<div dir="ltr"><div><div><div><div><div><div>Your det.stub contains:<br> <br>C NCLFORTSTART<br> subroutine TSRGT (eps, n, A, it, C, Kp, Lp) <br> real*8 eps, po, t0<br> integer n, it<br> dimension A(n,n), C(n,n), Kp(n), Lp(n) <br>C NCLEND<br>C NCLFORTSTART<br> <b>FUNCTION</b> DMGT (eps, n, A)<br> integer n<br> real*8 eps, d0<br> <b>dimension </b>A(n,n) <br>C NCLEND<br>---------------------------<br>[1] Comment: A stub file is required <b>*only* </b>for the fortran subroutine(s) invoked from NCL. <br><br> d = DET::<b>DMGT</b>(eps, N, a)<br><br> Hence, the TSRGT stub is not needed. No harm is done... just
not needed<br>-----------------------<br></div>[2] The errors:<br><br></div>The actual fortran function was typed as <b>real*8 </b>[<b>double precision</b>] and had 'A' typed as<b> real*8 [double precision]</b><br><br><b> real*8 Function</b> DMGT(eps, n, A)<br> integer n<br><b> real*8</b> eps, A(n,n)<br><br></div><div>or, equivalently<br><br></div> <b>double precision Function</b> DMGT(eps, n, A)<br></div><div> integer n<br></div><b> double precision </b>eps, A(n,n)<br><br></div>Your stub file had <br> <br> FUNCTION DMGT (eps, n, A)<br> <b>dimension </b>A(n,n) <br><br>When WRAPIT encounters '<b>dimension</b>', it will assign fortran default typing. For a variable starting with 'A' ['a'], that would be <b>real*4</b>. You must be careful about passing consistent argument (variable) types. <br><br>C NCLFORTSTART<br> FUNCTION DMGT (eps, n, A)<br> integer n<br> <b>double precision</b> eps, d0<br> <b>double precision</b> A(n,n)<br>C NCLEND<br></div><div><div><div><div><div><div><div><br>======================<br></div><div>%> WRAPIT det.stub det.f90<br><br></div><div>%> ncl check.ncl_new<br><br></div><div>It still did not return the correct answer. :-(<br><br></div><div>I suggest that you test the 'det.f90' entirely via fortran. I speculate the problem is with the fortran.<br><br></div><div>Good luck<br></div><div><br></div></div></div></div></div></div></div></div><div class="gmail_extra"><br><div class="gmail_quote">On Wed, Jul 11, 2018 at 5:08 AM, Lam Hoang <span dir="ltr"><<a href="mailto:lamhpvn@gmail.com" target="_blank">lamhpvn@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Dear Dennis and all,<div>I tied to use WRAPIT to wrap a fortran code to compute determinant. </div><div>However, I got a warning of "<b style="font-variant-ligatures:no-common-ligatures;color:rgb(0,0,0);font-family:Menlo;font-size:11px">implicit declaration of function "</b><b style="font-variant-ligatures:no-common-ligatures;color:rgb(0,0,0);font-family:Menlo;font-size:11px"><p class="m_5019605089317959032m_3371422303555131722gmail-p1" style="margin:0px;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;line-height:normal;display:inline!important"><span class="m_5019605089317959032m_3371422303555131722gmail-s1" style="font-variant-ligatures:no-common-ligatures"><b>tsrgt_</b></span><b style="font-variant-ligatures:no-common-ligatures">" is invalid in C99" </b><span style="font-variant-ligatures:no-common-ligatures">when I wrap tsrgt.f90 using command:</span></p></b></div><div><span style="font-variant-ligatures:no-common-ligatures;color:rgb(0,0,0);font-family:Menlo;font-size:11px">
<span></span>
<p class="m_5019605089317959032m_3371422303555131722gmail-p1" style="margin:0px;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;line-height:normal;background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_3371422303555131722gmail-s1" style="font-variant-ligatures:no-common-ligatures"><br></span></p><p class="m_5019605089317959032m_3371422303555131722gmail-p1" style="margin:0px;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;line-height:normal;background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_3371422303555131722gmail-s1" style="font-variant-ligatures:no-common-ligatures">WRAPIT det.stub det.f90</span></p>
