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# macros.h

    00001 //
    00002 // macros.h
    00003 //
    00004 // Copyright (C) 2001 Edward Valeev
    00005 //
    00006 // Author: Edward Valeev <edward.valeev@chemistry.gatech.edu>
    00007 // Maintainer: EV
    00008 //
    00009 // This file is part of the SC Toolkit.
    00010 //
    00011 // The SC Toolkit is free software; you can redistribute it and/or modify
    00012 // it under the terms of the GNU Library General Public License as published by
    00013 // the Free Software Foundation; either version 2, or (at your option)
    00014 // any later version.
    00015 //
    00016 // The SC Toolkit is distributed in the hope that it will be useful,
    00017 // but WITHOUT ANY WARRANTY; without even the implied warranty of
    00018 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    00019 // GNU Library General Public License for more details.
    00020 //
    00021 // You should have received a copy of the GNU Library General Public License
    00022 // along with the SC Toolkit; see the file COPYING.LIB.  If not, write to
    00023 // the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
    00024 //
    00025 // The U.S. Government is granted a limited license as per AL 91-7.
    00026 //
    00027
    00028 /* True if the integral is nonzero. */
    00029 #define INT_NONZERO(x) (((x)< -1.0e-15)||((x)> 1.0e-15))
    00030
    00031 /* Computes an index to a Cartesian function within a shell given
    00032  * am = total angular momentum
    00033  * i = the exponent of x (i is used twice in the macro--beware side effects)
    00034  * j = the exponent of y
    00035  * formula: (am - i + 1)*(am - i)/2 + am - i - j unless i==am, then 0
    00036  * The following loop will generate indices in the proper order:
    00037  *  cartindex = 0;
    00038  *  for (i=am; i>=0; i--) {
    00039  *    for (j=am-i; j>=0; j--) {
    00040  *      do_it_with(cartindex);
    00041  *      cartindex++;
    00042  *      }
    00043  *    }
    00044  */
    00045 #define INT_CARTINDEX(am,i,j) (((i) == (am))? 0 : (((((am) - (i) + 1)*((am) - (i)))>>1) + (am) - (i) - (j)))
    00046
    00047 /* This sets up the above loop over cartesian exponents as follows
    00048  * FOR_CART(i,j,k,am)
    00049  *   Stuff using i,j,k.
    00050  *   END_FOR_CART
    00051  */
    00052 #define FOR_CART(i,j,k,am) for((i)=(am);(i)>=0;(i)--) {\
    00053                            for((j)=(am)-(i);(j)>=0;(j)--) \
    00054                            { (k) = (am) - (i) - (j);
    00055 #define END_FOR_CART }}
    00056
    00057 /* This sets up a loop over all of the generalized contractions
    00058  * and all of the cartesian exponents.
    00059  * gc is the number of the gen con
    00060  * index is the index within the current gen con.
    00061  * i,j,k are the angular momentum for x,y,z
    00062  * sh is the shell pointer
    00063  */
    00064 #define FOR_GCCART(gc,index,i,j,k,sh)\
    00065     for ((gc)=0; (gc)<(sh)->ncon; (gc)++) {\
    00066     (index)=0;\
    00067     FOR_CART(i,j,k,(sh)->type[gc].am)
    00068
    00069 #define FOR_GCCART_GS(gc,index,i,j,k,sh)\
    00070     for ((gc)=0; (gc)<(sh)->ncontraction(); (gc)++) {\
    00071     (index)=0;\
    00072     FOR_CART(i,j,k,(sh)->am(gc))
    00073
    00074 #define END_FOR_GCCART(index)\
    00075     (index)++;\
    00076     END_FOR_CART\
    00077     }
    00078
    00079 #define END_FOR_GCCART_GS(index)\
    00080     (index)++;\
    00081     END_FOR_CART\
    00082     }
    00083
    00084 /* These are like the above except no index is kept track of. */
    00085 #define FOR_GCCART2(gc,i,j,k,sh)\
    00086     for ((gc)=0; (gc)<(sh)->ncon; (gc)++) {\
    00087     FOR_CART(i,j,k,(sh)->type[gc].am)
    00088
    00089 #define END_FOR_GCCART2\
    00090     END_FOR_CART\
    00091     }
    00092
    00093 /* These are used to loop over shells, given the centers structure
    00094  * and the center index, and shell index. */
    00095 #define FOR_SHELLS(c,i,j) for((i)=0;(i)<(c)->n;i++) {\
    00096                           for((j)=0;(j)<(c)->center[(i)].basis.n;j++) {
    00097 #define END_FOR_SHELLS }}
    00098
    00099 /* Computes the number of Cartesian function in a shell given
    00100  * am = total angular momentum
    00101  * formula: (am*(am+1))/2 + am+1;
    00102  */
    00103 #define INT_NCART(am) ((am>=0)?((((am)+2)*((am)+1))>>1):0)
    00104
    00105 /* Like INT_NCART, but only for nonnegative arguments. */
