diff --git a/analysis.html b/analysis.html new file mode 100644 index 0000000..233daec --- /dev/null +++ b/analysis.html @@ -0,0 +1,90 @@ + + + + Wave:Data Analysis + + + + +

Geophysical Data Analysis

+

+

+ + + +
+ + + + +
Method +Single Time Series +Multi-series + +
+
+     |
+     |
+     |
+Increasing
+Complexity
+(more
+variables)
+     |
+     |
+     |
+     |
+    \|/
+     V
+
+		 +Statistics +
  • mean, variance, skew, kurtosis +
  • curve-fitting +
  • autocorrelation +
+
  • multiple linear regression +
  • covariance, cross-correlation +
+ +
+Spectrum +
  • Fourier power spectrum (FFT) +
  • Maximum Entropy Method (MEM) +
  • Multi-Taper Method (MTM) +
+
  • Cross-spectrum, phase spectrum +
  • Coherency +
+ +
+Wavelet Transform +
  • Wavelet power spectrum +
  • Sliding FFT; evolutionary spectra +
+
  • Cross-wavelet spectrum, phase +
  • Wavelet coherency +
+ +
+Orthogonal Modes +
  • Singular Spectrum Analysis (SSA) +
+
  • Empirical Orthogonal Functions (EOF) +& Singular Value Decomposition (SVD) +
+
+ + + + + diff --git a/applications.html b/applications.html new file mode 100644 index 0000000..f7b79ef --- /dev/null +++ b/applications.html @@ -0,0 +1,56 @@ + + + + Wave:Applications + + + + +

Wavelet Applications

+ + 

+ + +

+ + 

+

Summary

+ 

+ +

+
¤
Wavelet analysis is a useful addition to methods of +geophysical data analysis.
+
¤
Most helpful in situations of locally-coherent signals, +or non-stationary time series.
+
¤
More research is needed on the perils & pitfalls, +choice of wavelet bases, and on statistical significance. +
+ +

+ + + diff --git a/bams_79_01_0061.ps.zip b/bams_79_01_0061.ps.zip new file mode 100644 index 0000000..b54d3d9 Binary files /dev/null and b/bams_79_01_0061.ps.zip differ diff --git a/favicon.ico b/favicon.ico new file mode 100644 index 0000000..8149549 Binary files /dev/null and b/favicon.ico differ diff --git a/history.html b/history.html new file mode 100644 index 0000000..8c64a3d --- /dev/null +++ b/history.html @@ -0,0 +1,50 @@ + + + + Wave:History + + + +

+ Sketchy History of Wavelet Analysis +

+ + +
1800'sJoseph Fourier + Fourier transform & series; heat diffusion +
+
1909Alfred Haar + rectangular Haar basis functions +
+
1946Dennis Gabor + time-frequency Gabor wavelets; communication theory +
+
1947 + Jean Ville & Hermann Wigner + Wigner-Ville transform; quantum mechanics +
+
1965Cooley & Tukey + Fast Fourier Transform (FFT) +
+
1984Grossman & Morlet + synthesis of theory; geophysics & earthquakes +
+
1985Yves Meyer + family of wavelets for complex phenomena +
+
1988-89 + Stephane Mallat & Ingrid Daubechies + discrete wavelet transform +
+ 

+ +Adapted from ``Signal processing: A historical perspective''
+(http://www.monash.edu.au/cmcm/wavelet/whistory.htm) + + +

