diff --git a/NAMESPACE b/NAMESPACE
index bf1e8a4ec4fea27995efec3caf11a52ed4066509..072919dafaa86df497c4a62e8cbabcfedf1d4e83 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -14,9 +14,11 @@ export(attributeTones)
export(cwt_morlet)
export(hilbert_extension)
export(mem)
+export(mfft)
export(mfft_anova)
export(mfft_complex)
export(mfft_real)
+export(mmfft)
export(periodogram)
export(powerspectrum.wavelet)
export(reconstruct_mfft)
diff --git a/R/mfft_complex.R b/R/mfft_complex.R
index 366d860c1a137fa8b560f5c47b2d408563ee1ef7..d8fedd769d5dbee36e174ecf0a40613655c07a82 100644
--- a/R/mfft_complex.R
+++ b/R/mfft_complex.R
@@ -9,9 +9,6 @@
#' `mfft` is a wrapper thar redirects the data
#' to `mfft_real` or `mfft_complex` depending on the nature of
#' the input data.
-#' TODO: this needs more work because the two routines
-#' do not yet take exactly the same inputs. In particular, the meaning
-#' the `correction` parameter is not the same
#' TODO: add Laskar reference and say that the correction=0 version
#' corresponds to Laskar's routine.
#' @param xdata The data provided either as a time series (advised), or as a vector.
@@ -20,20 +17,19 @@
#' more precisely angular velocities (2\pi / period), expressed in time-inverse units
#' with the time resolution encoded in `xdata` if the latter is a time series.
#' The computed frequencies are in the range given by minfreq and maxfreq.
-#' @param correction :
-#' The parameter is passed on to `mfft_real` or `mfft_complex` depending on
-#' `xdata` is real or complex, but the meaning of the parameter is not
-#' quite the same for both. This needs to be fixed.
-#' one approach would be to define scalars like 'fft', 'mfft', 'mfft_linear',
-#' 'mfft_second_order_correction'.
+#' @param correction: 0: no frequency correction (equivalent to Laskar); 1 : frequency correction using linear approximation ; 2: frequency correction using sythetic data;
+#' 3: second order-correction using synthetic data (all documented in the Sidlichovsky and Nesvorny reference). Note: 1 is not implemented for complex time series; 4 is
+#' not documented for real time series
#' @param nfreq is the number of frequencies returned, must be smaller that the length of xdata.
+#' @param force_complex : use the complex number implementation even if the time series is real.
#' @return a `mfft_deco` object, based on a data.frame with columns "Freq", "Ampl" and "Phases".
#' note that because of a language glitch (to be fixed), "Freq" actually means "Rate"
#' @author Michel Crucifix for the R code, and David Nesvorny for most of the supporting C code doing the
#' Frequency Modified Fourier transform for Complex Numbers
#' \insertRef{sidlichovsky97aa}{gtseries}
-mfft <- function(xdata, nfreq=30, minfreq=NULL, maxfreq=NULL, correction=1) {
- if (is.complex(xdata)) return(mfft_complex(xdata, nfreq, minfreq, maxfreq, correction)) else
+#' @export mfft
+mfft <- function(xdata, nfreq=15, minfreq=NULL, maxfreq=NULL, correction=1, force_complex = FALSE) {
+ if (is.complex(xdata) || force_complex) return(mfft_complex(xdata, nfreq, minfreq, maxfreq, correction)) else
return(mfft_real(xdata, nfreq, minfreq, maxfreq, correction))
}
@@ -76,10 +72,8 @@ mfft_complex <- function(xdata, nfreq=30, minfreq=NULL, maxfreq=NULL, correctio
xdata <- Re(xdata)
ndata <- length(xdata);
- flag <- correction + 1 # this is an ugly translation towards Sidlichovsky's convention
-
- if (!(flag == 1 || flag == 2 || flag == 3)) stop("flag must be either 1, 2, or 3")
-
+ flag <- c(1,'NA',2,3)[correction+1]
