c# parse pdf to xml : Delete metadata from pdf software SDK dll winforms wpf .net web forms xnumbers-tutorial10-part861

FOXES TEAM 
Reference for Xnumbers.xla 
Numeric Calculus  
in Excel  
Volume 
1
x
Delete metadata from pdf - add, remove, update PDF metadata in C#.net, ASP.NET, MVC, Ajax, WinForms, WPF
Allow C# Developers to Read, Add, Edit, Update and Delete PDF Metadata
pdf keywords metadata; view pdf metadata in explorer
Delete metadata from pdf - VB.NET PDF metadata library: add, remove, update PDF metadata in vb.net, ASP.NET, MVC, Ajax, WinForms, WPF
Enable VB.NET Users to Read, Write, Edit, Delete and Update PDF Document Metadata
batch edit pdf metadata; embed metadata in pdf
REFERENCE FOR XNUMBERS.XLA 
Numeric Calculus 
in EXCEL 
Oct 2007 
VB.NET PDF Page Delete Library: remove PDF pages in vb.net, ASP.
›› VB.NET PDF: Delete PDF Page. VB.NET PDF - How to Delete PDF Document Page in VB.NET. Visual Basic Sample Codes to Delete PDF Document Page in VB.NET Class.
pdf xmp metadata editor; adding metadata to pdf files
C# PDF Page Delete Library: remove PDF pages in C#.net, ASP.NET
Page: Delete Existing PDF Pages. |. Home ›› XDoc.PDF ›› C# PDF: Delete PDF Page. C#.NET PDF Library - Delete PDF Document Page in C#.NET.
change pdf metadata; rename pdf files from metadata
Xnumbers Tutorial 
Index 
About this Tutorial.....................................................................................................................8
Array functions...........................................................................................................................9
What is an array-function?.......................................................................................................9
How to insert an array function................................................................................................9
How to get the help on line......................................................................................................12
Xnumbers installation..............................................................................................................13
How to install..........................................................................................................................13
How to uninstall......................................................................................................................14
Installation troubles................................................................................................................14
Multiprecision Floating Point Arithmetic...............................................................................15
Why using extended precision numbers?..............................................................................15
Multiprecision methods...........................................................................................................17
How to store long number......................................................................................................17
Functions..................................................................................................................................19
General Description................................................................................................................19
Using Xnumbers functions.....................................................................................................19
Using extended numbers in Excel..........................................................................................20
Functions Handbook..............................................................................................................21
Precision.................................................................................................................................22
Formatting Result...................................................................................................................22
Arithmetic Functions...............................................................................................................23
Addition.............................................................................................................................................23
Subtraction........................................................................................................................................23
Multiplication.....................................................................................................................................24
Division.............................................................................................................................................24
Inverse..............................................................................................................................................24
Integer Division.................................................................................................................................24
Integer Remainder............................................................................................................................25
Sum..................................................................................................................................................27
Product.............................................................................................................................................27
Raise to power..................................................................................................................................27
Square Root......................................................................................................................................28
N
th
- Root...........................................................................................................................................28
Absolute............................................................................................................................................28
Change sign......................................................................................................................................28
Integer part.......................................................................................................................................29
Decimal part......................................................................................................................................29
Truncating.........................................................................................................................................29
Rounding..........................................................................................................................................29
Relative Rounding............................................................................................................................30
Extended Numbers manipulation...........................................................................................31
Digits count.......................................................................................................................................31
Significant Digits count......................................................................................................................31
Numbers comparison........................................................................................................................31
Extended number check...................................................................................................................32
Format extended number..................................................................................................................32
Check digits......................................................................................................................................32
SortRange.........................................................................................................................................33
Digits sum.........................................................................................................................................33
Vector flip..........................................................................................................................................33
Scientific format................................................................................................................................34
Split scientific format.........................................................................................................................34
Converting multiprecision into double...............................................................................................34
Macros X-Edit...................................................................................................................................35
Macro X-Converter...........................................................................................................................36
Statistical Functions...............................................................................................................39
Factorial............................................................................................................................................39
Factorial with double-step.................................................................................................................39
VB.NET PDF Library SDK to view, edit, convert, process PDF file
Offer professional PDF document metadata editing APIs, using which VB.NET developers can redact, delete, view and save PDF metadata. PDF Document Protection.
