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parser/*.c: correct the `pwr' derivative

This commit is contained in:
dwarning 2013-06-02 18:20:46 +02:00 committed by rlar
parent c747498324
commit 2dcea6d7c1
1 changed files with 50 additions and 30 deletions
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80
src/spicelib/parser/inpptree.c
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@ -600,49 +600,69 @@ static INPparseNode *PTdifferentiate(INPparseNode * p, int varnum)
pwr(a,b)
p->left: ',' p->left->left: a p->left->right: b
*/
if (p->left->right->type == PT_CONSTANT) {
/*
* f(a,b) = signum(a) * abs(a)^b
* D(f(a,b)) = signum(a) * abs(a)^b * b / a
#define a p->left->left
#define b p->left->right
if (b->type == PT_CONSTANT) {
/* b is a constant
*
* f(a,b) = signum(a) * abs(a)^b
* = signum(a) * exp(b*ln(abs(a)))
* D(f) = signum(a) * D(exp(b*ln(abs(a))))
* = signum(a) * exp(b*ln(abs(a))) * D(b*ln(abs(a)))
* = signum(a) * abs(a)^b * D(b*ln(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(p->left->left, varnum);
arg1 = PTdifferentiate(a, varnum);
newp = mkb(PT_TIMES,
mkf(PTF_SGN, p->left->left),
mkb(PT_DIVIDE, mkb(PT_TIMES,
mkcon(p->left->right->constant),
mkb(PT_POWER,
mkf(PTF_ABS, p->left->left),
mkcon(p->left->right->constant))),
p->left->left));
mkb(PT_TIMES,
mkcon(b->constant),
mkb(PT_POWER,
mkf(PTF_ABS, a),
mkcon(b->constant - 1.0))),
arg1);
#ifdef TRACE
printf("pwr, %s, returns; ", __func__);
printTree(newp);
printf("\n");
#endif
} else {
/*
* f(g) = signum(a) * abs(a)^g
* D(f^g) = signum(a) * D(exp(g*ln(f)))
* = signum(a) * exp(g*ln(f)) * D(g*ln(f))
* = signum(a) * exp(g*ln(f)) * (D(g)*ln(f) + g*D(f)/f)
/* b is a function
*
* f(a,b) = signum(a) * abs(a)^b
* = signum(a) * exp(b*ln(abs(a)))
* D(f) = signum(a) * D(exp(b*ln(abs(a))))
* = signum(a) * exp(b*ln(abs(a))) * D(b*ln(abs(a)))
* = signum(a) * exp(b*ln(abs(a))) * (D(b) * ln(abs(a)) + b * D(ln(abs(a))))
* = signum(a) * exp(b*ln(abs(a))) * (D(b) * ln(abs(a)) + b * 1/abs(a) * D(abs(a)))
* = signum(a) * exp(b*ln(abs(a))) * (D(b) * ln(abs(a)) + b * 1/abs(a) * signum(a)*D(a))
* = signum(a) * exp(b*ln(abs(a))) * (D(b) * ln(abs(a)) + b/a*D(a))
* = signum(a) * exp(b*ln(abs(a))) * D(b) * ln(abs(a) + signum(a) * exp(b*ln(abs(a))) / a * b * D(a)
* = signum(a) * exp(b*ln(abs(a))) * D(b) * ln(abs(a) + abs(a)^(b-1) * b * D(a)
*/
arg1 = PTdifferentiate(p->left->left, varnum);
arg2 = PTdifferentiate(p->left->right, varnum);
newp = mkb(PT_TIMES,
mkf(PTF_SGN, p->left->left),
mkb(PT_TIMES, mkf(PTF_EXP, mkb(PT_TIMES,
p->left->right, mkf(PTF_LN,
p->left->left))),
mkb(PT_PLUS,
mkb(PT_TIMES, p->left->right,
mkb(PT_DIVIDE, arg1, p->left->left)),
mkb(PT_TIMES, arg2, mkf(PTF_LN, p->left->left)))));
arg1 = PTdifferentiate(a, varnum);
arg2 = PTdifferentiate(b, varnum);
newp = mkb(PT_PLUS,
mkb(PT_TIMES,
mkf(PTF_SGN, a),
mkb(PT_TIMES,
mkb(PT_POWER, mkf(PTF_ABS, a), b),
mkb(PT_TIMES, arg2,
mkf(PTF_LN, mkf(PTF_ABS, a))))),
mkb(PT_TIMES,
mkb(PT_TIMES,
mkb(PT_POWER,
mkf(PTF_ABS, a),
mkb(PT_MINUS, b, mkcon(1.0))),
b),
arg1));
}
return mkfirst(newp, p);
#undef b
#undef a
}
default: