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  • How do I calculate the motion of 2 massive bodies in space?

    - by 1224
    I'm writing code simulating the 2-dimensional motion of two massive bodies with gravitational fields. The bodies' masses are known and I have a gravitational force equation. I know from that force I can get a differential equation for coordinates. I know that I once I solve this equation I will get the coordinates. I will need to make up some initial position and some initial velocity. I'd like to end up with a numeric solver for the ordinal differential equation for coordinates to get the formulas that I can write in code. Could someone break down how from laws and initial conditions we get to the formulas that calculate x and y at time t?

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  • Excel table auto update

    - by Mike
    So I have a table in Excel with formulas. When I add a new row, the new row automatically fills in the formulas as well, which is great. My problem is that it also changes the formula in the row above the added row as well. Here's what happens specifically: My table's last row is row 24. A formula I have in that row is the following: =COUNTIF(C$11:C24,"y")/(COUNTIF(C$11:C24,"Y")+COUNTIF(C$11:C24,"N")) When I add in data in row 25 the formula is updated in row 25 as well, which is what I want, to the following: =COUNTIF(C$11:C25,"y")/(COUNTIF(C$11:C25,"Y")+COUNTIF(C$11:C25,"N")) My problem is that the row above also updates - my row 24 changes to the same as row 25 (the C24 goes to C25). Why is my row 24 formula changing when I add a row 25? Note, my formulas above row 24 stay the same when I add in row 25 - only row 24 changes when I add in 25. Is there a way to not update the row above the row being added? This problem continues when additional rows are added - If I add in a row 26, then the formula in rows 24-26 then all reference C26. Why are they all updating?

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  • Proving the ROI of a technology?

    - by leeand00
    How does one prove the ROI of a technology to their manager? The closest thing I have found to a document on how to do this is: http://www.agilejournal.com/pdf/Finding-ROI-in-Build-Automation.pdf There are formulas in this document, but I can't really tell if they are just alot of marketing or if they are accurate formulas on how to calculate ROI. I'm not really trying to calculate the ROI of the build tool in the above paper, I was just trying to calculate the ROI of a simple build tool like ANT.

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  • How to count each digit in a range of integers?

