Re: FW: lspoly didn't wok when the number of data points equal to the number of coefficients

The lspoly used thru NCL v6.1.2 has some known limitations.
The next release (v6.2.0) will hopefully contain an updated version of
lspoly. Here called 'slatec_lspoly'. The following test script
and the results illustrates the issues.

A comparison to R results follows.

==> NCL script

  x = (/-4.5, -3.2, -1.4/)
  y = (/ 0.7, 2.3, 3.8/)

  n = dimsizes(y)

  print(" ")
  print("===========> 6.1.2 <===========")
  print(" ")

  n1 = n-1 ; max # of coef returned by lspoly
                 ; n1=2
  c = lspoly(x,y, 1, n1) ; up thru 6.1.2
  cc = slatec_lspoly(x,y, 1, n1) ; 6.2.0

  print(c)
  print(cc)

  cx = lspoly(x,y, 1, n) ; n=3 will fail
  print(cx)

  print(" ")
  print("===========> 6.2.0 <===========")
  print(" ")

  cc3 = slatec_lspoly(x,y, 1, n) ; n=3 here
  print(cc3)

*************************************************

(0)
(0) ===========> 6.1.2 <===========
(0)

Variable: c
Type: float
Total Size: 8 bytes
             2 values
Number of Dimensions: 1
Dimensions and sizes: [2]
Coordinates:
(0) 5.268707
(1) 0.9896836

Variable: cc
Type: float
Total Size: 8 bytes
             2 values
Number of Dimensions: 1
Dimensions and sizes: [2]
Coordinates:
(0) 5.268707
(1) 0.9896836

Variable: cx <=== fail
Type: float
Total Size: 12 bytes
             3 values
Number of Dimensions: 1
Dimensions and sizes: [3]
Coordinates:
(0) 1e+20
(1) 1e+20
(2) 1e+20

(0)
(0) ===========> 6.2.0 <===========
(0)

Variable: cc3 match R results
Type: float
Total Size: 12 bytes
             3 values
Number of Dimensions: 1
Dimensions and sizes: [3]
Coordinates:
(0) 4.392307
(1) 0.2435896
(2) -0.1282052

***********************************************
------ Using R --------------------------------
************************************************

> x <- c(-4.5, -3.2, -1.4)
> y <- c(0.7, 2.3, 3.8)
> n <- 1 # degree of polynomial
> result <- lm( y ~ poly( x, n, raw=T))

> result

Call:
lm(formula = y ~ poly(x, n, raw = T))

Coefficients:
         (Intercept) poly(x, n, raw = T)
              5.2687 0.9897

---------------------

> n <- 2 # degree of polynomial
> result <- lm( y ~ poly(x,n, raw=T))
> result

Call:
lm(formula = y ~ poly(x, n, raw = T))

Coefficients:
          (Intercept) poly(x, n, raw = T)1 poly(x, n, raw = T)2
               4.3923 0.2436 -0.1282

On 12/31/13, 8:18 PM, Richard Liang wrote:
> Thanks. Dennis. But the problem remain: Mathematically, if I have 3 points, I can make an second order polynomial to fit these points , in which I should have 3 coefficients.
> Thanks
>
>> Date: Mon, 30 Dec 2013 09:35:37 -0700
>> From: shea@ucar.edu
>> To: richardljy@hotmail.co.uk; ncl-talk@ucar.edu
>> Subject: Re: FW: lspoly didn't wok when the number of data points equal to the number of coefficients
>>
>> The Description section documentation was not correct. It has been changed.
>>
>> On 12/29/13, 9:53 AM, Richard Liang wrote:
>>> Thanks, Dennis
>>> The document said "It is necessary that the number of data points) be greater than or equal to n(the number of coefficients)."
>>> As I understand , for example, if I have 3 points, the max number of coefficients can be 3.
>>> Mathematically, if I have 3 points, I can make an secend order polynomial to fit these points , in which I should have 3 coefficients.
>>>
>>> Best
>>>
>>>> Date: Sat, 28 Dec 2013 08:26:49 -0700
>>>> From: shea@ucar.edu
>>>> To: richardljy@hotmail.co.uk; ncl-talk@ucar.edu
>>>> Subject: Re: FW: lspoly didn't wok when the number of data points equal to the number of coefficients
>>>>
>>>> As noted in the documentation:
>>>>
>>>> n
>>>>
>>>> The number of coefficients desired (i.e., n-1 will be the degree of the
>>>> polynomial). Due to the method used, n should be less than or equal to
>>>> five.
>>>>
>>>> ===
>>>>
>>>> In your case with 3 points, the max number of coefficients would be 2
>>>>
>>>>
>>>> On 12/28/13, 5:01 AM, Richard Liang wrote:
>>>>>
>>>>>
>>>>> From: richardljy@hotmail.co.uk
>>>>> To: ncl-talk@ucar.edu
>>>>> Subject: lspoly didn't wok when the number of data points equal to the number of coefficients
>>>>> Date: Sat, 21 Dec 2013 15:45:08 -0500
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> lspoly didn't wok when the number of data points equal to the number of coefficientsI did the test
>>>>> x = (/-4.5, -3.2, -1.4/)y = (/ 0.7, 2.3, 3.8/)n = 3 c = lspoly(x,y, 1, n) print(c)c will be(0) 1e+20(1) 1e+20(2) 1e+20
>>>>>
>>>>>
>>>>> But if n=2 c will be(0) 5.268707(1) 0.9896836
>>>>> I also did the test in the 4 element array, when n=4, it didn't work. only when n is less than the number of data points
>>>>> Any body help me? thanks
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> ncl-talk mailing list
>>>>> List instructions, subscriber options, unsubscribe:
>>>>> http://mailman.ucar.edu/mailman/listinfo/ncl-talk
>>>>>
>>>
>>>
>
>
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Received on Wed Jan 01 09:13:19 2014