online pdf metadata viewer; add metadata to pdf
C# PDF Library SDK to view, edit, convert, process PDF file for C#
PDF SDK for .NET allows you to read, add, edit, update, and delete PDF file metadata, like Title, Subject, Author, Creator, Producer, Keywords, etc.
edit multiple pdf metadata; clean pdf metadata
Xnumbers Tutorial 
Combinations....................................................................................................................................39
Permutations.....................................................................................................................................40
Arithmetic Mean................................................................................................................................40
Geometric Mean...............................................................................................................................40
Quadratic Mean................................................................................................................................40
Standard Deviation...........................................................................................................................40
Variance............................................................................................................................................41
Probability distributions.....................................................................................................................41
Univariate Statistic............................................................................................................................46
Linear Regression Coefficients.........................................................................................................47
Linear Regression - Standard Deviation of Estimates......................................................................49
Linear Regression Formulas.............................................................................................................50
Linear Regression Covariance Matrix...............................................................................................51
Linear Regression Statistics.............................................................................................................52
Linear Regression Evaluation...........................................................................................................53
Polynomial Regression - Coefficient.................................................................................................54
Polynomial Regression - Standard Deviation of Estimates...............................................................54
Polynomial Regression Statistics......................................................................................................54
Macro - Regression..........................................................................................................................55
Linear Regression with Robust Method............................................................................................59
Linear Regression Min-Max..............................................................................................................60
NIST Certification Test......................................................................................................................61
Transcendental Functions......................................................................................................62
Logarithm natural (Napier’s).............................................................................................................62
Logarithm for any base.....................................................................................................................62
Exponential.......................................................................................................................................62
Exponential for any base..................................................................................................................62
Constant  e.......................................................................................................................................63
Constant Ln(2)..................................................................................................................................63
Constant Ln(10)................................................................................................................................63
Hyperbolic Sine.................................................................................................................................63
Hyperbolic ArSine.............................................................................................................................63
Hyperbolic Cosine.............................................................................................................................64
Hyperbolic ArCosine.........................................................................................................................64
Hyperbolic Tangent...........................................................................................................................64
Hyperbolic ArTangent.......................................................................................................................64
Euler constant 
γ
................................................................................................................................64
Trigonometric Functions.........................................................................................................65
Sin....................................................................................................................................................65
Cos...................................................................................................................................................65
Tan...................................................................................................................................................66
Arcsine..............................................................................................................................................66
Arccosine..........................................................................................................................................66
Arctan...............................................................................................................................................66
Constant 
π
........................................................................................................................................66
Complement of right angle................................................................................................................67
Polynomial Rootfinder............................................................................................................68
Input parameters...............................................................................................................................69
Output...............................................................................................................................................70
How to use rootfinder macros...........................................................................................................71
Integer roots......................................................................................................................................74
Multiple roots....................................................................................................................................76
Polynomial Functions.............................................................................................................77
Polynomial evaluation.......................................................................................................................77
Polynomial derivatives......................................................................................................................78
Polynomial coefficients.....................................................................................................................79
Polynomial writing.............................................................................................................................80
Polynomial addition...........................................................................................................................80
Polynomial multiplication...................................................................................................................80
Polynomial subtraction......................................................................................................................81
Polynomial division quotient..............................................................................................................81
Polynomial division remainder..........................................................................................................81
Polynomial shift.................................................................................................................................85
Polynomial center.............................................................................................................................85
Polynomial roots radius.....................................................................................................................86
Polynomial building from roots..........................................................................................................87
Polynomial building with multi-precision............................................................................................89
Polynomial Solving...........................................................................................................................90
Integer polynomial............................................................................................................................90
VB.NET PDF delete text library: delete, remove text from PDF file
VB.NET PDF - How to Delete Text from PDF File in VB.NET. VB.NET Programming Guide to Delete Text from PDF File Using XDoc.PDF SDK for VB.NET.
remove metadata from pdf file; extract pdf metadata
C# PDF delete text Library: delete, remove text from PDF file in
C#.NET PDF SDK - Delete Text from PDF File in C#.NET. How to Use C# Programming Demo Code to Delete Text from PDF File with .NET PDF Component.