    - by Carlos Gutiérrez
    Imagine you sell those metallic digits used to number houses, locker doors, hotel rooms, etc. You need to find how many of each digit to ship when your customer needs to number doors/houses: 1 to 100 51 to 300 1 to 2,000 with zeros to the left The obvious solution is to do a loop from the first to the last number, convert the counter to a string with or without zeros to the left, extract each digit and use it as an index to increment an array of 10 integers. I wonder if there is a better way to solve this, without having to loop through the entire integers range. Solutions in any language or pseudocode are welcome. Edit: Answers review John at CashCommons and Wayne Conrad comment that my current approach is good and fast enough. Let me use a silly analogy: If you were given the task of counting the squares in a chess board in less than 1 minute, you could finish the task by counting the squares one by one, but a better solution is to count the sides and do a multiplication, because you later may be asked to count the tiles in a building. Alex Reisner points to a very interesting mathematical law that, unfortunately, doesn’t seem to be relevant to this problem. Andres suggests the same algorithm I’m using, but extracting digits with %10 operations instead of substrings. John at CashCommons and phord propose pre-calculating the digits required and storing them in a lookup table or, for raw speed, an array. This could be a good solution if we had an absolute, unmovable, set in stone, maximum integer value. I’ve never seen one of those. High-Performance Mark and strainer computed the needed digits for various ranges. The result for one millon seems to indicate there is a proportion, but the results for other number show different proportions. strainer found some formulas that may be used to count digit for number which are a power of ten. Robert Harvey had a very interesting experience posting the question at MathOverflow. One of the math guys wrote a solution using mathematical notation. Aaronaught developed and tested a solution using mathematics. After posting it he reviewed the formulas originated from Math Overflow and found a flaw in it (point to Stackoverflow :). noahlavine developed an algorithm and presented it in pseudocode. A new solution After reading all the answers, and doing some experiments, I found that for a range of integer from 1 to 10n-1: For digits 1 to 9, n*10(n-1) pieces are needed For digit 0, if not using leading zeros, n*10n-1 - ((10n-1) / 9) are needed For digit 0, if using leading zeros, n*10n-1 - n are needed The first formula was found by strainer (and probably by others), and I found the other two by trial and error (but they may be included in other answers). For example, if n = 6, range is 1 to 999,999: For digits 1 to 9 we need 6*105 = 600,000 of each one For digit 0, without leading zeros, we need 6*105 – (106-1)/9 = 600,000 - 111,111 = 488,889 For digit 0, with leading zeros, we need 6*105 – 6 = 599,994 These numbers can be checked using High-Performance Mark results. Using these formulas, I improved the original algorithm. It still loops from the first to the last number in the range of integers, but, if it finds a number which is a power of ten, it uses the formulas to add to the digits count the quantity for a full range of 1 to 9 or 1 to 99 or 1 to 999 etc. Here's the algorithm in pseudocode: integer First,Last //First and last number in the range integer Number //Current number in the loop integer Power //Power is the n in 10^n in the formulas integer Nines //Nines is the resut of 10^n - 1, 10^5 - 1 = 99999 integer Prefix //First digits in a number. For 14,200, prefix is 142 array 0..9 Digits //Will hold the count for all the digits FOR Number = First TO Last CALL TallyDigitsForOneNumber WITH Number,1 //Tally the count of each digit //in the number, increment by 1 //Start of optimization. Comments are for Number = 1,000 and Last = 8,000. Power = Zeros at the end of number //For 1,000, Power = 3 IF Power 0 //The number ends in 0 00 000 etc Nines = 10^Power-1 //Nines = 10^3 - 1 = 1000 - 1 = 999 IF Number+Nines <= Last //If 1,000+999 < 8,000, add a full set Digits[0-9] += Power*10^(Power-1) //Add 3*10^(3-1) = 300 to digits 0 to 9 Digits[0] -= -Power //Adjust digit 0 (leading zeros formula) Prefix = First digits of Number //For 1000, prefix is 1 CALL TallyDigitsForOneNumber WITH Prefix,Nines //Tally the count of each //digit in prefix, //increment by 999 Number += Nines //Increment the loop counter 999 cycles ENDIF ENDIF //End of optimization ENDFOR SUBROUTINE TallyDigitsForOneNumber PARAMS Number,Count REPEAT Digits [ Number % 10 ] += Count Number = Number / 10 UNTIL Number = 0 For example, for range 786 to 3,021, the counter will be incremented: By 1 from 786 to 790 (5 cycles) By 9 from 790 to 799 (1 cycle) By 1 from 799 to 800 By 99 from 800 to 899 By 1 from 899 to 900 By 99 from 900 to 999 By 1 from 999 to 1000 By 999 from 1000 to 1999 By 1 from 1999 to 2000 By 999 from 2000 to 2999 By 1 from 2999 to 3000 By 1 from 3000 to 3010 (10 cycles) By 9 from 3010 to 3019 (1 cycle) By 1 from 3019 to 3021 (2 cycles) Total: 28 cycles Without optimization: 2,235 cycles Note that this algorithm solves the problem without leading zeros. To use it with leading zeros, I used a hack: If range 700 to 1,000 with leading zeros is needed, use the algorithm for 10,700 to 11,000 and then substract 1,000 - 700 = 300 from the count of digit 1. Benchmark and Source code I tested the original approach, the same approach using %10 and the new solution for some large ranges, with these results: Original 104.78 seconds With %10 83.66 With Powers of Ten 0.07 A screenshot of the benchmark application: If you would like to see the full source code or run the benchmark, use these links: Complete Source code (in Clarion): http://sca.mx/ftp/countdigits.txt Compilable project and win32 exe: http://sca.mx/ftp/countdigits.zip Accepted answer noahlavine solution may be correct, but l just couldn’t follow the pseudo code, I think there are some details missing or not completely explained. Aaronaught solution seems to be correct, but the code is just too complex for my taste. I accepted strainer’s answer, because his line of thought guided me to develop this new solution.

