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fix derivations in comments

This commit is contained in:
rlar 2016-12-21 21:00:35 +01:00
parent 4f6e89576c
commit de1965e22d
1 changed files with 58 additions and 41 deletions
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99
src/spicelib/parser/inpptree.c
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@ -296,12 +296,28 @@ static INPparseNode *PTdifferentiate(INPparseNode * p, int varnum)
break; break;
case PT_POWER: case PT_POWER:
/*
* ^ : a^b -> |a| math^ b
*
* D(pow(a,b))
* = D(exp(b*log(abs(a))))
* = exp(b*log(abs(a))) * D(b*log(abs(a)))
* = pow(a,b) * (D(b)*log(abs(a)) + b*D(abs(a))/abs(a))
* = pow(a,b) * (D(b)*log(abs(a)) + b*sgn(a)*D(a)/abs(a))
* = pow(a,b) * (D(b)*log(abs(a)) + b*D(a)/a)
*
* when D(b) == 0, then
*
* D(pow(a,b))
* = pow(a,b) * (D(b)*log(abs(a)) + b*D(a)/a)
* = pow(a,b) * b * D(a)/a
* = pow(a,b) * b * D(a)/(signum(a) * abs(a))
* = pow(a, b-1) * b * D(a) / signum(a)
* = pwr(a, b-1) * b * D(a)
*/
#define a p->left #define a p->left
#define b p->right #define b p->right
if (b->type == PT_CONSTANT) { if (b->type == PT_CONSTANT) {
/*
* D(a^C) = C * a^(C-1) * D(a)
*/
arg1 = PTdifferentiate(a, varnum); arg1 = PTdifferentiate(a, varnum);
newp = mkb(PT_TIMES, mkb(PT_TIMES, newp = mkb(PT_TIMES, mkb(PT_TIMES,
@ -310,11 +326,6 @@ static INPparseNode *PTdifferentiate(INPparseNode * p, int varnum)
mkcon(b->constant - 1))), mkcon(b->constant - 1))),
arg1); arg1);
} else { } else {
/*
* D(a^b) = D(exp(b*log(a)))
* = exp(b*log(a)) * D(b*log(a))
* = exp(b*log(a)) * (D(b)*log(a) + b*D(a)/a)
*/
arg1 = PTdifferentiate(a, varnum); arg1 = PTdifferentiate(a, varnum);
arg2 = PTdifferentiate(b, varnum); arg2 = PTdifferentiate(b, varnum);
newp = mkb(PT_TIMES, mkf(PTF_EXP, mkb(PT_TIMES, newp = mkb(PT_TIMES, mkf(PTF_EXP, mkb(PT_TIMES,
@ -551,6 +562,25 @@ static INPparseNode *PTdifferentiate(INPparseNode * p, int varnum)
break; break;
case PTF_POW: case PTF_POW:
/*
* pow : pow(a,b) -> |a| math^ b
*
* D(pow(a,b))
* = D(exp(b*log(abs(a))))
* = exp(b*log(abs(a))) * D(b*log(abs(a)))
* = pow(a,b) * (D(b)*log(abs(a)) + b*D(abs(a))/abs(a))
* = pow(a,b) * (D(b)*log(abs(a)) + b*sgn(a)*D(a)/abs(a))
* = pow(a,b) * (D(b)*log(abs(a)) + b*D(a)/a)
*
* when D(b) == 0, then
*
* D(pow(a,b))
* = pow(a,b) * (D(b)*log(abs(a)) + b*D(a)/a)
* = pow(a,b) * b * D(a)/a
* = pow(a,b) * b * D(a)/(signum(a) * abs(a))
* = pow(a, b-1) * b * D(a) / signum(a)
* = pwr(a, b-1) * b * D(a)
*/
{ {
/* /*
pow(a,b) pow(a,b)
@ -560,9 +590,6 @@ static INPparseNode *PTdifferentiate(INPparseNode * p, int varnum)
#define b p->left->right #define b p->left->right
if (b->type == PT_CONSTANT) { if (b->type == PT_CONSTANT) {
/*
* D(f^C) = C * f^(C-1) * D(f)
*/
arg1 = PTdifferentiate(a, varnum); arg1 = PTdifferentiate(a, varnum);
newp = mkb(PT_TIMES, mkb(PT_TIMES, newp = mkb(PT_TIMES, mkb(PT_TIMES,
