Linear-Constraints-Syntax
Table below lists the commonly used notations in writing linear constraints in non-linear curve fitting and provides few examples:
Simple Linear
=, <, <=, >, >= and +, -, *, / Five relational operators are supported only for simple linear constraints. Nonlinear combination such as a * b >3; 1/b > c + 3; are not supported.
a > b; a + 2 * b >= c * 2 − d; a < b < c; a / 3 < 9;
Initial Values
(i) refers to the initial value of a parameter
xc__2(i)-xc_2 <=0.3; xc__2-xc__2(i) <= 0.3; limit the parameter value of xc__2 within the range of +/- 0.3 of its initial value xc__2(i).
represents all the parameters of a family
A(a) < 1; All amplitudes (A) to be less than 1.
indicates all parameters of a family except the one preceding (e).
A__3 >= 2*A__3(e); ensures A__3 is at least twice as large as all the other amplitudes.
represents a serial of parameter family.
w(2*n-1) < w(2*n), n=1..5; equivalent to: w__1 < w__2; w__3 < w__4; w__5 < w__6; w__7 < w__8; w__9 < w__10;
(ie) refers to initial values of all parameters of a family except the one preceding (e). (ia) refers to initial values of all parameters of a family
xc(ia) - xc(a) <= 0.2; xc(a) - xc(ia) <= 0.2; Limits all peak centers within +/- 0.2 of their corresponding initial values.
parameter name + __n where n denotes the (n-1)th replica. Note that two underscores are used.
Assume that y0 is a parameter and there is a replica. Then the available notations would be: y0 refers to first peak y0__2 refers to first replica
parameter name+_n where n denotes the nth dataset.
Assume that a is a parameter and there are 2 datasets. Then the available notations would be: a refers to fitting parameter a for first dataset a_2 refers to fitting parameter a for second dataset