pdf xmp metadata; google search pdf metadata
Xnumbers Tutorial 
Polynomial System of 2
nd
degree......................................................................................................91
Bivariate Polynomial.........................................................................................................................92
Orthogonal Polynomials evaluation..................................................................................................97
Weight of Orhogonal Polynomials.....................................................................................................99
Zeros of Orthogonal Polynomials......................................................................................................99
Coefficients of Orthogonal Polynomials..........................................................................................100
Complex Arithmetic and Functions......................................................................................101
How to insert a complex number....................................................................................................101
Complex Addition............................................................................................................................102
Complex Subtraction......................................................................................................................102
Complex Multiplication....................................................................................................................102
Complex Division............................................................................................................................102
Polar Conversion............................................................................................................................103
Rectangular Conversion.................................................................................................................103
Complex absolute...........................................................................................................................103
Complex power...............................................................................................................................104
Complex Roots...............................................................................................................................104
Complex Log...................................................................................................................................105
Complex Exp..................................................................................................................................105
Complex inverse.............................................................................................................................105
Complex negative...........................................................................................................................105
Complex conjugate.........................................................................................................................105
Complex Sin...................................................................................................................................106
Complex Cos..................................................................................................................................106
Complex Tangent...........................................................................................................................106
Complex ArcCos.............................................................................................................................106
Complex ArcSin..............................................................................................................................106
Complex ArcTan.............................................................................................................................106
Complex Hyperbolic Sine................................................................................................................106
Complex Hyperbolic Cosine............................................................................................................107
Complex Hyperbolic Tan.................................................................................................................107
Complex Inverse Hyperbolic Cos....................................................................................................107
Complex Inverse Hyperbolic Sin.....................................................................................................107
Complex Inverse Hyperbolic Tan....................................................................................................107
Complex digamma..........................................................................................................................107
Complex Exponential Integral.........................................................................................................107
Complex Error Function..................................................................................................................108
Complex Complementary Error Function........................................................................................108
Complex Gamma Function.............................................................................................................108
Complex Logarithm Gamma Function............................................................................................108
Complex Zeta Function...................................................................................................................108
Complex Quadratic Equation..........................................................................................................109
Number Theory....................................................................................................................110
Maximum Common Divisor.............................................................................................................110
Minimum Common Multiple............................................................................................................110
Rational Fraction approximation.....................................................................................................111
Continued Fraction.........................................................................................................................112
Continued Fraction of Square Root................................................................................................113
Check Prime...................................................................................................................................113
Next Prime......................................................................................................................................113
Modular Addition.............................................................................................................................114
Modular Subtraction........................................................................................................................114
Modular Multiplication.....................................................................................................................114
Modular Division.............................................................................................................................114
Modular Power................................................................................................................................114
Perfect Square................................................................................................................................116
Check odd/even..............................................................................................................................116
Check Integer.................................................................................................................................116
Macro - Factorize............................................................................................................................117
Batch Factorization with Msieve.....................................................................................................118
Factorization function......................................................................................................................120
Macro - Prime Numbers Generator.................................................................................................121
Prime Test......................................................................................................................................121
Diophantine Equation.....................................................................................................................123
Brouncker-Pell Equation.................................................................................................................124
Euler's Totient function...................................................................................................................125
Integer relation................................................................................................................................126
Macro Integer Relation Finder........................................................................................................130
Linear Algebra Functions.....................................................................................................133
Matrix Addition................................................................................................................................133
VB.NET PDF File Compress Library: Compress reduce PDF size in vb.
Delete unimportant contents: Flatten form fields. Document and metadata. All object data. VB.NET Demo Code to Optimize An Exist PDF File in Visual C#.NET Project.