+ + + + diff --git a/images/morlet.pro b/images/morlet.pro new file mode 100644 index 0000000..7068f82 --- /dev/null +++ b/images/morlet.pro @@ -0,0 +1,46 @@ + + +FUNCTION psi,k,t,WAVE_PART=wave_part,AMP_PART=amp_part + + wave_part = COMPLEX(COS(k*t),SIN(k*t)) ; exp(ikt) = cos(kt) + i*sin(kt) + amp_part = EXP( -ABS(t)^2/2.) ; exp(-|t|^2/2) + RETURN,wave_part*amp_part ; morlet + +END + + + k0 = 6.0 + time = FINDGEN(401)/20. - 10. + + a = 2 + b = 0 + + morlet = (1./SQRT(a))*PSI(k0,(time - b)/a,WAVE=wave,AMP=amp) + + WINDOW,0,COLOR=256,XSIZE=512,YSIZE=128 + LOADCT,42 + !P.BACKGROUND = 255 + !P.COLOR = 0 + !P.FONT = -1 + !P.CHARSIZE = 1.5 + !X.STYLE = 5 + !Y.STYLE = 5 + !P.MULTI = [0,2,1] + !X.MARGIN = [2,2] + !Y.MARGIN = [0,0] + !Y.RANGE = [MIN(FLOAT(wave))*0.95, MAX(amp)*1.05] + dy = (!Y.CRANGE(1) - !Y.CRANGE(0))/5. + + PLOT,time,FLOAT(morlet), $ + THICK=2,COLOR=50 + XYOUTS,!X.CRANGE(0),!Y.CRANGE(1) - dy,'(a)',CHARSIZE=1.2,ALIGN=0.5 + + PLOT,time,FLOAT(wave)/SQRT(2), $ + COLOR=128,THICK=2 + OPLOT,time,amp,COLOR=208,THICK=2 + OPLOT,time,FLOAT(morlet),THICK=2,LINES=2,COLOR=50 + XYOUTS,!X.CRANGE(0),!Y.CRANGE(1) - dy,'(b)',CHARSIZE=1.2,ALIGN=0.5 + + + +END diff --git a/images/wave_bias_faq.gif b/images/wave_bias_faq.gif new file mode 100644 index 0000000..4d7af17 Binary files /dev/null and b/images/wave_bias_faq.gif differ diff --git a/images/wave_bias_faq.pro b/images/wave_bias_faq.pro new file mode 100644 index 0000000..89dca9f --- /dev/null +++ b/images/wave_bias_faq.pro @@ -0,0 +1,52 @@ + + dt = 1 + n = 128 + t = FINDGEN(n)*dt + t1 = 8 + t2 = 32 + x = SIN(2*!PI*t/t1) + SIN(2*!PI*t/t2) +; x = RANDOMN(s,n) + + f = SPECTRUM(x,dt,PERIOD=fperiod) + w = WAVELET(x,dt,PERIOD=wperiod,DJ=0.125) + gws = TOTAL(ABS(w)^2,1)/n^2 + + WINDOW,XSIZE=240,YSIZE=350 + LOADCT,39 + !P.COLOR = 192 + !P.MULTI = [0,1,3] + !X.STYLE = 9 + !Y.STYLE = 9 + !X.MARGIN = [8,2] + !Y.MARGIN = [4,3] + !Y.MINOR = 1 + !X.TICKLEN = -0.04 + !P.CHARSIZE = 1.75 + xticks = FIX(ALOG(n)/ALOG(2))-1 + xtickv = 2L^(LINDGEN(xticks+1)+1) + xrange = [MAX(xtickv),MIN(xtickv)] + + PLOT,t,x, $ + XRANGE=[0,n], $ + XMINOR=1,XTICKS=xticks-2, $ + XTITLE='Time (days)', $ + TITLE='Time series with two sine waves' + OPLOT,t,x,COLOR=254 + + PLOT,fperiod,f,/XTYPE, $ + XRANGE=xrange,YRANGE=[0,0.5],YTICKS=2, $ + XTICKS=xticks,XTICKV=xtickv, $ + XTITLE='Period (days)',YTITLE='Power', $ + TITLE='Fourier power spectrum' + OPLOT,fperiod,f,PSYM=-4,/NOCLIP,COLOR=254,SYMSIZE=0.75 + + PLOT,wperiod,gws,/XTYPE, $ + XRANGE=xrange,YRANGE=[0,0.25],YTICKS=2, $ + XTICKS=xticks,XTICKV=xtickv, $ + XTITLE='Period (days)',YTITLE='Power', $ + TITLE='Global wavelet spectrum' + OPLOT,wperiod,gws,PSYM=-4,/NOCLIP,COLOR=254,SYMSIZE=0.75 + + TVLCT,r,g,b,/GET + WRITE_GIF,'wave_bias_faq.gif',TVRD(),r,g,b +END diff --git a/index.html b/index.html index 0769794..c55af69 100644 --- a/index.html +++ b/index.html @@ -6,7 +6,7 @@ - + El Nino Wavelet @@ -17,9 +17,9 @@ Christopher Torrence
- Harris, Inc.
- Boulder, Colorado
- chris.torrence[AT]harris[DOT]com + National Snow and Ice Data Center
+ CIRES, CU Boulder
+ chris.torrence[AT]colorado[DOT]edu         Gilbert P. Compo
@@ -29,44 +29,35 @@
-
+
- -
    -
  1. Wavelet Analysis & Monte Carlo -

    -

  2. References & Web Sites -

    -

  3. Interactive Wavelet Plot is no longer available - + + Wavelet Analysis & Monte Carlo

    -

  4. Software for Fortran, IDL, Matlab, and Python + References & Web Sites

    -

  5. Frequently Asked Questions (FAQ) + Interactive Wavelet Plot (no longer available)

    -

  6. Article: - "A Practical Guide to Wavelet Analysis", - C. Torrence and G. P. Compo, 1998. - - Permission to place a copy of this work on this - server has been provided by the - American Meteorological Society.
    - The AMS does not guarantee that the copy provided - here is an accurate copy of the published work.     -

    -

  7. Wavelet Coherency and Phase -
+ Software for Fortran, IDL, Matlab, and Python +

+ Frequently Asked Questions (FAQ) +

+ Article: "A Practical Guide to Wavelet Analysis", + C. Torrence and G. P. Compo, 1998*.
+

+ Abstract & List of Topics
+ Additional information & Errata +
+

+ Wavelet Coherency and Phase

 

-

+
This site is hosted by the Department of Atmospheric and Oceanic Sciences at the University of Colorado Boulder
@@ -84,5 +75,10 @@ Wavelet web page statistics ] --> + * Permission to place a copy of this work on this + server has been provided by the + American Meteorological Society. + The AMS does not guarantee that the copy provided + here is an accurate copy of the published work. diff --git a/plot/data/mauna.dat b/plot/data/mauna.dat new file mode 100644 index 0000000..4bf8863 --- /dev/null +++ b/plot/data/mauna.dat @@ -0,0 +1,475 @@ +$submit + Submit +$dataset +soi +$title +Mauna Loa Carbon Dioxide +$source +Carbon Dioxide Info. Anal. 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+1,16 @@ + + + + + +

