﻿

# asp.net c# pdf viewer : Break a pdf file SDK control API .net web page windows sharepoint octave62-part533

Chapter26: Statistics
605
 Becker,R.A.,Chambers,J.M.andWilks,A.R.(1988)TheNewSLanguage.
 Hyndman, , R. . J. and Fan, Y. (1996) Sample quantiles instatistical packages,
AmericanStatistician,50,361–365.
 R: : A A Language e and Environment for Statistical l Computing; http://cran.
r-project.org/doc/manuals/fullrefman.pdf.
Examples:
x = = randi (1000, , [10, , 1]); ; # # Create e empirical data a in n range 1-1000
q = = quantile e (x, [0, , 1]);
# Return n minimum, maximum of distribution
q = = quantile e (x, [0.25 0.5 0.75]); # # Return quartiles of distribution
Seealso: [prctile],page605.
[FunctionFile]
q = = prctile
(
x
)
[FunctionFile]
q = = prctile
(
x
,
p
)
[FunctionFile]
q = = prctile
(
x
,
p
,
dim
)
Forasamplex,computethequantiles,q,correspondingtothecumulativeprobability
values,p,inpercent.
Ifxisamatrix,computethepercentilesforeachcolumnandreturntheminamatrix,
suchthatthei-throwofy containsthep(i)thpercentilesofeachcolumnofx.
Ifpisunspeciﬁed,returnthequantilesfor[0255075100].
Theoptionalargumentdimdeterminesthedimensionalongwhichthepercentilesare
calculated. Ifdimisomitteditdefaultstotheﬁrstnon-singletondimension.
ProgrammingNote: Allnon-numericvalues(NaNs)ofx x areignored.
Seealso: [quantile],page604.
[FunctionFile]
statistics
(
x
)
[FunctionFile]
statistics
(
x
,
dim
)
Returnavectorwiththeminimum,ﬁrstquartile,median,thirdquartile,maximum,
mean,standarddeviation,skewness,andkurtosisoftheelementsofthevectorx.
Ifxisamatrix,calculatestatisticsovertheﬁrstnon-singletondimension.
Iftheoptionalargumentdimisgiven,operatealongthisdimension.
See also: [min], page445[max], page444[median], page 600[mean], page 599,
[std],page601,[skewness],page602,[kurtosis],page603.
26.2 BasicStatisticalFunctions
Octavesupports various helpful l statisticalfunctions. . Many y areusefulas initial l stepsto
basicdescriptivestatistics.
[FunctionFile]
center
(
x
)
[FunctionFile]
center
(
x
,
dim
)
Centerdatabysubtractingitsmean.
Break a pdf file - Split, seperate PDF into multiple files in C#.net, ASP.NET, MVC, Ajax, WinForms, WPF
Explain How to Split PDF Document in Visual C#.NET Application
pdf no pages selected; acrobat separate pdf pages
Break a pdf file - VB.NET PDF File Split Library: Split, seperate PDF into multiple files in vb.net, ASP.NET, MVC, Ajax, WinForms, WPF
VB.NET PDF Document Splitter Control to Disassemble PDF Document
acrobat split pdf into multiple files; break pdf file into parts
606
GNUOctave
Ifxisavector,subtractitsmean.
Ifxisamatrix,dotheaboveforeachcolumn.
Iftheoptionalargumentdimisgiven,operatealongthisdimension.
ProgrammingNote: centerhasobviousapplicationfornormalizingstatisticaldata.
Itisalsousefulforimprovingtheprecisionofgeneralnumericalcalculations.When-
ever there is a large value e that t is s common to o a batch of data, , the e mean can be
Seealso: [zscore],page606.
[FunctionFile]
z = = zscore
(
x
)
[FunctionFile]
z = = zscore
(
x
,
opt
)
[FunctionFile]
z = = zscore
(
x
,
opt
,
dim
)
[FunctionFile]
[z, mu, , sigma] = = zscore
(...)
