if there are no indexes in the expr or in find then it falls back on 'replace'simplifyAssertEq( a:replaceIndex(a, b), b )
|
${b} = {b}$
GOOD |
time: 0.229000ms stack: size: 7
|
| ||
variance must match in order for the replace to worksimplifyAssertEq( a'_a':replaceIndex(a'^u', b'^u'), a'_a' )
|
${{ a} _a} = {{ a} _a}$
GOOD |
time: 0.894000ms stack: size: 7
|
simplifyAssertEq( a'^a':replaceIndex(a'^b', b'^b'), b'^a' )
|
${{ b} ^a} = {{ b} ^a}$
GOOD |
time: 0.626000ms stack: size: 7
|
simplifyAssertEq( a'^a':replaceIndex(a'^b', b'^b' + c'^b'), b'^a' + c'^a' )
|
${{{ b} ^a} + {{ c} ^a}} = {{{ b} ^a} + {{ c} ^a}}$
GOOD |
time: 1.900000ms stack: size: 8
|
the sum indexes won't use the same symbol, because the symbols are not preserved and instead chosen among unused symbols in the result expressionsimplifyAssertEq( a'^a':replaceIndex(a'^b', b'^bc' * c'_c'), b'^ab' * c'_b' )
|
${{{{{ b} ^a} ^b}} {{{ c} _b}}} = {{{{{ b} ^a} ^b}} {{{ c} _b}}}$
GOOD |
time: 2.068000ms stack: size: 8
|
simplifyAssertEq( a'^a':replaceIndex(a'^b', b'^b' + c'^bc' * d'_c'), b'^a' + c'^ab' * d'_b' )
|
${{{ b} ^a} + {{{{{ c} ^a} ^b}} {{{ d} _b}}}} = {{{ b} ^a} + {{{{{ c} ^a} ^b}} {{{ d} _b}}}}$
GOOD |
time: 3.198000ms stack: size: 9
|
| ||
simplifyAssertEq( a'_ab':replaceIndex(a'_uv', b'_uv'), b'_ab' )
|
${{{ b} _a} _b} = {{{ b} _a} _b}$
GOOD |
time: 0.457000ms stack: size: 7
|
simplifyAssertEq( a'_ab':replaceIndex(a'_uv', b'_vu'), b'_ba' )
|
${{{ b} _b} _a} = {{{ b} _b} _a}$
GOOD |
time: 0.410000ms stack: size: 7
|
simplifyAssertEq( a'_ba':replaceIndex(a'_uv', b'_vu'), b'_ab' )
|
${{{ b} _a} _b} = {{{ b} _a} _b}$
GOOD |
time: 0.477000ms stack: size: 7
|
simplifyAssertEq( a'_ab':replaceIndex(a'_vu', b'_uv'), b'_ba' )
|
${{{ b} _b} _a} = {{{ b} _b} _a}$
GOOD |
time: 0.379000ms stack: size: 7
|
simplifyAssertEq( a'_ba':replaceIndex(a'_vu', b'_uv'), b'_ab' )
|
${{{ b} _a} _b} = {{{ b} _a} _b}$
GOOD |
time: 0.392000ms stack: size: 7
|
| ||
| ||
simplifyAssertEq( (g'^am' * c'_mbc'):replaceIndex( g'^am' * c'_mbc', c'^a_bc' ), c'^a_bc')
|
${{{{ c} ^a} _b} _c} = {{{{ c} ^a} _b} _c}$
GOOD |
time: 1.014000ms stack: size: 7
|
mapping the sum indexsimplifyAssertEq( (g'^am' * c'_mbc'):replaceIndex( g'^an' * c'_nbc', c'^a_bc' ), c'^a_bc')
|
${{{{ c} ^a} _b} _c} = {{{{ c} ^a} _b} _c}$
GOOD |
time: 0.960000ms stack: size: 7
|
mapping the fixed indexessimplifyAssertEq( (g'^am' * c'_mbc'):replaceIndex( g'^im' * c'_mjk', c'^i_jk' ), c'^a_bc')
|
${{{{ c} ^a} _b} _c} = {{{{ c} ^a} _b} _c}$
GOOD |
time: 0.834000ms stack: size: 7
|