+ if (is.na(flag)) stop('this correction scheme is not implemented for complex time series')
if (is.null(minfreq)){
my_minfreq <- -pi
@@ -108,21 +102,15 @@ mfft_complex <- function(xdata, nfreq=30, minfreq=NULL, maxfreq=NULL, correctio
# if this is input is a real vector, there will be positive and negative frequencies
# corresponding to the same amplitude
- # however, better use mfft_real in this case
OUT <- data.frame(Freq=Freq, Amp=Ampl, Phases=Phase)
- attr(OUT,"class") <- "mfft_deco"
+ class(OUT) <- c("mfft_deco", "data.frame")
attr(OUT,"nfreq") <- nfreq
attr(OUT,"data") <- xdata
return(OUT)
}
-
-
-
-#
-
#
# return(OUTVEC)
# dyn.load('fmft.so')
diff --git a/R/mfft_real.R b/R/mfft_real.R
index f3dceb70c42a162bfb05befff9bcb3c3b5ddb294..b8f60c3f6e7f6536c55045f22366f011b647f08c 100644
--- a/R/mfft_real.R
+++ b/R/mfft_real.R
@@ -337,7 +337,8 @@ mfft_analyse <- function(xdata, nfreq, fast = TRUE, nu = NULL, minfreq=NULL, max
#' @param minfreq,maxfreq If provided, bracket the frequencies to be probed. Note this are
#' more precisely angular velocities (2\pi / period), expressed in time-inverse units
#' with the time resolution encoded in `xdata` if the latter is a time series.
-#' @param correction: 0: no frequency correction (equivalent to Laskar); 1 : frequency correction using linear approximation ; 2: frequency correction using sythetic data (both are documented in the Sidlichovsky and Nesvorny paper.
+#' @param correction: 0: no frequency correction (equivalent to Laskar); 1 : frequency correction using linear approximation ; 2: frequency correction using sythetic data;
+#' 3: second order-correction using synthetic data (all documented in the Sidlichovsky and Nesvorny reference)
#' @param nfreq is the number of frequencies returned, must be smaller that the length of xdata.
#' @param fast (default = TRUE) uses analytical formulations for the crossproducts involving sines and cosines.
#' note: this is not really faster because the bottleneck is actually the goden section search. But more elegant.
@@ -354,6 +355,8 @@ mfft_analyse <- function(xdata, nfreq, fast = TRUE, nu = NULL, minfreq=NULL, max
#' @export mfft_real
mfft_real <- function(xdata, nfreq=5, minfreq=NULL, maxfreq=NULL, correction = 1 , fast=TRUE){
+
+ if (correction == 4) "this correction scheme is currently not implemented for real time series"
N <- length(xdata)
N2 <- N/2.
xdata = stats::as.ts(xdata)
@@ -427,7 +430,7 @@ mfft_real <- function(xdata, nfreq=5, minfreq=NULL, maxfreq=NULL, correction =
# rename for class compatibility
names(OUT) <- c("Freq","Amp","Phases")
- attr(OUT, "class") <- "mfft_deco"
+ class(OUT) <- c("mfft_deco", "data.frame")
attr(OUT, "data") <- xdata
attr(OUT, "nfreq") <- nfreq
return(OUT)
diff --git a/R/mfft_support.R b/R/mfft_support.R
index 662afe43ed4fe692e7bb6b45bcd16236fe924427..cb8dfc7839cb3f555f7e9863593c11e5cfbf7615 100644
--- a/R/mfft_support.R
+++ b/R/mfft_support.R
@@ -52,9 +52,9 @@ plot.mfft_deco <- function (M,periods=FALSE,labels=NULL,...){
plot(abs(M$Freq), abs(M$Amp),'h',ylab="Amplitudes", xlab="", ...)
if (periods) {
frequencies <- pretty(range(M$Freq/(2*pi)))
- labels <- as.character(1/frequencies)
- if (0 %in% frequencies) labels[which(frequencies == 0)] = "∞"
- axis(1, line=3, at=2*pi*frequencies, labels=labels)
+ plabels <- as.character(1/frequencies)
+ if (0 %in% frequencies) plabels[which(frequencies == 0)] = "∞"
+ axis(1, line=3, at=2*pi*frequencies, labels=plabels)
mtext("Rate", 1, 2)
mtext("Period", 1, 4)
} else {
@@ -62,8 +62,8 @@ plot.mfft_deco <- function (M,periods=FALSE,labels=NULL,...){
}
points(abs(M$Freq), abs(M$Amp),'p',...)