ComputetheZscoreofx
Ifxisavector,subtractitsmeananddividebyitsstandarddeviation. Ifthestandard
Theoptionalparameteroptdeterminesthenormalizationtousewhencomputingthe
standarddeviationandhasthesamedeﬁnitionas thecorrespondingparameterfor
std.
Ifxisamatrix,calculatealongtheﬁrstnon-singletondimension.Ifthethirdoptional
argumentdimisgiven,operatealongthisdimension.
Theoptionaloutputsmuandsigmacontainthemeanandstandarddeviation.
Seealso: [mean],page599,[std],page601,[center],page605.
[FunctionFile]
n = = histc
(
x
,
edges
)
[FunctionFile]
n = = histc
(
x
,
edges
,
dim
)
[FunctionFile]
[n, idx] = = histc
(...)
Computehistogramcounts.
Whenx isavector,thefunctioncountsthenumberofelementsofxthatfallinthe
histogrambinsdeﬁnedbyedges. Thismustbeavectorofmonotonicallyincreasing
values that t deﬁne the edges s of f the histogram bins. . n(k) ) contains the number of
elementsinxforwhichedges(k)<=x<edges(k+1).Theﬁnalelementofncontains
thenumberofelementsofx exactlyequaltothelastelementofedges.
Whenx isanN-dimensionalarray,thecomputationiscarriedoutalongdimension
dim.Ifnotspeciﬁeddimdefaultstotheﬁrstnon-singletondimension.
Whenasecondoutputargumentisrequestedanindexmatrixisalsoreturned. The
idx matrix has thesamesize as x. . Eachelement t of idx x contains s theindex of the
histogrambininwhichthecorrespondingelementofxwascounted.
Seealso: [hist],page280.
[FunctionFile]
c = = nchoosek
(
n
,
k
)
[FunctionFile]
c = = nchoosek
(
set
,
k
)
Compute the binomialcoeﬃcient t of f n or list all possible combinations of a set of
items.
C# PDF Convert: How to Convert Jpeg, Png, Bmp, & Gif Raster Images
Success"); break; case ConvertResult.FILE_TYPE_UNSUPPORT: Console.WriteLine("Fail: can not convert to PDF, file type unsupport"); break; case ConvertResult
pdf specification; break pdf
C# Image Convert: How to Convert Word to Jpeg, Png, Bmp, and Gif
RasterEdge.XDoc.PDF.dll. case ConvertResult.NO_ERROR: Console.WriteLine("Success"); break; case ConvertResult Fail: can not convert to JPEG, file type unsupport
cannot select text in pdf; break pdf into separate pages
Chapter26: Statistics
607
Ifnisascalarthencalculatethebinomialcoeﬃcientofnandk whichisdeﬁnedas
n
k
!
=
n(n 1)(n 2)(n k+1)
k!
=
n!
k!(n k)!
Thisisthenumberofcombinationsofnitemstakeningroupsofsizek.
Iftheﬁrstargumentisavector,set,thengenerateallcombinationsoftheelements
andnchoosek(length(set),k)rows.
Forexample:
Howmanywayscanthreeitemsbegroupedintopairs?
nchoosek (3, , 2)
)
3
Whatarethepossiblepairs?
nchoosek (1:3, , 2)
)
1
2
1
3
2
3
ProgrammingNote: Whencalculatingthebinomialcoeﬃcientnchoosekworksonly
fornon-negative,integerarguments.Usebincoefffornon-integerandnegativescalar
arguments,orforcomputingmanybinomialcoeﬃcients atoncewithvector inputs
fornork.
Seealso: [bincoeﬀ],page453,[perms],page607.
[FunctionFile]
perms
(
v
)
Generateallpermutationsofvwithonerowperpermutation.
Theresulthassizefactorial(n)*n,wherenisthelengthofv.
Example
perms ([1, , 2, , 3])
)
1
2
3
2
1
3
1
3
2
2
3
1
3
1
2
3
2
1
ProgrammingNote: Themaximumlengthofv v shouldbelessthanorequalto10to
limitmemoryconsumption.
Seealso: [permute],page411,[randperm],page426,[nchoosek],page606.
[FunctionFile]
ranks
(
x
,
dim
)
Iftheoptionalargumentdimisgiven,operatealongthisdimension.