pdf metadata reader; edit pdf metadata online
How to C#: Basic SDK Concept of XDoc.PDF for .NET
load, combine, and split PDF file(s), and add, create, insert, delete, re-order XDoc.PDF for .NET supports editing PDF document metadata, like Title
delete metadata from pdf; pdf xmp metadata viewer
Xnumbers Tutorial 
Matrix Subtraction...........................................................................................................................133
Matrix Multiplication........................................................................................................................133
Matrix Inverse.................................................................................................................................133
Matrix Determinant.........................................................................................................................133
Matrix Modulus...............................................................................................................................134
Scalar Product................................................................................................................................134
Similarity Transform........................................................................................................................134
Matrix Power...................................................................................................................................134
Matrix LU decomposition................................................................................................................135
Matrix LL
T
decomposition...............................................................................................................135
Vector Product................................................................................................................................136
Solve Linear Equation System........................................................................................................136
Square Delta Extrapolation.............................................................................................................137
Macro for Multiprecision Matrix Operations.....................................................................................139
Integrals & Series.................................................................................................................141
Discrete Fourier Transform.............................................................................................................141
Discrete Fourier Inverse Transform................................................................................................143
Discrete Fourier Spectrum..............................................................................................................144
Inverse Discrete Fourier Spectrum.................................................................................................144
2D Discrete Fourier Transform.......................................................................................................145
2D Inverse Discrete Fourier Transform...........................................................................................145
Macro DFT (Discrete Fourier Transform)........................................................................................146
Macro Sampler...............................................................................................................................149
Integral function..............................................................................................................................151
Zeros of integral function................................................................................................................154
Function Integration (Romberg method).........................................................................................155
Function Integration (Double Exponential method).........................................................................156
Function Integration (mixed method)..............................................................................................158
Complex Function Integration (Romberg method)..........................................................................160
Data Integration (Newton-Cotes)....................................................................................................161
Function Integration (Newton-Cotes)..............................................................................................163
Integration: symbolic and numeric approaches...............................................................................165
Integration of oscillating functions (Filon formulas).........................................................................166
Integration of oscillating functions (Fourier transform)....................................................................168
Infinite Integration of oscillating functions.......................................................................................169
Double Integral...............................................................................................................................172
Macro for Double Integration..........................................................................................................172
Macro for Triple Integration.............................................................................................................175
Double integration function.............................................................................................................178
Infinite integral................................................................................................................................181
Double Data integration..................................................................................................................183
Series Evaluation............................................................................................................................186
Series acceleration with 
^2...........................................................................................................187
Complex Series Evaluation.............................................................................................................188
Double Series.................................................................................................................................189
Trigonometric series.......................................................................................................................190
Trigonometric double serie.............................................................................................................192
Discrete Convolution.......................................................................................................................193
Interpolation..........................................................................................................................195
Polynomial interpolation..................................................................................................................195
Interpolation schemas.....................................................................................................................197
Interpolation with continued fraction...............................................................................................199
Interpolation with Cubic Spline........................................................................................................201
Cubic Spline 2nd derivatives...........................................................................................................201
Cubic Spline Coefficients................................................................................................................203
2D Mesh Interpolation.....................................................................................................................204
Macro Mesh Fill..............................................................................................................................205
Differential Equations...........................................................................................................211
ODE Runge-Kutta 4........................................................................................................................211
ODE Multi-Steps.............................................................................................................................215
Multi-step coefficents tables............................................................................................................216
Predictor- Corrector........................................................................................................................218
PECE algorithm of 2
nd
order...........................................................................................................218
ODE Predictor-Corrector 4..............................................................................................................221
ODE Implicit Predictor-Corrector....................................................................................................223
Differential Systems........................................................................................................................226
OD Linear System..........................................................................................................................226
High order linear ODE.....................................................................................................................227
ODE for integral function solving....................................................................................................230
Xnumbers Tutorial 
Macro ODE Solver..........................................................................................................................232
Macro ODE - Slope Grid.................................................................................................................233
Nonlinear Equations.............................................................................................................235
