Bernstein basis polynomials: Difference between revisions
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bern ( 1 , 1 , 1 ) --> bern ( 1 , 1 , 1 , 1 )
bern ( 1 , 2 , 6 ) --> bern ( 1 , 1.66666666667 , 3.33333333333 , 6 )</pre>
=={{header|jq}}==
'''Adapted from [[#Wren|Wren]]'''
'''Works with jq and gojq, the C and Go implementations of jq'''
<syntaxhighlight lang=jq>
def toBern2(a):
[a[0], a[0] + a[1] / 2,
a[0] + a[1] + a[2]];
# uses de Casteljau's algorithm
def evalBern2($b; $t):
(1 - $t) as $s
| ($s * $b[0] + $t * $b[1]) as $b01
| ($s * $b[1] + $t * $b[2]) as $b12
| $s * $b01 + $t * $b12;
def toBern3(a):
[a[0],
a[0] + a[1] / 3,
a[0] + a[1] * 2/3 + a[2] / 3,
a[0] + a[1] + a[2] + a[3] ];
# uses de Casteljau's algorithm
def evalBern3($b; $t):
(1 - $t) as $s
| ($s * $b[0] + $t * $b[1]) as $b01
| ($s * $b[1] + $t * $b[2]) as $b12
| ($s * $b[2] + $t * $b[3]) as $b23
| ($s * $b01 + $t * $b12) as $b012
| ($s * $b12 + $t * $b23) as $b123
| $s * $b012 + $t * $b123;
def bern2to3(q):
[q[0],
q[0] / 3 + q[1] * 2/3,
q[1] * 2/3 + q[2] / 3,
q[2]] ;
def pm: [1, 0, 0];
def qm: [1, 2, 3];
def rm: [1, 2, 3, 4];
def pb2: toBern2(pm);
def qb2: toBern2(qm);
"Subprogram(1) examples:",
"mono\(pm) --> bern\(pb2)",
"mono\(qm) --> bern\(qb2)",
"\nSubprogram(2) examples:",
({x: 0.25}
| .y = evalBern2(pb2; .x)
| "p(\(.x)) = \(.y)" ),
({x: 7.5}
| .y = evalBern2(pb2; .x)
| "p(\(.x)) = \(.y)" ),
({x: 0.25}
| .y = evalBern2(qb2; .x)
| "q(\(.x)) = \(.y)" ),
({x: 7.5}
| .y = evalBern2(qb2; .x)
| "q(\(.x)) = \(.y)" ),
"\nSubprogram(3) examples:",
({}
| .pm0 = pm + [0]
| .qm0 = qm + [0]
| .pb3 = toBern3(.pm0)
| .qb3 = toBern3(.qm0)
| .rb3 = toBern3(rm)
| "mono\(.pm0) --> bern\(.pb3)",
"mono\(.qm0) --> bern\(.qb3)",
"mono\(rm) --> bern\(.rb3)",
"\nSubprogram(4) examples:",
( .x = 0.25
| .y = evalBern3(.pb3; .x)
| "p(\(.x)) = \(.y)" ),
( .x = 7.5
| .y = evalBern3(.pb3; .x)
| "p(\(.x)) = \(.y)" ),
( .x = 0.25
| .y = evalBern3(.qb3; .x)
| "q(\(.x)) = \(.y)" ),
( .x = 7.5
| .y = evalBern3(.qb3; .x)
| "q(\(.x)) = \(.y)" ),
( .x = 0.25
| .y = evalBern3(.rb3; .x)
| "r(\(.x)) = \(.y)" ),
( .x = 7.5
| .y = evalBern3(.rb3; .x)
| "r(\(.x)) = \(.y)" ),
"\nSubprogram(5) examples:",
"mono\(pb2) --> bern\( bern2to3(pb2))",
"mono\(qb2) --> bern\( bern2to3(qb2) )"
)
</syntaxhighlight>
{{output}}
<pre>
Subprogram(1) examples:
mono[1,0,0] --> bern[1,1,1]
mono[1,2,3] --> bern[1,2,6]
Subprogram(2) examples:
p(0.25) = 1
p(7.5) = 1
q(0.25) = 1.6875
q(7.5) = 184.75
Subprogram(3) examples:
mono[1,0,0,0] --> bern[1,1,1,1]
mono[1,2,3,0] --> bern[1,1.6666666666666665,3.333333333333333,6]
mono[1,2,3,4] --> bern[1,1.6666666666666665,3.333333333333333,10]
Subprogram(4) examples:
p(0.25) = 1
p(7.5) = 1
q(0.25) = 1.6874999999999998
q(7.5) = 184.75000000000034
r(0.25) = 1.7499999999999998
r(7.5) = 1872.25
Subprogram(5) examples:
mono[1,1,1] --> bern[1,1,1,1]
mono[1,2,6] --> bern[1,1.6666666666666665,3.333333333333333,6]
</pre>
=={{header|Julia}}==
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