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  • Excel VBA Select Case Loop Sub

    - by Zack
    In my excel file, I have a table setup with formulas. with Cells from Range("B2:B12"), Range ("D2:D12"), and etc every other row containing the answers to these formulas. for these cells (with the formula answers), I need to apply conditional formatting, but I have 7 conditions, so I've been using "select case" in VBA to change their interior background based on their number. I have the select case function currently set up within the sheet code, as opposed to it's own macro Private Sub Worksheet_Change(ByVal Target As Range) Dim iColor As Integer If Not Intersect(Target, Range("B2:L12")) Is Nothing Then Select Case Target Case 0 iColor = 2 Case 0.01 To 0.49 iColor = 36 Case 0.5 To 0.99 iColor = 6 Case 1 To 1.99 iColor = 44 Case 2 To 2.49 iColor = 45 Case 2.5 To 2.99 iColor = 46 Case 3 To 5 iColor = 3 End Select Target.Interior.ColorIndex = iColor End If End Sub but using this method, you must be actually entering the value into the cell for the formatting to work. which is why I want to write a subroutine to to do this as a macro. I can input my data, let the formulas work, and when everything is ready, I can run the macro and format those specific cells. I want an easy way to do this, obviously I could waste a load of time, typing out all the cases for every cell, but I figured it'd be easier with a loop. how would I go about writing a select case loop to change the formatting on a a specific range of cells every other row? thank you in advance.

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  • A Taxonomy of Numerical Methods v1