<br></span></div><div><span style="font-variant-ligatures:no-common-ligatures;color:rgb(0,0,0);font-family:Menlo;font-size:11px">It compiled the code still and generated "det.so" file, however the determinant result was wrong (det=0.0 compared to det=30. using determinant() function) when I run the code in "check.ncl" file</span></div><div><br></div><div><font face="Menlo" color="#000000"><span style="font-size:11px;font-variant-ligatures:no-common-ligatures">I think there is something wrong with subroutine TSRGT() because when </span></font><span style="font-size:11px;font-variant-ligatures:no-common-ligatures;color:rgb(0,0,0);font-family:Menlo">I tried to put subroutine TSRGT() in a separated file and retry to wrap and I still got the above warning of implicit declaration.</span></div><div><font face="Menlo" color="#000000"><span style="font-size:11px;font-variant-ligatures:no-common-ligatures"><br></span></font></div><div><font face="Menlo" color="#000000"><span style="font-size:11px;font-variant-ligatures:no-common-ligatures">Attachments are all my used files. Could you please have a check and tell me what's wrong.</span></font></div><div><font face="Menlo" color="#000000"><span style="font-size:11px;font-variant-ligatures:no-common-ligatures"><br></span></font></div><div><font face="Menlo" color="#000000"><span style="font-size:11px;font-variant-ligatures:no-common-ligatures">Regards,</span></font></div><div><font face="Menlo" color="#000000"><span style="font-size:11px;font-variant-ligatures:no-common-ligatures">Lam</span></font></div><div><br></div></div><div class="HOEnZb"><div class="h5"><div class="gmail_extra"><br><div class="gmail_quote">On Wed, Jul 11, 2018 at 9:43 AM, Lam Hoang <span dir="ltr"><<a href="mailto:lamhpvn@gmail.com" target="_blank">lamhpvn@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Thank you Dennis for your kind support.<div>I will used WRAPIT and fortran code to compute determinant instead.</div><div><br></div><div>Thanks again!</div><span class="m_5019605089317959032HOEnZb"><font color="#888888"><div><br></div><div>Lam</div></font></span></div><div class="m_5019605089317959032HOEnZb"><div class="m_5019605089317959032h5"><div class="gmail_extra"><br><div class="gmail_quote">On Wed, Jul 11, 2018 at 5:34 AM, Dennis Shea <span dir="ltr"><<a href="mailto:shea@ucar.edu" target="_blank">shea@ucar.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div>Yes. The 'determinant' function is taking a <b>very</b> long time for a 41x41 square matrix.<br><br>The underlying fortran code uses a partial-pivoting Gaussian elimination scheme.This method is quick enough for small matrices. Likely, some convergence criterion is not being met. It has been a long time since I have looked at this approach. I speculate that it may behave like N^2 (41^2) time,<br><br>For larger matrices, A better method might be a QR decomposition. Still , this method has issues also.<br><br></div><div>The NCL function<br> <a href="https://test.www.ncl.ucar.edu/Document/Functions/Built-in/solve_linsys.shtml" target="_blank">https://test.www.ncl.ucar.edu/<wbr>Document/Functions/Built-in/so<wbr>lve_linsys.shtml</a><br></div><div>uses LU-decomposition to solve a <br></div><div><br></div><div>The LAPACK numerical analysts have a solid reason for not developing an <b>explicit</b> determinant subroutine. Too many numerical issues.<br>Often, computing the determinant is <em>not</em> what you should be doing
to solve a given problem.