if (!is.null(labels)) {
- yshift <- 0.05*range(M$Amp)
- text(M$Freq, M$Amp + yshift, labels, srt=90, pos=4)
+ yshift <- 0.05*diff(range(M$Amp))
+ text(M$Freq, M$Amp, labels, srt=90, , adj=-0.4)
}
}
diff --git a/R/mmfft.R b/R/mmfft.R
new file mode 100644
index 0000000000000000000000000000000000000000..ae445c841d4af782c74cdb4597b38d4a4d1a58f8
--- /dev/null
+++ b/R/mmfft.R
@@ -0,0 +1,72 @@
+#' Moving Modified Fourier Transform
+#'
+#' @param xdata The data provided either as a time series (advised), or as a vector.
+#' may be complex
+#' @param seglength Length of moving segment. Both xdata length and seglenthm are adviced to be a power of 2 (faster)
+#' @param ... passed to mmft
+#' @return a `mmfft` object
+#' @note in the current implementation, the right-hand-side of xdata that is left after an integer division
+#' by seglenth is discarded
+#' @author Michel Crucifix
+#' @export mmfft
+mmfft <- function(xdata, seglength = length(xdata) %/% 16, ...){
+ N <- length(xdata)
+ nsections <- (N %/% seglength)
+ N0 <- nsections * seglength
+# remainder <- seglength - N0
+ xdata0 <- matrix( xdata[1:N0], byrow=FALSE, seglength, nsections)
+ myMfft <- function(x) mfft(x, ...)
+ OUT <- apply(xdata0, 2, myMfft)
+ class(OUT) <- "mmfft"
+ attr(OUT, "nsections") <- nsections
+ attr(OUT, "seglength") <- seglength
+ attr(OUT, "start") <- ifelse(is.ts(xdata), stats::start(xdata), 1)
+ attr(OUT, "deltat") <- ifelse(is.ts(xdata), stats::deltat(xdata), 1)
+ return(OUT)
+}
+
+#' @rdname mmfft
+plot.mmfft <- function(x){
+ freqrange <-
+ c(min(sapply(x, function(xs) min(xs$Freq))),
+ max(sapply(x, function(xs) max(xs$Freq))))
+
+ amprange <-
+ c(min(sapply(x, function(xs) min(xs$Amp))),
+ max(sapply(x, function(xs) max(xs$Amp))))
+
+ print(amprange)
+ amp2lwd <- function(amp){ 3*amp/amprange[2] }
+
+ length <- attr(x, "nsections") *
+ attr(x, "seglength")
+
+ nsec <- length(x)
+ dt <- attr(x,"deltat")
+ tsec <- attr(x,"seglength")*dt
+
+ tstart <- attr(x,"start")
+ tend <- tstart + nsec * tsec
+
+ print(freqrange)
+ print(c(tstart, tend))
+ plot(c(tstart, tend), freqrange, type='n', xlab='Time', ylab='Rate')
+
+ for (iseq in seq(nsec)){
+ trange <- tstart + c(iseq-1,iseq)*tsec
+ obj <- x[[iseq]]
+ nfreq <- length(obj$Freq)
+ print(obj$Amp)
+ lwds <- sapply(obj$Amp, amp2lwd)
+ print(lwds)
+ for (j in seq(nfreq)){
+ lines(trange, rep(obj$Freq[j],2), lwd=lwds[j])
+ }
+ }
+
+}
+
+
+
+
+
diff --git a/man/mfft.Rd b/man/mfft.Rd
index 7fc6a0c4de07b370016a7b3588953e425ce77ca4..5d229ac6cb71dd630d397f61d14ce365ed94b7a9 100644
--- a/man/mfft.Rd
+++ b/man/mfft.Rd
@@ -4,7 +4,14 @@
\alias{mfft}
\title{Modified Fourier transform}
\usage{
-mfft(xdata, nfreq = 30, minfreq = NULL, maxfreq = NULL, correction = 1)
+mfft(
+ xdata,
+ nfreq = 15,
+ minfreq = NULL,
+ maxfreq = NULL,
+ correction = 1,
+ force_complex = FALSE
+)
}
\arguments{
\item{xdata}{The data provided either as a time series (advised), or as a vector.