mapping bothsimplifyAssertEq( (g'^am' * c'_mbc'):replaceIndex( g'^id' * c'_djk', c'^i_jk' ), c'^a_bc')
|
${{{{ c} ^a} _b} _c} = {{{{ c} ^a} _b} _c}$
GOOD |
time: 0.571000ms stack: size: 7
|
| ||
simplifyAssertEq( (a'_a' + b'_ab' * c'^b'):replaceIndex(a'_u', b'_u'), b'_a' + b'_ab' * c'^b' )
|
${{{ b} _a} + {{{{{ b} _a} _b}} {{{ c} ^b}}}} = {{{ b} _a} + {{{{{ b} _a} _b}} {{{ c} ^b}}}}$
GOOD |
time: 2.052000ms stack: size: 9
|
| ||
TODO this should preserve the order of b_ab -> c_absimplifyAssertEq( (a'_a' + b'_ab' * c'^b'):replaceIndex(b'_uv', c'_uv'), a'_a' + c'_ab' * c'^b' )
|
${{{ a} _a} + {{{{{ c} _a} _b}} {{{ c} ^b}}}} = {{{ a} _a} + {{{{{ c} _a} _b}} {{{ c} ^b}}}}$
GOOD |
time: 2.293000ms stack: size: 9
|
| ||
TODO this should preserve the order of b_ab -> d_absimplifyAssertEq( (a'_a' + b'_ab' * c'^b'):replaceIndex(b'_uv', d'_uv'), a'_a' + d'_ab' * c'^b' )
|
${{{ a} _a} + {{{{{ d} _a} _b}} {{{ c} ^b}}}} = {{{ a} _a} + {{{{{ d} _a} _b}} {{{ c} ^b}}}}$
GOOD |
time: 2.223000ms stack: size: 9
|
| ||
simplifyAssertEq( a'^a_a':replaceIndex(a'^a_a', b'^a_a'), b'^a_a')
|
${{{ b} ^a} _a} = {{{ b} ^a} _a}$
GOOD |
time: 0.429000ms stack: size: 7
|
simplifyAssertEq( a'^a_a':replaceIndex(a'^u_u', b'^u_u'), b'^a_a')
|
${{{ b} ^a} _a} = {{{ b} ^a} _a}$
GOOD |
time: 0.428000ms stack: size: 7
|
| ||
simplifyAssertEq( (a'^a_a' * a'^b_b'):replaceIndex(a'^u_u', b'^u_u'), b'^a_a' * b'^b_b')
|
${{{{{ b} ^a} _a}} {{{{ b} ^b} _b}}} = {{{{{ b} ^a} _a}} {{{{ b} ^b} _b}}}$
GOOD |
time: 1.077000ms stack: size: 8
|
| ||
simplifyAssertEq( a'^a_ab':replaceIndex(a'^a_ab', b'_b'), b'_b' )
|
${{ b} _b} = {{ b} _b}$
GOOD |
time: 0.287000ms stack: size: 7
|
simplifyAssertEq( a'^a_ab':replaceIndex(a'^a_ab', b'_b' + c'_a^a_b'), b'_b' + c'_a^a_b' )
|
${{{ b} _b} + {{{{ c} _a} ^a} _b}} = {{{ b} _b} + {{{{ c} _a} ^a} _b}}$
GOOD |
time: 1.092000ms stack: size: 8
|
| ||
hmm, how to account for this? if the fixed indexes don't match then I still want it to fall back on a plain replace() | ||
simplifyAssertEq( a'_t':replaceIndex(a'_t', b), b)
|
${b} = {b}$
GOOD |
time: 0.150000ms stack: size: 0 |
simplifyAssertEq( a'_t':replaceIndex(a'_t', b'_u'), b'_u')
|
${{ b} _u} = {{ b} _u}$
GOOD |
time: 0.229000ms stack: size: 7
|
but in the event of a regular replace, I still want it to not collide sum indexes | ||
simplifyAssertEq( (a'_t' * b'^a_a'):replaceIndex(a'_t', c'_u' * d'^a_a'), c'_u' * b'^a_a' * d'^b_b')
|
${{{{{{ c} _u}} {{{{ d} ^b} _b}}}} {{{{ b} ^a} _a}}} = {{{{ c} _u}} {{{{ b} ^a} _a}} {{{{ d} ^b} _b}}}$
GOOD |
time: 2.736000ms stack: size: 8
|
what does this mean? the fixed indexes shouldn't have to match ... | ||