<br><br></div><div>I will update the 'determinant' documentation to reflect some of the above issues.<br><br>===<br></div><div>I suggest calling a fortran or C code that performs an LU decomposition and compute the determinant if that is what you need.<br><br></div><div>Regards<br></div><div><br></div> <br></div><div class="m_5019605089317959032m_-5168134323553592039HOEnZb"><div class="m_5019605089317959032m_-5168134323553592039h5"><div class="gmail_extra"><br><div class="gmail_quote">On Tue, Jul 10, 2018 at 8:20 AM, Lam Hoang <span dir="ltr"><<a href="mailto:lamhpvn@gmail.com" target="_blank">lamhpvn@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Please find the attachment for my "x" matrix <div>I run determinant(x) and still waiting for the result after 2mins</div></div><div class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801HOEnZb"><div class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801h5"><div class="gmail_extra"><br><div class="gmail_quote">On Tue, Jul 10, 2018 at 9:13 PM, Lam Hoang <span dir="ltr"><<a href="mailto:lamhpvn@gmail.com" target="_blank">lamhpvn@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Dear Dennis,<div>uname -a gives:</div><div><br></div><div>
<span></span>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-s1" style="font-variant-ligatures:no-common-ligatures">Darwin MACBooks-MBP 16.7.0 Darwin Kernel Version 16.7.0: Thu Jan 11 22:59:40 PST 2018; root:xnu-3789.73.8~1/RELEASE_X<wbr>86_64 x86_64</span></p>
<br></div><div>and gcc --version gives:</div><div>
<span></span>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-s1" style="font-variant-ligatures:no-common-ligatures"><br></span></p><p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-s1" style="font-variant-ligatures:no-common-ligatures">Configured with: --prefix=/Applications/Xcode.a<wbr>pp/Contents/Developer/usr --with-gxx-include-dir=/usr/in<wbr>clude/c++/4.2.1</span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-s1" style="font-variant-ligatures:no-common-ligatures">Apple LLVM version 8.1.0 (clang-802.0.42)</span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-s1" style="font-variant-ligatures:no-common-ligatures">Target: x86_64-apple-darwin16.7.0</span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-s1" style="font-variant-ligatures:no-common-ligatures">Thread model: posix</span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail-s1" style="font-variant-ligatures:no-common-ligatures">InstalledDir: /Applications/Xcode.app/Conten<wbr>ts/Developer/Toolchains/XcodeD<wbr>efault.xctoolchain/usr/bin</span></p>
<br></div><div><br></div><div>anything looks suspicious?</div><div>Regards,</div><div><br></div></div><div class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628HOEnZb"><div class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628h5"><div class="gmail_extra"><br><div class="gmail_quote">On Tue, Jul 10, 2018 at 8:59 PM, Dennis Shea <span dir="ltr"><<a href="mailto:shea@ucar.edu" target="_blank">shea@ucar.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div><div>Normally, NCL would use an LAPACK code to compute a mathematical quantity. However, LAPACK contains no such subroutine due to issues with accuracy and stability: <br></div><br> <a href="http://www.netlib.org/lapack/faq.html#_are_there_routines_in_lapack_to_compute_determinants" target="_blank">http://www.netlib.org/lapack/f<wbr>aq.html#_are_there_routines_in<wbr>_lapack_to_compute_determinant<wbr>s</a><br><br></div>Really, 'they' (applied mathematicians) do not want people calculating the determinant.<br><div>===<br><br>NCL uses a computer program from:<br><br> An Introduction
to Computational Physics, Tao Pang (Cambridge University
Press,1997).<br>===<br><br></div><div>The use of integer or float values as input should have no effect. All non-double input is promoted to double prior to input to the fortran code used to perform the calculations. <br><br></div><div>I have no idea why you are encountering extremely long execution times. My 6.3.0 [MAC] returns a result more or less immediately. What version of gcc do you have installed? Please send the output from the following:<br><br></div><div>%> uname -a<br><br></div><div>%> gcc --version<br></div><div><br>====<br></div><div>That said: I have tried to calculate the determinant with N=41<br><br></div><div> N = 41<br></div><div> x = random_uniform(0,5,(/N,N/))<br></div><div> d = determinant(x) <wbr> ; VERY fast; instantaneous return value<br></div><div> print(d)<br></div><div><br></div><div>Variable: d<br>Type: float<br>Total Size: 4 bytes<br> 1 values<br>Number of Dimensions: 1<br>Dimensions and sizes: [1]<br>Coordinates: <br>(0) <b>1.767279e+31 <==== ???? I have no idea what the correct answer is<br><br></b></div><div>Ummm, rather large number!!!