通过Maple中的for循环定义一组函数

Question

在Maple中，我想通过两个for循环来定义一组函数：

printlevel:=2;

# Node coordinates.
N_x:=5;
N_y:=4;
N_elx:=N_x-1;
N_ely:=N_y-1;
h_x:=(x_e-x_s)/N_elx;
h_y:=(y_e-y_s)/N_ely;
x_n:=[seq(x_s+j*h_x,j=0..N_elx)];
y_n:=[seq(y_s+j*h_y,j=0..N_ely)];

# Partition of unity.
for j from 2 by 1 to N_x-1 do
    for k from 2 by 1 to N_y-1 do
        phi[j,k]:=(x,y)->(x-x_n[j-1])*(x-x_n[j+1])*(y-y_n[k-1])*(y-y_n[k+1])/((x_n[j]-x_n[j-1])*(x_n[j]-x_n[j+1])*(y_n[k]-y_n[k-1])*(y_n[k]-y_n[k+1]));
    od;
od;

但是，这会产生[j,k]变化的输出，但不评估x_n[j-1]，x_n[j+1]，y_n[j-1]和y_n[j+1]。因此，功能未正确定义。例如，使用j=4,k=2调用phi[4,2](x,y);函数，我得到输出

phi[4, 2] called with arguments: x, y
#(phi[4,2],1): (x-x_n[j-1])*(x-x_n[j+1])*(y-y_n[k-1])*(y-y_n[k+1])/(x_n[j]-x_n[j-1])/(x_n[j]-x_n[j+1])/(y_n[k]-y_n[k-1])/(y_n[k]-y_n[k+1])
Error, (in phi[4, 2]) invalid subscript selector

而不是所需的输出

$ \ phi_ {4,2}：= \ dfrac {（X-X_3）（X-x_5）（Y-Y_1）（Y-Y_3）} {（X_4-X_3）（X_4-x_5）（Y_2 -y_1）（Y_2-Y_3）} = \ dfrac {（X-\ dfrac {1} {2}）（X-1）（Y-O）（y轴\ dfrac {2} {3}）} {（ \ dfrac {3} {4} - \ dfrac {1} {2}）（\ dfrac {3} {4} -1）/（\ dfrac {1} {3} -0）（\ dfrac {1} { 3} - \ dfrac {2} {3}）} $

我该如何解决这个问题？

Answer 1

宏碁的回答：

如果您想要运算符而不是表达式，请使用函数unapply：

N_x:=5;
N_y:=4;
N_elx:=N_x-1;
N_ely:=N_y-1;
h_x:=(x_e-x_s)/N_elx;
h_y:=(y_e-y_s)/N_ely;
x_n:=[seq(x_s+j*h_x,j=0..N_elx)];
y_n:=[seq(y_s+j*h_y,j=0..N_ely)];

# Partition of unity.
for j from 2 by 1 to N_x-1 do
    for k from 2 by 1 to N_y-1 do
        phi[j,k]:=unapply( (x-x_n[j-1])*(x-x_n[j+1])
                           *(y-y_n[k-1])*(y-y_n[k+1])
                           /((x_n[j]-x_n[j-1])*(x_n[j]-x_n[j+1])
                            *(y_n[k]-y_n[k-1])*(y_n[k]-y_n[k+1])),
                           [x,y]);
    od;
od;