY][ZZ]-a[YY][YY]*a[XX][ZZ]));
697 static gmx_inline void m_add(gmx_cxx_const matrix a, gmx_cxx_const matrix b, matrix dest)
699 dest[XX][XX] = a[XX][XX]+b[XX][XX];
700 dest[XX][YY] = a[XX][YY]+b[XX][YY];
701 dest[XX][ZZ] = a[XX][ZZ]+b[XX][ZZ];
702 dest[YY][XX] = a[YY][XX]+b[YY][XX];
703 dest[YY][YY] = a[YY][YY]+b[YY][YY];
704 dest[YY][ZZ] = a[YY][ZZ]+b[YY][ZZ];
705 dest[ZZ][XX] = a[ZZ][XX]+b[ZZ][XX];
706 dest[ZZ][YY] = a[ZZ][YY]+b[ZZ][YY];
707 dest[ZZ][ZZ] = a[ZZ][ZZ]+b[ZZ][ZZ];
710 static gmx_inline void m_sub(gmx_cxx_const matrix a, gmx_cxx_const matrix b, matrix dest)
712 dest[XX][XX] = a[XX][XX]-b[XX][XX];
713 dest[XX][YY] = a[XX][YY]-b[XX][YY];
714 dest[XX][ZZ] = a[XX][ZZ]-b[XX][ZZ];
715 dest[YY][XX] = a[YY][XX]-b[YY][XX];
716 dest[YY][YY] = a[YY][YY]-b[YY][YY];
717 dest[YY][ZZ] = a[YY][ZZ]-b[YY][ZZ];
718 dest[ZZ][XX] = a[ZZ][XX]-b[ZZ][XX];
719 dest[ZZ][YY] = a[ZZ][YY]-b[ZZ][YY];
720 dest[ZZ][ZZ] = a[ZZ][ZZ]-b[ZZ][ZZ];
723 static gmx_inline void msmul(gmx_cxx_const matrix m1, real r1, matrix dest)
725 dest[XX][XX] = r1*m1[XX][XX];
726 dest[XX][YY] = r1*m1[XX][YY];
727 dest[XX][ZZ] = r1*m1[XX][ZZ];
728 dest[YY][XX] = r1*m1[YY][XX];
729 dest[YY][YY] = r1*m1[YY][YY];
730 dest[YY][ZZ] = r1*m1[YY][ZZ];
731 dest[ZZ][XX] = r1*m1[ZZ][XX];
732 dest[ZZ][YY] = r1*m1[ZZ][YY];
733 dest[ZZ][ZZ] = r1*m1[ZZ][ZZ];
736 static gmx_inline void m_inv_ur0(gmx_cxx_const matrix src, matrix dest)
738 double tmp = src[XX][XX]*src[YY][YY]*src[ZZ][ZZ];
739 if (fabs(tmp) <= 100*GMX_REAL_MIN)
741 gmx_fatal(FARGS, "Can not invert matrix, determinant is zero");
744 dest[XX][XX] = 1/src[XX][XX];
745 dest[YY][YY] = 1/src[YY][YY];
746 dest[ZZ][ZZ] = 1/src[ZZ][ZZ];
747 dest[ZZ][XX] = (src[YY][XX]*src[ZZ][YY]*dest[YY][YY]
748 - src[ZZ][XX])*dest[XX][XX]*dest[ZZ][ZZ];
749 dest[YY][XX] = -src[YY][XX]*dest[XX][XX]*dest[YY][YY];
750 dest[ZZ][YY] = -src[ZZ][YY]*dest[YY][YY]*dest[ZZ][ZZ];
756 static gmx_inline void m_inv(gmx_cxx_const matrix src, matrix dest)
758 const real smallreal = (real)1.0e-24;
759 const real largereal = (real)1.0e24;
766 if ((fc <= smallreal) || (fc >= largereal))
768 gmx_fatal(FARGS, "Can not invert matrix, determinant = %e", deter);
771 dest[XX][XX] = c*(src[YY][YY]*src[ZZ][ZZ]-src[ZZ][YY]*src[YY][ZZ]);
772 dest[XX][YY] = -c*(src[XX][YY]*src[ZZ][ZZ]-src[ZZ][YY]*src[XX][ZZ]);
773 dest[XX][ZZ] = c*(src[XX][YY]*src[YY][ZZ]-src[YY][YY]*src[XX][ZZ]);
774 dest[YY][XX] = -c*(src[YY][XX]*src[ZZ][ZZ]-src[ZZ][XX]*src[YY][ZZ]);
775 dest[YY][YY] = c*(src[XX][XX]*src[ZZ][ZZ]-src[ZZ][XX]*src[XX][ZZ]);
776 dest[YY][ZZ] = -c*(src[XX][XX]*src[YY][ZZ]-src[YY][XX]*src[XX][ZZ]);
777 dest[ZZ][XX] = c*(src[YY][XX]*src[ZZ][YY]-src[ZZ][XX]*src[YY][YY]);