Interactive Wavelets in ION +

+ + + + + diff --git a/plot/make_waveplot b/plot/make_waveplot new file mode 100644 index 0000000..c7699ac --- /dev/null +++ b/plot/make_waveplot @@ -0,0 +1,4 @@ +#!/bin/sh -f +gcc -c util.c +gcc -c waveplot.c +gcc waveplot.c util.o -o waveplot.cgi diff --git a/plot/nino3sst.gif b/plot/nino3sst.gif new file mode 100644 index 0000000..60548dc Binary files /dev/null and b/plot/nino3sst.gif differ diff --git a/plot/util.c b/plot/util.c new file mode 100644 index 0000000..358f617 --- /dev/null +++ b/plot/util.c @@ -0,0 +1,152 @@ +#include +#include +#include +#include "util.h" + +#define LF 10 +#define CR 13 + +void getword(char *word, char *line, char stop) { + int x = 0,y; + + for(x=0;((line[x]) && (line[x] != stop));x++) + word[x] = line[x]; + + word[x] = '\0'; + if(line[x]) ++x; + y=0; + + while(line[y++] = line[x++]); +} + +char *makeword(char *line, char stop) { + int x = 0,y; + char *word = (char *) malloc(sizeof(char) * (strlen(line) + 1)); + + for(x=0;((line[x]) && (line[x] != stop));x++) + word[x] = line[x]; + + word[x] = '\0'; + if(line[x]) ++x; + y=0; + + while(line[y++] = line[x++]); + return word; +} + +char *fmakeword(FILE *f, char stop, int *cl) { + int wsize; + char *word; + int ll; + + wsize = 102400; + ll=0; + word = (char *) malloc(sizeof(char) * (wsize + 1)); + + while(1) { + word[ll] = (char)fgetc(f); + if(ll==wsize) { + word[ll+1] = '\0'; + wsize+=102400; + word = (char *)realloc(word,sizeof(char)*(wsize+1)); + } + --(*cl); + if((word[ll] == stop) || (feof(f)) || (!(*cl))) { + if(word[ll] != stop) ll++; + word[ll] = '\0'; + word = (char *) realloc(word, ll+1); + return word; + } + ++ll; + } +} + +char x2c(char *what) { + register char digit; + + digit = (what[0] >= 'A' ? ((what[0] & 0xdf) - 'A')+10 : (what[0] - '0')); + digit *= 16; + digit += (what[1] >= 'A' ? ((what[1] & 0xdf) - 'A')+10 : (what[1] - '0')); + return(digit); +} + +void unescape_url(char *url) { + register int x,y; + + for(x=0,y=0;url[y];++x,++y) { + if((url[x] = url[y]) == '%') { + url[x] = x2c(&url[y+1]); + if (url[x] == CR) x--; /*CT 11/7/97 get rid of Carriage Returns */ + y+=2; + } + } + url[x] = '\0'; +} + +void plustospace(char *str) { + register int x; + + for(x=0;str[x];x++) if(str[x] == '+') str[x] = ' '; +} + +int rind(char *s, char c) { + register int x; + for(x=strlen(s) - 1;x != -1; x--) + if(s[x] == c) return x; + return -1; +} + +int getline(char *s, int n, FILE *f) { + register int i=0; + + while(1) { + s[i] = (char)fgetc(f); + + if(s[i] == CR) + s[i] = fgetc(f); + + if((s[i] == 0x4) || (s[i] == LF) || (i == (n-1))) { + s[i] = '\0'; + return (feof(f) ? 1 : 0); + } + ++i; + } +} + +void send_fd(FILE *f, FILE *fd) +{ + int num_chars=0; + char c; + + while (1) { + c = fgetc(f); + if(feof(f)) + return; + fputc(c,fd); + } +} + +int ind(char *s, char c) { + register int x; + + for(x=0;s[x];x++) + if(s[x] == c) return x; + + return -1; +} + +void escape_shell_cmd(char *cmd) { + register int x,y,l; + + l=strlen(cmd); + for(x=0;cmd[x];x++) { + if(ind("&;`'\"|*?~<>^()[]{}$\\\x0A",cmd[x]) != -1){ + for(y=l+1;y>x;y--) + cmd[y] = cmd[y-1]; + l++; /* length has been increased */ + cmd[x] = '\\'; + x++; /* skip the character */ + } + } +} + diff --git a/plot/util.h b/plot/util.h new file mode 100644 index 0000000..eded336 --- /dev/null +++ b/plot/util.h @@ -0,0 +1,12 @@ + +void getword(char *word, char *line, char stop); +char *makeword(char *line, char stop); +char *fmakeword(FILE *f, char stop, int *cl); +char x2c(char *what); +void unescape_url(char *url); +void plustospace(char *str); +int rind(char *s, char c); +int getline(char *s, int n, FILE *f); +void send_fd(FILE *f, FILE *fd); +int ind(char *s, char c); +void escape_shell_cmd(char *cmd); diff --git a/plot/util.o b/plot/util.o new file mode 100644 index 0000000..f68c597 Binary files /dev/null and b/plot/util.o differ diff --git a/plot/wavemake.idl b/plot/wavemake.idl new file mode 100644 index 0000000..b484e64 --- /dev/null +++ b/plot/wavemake.idl @@ -0,0 +1,4 @@ +.compile waveplot +RESOLVE_ALL +SAVE,FILENAME='waveplot.sav',/ROUTINES,/VERBOSE +EXIT diff --git a/plot/waveopt.html b/plot/waveopt.html new file mode 100644 index 0000000..32dd788 --- /dev/null +++ b/plot/waveopt.html @@ -0,0 +1,220 @@ + + +Wave:Interactive Wavelets:Plot + + + +
+ + +
+ +# str0 = ''+alt+'' +# str2 = ' 

click here for postscript file

' +# IF (N_ELEMENTS(errors) GT 1) THEN FOR i=0,N_ELEMENTS(errors)-1 DO PRINTF,outf,errors(i) +# IF (N_ELEMENTS(errors) LE 1) THEN IF (postscript) THEN PRINTF,outf,str2 ELSE PRINTF,outf,str1 +
+# IF (N_ELEMENTS(errors) GT 1) THEN PRINTF,outf,'