@@ -17,12 +24,11 @@ more precisely angular velocities (2\pi / period), expressed in time-inverse uni
with the time resolution encoded in `xdata` if the latter is a time series.
The computed frequencies are in the range given by minfreq and maxfreq.}
-\item{correction}{:
-The parameter is passed on to `mfft_real` or `mfft_complex` depending on
-`xdata` is real or complex, but the meaning of the parameter is not
-quite the same for both. This needs to be fixed.
-one approach would be to define scalars like 'fft', 'mfft', 'mfft_linear',
-'mfft_second_order_correction'.}
+\item{force_complex}{: use the complex number implementation even if the time series is real.}
+
+\item{correction:}{0: no frequency correction (equivalent to Laskar); 1 : frequency correction using linear approximation ; 2: frequency correction using sythetic data;
+3: second order-correction using synthetic data (all documented in the Sidlichovsky and Nesvorny reference). Note: 1 is not implemented for complex time series; 4 is
+not documented for real time series}
}
\value{
a `mfft_deco` object, based on a data.frame with columns "Freq", "Ampl" and "Phases".
@@ -38,9 +44,6 @@ by M. Crucifix when the input signal is real.
`mfft` is a wrapper thar redirects the data
to `mfft_real` or `mfft_complex` depending on the nature of
the input data.
-TODO: this needs more work because the two routines
-do not yet take exactly the same inputs. In particular, the meaning
-the `correction` parameter is not the same
TODO: add Laskar reference and say that the correction=0 version
corresponds to Laskar's routine.
}
diff --git a/man/mfft_deco.Rd b/man/mfft_deco.Rd
index 1dd89634da5c781c9812f0c3fc97054b0a6c655c..b85616c3c53aa4e8656de358b086addb15fef44e 100644
--- a/man/mfft_deco.Rd
+++ b/man/mfft_deco.Rd
@@ -15,7 +15,7 @@ mfft_anova(M)
\method{as.data.frame}{mfft_deco}(x)
-\method{plot}{mfft_deco}(M, periods = FALSE, ...)
+\method{plot}{mfft_deco}(M, periods = FALSE, labels = NULL, ...)
\method{lines}{mfft_deco}(M, ...)
@@ -25,6 +25,12 @@ mfft_anova(M)
\item{M}{: mfft_deco object}
\item{sum}{: TRUE if user wants to sum components in the reconstruction}
+
+\item{periods}{if TRUE will add a lower axis with period labels}
+
+\item{labels}{to be set above the frequency peaks. Can be the output of `attributeTone`}
+
+\item{a}{`mfft_deco` object, typically the output of a `mfft` call.}
}
\value{
list of reconstructed components if sum=FALSE, full
diff --git a/man/mfft_real.Rd b/man/mfft_real.Rd
index 3d21180787c2e2ec4210eb562d8e260718272cd7..791d76b3b0be396784f60e261d2a21a9f56d01d4 100644
--- a/man/mfft_real.Rd
+++ b/man/mfft_real.Rd
@@ -25,7 +25,8 @@ with the time resolution encoded in `xdata` if the latter is a time series.}
\item{fast}{(default = TRUE) uses analytical formulations for the crossproducts involving sines and cosines.
note: this is not really faster because the bottleneck is actually the goden section search. But more elegant.}
-\item{correction:}{0: no frequency correction (equivalent to Laskar); 1 : frequency correction using linear approximation ; 2: frequency correction using sythetic data (both are documented in the Sidlichovsky and Nesvorny paper.}
+\item{correction:}{0: no frequency correction (equivalent to Laskar); 1 : frequency correction using linear approximation ; 2: frequency correction using sythetic data;
+3: second order-correction using synthetic data (all documented in the Sidlichovsky and Nesvorny reference)}
}
\value{
a `mfft_deco` object, based on a data.frame with columns "Freq", "Ampl" and "Phases".