if they don't match then assume they are not correlated between the 'find' and 'replace' | ||
| ||
simplifyAssertEq( (a'_ij' + c'_,t' * b'_ij'):replaceIndex( c'_,t', c * d'^i_i' ), a'_ij' + c * d'^a_a' * b'_ij' )
|
${{{{ a} _i} _j} + {{{{{c}} {{{{ d} ^a} _a}}}} {{{{ b} _i} _j}}}} = {{{{ a} _i} _j} + {{{c}} {{{{ d} ^a} _a}} {{{{ b} _i} _j}}}}$
GOOD |
time: 4.168000ms stack: size: 9
|
simplifyAssertEq( (a'_ab' + c'_,t' * b'_ab'):replaceIndex( c'_,t', c * d'^a_a' ), a'_ab' + c * d'^c_c' * b'_ab' )
|
${{{{ a} _a} _b} + {{{{{c}} {{{{ d} ^c} _c}}}} {{{{ b} _a} _b}}}} = {{{{ a} _a} _b} + {{{c}} {{{{ d} ^c} _c}} {{{{ b} _a} _b}}}}$
GOOD |
time: 3.365000ms stack: size: 9
|
| ||
TODO so it looks like, when the replace expression has sum terms *AND* it is an Expression instead of just a TensorRef | ||
that's when the sum indexes aren't replaced correctly | ||
simplifyAssertEq( (a'_ij' + c'_,t' * b'_ij'):replaceIndex( c'_,t', c * d'^i_i' + e'^i_i' ), a'_ij' + (c * d'^a_a' + e'^a_a') * b'_ij' )
|
${{{{ a} _i} _j} + {{{\left({{{{c}} {{{{ d} ^a} _a}}} + {{{ e} ^a} _a}}\right)}} {{{{ b} _i} _j}}}} = {{{{ a} _i} _j} + {{{\left({{{{c}} {{{{ d} ^a} _a}}} + {{{ e} ^a} _a}}\right)}} {{{{ b} _i} _j}}}}$
GOOD |
time: 4.588000ms stack: size: 18
|
| ||
printbr( g'_ij,t':eq(d * (d * b'^k_,i' * g'_kj' + d * b'^k_,j' * g'_ki' + d * b'^k' * c'_ijk' + d * b'^k' * c'_jik' + 2 * d'_,t' * g'_ij' - 2 * d * a * e'_ij') ):replaceIndex( d'_,t', frac(1,3) * (3 * d'_,i' * b'^i' - d * b'^i_,i' - frac(1,2) * d * b'^i' * g'_,i' / g + e * d * a) ) )
|
${{{{ g} _i} _j} _{,t}} = {{{d}} {{\left({{{{d}} {{{{ b} ^k} _{,i}}} {{{{ g} _k} _j}}} + {{{d}} {{{{ b} ^k} _{,j}}} {{{{ g} _k} _i}}} + {{{d}} {{{ b} ^k}} {{{{{ c} _i} _j} _k}}} + {{{d}} {{{ b} ^k}} {{{{{ c} _j} _i} _k}}} + {{{2}} {{{{\frac{1}{3}}} {{\left({{{{3}} {{{ d} _{,a}}} {{{ b} ^a}}}{-{{{d}} {{{{ b} ^a} _{,a}}}}}{-{{\frac{1}{g}} {{{\frac{1}{2}}} {{d}} {{{ b} ^a}} {{{ g} _{,a}}}}}} + {{{e}} {{d}} {{a}}}}\right)}}}} {{{{ g} _i} _j}}}{-{{{2}} {{d}} {{a}} {{{{ e} _i} _j}}}}}\right)}}}$
GOOD |
time: 2.871000ms stack: size: 0 |
| ||
only if extra indexes match. in this case, extra is 'k'. | ||
simplifyAssertEq( (g'_ab,t' * g'_cd,e'):replaceIndex(g'_ij,k', c'_ij'), g'_ab,t' * g'_cd,e')
|
${{{{{{ g} _a} _b} _{,t}}} {{{{{ g} _c} _d} _{,e}}}} = {{{{{{ g} _a} _b} _{,t}}} {{{{{ g} _c} _d} _{,e}}}}$
GOOD |
time: 1.217000ms stack: size: 8
|
simplifyAssertEq( (g'_ab,t' * g'_cd,e'):replaceIndex(g'_ij,t', c'_ij'), c'_ab' * g'_cd,e')
|
${{{{{ c} _a} _b}} {{{{{ g} _c} _d} _{,e}}}} = {{{{{ c} _a} _b}} {{{{{ g} _c} _d} _{,e}}}}$