+ +Fig. 1: (a) +# str1 = '.' +# IF (source NE '') THEN str1 = ' (from ' + source + ')' + str1 +# PRINTF,outf,'Time series' +# PRINTF,outf,' of ' + dataset1 + str1 + + +(b) The wavelet power spectrum. + +# str1 = 'The power has been scaled by the global wavelet spectrum (at right).' +# str2 = 'The contour levels are chosen so that 75%, 50%, 25%, and 5% of the wavelet power is above each level, respectively. +# IF (gws) THEN PRINTF,outf,str1 ELSE PRINTF,outf,str2 + +# str1 = 'Cross-hatched region is the cone of influence, where zero padding has reduced the variance.' +# IF (coi1) THEN PRINTF,outf,str1 + +# background_str = 'using a white-noise background spectrum' +# lag1_string = ' lag1=' + ROUND_ANY(lag1) +# IF (lag1 GT 0.0) THEN background_str = 'using a red-noise (autoregressive' + lag1_string + ') background spectrum' +# background_str = [background_str,'using the global wavelet spectrum as the background'] + +# str1 = 'Black contour is the '+ROUND_ANY(siglvl)+'% significance level, ' +# IF (siglvl NE 0) THEN PRINTF,outf,str1+background_str[do_global]+'.' + +# str1 = '(c) The global wavelet power spectrum +# str2 = ' (black line). The dashed line is the '+ROUND_ANY(siglvl)+'% significance level for the global wavelet spectrum, ' +# str2 = str2 + background_str[0] +# IF ((siglvl NE 0) AND (N_ELEMENTS(globalsignif) GT 1)) THEN str1 = str1 + str2 +# PRINTF,outf,str1+'.' + +# IF (N_ELEMENTS(errors) GT 1) THEN PRINTF,outf,'-->' ;comment out the caption + +
+ + +
+ + +
+ +

Wavelet Options:

+# select = (['',' SELECTED']) +# morlet = (mother EQ "Morlet") +# paul = (mother EQ "Paul") +# dog = (mother EQ "DOG") +Wavelet: + +# PRINTF,outf,'' + +Param: +# str1 = '' +
+ +s0/dt = +# str1 = '' +Starting scale, multiple of dt +
+ +    dj = +# str1 = '' +delta-j, scale width +
+ +  Oct = +# str1 = '' + #octaves, max scale is s0 2Oct +
+ +# str1 = '' + Pad with zeroes +
+ +# str1 = '' + Normalize by global wavelet +
+ +Significance level = +# str1 = '' +% (0=don't plot) +

+ +Background spectrum for significance:
+# str1 = ' ' + Global wavelet spectrum, or
+# str1 = ' ' + Red noise (lag1 autoregressive) +

+ +Lag1* = +# str1 = '' +(white noise=0.0) +

+ + +

 + +

Plotting Options:

+ +# str1 = '' +Screen +
+# str1 = '' +Postscript file +
+# str1 = '' +Encapsulated postscript file + +

+ +#; PRINTF,outf,'t0=' + ROUND_ANY(t0) + ',' +#; PRINTF,outf,'dt=' + ROUND_ANY(dt) + '
' +From +# str1 = '' +until +# str1 = '' +
+# PRINTF,outf,'Range = ' + ROUND_ANY(time0) + ' - ' + ROUND_ANY(time1) +
+ +# str1 = '' + Cone of influence +
+ +# str1 = '' + Black & white +
+ +x-label: +# str1 = '' +
+ +y-label: +# str1 = '' +# PRINTF,outf,'' +
+ +Long name: +# str1 = '' +
+ +Short name: +# str1 = '' +
+ +Data units: +# str1 = '' +
+ +Time units: +# str1 = '' + +

+ + +

+ +
+ 
+   +  + +
+
+*The initial Lag1 is estimated from +(a1 + a21/2)/2, where a1 and a2 +are the lag1 and lag2 autocorrelations. +

+[return to Wavelet Analysis homepage] +

+

+ + diff --git a/plot/waveplot.c b/plot/waveplot.c new file mode 100644 index 0000000..2eea0c2 --- /dev/null +++ b/plot/waveplot.c @@ -0,0 +1,122 @@ +#include +#ifndef NO_STDLIB_H +#include +#else +char *getenv(); +#endif +#include +#include +#include +#include +#include +#include +#include + +#define MAX_ENTRIES 2500 + +typedef struct { + char *name; + char *val; +} entry; + +char *makeword(char *line, char stop); +char *fmakeword(FILE *f, char stop, int *len); +char x2c(char *what); +void unescape_url(char *url); +void plustospace(char *str); + +FILE *infp,*outfp; + +main(int argc, char *argv[]) { + entry entries[MAX_ENTRIES]; + register int x,m=0; + int cl; + char data[255],filename[255],file2[255],dir[255],command[255],time_str[20]; + clock_t clocktime; + time_t curtime; + struct tm *loctime; + + printf("Content-type: text/html%c%c",10,10); + + curtime = time (NULL); /* Get the current time. */ + loctime = localtime (&curtime); /* Convert to localtime representation.*/ + strftime (time_str,20,"%H%M%S",loctime); /* Convert to string */ + +/* local directories */ + sprintf(dir, "/export/home/httpd/htdocs/research/wavelets/plot/"); + sprintf(filename, "out/wave_%s", getenv("REMOTE_HOST")); + + if(strcmp(getenv("REQUEST_METHOD"),"POST")) { + goto skip; +/* printf("This script should be referenced using "); + printf("Wavelet Plot.%c",10); + exit(1); +*/ + } + +/* not sure what this does... */ + if(strcmp(getenv("CONTENT_TYPE"),"application/x-www-form-urlencoded")) { + printf("This script can only be used to decode form results. \n"); + exit(1); + } + cl = atoi(getenv("CONTENT_LENGTH")); + +/* decode the form data */ + for(x=0;cl && (!feof(stdin));x++) { + m=x; + entries[x].val = fmakeword(stdin,'&',&cl); + plustospace(entries[x].val); + unescape_url(entries[x].val); + entries[x].name = makeword(entries[x].val,'='); + } + +/* read in options */ + if (strcmp(entries[1].name,"$dataset")==0) { + sprintf(command,"rm -f %s%s.opt",dir,filename); + system(command); + sprintf(file2,"%s%s.dat",dir,filename);} + else + sprintf(file2,"%s%s.opt",dir,filename); + +/* remove previous gif & postscript files */ + sprintf(command,"rm -f %s%s*.gif %s%s*.ps",dir,filename,dir,filename); + system(command); + +/* write out options */ + outfp = fopen(file2,"w"); + for(x=0; x <= m; x++) + fprintf(outfp,"%s\n%s\n",entries[x].name,entries[x].val); + fclose(outfp); + +skip: +/* construct IDL batch file */ + sprintf(file2,"%s%s.idl",dir,filename); + outfp = fopen(file2,"w"); + fprintf(outfp,"CATCH,error_status\n"); + fprintf(outfp,"IF (error_status NE 0) THEN EXIT\n"); + fprintf(outfp,"CD,'%s'\n",dir); + fprintf(outfp,"RESTORE,'waveplot.sav'\n"); + fprintf(outfp,".run waveplot\n"); + fprintf(outfp,"waveplot,'%s','%s'\n",filename,time_str); + fprintf(outfp,"EXIT\n"); + fclose(outfp); + +/* run IDL batch file */ + sprintf(command,"/usr/local/rsi/idl/bin/idl %s",file2); + system(command); + +/* read in HTML & dump to browser */ + sprintf(file2,"%s%s.html",dir,filename); + infp = fopen(file2,"r"); + (void) fgets(data,sizeof(data),infp); + while (!feof(infp)) { + printf("%s\n",data); + (void) fgets(data,sizeof(data),infp); + } + fclose(infp); + +/* automatically remove data & gif files more than 4 days old... */ + sprintf(command,"find %sout -name 'wave_*' -mtime +4 -exec rm {} \\;",dir); + system(command); + +} diff --git a/plot/waveplot.cgi b/plot/waveplot.cgi new file mode 100644 index 0000000..7cd5e3f Binary files /dev/null and b/plot/waveplot.cgi differ diff --git a/plot/waveplot.html b/plot/waveplot.html new file mode 100644 index 0000000..2e90759 --- /dev/null +++ b/plot/waveplot.html @@ -0,0 +1,98 @@ + + + +Wave:Interactive Wavelets:Choose data + + + +
+ + +
+ + + + +
+ +
+Interactive Wavelets
+Please send comments or suggestions to +C.Torrence: torrence@NOSPAMmonsoon.colorado.edu + +		 + +      +   or   + +      + +
+ +
+ +Choose a dataset and press "Submit":