Seealso: [spearman],page610,[kendall],page611.
C# PDF Page Insert Library: insert pages into PDF file in C#.net
Offer PDF page break inserting function. offers easy & mature APIs for developers to add & insert an (empty) page into an existing PDF document file.
break pdf; break a pdf into parts
VB.NET PDF Page Insert Library: insert pages into PDF file in vb.
Offer PDF page break inserting function. And this page will give comprehensive VB example codes to create a new page to any designed location of the PDF file.
break pdf documents; break pdf into multiple pages
608
GNUOctave
[FunctionFile]
run_count
(
x
,
n
)
[FunctionFile]
run_count
(
x
,
n
,
dim
)
Counttheupwardrunsalongtheﬁrst non-singletondimensionof x oflength1,2,
...,n-1andgreaterthanorequalton.
Iftheoptionalargumentdimisgiventhenoperatealongthisdimension.
Seealso: [runlength],page608.
[FunctionFile]
count = runlength
(
x
)
[FunctionFile]
[count, value] = = runlength
(
x
)
Findthelengthsofallsequencesofcommonvalues.
countisavectorwiththelengthsofeachrepeatedvalue.
Theoptionaloutputvaluecontainsthevaluethatwasrepeatedinthesequence.
runlength ([2, 2, 0, 4, 4, 4, 0, 1, , 1, 1, 1])
)
[2, 1, 3, , 1, 4]
Seealso: [run
count],page608.
[FunctionFile]
probit
(
p
)
Returntheprobit(thequantileofthestandardnormaldistribution)foreachelement
ofp.
Seealso: [logit],page608.
[FunctionFile]
logit
(
p
)
Computethelogitforeachvalueofp
Thelogitisdeﬁnedas
logit(p)=log
p
1 p
Seealso: [probit],page608,[logistic
cdf],page616.
[FunctionFile]
cloglog
(
x
)
Returnthecomplementarylog-logfunctionofx.
Thecomplementarylog-logfunctionisdeﬁnedas
cloglog(x)= log( log(x))
[FunctionFile]
mahalanobis
(
x
,
y
)
ReturntheMahalanobis’D-squaredistancebetweenthemultivariatesamplesx and
y.
[FunctionFile]
[t, l_x] = = table
(
x
)
[FunctionFile]
[t, l_x, l_y] ] = table
(
x
,
y
)
Createacontingencytabletfromdatavectors.
Thel
xandl
y vectorsarethecorrespondinglevels.
Currently,only1-and2-dimensionaltablesaresupported.
C# TWAIN - Query & Set Device Abilities in C#
TWSX_NATIVE; // See if the device supports file transfer. device.TwainTransferMode = method; break; } if (method == TwainTransferMethod.TWSX_FILE) device
pdf split; pdf insert page break
C# TWAIN - Install, Deploy and Distribute XImage.Twain Control
RasterEdge.XDoc.PDF.dll. See if the device supports file transfer device. TwainTransferMode = method; break; } if (method == TwainTransferMethod.TWSX_FILE)
pdf print error no pages selected; break password pdf
Chapter26: Statistics
609
26.3 StatisticalPlots
OctavecancreateQuantilePlots(QQ-Plots),andProbabilityPlots(PP-Plots).Theseare
NotethatOctavecanalsoshowhistogramsofdatausingthehistfunctionasdescribed
inSection15.2.1[Two-DimensionalPlots],page273.
[FunctionFile]
[q, s] ] = = qqplot
(
x
)
[FunctionFile]
[q, s] ] = = qqplot
(
x
,
y
)
[FunctionFile]
[q, s] ] = = qqplot
(
x
,
dist
)
[FunctionFile]
[q, s] ] = = qqplot
(
x
,
y
,
params
)
[FunctionFile]
qqplot
(...)
PerformaQQ-plot(quantileplot).
IfFistheCDF ofthedistributiondistwithparametersparams andGits inverse,
andx asamplevectoroflengthn,theQQ-plotgraphs ordinates(i)=i-thlargest
elementofxversusabscissaq(if)=G((i-0.5)/n).