<br><br>====<br></div><div>I will open a JIRA trouble ticket and ask the core NCL developers if everything looks good.<br><br>====<br></div><div>Again, echoing LAPACK, calculating a determinant has issues.<br><br></div><div>Regards<br></div><div><b></b></div></div><div class="gmail_extra"><br><div class="gmail_quote"><div><div class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519h5">On Tue, Jul 10, 2018 at 6:34 AM, Lam Hoang <span dir="ltr"><<a href="mailto:lamhpvn@gmail.com" target="_blank">lamhpvn@gmail.com</a>></span> wrote:<br></div></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519h5"><div dir="ltr">Dear all,<div>I want to calculate determinant of a 41x41 real (float) matrix. I used determinant() function <div><a href="https://www.ncl.ucar.edu/Document/Functions/Built-in/determinant.shtml" target="_blank">https://www.ncl.ucar.edu/Docum<wbr>ent/Functions/Built-in/determi<wbr>nant.shtml</a></div><div><br></div><div>However it is very slow.</div><div><br></div><div>I try to run the sample in the above page, it's quick. Even if I replace integer values by float values (i.e replace 1 by 1.0, 0 by 0.0 and so on)</div><div>I try to create a 4x4 real matrix, give all members a value of 1.0</div><div>It seems that the determinant() function runs forever and does not return any value</div><div><br></div><div>In the following illustration, a is sample matrix after replacing integer by float values. It takes NCL few seconds to return the value d = 30</div><div><br></div><div>x is new 4x4 matrix created by my new() function, it never gives me any result.</div><div><br></div><div>
<i><span></span>
</i><p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i>Variable: a</i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i>Type: float</i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i>Total Size: 64 bytes</i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-Apple-converted-space"> </span>16 values</i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i>Number of Dimensions: 2</i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i>Dimensions and sizes:<span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-Apple-tab-span" style="white-space:pre-wrap"> </span>[4] x [4]</i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i>Coordinates:<span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-Apple-converted-space"> </span></i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i>(0)<span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-Apple-tab-span" style="white-space:pre-wrap"> </span>d = 30</i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p2" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255);min-height:13px"><i><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"></span><br></i></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i>Variable: x</i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i>Type: float</i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i>Total Size: 64 bytes</i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-Apple-converted-space"> </span>16 values</i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i>Number of Dimensions: 2</i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i>Dimensions and sizes:<span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-Apple-tab-span" style="white-space:pre-wrap"> </span>[4] x [4]</i></span></p>
<p class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-weight:normal;font-stretch:normal;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(0,0,0);background-color:rgb(255,255,255)"><span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-s1" style="font-variant-ligatures:no-common-ligatures"><i>Coordinates:<span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail-Apple-converted-space"> </span></i></span></p>