+ + +

+

+ +
+ +		 + +Or enter new data: + + +
Long name: + + +
+
Data source: + + +
+
Short name: + + +
+
Data units: + + +
+
Initial time t0 = + + +
+
time between data values dt = + + +
+
Time units: + + +
Data Values: +

+Data values should be separated by spaces
or returns, +maximum of 2048 values. +

+If this field is left empty, then the default dataset (to the left) +will be used. +

 +
+ + +
+ +
+
+ + + diff --git a/plot/waveplot.pro b/plot/waveplot.pro new file mode 100644 index 0000000..13862cc --- /dev/null +++ b/plot/waveplot.pro @@ -0,0 +1,448 @@ +PRO waveplot,filename,time_str,TEST=test + + errors = ['
 
*** ERROR ***'] + error_status = 0 + CATCH,error_status + IF (error_status NE 0) THEN BEGIN + errors = [errors,'[IDL] '+!ERR_STRING+'
'] + '

' + error_status = 0 + GOTO,oops + ENDIF + +;********************************************************** INITIALIZE + dataset = 'nino3sst' + mother = 'Morlet' + mother_old = '' + param = 6d + pad = 0b + coi = 0b + gws = 0b + tstart = -1E37 + tend = 1E37 + dj = 1./4 + oct = 10 +; lag1 = 0.0 + siglvl = 10 + do_global = 1 + title = ' ' + xtitle = 'Time' + ytitle = 'Period' + t_units = 'years' + eqn_string = '' + units = '' + data = FLTARR(4096) + dataset1 = '' + source = '' + printflag = 0 + do_color = 1b ; color + encapsulated = 0b ; PS or EPSF + window_size = [600,400] + test = KEYWORD_SET(test) + IF (test) THEN BEGIN + filename = 'test' + time_str = '' + ENDIF + +;********************************************************** READ DATAFILES + +;---------------------------------------------------------- Read user files + file_in = filename + flag = 0 + str = '' + number = '' + ON_IOERROR,skip + OPENW,2,'/tmp/wave' + FOR i=0,1 DO BEGIN + link = file_in + '.dat' + readfile = ([file_in+'.dat',filename+'.opt'])(i) + OPENR,1,readfile + READF,1,str + WHILE (str NE 'data') DO BEGIN + READF,1,number + IF (STRMID(str,0,1) EQ '$') THEN BEGIN + temp = number + str_exec = STRMID(str,1,79) + '=temp' + ENDIF ELSE str_exec = str + '=' + STRING(number) + r = EXECUTE(str_exec) + PRINTF,2,readfile+' '+str_exec + IF (EOF(1)) THEN GOTO,skip + READF,1,str + ENDWHILE + IF (i EQ 0) THEN READF,1,data +skip: + IF (STRTRIM(eqn_string,2) NE '') THEN BEGIN ; user-defined eqn + n = 2048 + pi = !PI + t = t0 + dt*FINDGEN(n) +; get rid of multiple statements + cutamp = STRPOS(eqn_string,'&') + IF (cutamp GT 0) THEN eqn_string = STRMID(eqn_string,0,cutamp-1) + r = EXECUTE('data = ' + eqn_string) + ENDIF + n = MAX(WHERE(data NE 0)) + 1 + IF (n EQ 0) THEN BEGIN ;---------------------- Read default data files + IF (flag) THEN BEGIN + errors=[errors,'[IDL] '+!ERR_STRING+''] + '