Ifthesample comes fromF,exceptfor atransformationoflocationandscale,the
pairswillapproximatelyfollowastraightline.
Ifthesecondargumentisavectory theempiricalCDFofy isusedasdist.
The default for r dist is the e standard normal distribution. . The e optionalargument
paramscontainsalistofparametersofdist. Forexample,foraquantileplotofthe
uniformdistributionon[2,4]andx,use
qqplot (x, "unif", 2, 4)
distcanbeanystringforwhichafunctiondistinv ordist
inv existsthatcalculates
theinverseCDFofdistributiondist.
Ifnooutputargumentsaregiven,thedataareplotteddirectly.
[FunctionFile]
[p, y] ] = = ppplot
(
x
,
dist
,
params
)
PerformaPP-plot(probabilityplot).
IfFistheCDFofthedistributiondistwithparametersparamsandxasamplevector
oflengthn,thePP-plotgraphsordinatey(i)=F(i-thlargestelementofx)versus
abscissap(i)=(i-0.5)/n. IfthesamplecomesfromF,thepairswillapproximately
followastraightline.
Thedefaultfordististhestandardnormaldistribution.
Theoptionalargumentparams containsalistofparametersofdist.
Forexample,foraprobabilityplotoftheuniformdistributionon[2,4]andx,use
ppplot (x, "uniform", 2, , 4)
dist can n be any y string g for r which a a function n dist
cdf that t calculates the CDF of
distributiondistexists.
Ifnooutputisrequestedthenthedataareplottedimmediately.
C# TWAIN - Acquire or Save Image to File
RasterEdge.XDoc.PDF.dll. is necessary in order to set the file format later Group4) device.Compression = TwainCompressionMode.Group3; break; } } acq.FileTranfer
a pdf page cut; reader split pdf
C# TWAIN - Specify Size and Location to Scan
How to Save Acquired Image to File in C#.NET with in frames) { if (frame == TwainStaticFrameSizeType.LetterUS) { this.device.FrameSize = frame; break; } } }.
break a pdf into smaller files; break a pdf into multiple files
610
GNUOctave
26.4 CorrelationandRegressionAnalysis
[FunctionFile]
cov
(
x
)
[FunctionFile]
cov
(
x
,
opt
)
[FunctionFile]
cov
(
x
,
y
)
[FunctionFile]
cov
(
x
,
y
,
opt
)
Computethecovariancematrix.
Ifeachrow of x andy y is s an n observation, andeachcolumnis s a variable, , thenthe
(i,j)-thentryofcov(x,y)isthecovariancebetweenthei-thvariableinxandthe
j-thvariableiny.
ij
=
1
N 1
XN
i=1
(x
i
¯x)(y
i
¯y)
where¯xand¯yarethemeanvaluesofxandy.
Ifcalledwithoneargument,computecov(x,x),thecovariancebetweenthecolumns
ofx.
Theargumentoptdeterminesthetypeofnormalizationtouse.Validvaluesare
0:
normalizewithN 1,providesthebestunbiasedestimatorofthecovari-
ance[default]
1:
normalizewithN,thisprovidesthesecondmomentaroundthemean
CompatibilityNote::Octavealwayscomputesthecovariancematrix. Fortwoinputs,
however,matlabwillcalculatecov(x(:),y(:))wheneverthenumberofelements
inx andy areequal. . Thiswillresultinascalarratherthanamatrixoutput. Code
relyingonthisodddeﬁnitionwillneedtobechangedwhenrunninginOctave.
Seealso: [corr],page610.
[FunctionFile]
corr
(
x
)
[FunctionFile]
corr
(
x
,
y
)
Computematrixofcorrelationcoeﬃcients.
If each row of x x and y is s an n observation and each columnis avariable, thenthe
(i,j)-thentryofcorr(x,y)isthecorrelationbetweenthei-thvariableinxandthe
j-thvariableiny.
corr(x;y)=
cov(x;y)
std(x)std(y)
If called with one argument, , compute e corr(x,x), , the correlation n between the
columnsofx.