<br></div><div><br></div><div><br></div><div>Any suggestion or solution for this?</div><div><br></div><div>Regards,</div><div><br></div><div><br></div><div>p/s: I am using NCL v6.3.0 <span class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621HOEnZb"><font color="#888888"><div><div><br></div>-- <br><div class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519m_7738002602217992621m_7003381718460655705gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>Lam Hoang, PhD<br>Chief of Climate Prediction Division,</div><div>Viet Nam National Center of Hydro-Meteorology Forecasting<br>National Hydro-Meteorological Services of Vietnam</div><div><a href="https://maps.google.com/?q=8+Phao+Dai+Lang+street,+Lang+Thuong,+Dong+Da,+Ha+Noi,+Vietnam&entry=gmail&source=g" target="_blank">8 Phao Dai Lang street, Lang Thuong, Dong Da, Ha Noi, Vietnam</a><br><span style="font-size:12.8px">Mob: +84 9 682 34 682 </span><br style="font-size:12.8px"><br></div><div>Associate Researcher,<br>School of Earth, Atmosphere and Environment <br>Monash University, VIC 3800<br>Email: <a href="mailto:lam.hoang@monash.edu" target="_blank">lam.hoang@monash.edu</a></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div>
</div></font></span></div></div></div>
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<br></blockquote></div><br></div>
</blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628m_6770581555639705519gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>Lam Hoang, PhD<br>Chief of Climate Prediction Division,</div><div>Viet Nam National Center of Hydro-Meteorology Forecasting<br>National Hydro-Meteorological Services of Vietnam</div><div><a href="https://maps.google.com/?q=8+Phao+Dai+Lang+street,+Lang+Thuong,+Dong+Da,+Ha+Noi,+Vietnam&entry=gmail&source=g" target="_blank">8 Phao Dai Lang street, Lang Thuong, Dong Da, Ha Noi, Vietnam</a><br><span style="font-size:12.8px">Mob: +84 9 682 34 682 </span><br style="font-size:12.8px"><br></div><div>Associate Researcher,<br>School of Earth, Atmosphere and Environment <br>Monash University, VIC 3800<br>Email: <a href="mailto:lam.hoang@monash.edu" target="_blank">lam.hoang@monash.edu</a></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div>
</div>
</div></div></blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="m_5019605089317959032m_-5168134323553592039m_-2002830973015143801m_-2237439823103543628gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>Lam Hoang, PhD<br>Chief of Climate Prediction Division,</div><div>Viet Nam National Center of Hydro-Meteorology Forecasting<br>National Hydro-Meteorological Services of Vietnam</div><div><a href="https://maps.google.com/?q=8+Phao+Dai+Lang+street,+Lang+Thuong,+Dong+Da,+Ha+Noi,+Vietnam&entry=gmail&source=g" target="_blank">8 Phao Dai Lang street, Lang Thuong, Dong Da, Ha Noi, Vietnam</a><br><span style="font-size:12.8px">Mob: +84 9 682 34 682 </span><br style="font-size:12.8px"><br></div><div>Associate Researcher,<br>School of Earth, Atmosphere and Environment <br>Monash University, VIC 3800<br>Email: <a href="mailto:lam.hoang@monash.edu" target="_blank">lam.hoang@monash.edu</a></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div>
</div>
</div></div></blockquote></div><br></div>
</div></div></blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="m_5019605089317959032m_-5168134323553592039gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>Lam Hoang, PhD<br>Chief of Climate Prediction Division,</div><div>Viet Nam National Center of Hydro-Meteorology Forecasting<br>National Hydro-Meteorological Services of Vietnam</div><div><a href="https://maps.google.com/?q=8+Phao+Dai+Lang+street,+Lang+Thuong,+Dong+Da,+Ha+Noi,+Vietnam&entry=gmail&source=g">8 Phao Dai Lang street, Lang Thuong, Dong Da, Ha Noi, Vietnam</a><br><span style="font-size:12.8px">Mob: +84 9 682 34 682 </span><br style="font-size:12.8px"><br></div><div>Associate Researcher,<br>School of Earth, Atmosphere and Environment <br>Monash University, VIC 3800<br>Email: <a href="mailto:lam.hoang@monash.edu" target="_blank">lam.hoang@monash.edu</a></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div>
</div>
</div></div></blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="m_5019605089317959032gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>Lam Hoang, PhD<br>Chief of Climate Prediction Division,</div><div>Viet Nam National Center of Hydro-Meteorology Forecasting<br>National Hydro-Meteorological Services of Vietnam</div><div><a href="https://maps.google.com/?q=8+Phao+Dai+Lang+street,+Lang+Thuong,+Dong+Da,+Ha+Noi,+Vietnam&entry=gmail&source=g">8 Phao Dai Lang street, Lang Thuong, Dong Da, Ha Noi, Vietnam</a><br><span style="font-size:12.8px">Mob: +84 9 682 34 682 </span><br style="font-size:12.8px"><br></div><div>Associate Researcher,<br>School of Earth, Atmosphere and Environment <br>Monash University, VIC 3800<br>Email: <a href="mailto:lam.hoang@monash.edu" target="_blank">lam.hoang@monash.edu</a></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div>
</div>
</div></div></blockquote></div><br></div>