' + ON_IOERROR, NULL + GOTO,oops + ENDIF + flag = 1 ; should only reach this point once + file_in = 'data/' + dataset + i = -1 ; loop again to read in default.dat and user.opt + ENDIF + CLOSE,1 + ENDFOR +ON_IOERROR,NULL +CLOSE,2 + +;********************************************************** CALCULATE WAVELET + IF (N_ELEMENTS(s0) LT 1) THEN BEGIN + s0 = 2. + coi = 1b + pad = 1b + ENDIF + dj = 0.1 > dj < 1 + IF (dt LT 1E-9) THEN errors = [errors,'dt must be greater than 0.0'] + IF (n LT 5) THEN errors = [errors,'Dataset must have at least 5 points'] + + s0dt = s0*dt ; put back in the delta-t scaling + data = data(0:n-1) + data0 = data + data = data - TOTAL(data)/n ;*** remove the mean + variance = STDEV(data)^2 +; data = data/SQRT(variance) ;*** normalize by standard deviation + time = t0 + dt*FINDGEN(n) + coi1 = KEYWORD_SET(coi) ;*** save a copy + IF (mother_old NE mother) THEN dummy = TEMPORARY(param) ; use default + CASE (mother) OF + 'Morlet': BEGIN + IF (N_ELEMENTS(param) LT 1) THEN param = 6d ; default + param = 2d > param < 20d + param_str = ROUND_ANY(param,SIG=4) + END + 'Paul': BEGIN + IF (N_ELEMENTS(param) LT 1) THEN param = 4d ; default + param = 1d > FIX(param) < 20d + param_str = STRTRIM(FIX(param),2) + END + 'DOG': BEGIN + IF (N_ELEMENTS(param) LT 1) THEN param = 2d ; default + param = 1d > FIX(param) < 20d + param_str = STRTRIM(FIX(param),2) + END + ENDCASE + base2 = FIX(ALOG(n/s0)/ALOG(2) + 0.4999) + oct = 1 > oct < base2 + + IF (N_ELEMENTS(errors) GT 1) THEN BEGIN ;************ E R R O R ********** + errors = [errors,''] + '