Seealso: [cov],page610.
[FunctionFile]
spearman
(
x
)
[FunctionFile]
spearman
(
x
,
y
)
ComputeSpearman’srankcorrelationcoeﬃcientrho.
For two data vectors x x andy, , Spearman’s s rho is s the e correlationcoeﬃcient of the
ranksofx andy.
Chapter26: Statistics
611
Ifxandyaredrawnfromindependentdistributions,rhohaszeromeanandvariance
1/(n-1),andisasymptoticallynormallydistributed.
spearman(x)isequivalenttospearman(x,x).
Seealso: [ranks],page607,[kendall],page611.
[FunctionFile]
kendall
(
x
)
[FunctionFile]
kendall
(
x
,
y
)
ComputeKendall’stau.
Fortwodatavectorsx,yofcommonlengthn,Kendall’stauisthecorrelationofthe
signsofallrankdiﬀerencesofxandy;i.e.,ifbothxandyhavedistinctentries,then
 =
1
n(n 1)
X
i;j
sign(q
i
q
j
)sign(r
i
r
j
)
inwhichtheq
i
andr
i
aretheranksofx andy,respectively.
Ifxandyaredrawnfromindependentdistributions,Kendall’stauisasymptotically
normalwithmean0andvariance
2(2n+5)
9n(n 1)
.
kendall(x)isequivalenttokendall(x,x).
Seealso: [ranks],page607,[spearman],page610.
[FunctionFile]
[theta, beta, dev, dl, , d2l, p] = = logistic_regression
(
y
,
x
,
print
,
theta
,
beta
)
Performordinallogisticregression.
Supposeytakesvaluesinkorderedcategories,andletgamma_i(x)bethecumulative
probabilitythaty fallsinoneoftheﬁrsticategoriesgiventhecovariatex.Then
[theta, beta] ] = = logistic_regression n (y, , x)
ﬁtsthemodel
logit (gamma_i i (x)) ) = = theta_i - beta’ * x,
i = = 1 ... k-1
Thenumberofordinalcategories,k,istakentobethenumberofdistinctvaluesof
round(y). Ifk k equals 2,y isbinaryandthemodelis ordinarylogisticregression.
Thematrixxisassumedtohavefullcolumnrank.
Giveny only,theta=logistic_regression(y)ﬁtsthemodelwithbaselinelogit
oddsonly.
Thefullformis
[theta, beta, , dev, , dl, d2l, , gamma]
= logistic_regression n (y, , x, print, , theta, , beta)
inwhichalloutputargumentsandallinputargumentsexcepty areoptional.
Othervaluesrequestnoinformationtobedisplayed. Theinputargumentsthetaand
betagiveinitialestimatesforthetaandbeta.
Thereturnedvaluedev holdsminustwicethelog-likelihood.
The returned d values dl l and d d2l l are e the e vector of ﬁrst and the matrix of second
derivativesofthelog-likelihoodwithrespecttothetaandbeta.
pholdsestimatesfortheconditionaldistributionofy givenx.
612
GNUOctave
26.5 Distributions
Octavehas functionsforcomputingtheProbabilityDensityFunction(PDF),theCumu-
lativeDistributionfunction(CDF),andthequantile(theinverseoftheCDF)foralarge
numberofdistributions.
Thefollowingtablesummarizesthesupporteddistributions(inalphabeticalorder).