778 dest[ZZ][YY] = -c*(src[XX][XX]*src[ZZ][YY]-src[ZZ][XX]*src[XX][YY]);
779 dest[ZZ][ZZ] = c*(src[XX][XX]*src[YY][YY]-src[YY][XX]*src[XX][YY]);
782 static gmx_inline void mvmul(gmx_cxx_const matrix a, const rvec src, rvec dest)
784 dest[XX] = a[XX][XX]*src[XX]+a[XX][YY]*src[YY]+a[XX][ZZ]*src[ZZ];
785 dest[YY] = a[YY][XX]*src[XX]+a[YY][YY]*src[YY]+a[YY][ZZ]*src[ZZ];
786 dest[ZZ] = a[ZZ][XX]*src[XX]+a[ZZ][YY]*src[YY]+a[ZZ][ZZ]*src[ZZ];
790 static gmx_inline void mvmul_ur0(gmx_cxx_const matrix a, const rvec src, rvec dest)
792 dest[ZZ] = a[ZZ][XX]*src[XX]+a[ZZ][YY]*src[YY]+a[ZZ][ZZ]*src[ZZ];
793 dest[YY] = a[YY][XX]*src[XX]+a[YY][YY]*src[YY];
794 dest[XX] = a[XX][XX]*src[XX];
797 static gmx_inline void tmvmul_ur0(gmx_cxx_const matrix a, const rvec src, rvec dest)
799 dest[XX] = a[XX][XX]*src[XX]+a[YY][XX]*src[YY]+a[ZZ][XX]*src[ZZ];
800 dest[YY] = a[YY][YY]*src[YY]+a[ZZ][YY]*src[ZZ];
801 dest[ZZ] = a[ZZ][ZZ]*src[ZZ];
804 static gmx_inline void unitv(const rvec src, rvec dest)
808 linv = gmx_invsqrt(norm2(src));
809 dest[XX] = linv*src[XX];
810 dest[YY] = linv*src[YY];
811 dest[ZZ] = linv*src[ZZ];
814 static gmx_inline void unitv_no_table(const rvec src, rvec dest)
818 linv = 1.0/sqrt(norm2(src));
819 dest[XX] = linv*src[XX];
820 dest[YY] = linv*src[YY];
821 dest[ZZ] = linv*src[ZZ];
824 static void calc_lll(const rvec box, rvec lll)
826 lll[XX] = 2.0*M_PI/box[XX];
827 lll[YY] = 2.0*M_PI/box[YY];
828 lll[ZZ] = 2.0*M_PI/box[ZZ];
831 static gmx_inline real trace(gmx_cxx_const matrix m)
833 return (m[XX][XX]+m[YY][YY]+m[ZZ][ZZ]);
836 static gmx_inline real _divide_err(real a, real b, const char *file, int line)
838 if (fabs(b) <= GMX_REAL_MIN)
840 gmx_fatal(FARGS, "Dividing by zero, file %s, line %d", file, line);
845 static gmx_inline int _mod(int a, int b, char *file, int line)
849 gmx_fatal(FARGS, "Modulo zero, file %s, line %d", file, line);
854 /* Operations on multidimensional rvecs, used e.g. in edsam.c */
855 static gmx_inline void m_rveccopy(int dim, gmx_cxx_const rvec *a, rvec *b)
860 for (i = 0; i < dim; i++)
862 copy_rvec(a[i], b[i]);
866 /*computer matrix vectors from base vectors and angles */
867 static gmx_inline void matrix_convert(matrix box, const rvec vec, rvec angle)
869 svmul(DEG2RAD, angle, angle);
870 box[XX][XX] = vec[XX];
871 box[YY][XX] = vec[YY]*cos(angle[ZZ]);
872 box[YY][YY] = vec[YY]*sin(angle[ZZ]);
873 box[ZZ][XX] = vec[ZZ]*cos(angle[YY]);
874 box[ZZ][YY] = vec[ZZ]
875 *(cos(angle[XX])-cos(angle[YY])*cos(angle[ZZ]))/sin(angle[ZZ]);
876 box[ZZ][ZZ] = sqrt(sqr(vec[ZZ])
877 -box[ZZ][XX]*box[ZZ][XX]-box[ZZ][YY]*box[ZZ][YY]);
880 #define divide_err(a, b) _divide_err((a), (b), __FILE__, __LINE__)
881 #define mod(a, b) _mod((a), (b), __FILE__, __LINE__)