' + GOTO,oops + ENDIF + + wave = WAVELET(data,dt, $ ;*** required inputs + S0=s0dt,OCT=oct,DJ=dj, $ ;*** optional inputs + PAD=pad,MOTHER=mother,PARAM=param, $ ;*** optional inputs + SCALE=scale,PERIOD=period,COI=coi) ;*** optional outputs + +;----------------------------------------------------- truncate data + time0 = time[0] + time1 = time[n-1] + IF (tstart EQ -1E37) THEN tstart = time0 + IF (tend EQ 1E37) THEN tend = time1 + tstart = tstart < time(n-5) + tend = time(4) > tend + keep = WHERE((time GE tstart) AND (time LE tend),n) + time = time(keep) + data = data(keep) + data0 = data0(keep) + wave = wave(keep,*) + coi = coi(keep) + +; construct power, global wavelet + power = ABS(wave)^2 + nt = N_ELEMENTS(time) + na = N_ELEMENTS(period) + global_ws = TOTAL(power,1)/nt + +; significance level + IF (N_ELEMENTS(lag1) LT 1) THEN BEGIN + lag1 = A_CORRELATE(data,[1,2]) + lag1 = (lag1(0) + SQRT(lag1(1)))/2. + lag1 = FIX(lag1*100. + 0.5)/100. + ENDIF + lag1 = (-1) > lag1 < 1 + IF (do_global) THEN BEGIN ; use GWS as background + fft_theor = global_ws + ENDIF ELSE BEGIN ; use AR1 as background + freq = dt/period ; normalized frequency + fft_theor = (1-lag1^2)/(1-2*lag1*COS(freq*2*!PI)+lag1^2) ; [Eqn(16)] + fft_theor = variance*fft_theor + ENDELSE + + siglvl = 0 > siglvl < 50 + signif = fft_theor*CHISQR_CVF((0>siglvl<50)/100.,2)/2. + +; check if normalized by GWS + IF (gws) THEN BEGIN + power = TEMPORARY(power)/REBIN(TRANSPOSE(global_ws),nt,na) + signif = signif/global_ws + levels = [0.5,1,2,3] + ENDIF ELSE BEGIN + p1 = power(SORT(power)) + n1 = N_ELEMENTS(p1) +; boxsize = [0.5,0.75,0.95] + boxsize = [0.25,0.5,0.75,0.95] + levels = [p1(boxsize*n1)] + ENDELSE + + labels = levels ; make a copy for MAKE_KEY + +;----------------------------------------------------- Global significance + IF (siglvl GT 0) THEN BEGIN + dof = n;-scale ;*** the -scale corrects for the edge effects + globalsignif = WAVE_SIGNIF(data,dt,scale,1, $ + DOF=dof,LAG1=lag1,SIGLVL=1.-(siglvl<50)/100., $ + MOTHER=mother,PARAM=param) + ENDIF + + + +;********************************************************** START PLOTTING + postscript = (printflag GT 0) + CASE (printflag) OF + 0: BEGIN + SET_PLOT,'Z' + DEVICE,Z_BUFFERING=0,SET_RESOLUTION=window_size + END + 1: BEGIN + SET_PLOT,'ps' + DEVICE,FILE=filename + time_str + '.ps', $ + BITS=8,/COLOR, $ + ISOLATIN=0, $ + /LANDSCAPE, $ + /INCHES,XSIZE=9,XOFFSET=1,YSIZE=6.5,YOFFSET=10 + DEVICE,FONT_INDEX=5,/HELV,/BOLD + END + 2: BEGIN + SET_PLOT,'ps' + DEVICE,FILE=filename + time_str + '.ps', $ + BITS=8,/COLOR, $ + ISOLATIN=0, $ + /ENCAPSULATED, $ + /INCHES,XSIZE=8,YSIZE=6 + DEVICE,FONT_INDEX=5,/HELV,/BOLD + END + ENDCASE + + LOADCT,42*do_color,/SILENT +; LOADCT,49,/SILENT + !P.BACKGROUND = 255b + !P.COLOR = 0 + !X.STYLE = 1 + !Y.STYLE = 1 + !P.FONT = -1 + postscript + !P.CHARSIZE = 0.8 + 0.2*postscript + !P.CHARTHICK = 1 - postscript + !X.TICKLEN = -0.03 + !Y.TICKLEN = -0.01 + + grid = ([1,5])(postscript) + yrange = [MAX(period),MIN(period)] + ytickv = 2.^(INDGEN(oct) + FIX(ALOG(MIN(period))/ALOG(2.))) + xtitle1 = xtitle + ytitle1 = ytitle + ytitle2 = 'Scale' + IF (N_ELEMENTS(dataset1) LT 1) THEN dataset1 = dataset + dataset2 = dataset1 + IF (STRLEN(t_units) GT 0) THEN BEGIN ;*** if "units", then tack onto labels + xtitle1 = xtitle1 + ' (' + t_units + ')' + ytitle1 = ytitle1 + ' (' + t_units + ')' + ytitle2 = ytitle2 + ' (' + t_units + ')' + ENDIF + IF (STRLEN(units) GT 0) THEN BEGIN ;*** if "units", then tack onto labels + dataset2 = dataset1 + ' (' + units + ')' + ENDIF + +;---------------------------------------------------------- Time Series Plot + !P.MULTI = 0 + pcolor = 16*do_color + pos1 = [0.1,0.7,0.7,0.945] + PLOT,time,data0, $ + XSTYLE=9,YSTYLE=9, $ + XRANGE=[tstart,tend], $ + XTITLE=xtitle1,YTITLE=dataset2,/NODATA,YMINOR=2,POSITION=pos1 + OPLOT,time,data0,THICK=1+postscript,COLOR=pcolor + dummy = PLOT_LABEL(0,0.75,/AFTER,NUMBER=1,TITLE=title) + +;---------------------------------------------------------- Wavelet Contour Plot + colors = BYTSCL(FINDGEN(N_ELEMENTS(levels)),TOP=200) + 48 + colors = [208,176,128,80] + IF (do_color) THEN colors = [64,144,180,240] + pos2 = [pos1(0),0.21,pos1(2),0.55] + + CONTOUR,power,time,period,/NOERASE, $ + XRANGE=[tstart,tend], $ + POSITION=pos2, $ + YRANGE=yrange,YSTYLE=1, $ + /YTYPE,/FILL,LEVELS=levels,C_COLORS=colors, $ + YTICKS=N_ELEMENTS(ytickv)-1,YTICKV=ytickv,YMINOR=1, $ + XTITLE=xtitle1,YTITLE=ytitle1 +; XGRIDS=grid,YGRIDS=grid,XTICKLEN=0.5,YTICKLEN=1 +; FIT_IN_WINDOW,postscript,ROTATE(SQRT(power),7),TOP=254,BOTTOM=48 + +;---------------------------------------------------------- signif level + IF (siglvl GT 0) THEN BEGIN + signif = power/REBIN(TRANSPOSE(signif),n,na) + CONTOUR,signif,time,period,/OVERPLOT,LEVEL=1.0,THICK=2+3*postscript + ENDIF + +;---------------------------------------------------------- COI + IF (coi1) THEN BEGIN + color = ([100,4])(do_color) + maxx = MAX(coi) > MAX(period) + POLYFILL,[time(0),time,MAX(time)],[maxx,coi,maxx], $ + ORIEN=+45,SPACING=0.5,COLOR=color,NOCLIP=0,THICK=1 + POLYFILL,[time(0),time,MAX(time)],[maxx,coi,maxx], $ + ORIEN=-45,SPACING=0.5,COLOR=color,NOCLIP=0,THICK=1 + PLOTS,time,coi,COLOR=color,NOCLIP=0,THICK=1 + xx=0.33 & yy=-0.07 + ENDIF + +;---------------------------------------------------------- WPS