@ -576,11 +603,6 @@ static INPparseNode *PTdifferentiate(INPparseNode * p, int varnum)
printf("\n"); printf("\n");
#endif #endif
} else { } else {
/*
* D(f^g) = D(exp(g*log(f)))
* = exp(g*log(f)) * D(g*log(f))
* = exp(g*log(f)) * (D(g)*log(f) + g*D(f)/f)
*/
arg1 = PTdifferentiate(a, varnum); arg1 = PTdifferentiate(a, varnum);
arg2 = PTdifferentiate(b, varnum); arg2 = PTdifferentiate(b, varnum);
newp = mkb(PT_TIMES, mkf(PTF_EXP, mkb(PT_TIMES, newp = mkb(PT_TIMES, mkf(PTF_EXP, mkb(PT_TIMES,
@ -599,6 +621,26 @@ static INPparseNode *PTdifferentiate(INPparseNode * p, int varnum)
break; break;
case PTF_PWR: case PTF_PWR:
/*
* pwr : pwr(a,b) -> signum(a) * (|a| math^ b)
* -> signum(a) * pow(a, b)
*
* Note:
* D(pow(a,b)) = pow(a,b) * (D(b)*log(abs(a)) + b*D(a)/a)
*
* D(pwr(a,b))
* = D(signum(a) * pow(a,b))
* = D(signum(a)) * pow(a,b) + signum(a) * D(pow(a,b))
* = 0 + signum(a) * pow(a,b) * (D(b)*log(abs(a)) + b*D(a)/a)
* = pwr(a,b) * (D(b)*log(abs(a)) + b*D(a)/a)
*
* with D(b) == 0
*
* D(pwr(a,b))
* = pwr(a,b) * b * D(a)/a
* = signum(a) * pow(a,b) * b * D(a)/(signum(a) * abs(a))
* = pow(a, b-1) * b * D(a)
*/
{ {
/* /*
pwr(a,b) pwr(a,b)
@ -607,18 +649,6 @@ static INPparseNode *PTdifferentiate(INPparseNode * p, int varnum)
#define a p->left->left #define a p->left->left
#define b p->left->right #define b p->left->right
if (b->type == PT_CONSTANT) { if (b->type == PT_CONSTANT) {
/* b is a constant
*
* f(a,b) = signum(a) * abs(a)^b
* = signum(a) * exp(b*log(abs(a)))
* D(f) = signum(a) * D(exp(b*log(abs(a))))
* = signum(a) * exp(b*log(abs(a))) * D(b*log(abs(a)))
* = signum(a) * abs(a)^b * D(b*log(abs(a)))
* = signum(a) * abs(a)^b * b * 1/abs(a) * D(abs(a))
* = signum(a) * abs(a)^(b-1) * b * D(abs(a))
* = signum(a) * abs(a)^(b-1) * b * signum(a) * D(a)
* = abs(a)^(b-1) * b * D(a)
*/
arg1 = PTdifferentiate(a, varnum); arg1 = PTdifferentiate(a, varnum);
newp = mkb(PT_TIMES, newp = mkb(PT_TIMES,
@ -634,19 +664,6 @@ static INPparseNode *PTdifferentiate(INPparseNode * p, int varnum)
printf("\n"); printf("\n");
#endif #endif
} else { } else {
/* b is a function
*
* f(a,b) = signum(a) * abs(a)^b
* = signum(a) * exp(b*log(abs(a)))
* D(f) = signum(a) * D(exp(b*log(abs(a))))
* = signum(a) * exp(b*log(abs(a))) * D(b*log(abs(a)))
* = signum(a) * exp(b*log(abs(a))) * (D(b) * log(abs(a)) + b * D(log(abs(a))))
* = signum(a) * exp(b*log(abs(a))) * (D(b) * log(abs(a)) + b * 1/abs(a) * D(abs(a)))
* = signum(a) * exp(b*log(abs(a))) * (D(b) * log(abs(a)) + b * 1/abs(a) * signum(a)*D(a))
* = signum(a) * exp(b*log(abs(a))) * (D(b) * log(abs(a)) + b/a*D(a))
* = signum(a) * exp(b*log(abs(a))) * D(b) * log(abs(a) + signum(a) * exp(b*log(abs(a))) / a * b * D(a)
* = signum(a) * exp(b*log(abs(a))) * D(b) * log(abs(a) + abs(a)^(b-1) * b * D(a)
*/
arg1 = PTdifferentiate(a, varnum); arg1 = PTdifferentiate(a, varnum);
arg2 = PTdifferentiate(b, varnum); arg2 = PTdifferentiate(b, varnum);
newp = mkb(PT_PLUS, newp = mkb(PT_PLUS,