diff --git a/man/toneCombinations.Rd b/man/toneCombinations.Rd
index 9be4371e80e38c3fc96b926f7ef938e5162009c6..a716e1b81973d234492c0871128497f73c75ee45 100644
--- a/man/toneCombinations.Rd
+++ b/man/toneCombinations.Rd
@@ -21,7 +21,7 @@ explicit label names, up to order 3 (this could be made more flexible is the fut
}
\examples{
omegas <- c( 0.123, 0.14312, 0.33251, 0.554313)
-print(toneCombinations(omegas)
+print(toneCombinations(omegas))
}
\author{
Michel Crucifix
diff --git a/notebook/Untitled.ipynb b/notebook/Untitled.ipynb
index bc54ce5aa632731c24245aabb2d90e0aff772636..49d8e0fc0d2b8f000444be8c5b894f89fa78df09 100644
--- a/notebook/Untitled.ipynb
+++ b/notebook/Untitled.ipynb
@@ -101,7 +101,7 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 6,
"id": "eddee22d-bfb4-40bb-a009-2f59a1152172",
"metadata": {},
"outputs": [],
@@ -111,7 +111,7 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 7,
"id": "795d94ae-46c9-42a4-96d8-9058ff209056",
"metadata": {},
"outputs": [],
@@ -124,50 +124,212 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 8,
"id": "14b06778-5775-4bfc-9f08-a16c9c508c3b",
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "plot without title"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 420,
+ "width": 420
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
"source": [
"plot(M, labels=tones)"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 9,
"id": "612ded56-53be-400c-971a-0fa9b1b762bf",
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<style>\n",
+ ".list-inline {list-style: none; margin:0; padding: 0}\n",
+ ".list-inline>li {display: inline-block}\n",
+ ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
+ "</style>\n",
+ "<ol class=list-inline><li>2.64933608960962</li><li>2.80151358146866</li><li>3.31110959465901</li><li>3.2802406825405</li><li>3.26211771637853</li><li>2.69742349946146</li></ol>\n"
+ ],
+ "text/latex": [
+ "\\begin{enumerate*}\n",
+ "\\item 2.64933608960962\n",
+ "\\item 2.80151358146866\n",
+ "\\item 3.31110959465901\n",
+ "\\item 3.2802406825405\n",
+ "\\item 3.26211771637853\n",
+ "\\item 2.69742349946146\n",
+ "\\end{enumerate*}\n"
+ ],
+ "text/markdown": [
+ "1. 2.64933608960962\n",
+ "2. 2.80151358146866\n",
+ "3. 3.31110959465901\n",
+ "4. 3.2802406825405\n",
+ "5. 3.26211771637853\n",
+ "6. 2.69742349946146\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ "[1] 2.649336 2.801514 3.311110 3.280241 3.262118 2.697423"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"Astro$omepre"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 10,
"id": "00b4c33b-caf2-443c-b1de-cccd7f6773da",
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<style>\n",
+ ".list-inline {list-style: none; margin:0; padding: 0}\n",
+ ".list-inline>li {display: inline-block}\n",
+ ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
+ "</style>\n",
+ "<ol class=list-inline><li>'p1'</li><li>'p2'</li><li>'p3'</li><li>'p4'</li><li>'p5'</li><li>'p6'</li><li>'o1'</li><li>'o2'</li><li>'o3'</li><li>'o4'</li><li>'o5'</li><li>'o6'</li></ol>\n"
+ ],
+ "text/latex": [
+ "\\begin{enumerate*}\n",
+ "\\item 'p1'\n",
+ "\\item 'p2'\n",