title + units_sqr = '' + IF (units NE '') THEN units_sqr = ' (' + units + ')!U2!N' +; variance_str = ROUND_ANY(variance,SIG=3) + units_sqr + IF (gws) THEN title1=' (normalized by global)' ELSE title1='' + dummy = PLOT_LABEL(0,1,/AFTER,NUMBER=2, $ + TITLE='Wavelet Power Spectrum'+title1) + +;---------------------------------------------------------- Make color key + pos3 = [pos2[0],pos2(1),pos2[2]-(pos2[2]-pos2[0])/3.,pos2(3)] + PLOT,[0,1],/NODATA,XSTYLE=5,YSTYLE=5,POSITION=pos3,/NOERASE + nlab = N_ELEMENTS(labels) + labels = [0.,labels] +; labels = ROUND_ANY(labels,SIG=2) +; labels(nlab-1) = ' ' + labels(nlab-1) + '!U !Ns!U2!N' + labels = STRING(DOUBLE(labels),FORMAT='(G9.2)') + FOR i=0,N_ELEMENTS(labels)-1 DO BEGIN + expo = STRPOS(labels[i],'E') + IF (expo GE 1) THEN BEGIN + num = STRMID(labels[i],0,expo) + expnt = FIX(STRMID(labels[i],expo+1,255)) + labels[i] = num + 'x10!U' + STRING(expnt) + '!N' + ENDIF + ENDFOR + labels = STRCOMPRESS(labels,/REMOVE_ALL) + colors = [!P.BACKGROUND,colors] +; IF (N_ELEMENTS(boxsize) GT 0) THEN extra = {BOXSIZE:[boxsize,1]-[0,boxsize]} + IF (gws) THEN units2=' (relative to global)' ELSE units2=units_sqr + MAKE_KEY,LABELS=labels,COLORS=colors,_EXTRA=extra, $ + TITLE='Power'+units2 + +;---------------------------------------------------------- Title + XYOUTS,0.84,0.9, $ + '!5INTERACTIVE WAVELET PLOT!X'+$ + '!C!CC. Torrence & G.P. Compo'+$ + '!C!Chttp://paos.colorado.edu/!Cresearch/wavelets/', $ + /NORMAL,ALIGN=0.5,CHARSIZE=0.8 + + +;********************************************************** PLOTTING GLOBAL + pos4 = [0.74,pos2(1),0.95,pos2(3)] + blank = REPLICATE(' ',29) + + PLOT,global_ws,period,/NOERASE, $ + XSTYLE=4,YSTYLE=9, $ + /XTYPE, $ + XTICK_GET=xtick_get, $ + YRANGE=yrange,/YTYPE, $ + YTICKS=N_ELEMENTS(ytickv)-1,YTICKV=ytickv,YTICKNAME=blank, $ + YTICKLEN=-0.02, $ + POSITION=pos4, $ + THICK=2+2*postscript +; xtickname = ROUND_ANY(DOUBLE(xtick_get),SIG=2) + xtickname = STRING(DOUBLE(xtick_get),FORMAT='(G9.2)') + FOR i=0,N_ELEMENTS(xtickname)-1 DO BEGIN + expo = STRPOS(xtickname[i],'E') + IF (expo GE 1) THEN BEGIN + num = STRMID(xtickname[i],0,expo) + expnt = FIX(STRMID(xtickname[i],expo+1,255)) + xtickname[i] = '10!U' + STRING(expnt) + '!N' + ENDIF + ENDFOR + xtickname = STRCOMPRESS(xtickname,/REMOVE_ALL) + AXIS,XAXIS=0,XTICKNAME=xtickname, $ + XTITLE='Variance'+units_sqr + IF ((siglvl GT 0) AND (N_ELEMENTS(globalsignif) GT 1)) THEN BEGIN + OPLOT,globalsignif,period, $ + COLOR=208*do_color, $ + LINES=2-postscript, $ + NOCLIP=0 + ENDIF + dummy = PLOT_LABEL(0,1,/AFTER,NUMBER=3,TITLE='Global Wavelet') + +;********************************************************** PLOTTING MOTHER + I = COMPLEX(0,1) + t0 = (DINDGEN(101)-50)/10. + pname = 'm' + CASE (mother) OF + 'Morlet': BEGIN + psi = EXP(I*param*t0)*EXP(-t0^2/2) + pname = 'k!D0!N' + END + 'Paul': BEGIN + psi = (1-I*t0)^(-param+1) + END + 'DOG': BEGIN + sw = 8*2*!DPI*DINDGEN(101)/100d + psi = FLOAT(FFT(-I^param*(sw^param)*EXP(-sw^2/2),1,/DOUBLE)) + psi = [psi[50:*],psi[0:49]] + END + ENDCASE + keep = WHERE(ABS(psi) GE 0.001*MAX(ABS(psi))) + t0 = t0[keep] + psi = psi[keep] + psiReal = FLOAT(psi) + psiImag = IMAGINARY(COMPLEX(psi)) + mn = MIN([psiReal,psiImag],MAX=mx) + + PLOT,t0,psiImag,/NOERASE,LINES=1, $ + XSTYLE=5,YSTYLE=5, $ + /NOCLIP, $ + YRANGE=[mn,mx], $ + POSITION=[pos2[2]-(pos2[2]-pos2[0])/4.,0.02,pos2[2],pos2[1]-0.06] +; OPLOT,t0,psiImag,LINES=1,COLOR=!P.BACKGROUND + OPLOT,t0,psiReal + title1 = '' + IF (MAX(ABS(psiImag)) GT 0) THEN title1='!C !Dsolid=Real, dashed=Imaginary' + XYOUTS,MAX(t0),0,' ' + mother + ' ' + $ + pname + '=' + param_str + title1,/NOCLIP + + +oops: + CATCH,error_status + IF (error_status NE 0) THEN EXIT + +;********************************************************** OUTPUT OPTIONS .html + OPENR,1,'waveopt.html' + outf = 2 + OPENW,outf,filename + '.html' + WHILE NOT EOF(1) DO BEGIN + READF,1,str + CASE (STRMID(str,0,1)) OF + '#': r = EXECUTE(STRMID(str,1,255)) + ELSE: PRINTF,outf,str + ENDCASE + ENDWHILE + CLOSE,/ALL + +;********************************************************** OUTPUT .gif FILE + IF (N_ELEMENTS(errors) LT 2) THEN BEGIN + IF (postscript) THEN BEGIN + DEVICE,/CLOSE + ENDIF ELSE BEGIN + image1 = TVRD() + WRITE_GIF,filename + time_str + '.gif',image1 + ENDELSE + ENDIF +END diff --git a/plot/waveplot.sav b/plot/waveplot.sav new file mode 100644 index 0000000..26d56b4 Binary files /dev/null and b/plot/waveplot.sav differ diff --git a/plot/waveploteqn.html b/plot/waveploteqn.html new file mode 100644 index 0000000..ce112cf --- /dev/null +++ b/plot/waveploteqn.html @@ -0,0 +1,103 @@ + + + +Wave:Interactive Wavelets:Choose data + + + +

+ + +
+ + + + +
+ +
+Interactive Wavelets
+Please send comments or suggestions to +C.Torrence: torrence@NOSPAMmonsoon.colorado.edu + +		 + +      +   or   + +      + +
+ +
+ +Choose a dataset and press "Submit":

+ + +

+

+ +
+ +		 + +Or enter new data: + + +
Long name: + + +
+
Data source: + + +
+
Short name: + + +
+
Data units: + + +
+
Initial time t0 = + + +
+
time between data values dt = + + +
+
Time units: + + +
+ 
+Enter either an equation or data values:

+

Equation data(t,t0,dt,pi) = +

+

 + + +
Data Values: +

+Data values should be separated
by spaces or returns,
+maximum of 2048 values. +

 +
+ + +
+ +
+
+ + +