GOOD |
time: 0.908000ms stack: size: 8
|
| ||
TODO make sure summed indexes aren't matched incorreclty | ||
replaceIndex with more general indexes should worksimplifyAssertEq( a'^a_a':replaceIndex( a'^a_b', b'^a_b'), b'^a_a')
|
${{{ b} ^a} _a} = {{{ b} ^a} _a}$
GOOD |
time: 0.296000ms stack: size: 7
|
replaceIndex with more specific (summed) indexes shouldn'tsimplifyAssertEq( a'^a_b':replaceIndex( a'^a_a', b'^a_a'), a'^a_b')
|
${{{ a} ^a} _b} = {{{ a} ^a} _b}$
GOOD |
time: 0.206000ms stack: size: 7
|
and the two should be discernablesimplifyAssertEq( (a'^a_b' * a'^c_c'):replaceIndex( a'^a_a', b'^a_a'), (a'^a_b' * b'^c_c'))
|
${{{{{ a} ^a} _b}} {{{{ b} ^c} _c}}} = {{{{{ a} ^a} _b}} {{{{ b} ^c} _c}}}$
GOOD |
time: 0.508000ms stack: size: 8
|
same but replace with scalars | ||
in this case, a^a_b's indexes are considered extra since they are not in b as well, so they will be exactly matched in the expression. since no a^a_b exists, it will not match and not replace.simplifyAssertEq( a'^a_a':replaceIndex( a'^a_b', b), a'^a_a')
|
${{{ a} ^a} _a} = {{{ a} ^a} _a}$
GOOD |
time: 0.175000ms stack: size: 7
|
simplifyAssertEq( a'^a_b':replaceIndex( a'^a_a', b), a'^a_b')
|
${{{ a} ^a} _b} = {{{ a} ^a} _b}$
GOOD |
time: 0.235000ms stack: size: 7
|
simplifyAssertEq( (a'^a_b' * a'^c_c'):replaceIndex( a'^a_a', b), (a'^a_b' * b))
|
${{{{{ a} ^a} _b}} {{b}}} = {{{{{ a} ^a} _b}} {{b}}}$
GOOD |
time: 0.516000ms stack: size: 8
|
| ||
printbr( d'_,t':eq( frac(1,6) * ( d * ( 2 * e * a - b'^k_,i' * g'^ij' * g'_jk' - b'^k_,j' * g'_ik' * g'^ij' - b'^k' * g'^ij' * g'_ij,k' ) )):replaceIndex( g'_ij', c'_ij' / d^2 ) )
|
${{ d} _{,t}} = {{{\frac{1}{6}}} {{d}} {{\left({{{{2}} {{e}} {{a}}}{-{{{{{ b} ^k} _{,i}}} {{{{ g} ^i} ^j}} {{\frac{{{ c} _j} _k}{{d}^{2}}}}}}{-{{{{{ b} ^k} _{,j}}} {{\frac{{{ c} _i} _k}{{d}^{2}}}} {{{{ g} ^i} ^j}}}}{-{{{{ b} ^k}} {{{{ g} ^i} ^j}} {{{{{ g} _i} _j} _{,k}}}}}}\right)}}}$
GOOD |
time: 1.748000ms stack: size: 0 |
printbr( d'_,t':eq( 2 * e * a - b'^k_,i' * g'^ij' * g'_jk' - b'^k_,j' * g'_ik' * g'^ij' - b'^k' * g'^ij' * g'_ij,k' ):replaceIndex( g'_ij', c'_ij' / d^2 ) )
|
${{ d} _{,t}} = {{{{{{2}} {{e}} {{a}}}{-{{{{{ b} ^k} _{,i}}} {{{{ g} ^i} ^j}} {{\frac{{{ c} _j} _k}{{d}^{2}}}}}}}{-{{{{{ b} ^k} _{,j}}} {{\frac{{{ c} _i} _k}{{d}^{2}}}} {{{{ g} ^i} ^j}}}}}{-{{{{ b} ^k}} {{{{ g} ^i} ^j}} {{{{{ g} _i} _j} _{,k}}}}}}$
GOOD |
time: 1.643000ms stack: size: 0 |
| ||
simplifyAssertEq( d'_,t':eq( b'^k_,i' * g'^ij' * g'_jk' ):replaceIndex( g'_ij', c'_ij' / d^2 ), d'_,t':eq(b'^k_,i' * g'^ij' * c'_jk' / d^2) )
|