Distribution
PDF
CDF
Quantile
Beta
betapdf
betacdf
betainv
Binomial
binopdf
binocdf
binoinv
Cauchy
cauchy
pdf
cauchy
cdf
cauchy
inv
Chi-Square
chi2pdf
chi2cdf
chi2inv
UnivariateDiscrete
discrete
pdf
discrete
cdf
discrete
inv
Empirical
empirical
pdf
empirical
cdf
empirical
inv
Exponential
exppdf
expcdf
expinv
F
fpdf
fcdf
ﬁnv
Gamma
gampdf
gamcdf
gaminv
Geometric
geopdf
geocdf
geoinv
Hypergeometric
hygepdf
hygecdf
hygeinv
KolmogorovSmirnov
NotAvailable
kolmogorov
NotAvailable
smirnov
cdf
Laplace
laplace
pdf
laplace
cdf
laplace
inv
Logistic
logistic
pdf
logistic
cdf
logistic
inv
Log-Normal
lognpdf
logncdf
logninv
UnivariateNormal
normpdf
normcdf
norminv
Pascal
nbinpdf
nbincdf
nbininv
Poisson
poisspdf
poisscdf
poissinv
StandardNormal
stdnormal
pdf
stdnormal
cdf
stdnormal
inv
t(Student)
tpdf
tcdf
tinv
UniformDiscrete
unidpdf
unidcdf
unidinv
Uniform
unifpdf
unifcdf
uniﬁnv
Weibull
wblpdf
wblcdf
wblinv
[FunctionFile]
betapdf
(
x
,
a
,
b
)
Foreachelementofx,computetheprobabilitydensityfunction(PDF)at x ofthe
[FunctionFile]
betacdf
(
x
,
a
,
b
)
Foreachelement ofx,computethecumulativedistributionfunction(CDF)atx of
[FunctionFile]
betainv
(
x
,
a
,
b
)
Foreachelementofx,computethequantile(theinverseoftheCDF)atxoftheBeta
distributionwithparametersaandb.
Chapter26: Statistics
613
[FunctionFile]
binopdf
(
x
,
n
,
p
)
Foreachelementofx,computetheprobabilitydensityfunction(PDF)at x ofthe
binomialdistributionwithparametersnandp,wherenisthenumberoftrialsand
pistheprobabilityofsuccess.
[FunctionFile]
binocdf
(
x
,
n
,
p
)
Foreachelement ofx,computethecumulativedistributionfunction(CDF)atx of
thebinomialdistributionwithparameters nandp,wherenisthenumberoftrials
andpistheprobabilityofsuccess.
[FunctionFile]
binoinv
(
x
,
n
,
p
)
For eachelement of x,computethe quantile (the inverseofthe CDF) at x x of f the
binomialdistributionwithparametersnandp,wherenisthenumberoftrialsand
pistheprobabilityofsuccess.
[FunctionFile]
cauchy_pdf
(
x
)
[FunctionFile]
cauchy_pdf
(
x
,
location
,
scale
)
Foreachelementofx,computetheprobabilitydensityfunction(PDF)at x ofthe
Cauchydistributionwithlocationparameterlocationandscaleparameterscale >0.
Defaultvaluesarelocation=0,scale=1.
[FunctionFile]
cauchy_cdf
(
x
)
[FunctionFile]
cauchy_cdf
(
x
,
location
,
scale
)
Foreachelement ofx,computethecumulativedistributionfunction(CDF)atx of
theCauchydistributionwithlocationparameterlocationandscaleparameterscale.
Defaultvaluesarelocation=0,scale=1.
[FunctionFile]
cauchy_inv
(
x
)
[FunctionFile]
cauchy_inv
(
x
,
location
,
scale
)
For eachelement of x,computethe quantile (the inverseofthe CDF) at x x of f the
Cauchydistributionwithlocationparameterlocationandscaleparameterscale.
Defaultvaluesarelocation=0,scale=1.
[FunctionFile]
chi2pdf
(
x
,
n
)
Foreachelementofx,computetheprobabilitydensityfunction(PDF)at x ofthe
chi-squaredistributionwithndegreesoffreedom.
[FunctionFile]
chi2cdf
(
x
,
n
)
Foreachelement ofx,computethecumulativedistributionfunction(CDF)atx of
thechi-squaredistributionwithndegreesoffreedom.
[FunctionFile]
chi2inv
(
x
,
n
)
For eachelement of x,computethe quantile (the inverseofthe CDF) at x x of f the
chi-squaredistributionwithndegreesoffreedom.
[FunctionFile]
discrete_pdf
(
x
,
v
,
p
)
For each h element t of x, , compute the probability density y function n (PDF) ) at x x of f a
univariatediscretedistributionwhichassumesthevaluesinv withprobabilitiesp.