    00106 #define INT_NCART_NN(am) ((((am)+2)*((am)+1))>>1)
    00107
    00108 /* For a given ang. mom., am, with n cartesian functions, compute the
    00109  * number of cartesian functions for am+1 or am-1
    00110  */
    00111 #define INT_NCART_DEC(am,n) ((n)-(am)-1)
    00112 #define INT_NCART_INC(am,n) ((n)+(am)+2)
    00113
    00114 /* Computes the number of pure angular momentum functions in a shell
    00115  * given am = total angular momentum
    00116  */
    00117 #define INT_NPURE(am) (2*(am)+1)
    00118
    00119 /* Computes the number of functions in a shell given
    00120  * pu = pure angular momentum boolean
    00121  * am = total angular momentum
    00122  */
    00123 #define INT_NFUNC(pu,am) ((pu)?INT_NPURE(am):INT_NCART(am))
    00124
    00125 /* Given a centers pointer and a shell number, this evaluates the
    00126  * pointer to that shell. */
    00127 #define INT_SH(c,s) ((c)->center[(c)->center_num[s]].basis.shell[(c)->shell_num[s]])
    00128
    00129 /* Given a centers pointer and a shell number, get the angular momentum
    00130  * of that shell. */
    00131 #define INT_SH_AM(c,s) ((c)->center[(c)->center_num[s]].basis.shell[(c)->shell_num[s]].type.am)
    00132
    00133 /* Given a centers pointer and a shell number, get pure angular momentum
    00134  * boolean for that shell. */
    00135 #define INT_SH_PU(c,s) ((c)->center[(c)->center_num[s]].basis.shell[(c)->shell_num[s]].type.puream)
    00136
    00137 /* Given a centers pointer, a center number, and a shell number,
    00138  * get the angular momentum of that shell. */
    00139 #define INT_CE_SH_AM(c,a,s) ((c)->center[(a)].basis.shell[(s)].type.am)
    00140
    00141 /* Given a centers pointer, a center number, and a shell number,
    00142  * get pure angular momentum boolean for that shell. */
    00143 #define INT_CE_SH_PU(c,a,s) ((c)->center[(a)].basis.shell[(s)].type.puream)
    00144
    00145 /* Given a centers pointer and a shell number, compute the number
    00146  * of functions in that shell. */
    00147 /* #define INT_SH_NFUNC(c,s) INT_NFUNC(INT_SH_PU(c,s),INT_SH_AM(c,s)) */
    00148 #define INT_SH_NFUNC(c,s) ((c)->center[(c)->center_num[s]].basis.shell[(c)->shell_num[s]].nfunc)
    00149
    00150 /* These macros assist in looping over the unique integrals
    00151  * in a shell quartet.  The exy variables are booleans giving
    00152  * information about the equivalence between shells x and y.  The nx
    00153  * variables give the number of functions in each shell, x. The
    00154  * i,j,k are the current values of the looping indices for shells 1, 2, and 3.
    00155  * The macros return the maximum index to be included in a summation
    00156  * over indices 1, 2, 3, and 4.
    00157  * These macros require canonical integrals.  This requirement comes
    00158  * from the need that integrals of the shells (1 2|2 1) are not
    00159  * used.  The integrals (1 2|1 2) must be used with these macros to
    00160  * get the right nonredundant integrals.
    00161  */
    00162 #define INT_MAX1(n1) ((n1)-1)
    00163 #define INT_MAX2(e12,i,n2) ((e12)?(i):((n2)-1))
    00164 #define INT_MAX3(e13e24,i,n3) ((e13e24)?(i):((n3)-1))
    00165 #define INT_MAX4(e13e24,e34,i,j,k,n4) \
    00166   ((e34)?(((e13e24)&&((k)==(i)))?(j):(k)) \
    00167         :((e13e24)&&((k)==(i)))?(j):(n4)-1)
    00168 /* A note on integral symmetries:
    00169  *  There are 15 ways of having equivalent indices.
    00170  *  There are 8 of these which are important for determining the
    00171  *  nonredundant integrals (that is there are only 8 ways of counting
    00172  *  the number of nonredundant integrals in a shell quartet)
    00173  * Integral type   Integral    Counting Type
    00174  *     1           (1 2|3 4)      1
    00175  *     2           (1 1|3 4)      2
    00176  *     3           (1 2|1 4)       ->1
    00177  *     4           (1 2|3 1)       ->1
    00178  *     5           (1 1|1 4)      3
    00179  *     6           (1 1|3 1)       ->2
    00180  *     7           (1 2|1 1)       ->5
    00181  *     8           (1 1|1 1)      4
    00182  *     9           (1 2|2 4)       ->1
    00183  *    10           (1 2|3 2)       ->1
    00184  *    11           (1 2|3 3)      5
    00185  *    12           (1 1|3 3)      6
    00186  *    13           (1 2|1 2)      7
    00187  *    14           (1 2|2 1)      8    reduces to 7 thru canonicalization
    00188  *    15           (1 2|2 2)       ->5
    00189  */