Bisection.........................................................................................................................................235
Secant.............................................................................................................................................236
Derivatives............................................................................................................................239
First Derivative................................................................................................................................239
Second Derivative...........................................................................................................................240
Gradient..........................................................................................................................................240
Jacobian matrix...............................................................................................................................241
Hessian matrix................................................................................................................................241
Non-linear equation solving with derivatives...................................................................................243
Conversions.........................................................................................................................245
Decibel............................................................................................................................................245
Base conversion.............................................................................................................................245
Multiprecision Base Conversion......................................................................................................246
Log Relative Error...........................................................................................................................247
Special Functions.................................................................................................................249
Error Function  Erf(x)......................................................................................................................249
Exponential integral Ei(x)................................................................................................................249
Exponential integral En(x)...............................................................................................................249
Euler-Mascheroni Constant  
γ
.........................................................................................................250
Gamma function 
Γ
(x)......................................................................................................................250
Log Gamma function......................................................................................................................251
Gamma quotient.............................................................................................................................251
Gamma F-factor..............................................................................................................................252
Digamma function...........................................................................................................................252
Beta function...................................................................................................................................252
Incomplete Gamma function...........................................................................................................253
Incomplete Beta function................................................................................................................253
Combinations function....................................................................................................................253
Bessel  functions of integer order...................................................................................................254
Cosine Integral Ci(x).......................................................................................................................254
Sine Integral Si(x)...........................................................................................................................254
Fresnel sine Integral.......................................................................................................................255
Fresnel cosine Integral....................................................................................................................255
Fibonacci numbers.........................................................................................................................255
Hypergeometric function.................................................................................................................256
Zeta function  
ζ
(s)...........................................................................................................................256
Airy functions..................................................................................................................................257
Elliptic Integrals...............................................................................................................................257
Kummer confluent hypergeometric functions..................................................................................258
Integral of sine-cosine power..........................................................................................................259
Spherical Bessel functions of integer order.....................................................................................260
Formulas Evaluation.............................................................................................................261
Multiprecision Expression Evaluation.............................................................................................261
Complex Expression Evaluation.....................................................................................................265
Multiprecision Excel Formula Evaluation........................................................................................266
Math expression strings..................................................................................................................268
List of basic functions and operators..............................................................................................271
Function Optimization...........................................................................................................274
Macros for optimization on site.......................................................................................................274
Example 1 - Rosenbrock's parabolic valley....................................................................................276
Example 2 - Constrained minimization...........................................................................................277
Example 3 - Nonlinear Regression with Absolute Sum...................................................................279
Example 4 - Optimization of Integral function.................................................................................280
How to call  Xnumbers functions from VBA.........................................................................281
References & Resources.......................................................................................................284
Analytical index......................................................................................................................287
Xnumbers Tutorial 
WHITE PAGE
Xnumbers Tutorial 
About this tutorial 
About this Tutorial 
This document is the reference guide for all functions 
and macros contained in the Xnumbers addin. It is a 
printable version of the help-on-line, with a larger 
collection of examples. 
XNUMBERS.XLA 
is an Excel addin containing useful functions for numerical 
calculus in standard and multiprecision floating point arithmetic up to 200 
significant digits.  
The main purpose of this document is to be a reference guide for the functions of this package, 
showing how to work with multiprecision arithmetic in Excel. The most part of the material 
contained in this document comes from the Xnumbers help-on-line. You may print it in order to 
have a handle paper manual. Of course it speaks about math and numerical calculus but this is 
not a math book.  You rarely find here theorems and demonstrations. You can find, on the 
contrary, many explaining examples. 
Special thanks to everyone that have kindly collaborated. 
Leonardo Volpi 
Chapter 
Xnumbers Tutorial 
Array functions 
What is an array-function? 
A function that returns multiple values is called "array-function". Xnumbers contains many of 
these functions. Each function returning a matrix or a vector is an array functions. Function 
performing matrix operations such as inversion, multiplication, sum, etc. are examples of array-
functions. Also complex numbers are arrays of two cells. On the contrary, in the real domain, 
the logarithm, the exponential, the trigonometric functions, etc. are scalar functions because 
they return only one value. 
In a worksheet, an array-function always returns a (n x m) rectangular range 
of cells. To enter it, you must select this range, enter the function as usually 
and and give the keys sequence CTRL+SHIFT+ENTER. Keep down both 
keys CTRL and SHIFT (do not care the order) and then press ENTER. 
How to insert an array function 
The following example explains, step-by-step, how to insert an array-function 
The System Solution 
Assume to have to solve a 3x3 linear system. The solution is a vector of 3 values. 
Ax = b 
Where: 
The function SYSLIN returns the vector solution x, that is an (3 x 1) array.  
To see the three values you must select 
before the area where you want to insert 
these values. 
Now insert the function either from menu or 
by the icon 
Select the area of the matrix A "A5:C7" and 
the constant vector b "E5:E7" 
ª 
=
1 3 3 4
1 2 2 2
1 1 1 1
A
=
3
2
4
b
Documents you may be interested
Documents you may be interested