+ "\\item 'p3'\n",
+ "\\item 'p4'\n",
+ "\\item 'p5'\n",
+ "\\item 'p6'\n",
+ "\\item 'o1'\n",
+ "\\item 'o2'\n",
+ "\\item 'o3'\n",
+ "\\item 'o4'\n",
+ "\\item 'o5'\n",
+ "\\item 'o6'\n",
+ "\\end{enumerate*}\n"
+ ],
+ "text/markdown": [
+ "1. 'p1'\n",
+ "2. 'p2'\n",
+ "3. 'p3'\n",
+ "4. 'p4'\n",
+ "5. 'p5'\n",
+ "6. 'p6'\n",
+ "7. 'o1'\n",
+ "8. 'o2'\n",
+ "9. 'o3'\n",
+ "10. 'o4'\n",
+ "11. 'o5'\n",
+ "12. 'o6'\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ " [1] \"p1\" \"p2\" \"p3\" \"p4\" \"p5\" \"p6\" \"o1\" \"o2\" \"o3\" \"o4\" \"o5\" \"o6\""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"astroFreqnames"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 11,
"id": "bf2945fc-cbe0-48c4-85a2-a11cd8403003",
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<style>\n",
+ ".list-inline {list-style: none; margin:0; padding: 0}\n",
+ ".list-inline>li {display: inline-block}\n",
+ ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
+ "</style>\n",
+ "<ol class=list-inline><li>''</li><li>'-p1 + p3'</li><li>'o1'</li><li>'-p3 + p1 + o1'</li><li>'-p1 + p4'</li><li>'p1'</li><li>'-p1 + p2'</li><li>'-p2 + p3'</li><li>'p2'</li><li>'-p4 + p1 + o1'</li></ol>\n"
+ ],
+ "text/latex": [
+ "\\begin{enumerate*}\n",
+ "\\item ''\n",
+ "\\item '-p1 + p3'\n",
+ "\\item 'o1'\n",
+ "\\item '-p3 + p1 + o1'\n",
+ "\\item '-p1 + p4'\n",
+ "\\item 'p1'\n",
+ "\\item '-p1 + p2'\n",
+ "\\item '-p2 + p3'\n",
+ "\\item 'p2'\n",
+ "\\item '-p4 + p1 + o1'\n",
+ "\\end{enumerate*}\n"
+ ],
+ "text/markdown": [
+ "1. ''\n",
+ "2. '-p1 + p3'\n",
+ "3. 'o1'\n",
+ "4. '-p3 + p1 + o1'\n",
+ "5. '-p1 + p4'\n",
+ "6. 'p1'\n",
+ "7. '-p1 + p2'\n",
+ "8. '-p2 + p3'\n",
+ "9. 'p2'\n",
+ "10. '-p4 + p1 + o1'\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ " [1] \"\" \"-p1 + p3\" \"o1\" \"-p3 + p1 + o1\"\n",
+ " [5] \"-p1 + p4\" \"p1\" \"-p1 + p2\" \"-p2 + p3\" \n",
+ " [9] \"p2\" \"-p4 + p1 + o1\""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"tones"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 12,
"id": "509faec7-a7b0-44dc-9ca0-ddd2aba207d3",
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " [1] 0.000000 0.066177 0.153249 0.087072 0.063090 0.264934 0.015218 0.050960\n",
+ " [9] 0.280151 0.090159\n",
+ " [1] -Inf 94.94 41.00 72.16 99.59 23.72 412.88 123.30 22.43 69.69\n"
+ ]
+ }
+ ],
"source": [
"print(M$Freq,5)\n",
"print(2*pi/M$Freq, 4)"
@@ -175,20 +337,50 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 13,
"id": "69c4cf20-605e-402c-8d63-c2fab9f01679",
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " p1 p2 p3 p4 p5 p6 o1 o2 o3 o4 \n",
+ "0.26493 0.28015 0.33111 0.32802 0.32621 0.26974 0.15325 0.15815 0.11719 0.15506 \n",
+ " o5 o6 \n",
+ "0.21733 0.15016 \n"
+ ]
+ }
+ ],
"source": [
"print(astroFreqs, 5)"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 14,
"id": "2ebf1fb3-9797-4c16-891a-7ffc692623b5",
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "0.06618"
+ ],
+ "text/latex": [
+ "0.06618"
+ ],
+ "text/markdown": [
+ "0.06618"
+ ],
+ "text/plain": [
+ "[1] 0.06618"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
".33111-0.26493"
]