${{{ d} _{,t}} = {{{{{ b} ^k} _{,i}}} {{{{ g} ^i} ^j}} {{\frac{{{ c} _j} _k}{{d}^{2}}}}}} = {{{ d} _{,t}} = {\frac{{{{{ b} ^k} _{,i}}} {{{{ g} ^i} ^j}} {{{{ c} _j} _k}}}{{d}^{2}}}}$
GOOD |
time: 10.281000ms stack: size: 27
|
| ||
simplifyAssertEq( d'_,t':eq( g'^jk' * g'_jk' ):replaceIndex( g'_ij', c'_ij' / d^2 ), d'_,t':eq( g'^jk' * c'_jk' / d^2) )
|
${{{ d} _{,t}} = {{{{{ g} ^j} ^k}} {{\frac{{{ c} _j} _k}{{d}^{2}}}}}} = {{{ d} _{,t}} = {\frac{{{{{ g} ^j} ^k}} {{{{ c} _j} _k}}}{{d}^{2}}}}$
GOOD |
time: 7.246000ms stack: size: 24
|
| ||
does fixed in the find/repl to map into sums in the expr | ||
simplifyAssertEq( a'^i_i':replaceIndex(a'^i_j', b'^i_j'), b'^i_i')
|
${{{ b} ^i} _i} = {{{ b} ^i} _i}$
GOOD |
time: 0.347000ms stack: size: 7
|
| ||
why do neither of these work? because if there are *only* sum-indexes won't match, however if there are extra indexes then it will match. why do we have this constraint again? | ||
internal sum indexes do seem to work in replaceIndex, like A^a_a, but externally shared between two tensors don't: A^a * A_a ... why distinguish? | ||
print( (a'^a' * a'_a'):replaceIndex(a'^a' * a'_a', 2))
| ${{{ a} ^a}} {{{ a} _a}}$ GOOD |
time: 0.125000ms stack: size: 0 |
print( (a'^a' * a'_a'):replaceIndex(a'^a' * a'_a', b'^a' * b'_a'))
| ${{{ a} ^a}} {{{ a} _a}}$ GOOD |
time: 0.138000ms stack: size: 0 |
print( (c'_b' * a'^a' * a'_a'):replaceIndex(c'_b' * a'^a' * a'_a', 2))
| ${{{ c} _b}} {{{ a} ^a}} {{{ a} _a}}$ GOOD |
time: 0.218000ms stack: size: 0 |
| ||
and what about when find/replace has a partial number of fixed indexes | ||
what should this produce? Technically it is invalid match, since the from and to don't have matching fixed indexes. So... assert error?assertError(function() return (a'_a' + b'_ab' * c'^b'):replaceIndex(b'_uv', c'_bv') end )
|
${{ a} _a} + {{{{{ b} _a} _b}} {{{ c} ^b}}}$
BAD /home/chris/Projects/lua/symmath/tests/unit/unit.lua:206: expected an error, but found none stack traceback: /home/chris/Projects/lua/symmath/tests/unit/unit.lua:246: in function [C]: in function 'assert' /home/chris/Projects/lua/symmath/tests/unit/unit.lua:206: in function 'assertError' [string "assertError(function() return (a'_a' + b'_ab'..."]:1: in main chunk /home/chris/Projects/lua/symmath/tests/unit/unit.lua:238: in function [C]: in function 'xpcall' /home/chris/Projects/lua/symmath/tests/unit/unit.lua:237: in function 'exec' replaceIndex.lua:136: in function 'cb' /home/chris/Projects/lua/ext/timer.lua:58: in function 'timer' replaceIndex.lua:6: in main chunk [C]: at 0x5c687d641380 |
time: 0.203000ms stack: size: 0 |