    - by JoshReuben
    Numerical Analysis – When, What, (but not how) Once you understand the Math & know C++, Numerical Methods are basically blocks of iterative & conditional math code. I found the real trick was seeing the forest for the trees – knowing which method to use for which situation. Its pretty easy to get lost in the details – so I’ve tried to organize these methods in a way that I can quickly look this up. I’ve included links to detailed explanations and to C++ code examples. I’ve tried to classify Numerical methods in the following broad categories: Solving Systems of Linear Equations Solving Non-Linear Equations Iteratively Interpolation Curve Fitting Optimization Numerical Differentiation & Integration Solving ODEs Boundary Problems Solving EigenValue problems Enjoy – I did ! Solving Systems of Linear Equations Overview Solve sets of algebraic equations with x unknowns The set is commonly in matrix form Gauss-Jordan Elimination http://en.wikipedia.org/wiki/Gauss%E2%80%93Jordan_elimination C++: http://www.codekeep.net/snippets/623f1923-e03c-4636-8c92-c9dc7aa0d3c0.aspx Produces solution of the equations & the coefficient matrix Efficient, stable 2 steps: · Forward Elimination – matrix decomposition: reduce set to triangular form (0s below the diagonal) or row echelon form. If degenerate, then there is no solution · Backward Elimination –write the original matrix as the product of ints inverse matrix & its reduced row-echelon matrix à reduce set to row canonical form & use back-substitution to find the solution to the set Elementary ops for matrix decomposition: · Row multiplication · Row switching · Add multiples of rows to other rows Use pivoting to ensure rows are ordered for achieving triangular form LU Decomposition http://en.wikipedia.org/wiki/LU_decomposition C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-lu-decomposition-for-solving.html Represent the matrix as a product of lower & upper triangular matrices A modified version of GJ Elimination Advantage – can easily apply forward & backward elimination to solve triangular matrices Techniques: · Doolittle Method – sets the L matrix diagonal to unity · Crout Method - sets the U matrix diagonal to unity Note: both the L & U matrices share the same unity diagonal & can be stored compactly in the same matrix Gauss-Seidel Iteration http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method C++: http://www.nr.com/forum/showthread.php?t=722 Transform the linear set of equations into a single equation & then use numerical integration (as integration formulas have Sums, it is implemented iteratively). an optimization of Gauss-Jacobi: 1.5 times faster, requires 0.25 iterations to achieve the same tolerance Solving Non-Linear Equations Iteratively find roots of polynomials – there may be 0, 1 or n solutions for an n order polynomial use iterative techniques Iterative methods · used when there are no known analytical techniques · Requires set functions to be continuous & differentiable · Requires an initial seed value – choice is critical to convergence à conduct multiple runs with different starting points & then select best result · Systematic - iterate until diminishing returns, tolerance or max iteration conditions are met · bracketing techniques will always yield convergent solutions, non-bracketing methods may fail to converge Incremental method if a nonlinear function has opposite signs at 2 ends of a small interval x1 & x2, then there is likely to be a solution in their interval – solutions are detected by evaluating a function over interval steps, for a change in sign, adjusting the step size dynamically. Limitations – can miss closely spaced solutions in large intervals, cannot detect degenerate (coinciding) solutions, limited to functions that cross the x-axis, gives false positives for singularities Fixed point method http://en.wikipedia.org/wiki/Fixed-point_iteration C++: http://books.google.co.il/books?id=weYj75E_t6MC&pg=PA79&lpg=PA79&dq=fixed+point+method++c%2B%2B&source=bl&ots=LQ-5P_taoC&sig=lENUUIYBK53tZtTwNfHLy5PEWDk&hl=en&sa=X&ei=wezDUPW1J5DptQaMsIHQCw&redir_esc=y#v=onepage&q=fixed%20point%20method%20%20c%2B%2B&f=false Algebraically rearrange a solution to isolate a variable then apply incremental method Bisection method http://en.wikipedia.org/wiki/Bisection_method C++: http://numericalcomputing.wordpress.com/category/algorithms/ Bracketed - Select an initial interval, keep bisecting it ad midpoint into sub-intervals and then apply incremental method on smaller & smaller intervals – zoom in Adv: unaffected by function gradient à reliable Disadv: slow convergence False Position Method http://en.wikipedia.org/wiki/False_position_method C++: http://www.dreamincode.net/forums/topic/126100-bisection-and-false-position-methods/ Bracketed - Select an initial interval , & use the relative value of function at interval end points to select next sub-intervals (estimate how far between the end points the solution might be & subdivide based on this) Newton-Raphson method http://en.wikipedia.org/wiki/Newton's_method C++: http://www-users.cselabs.umn.edu/classes/Summer-2012/csci1113/index.php?page=./newt3 Also known as Newton's method Convenient, efficient Not bracketed – only a single initial guess is required to start iteration – requires an analytical expression for the first derivative of the function as input. Evaluates the function & its derivative at each step. Can be extended to the Newton MutiRoot method for solving multiple roots Can be easily applied to an of n-coupled set of non-linear equations – conduct a Taylor Series expansion of a function, dropping terms of order n, rewrite as a Jacobian matrix of PDs & convert to simultaneous linear equations !!! Secant Method http://en.wikipedia.org/wiki/Secant_method C++: http://forum.vcoderz.com/showthread.php?p=205230 Unlike N-R, can estimate first derivative from an initial interval (does not require root to be bracketed) instead of inputting it Since derivative is approximated, may converge slower. Is fast in practice as it does not have to evaluate the derivative at each step. Similar implementation to False Positive method Birge-Vieta Method http://mat.iitm.ac.in/home/sryedida/public_html/caimna/transcendental/polynomial%20methods/bv%20method.html C++: http://books.google.co.il/books?id=cL1boM2uyQwC&pg=SA3-PA51&lpg=SA3-PA51&dq=Birge-Vieta+Method+c%2B%2B&source=bl&ots=QZmnDTK3rC&sig=BPNcHHbpR_DKVoZXrLi4nVXD-gg&hl=en&sa=X&ei=R-_DUK2iNIjzsgbE5ID4Dg&redir_esc=y#v=onepage&q=Birge-Vieta%20Method%20c%2B%2B&f=false combines Horner's method of polynomial evaluation (transforming into lesser degree polynomials that are more computationally efficient to process) with Newton-Raphson to provide a computational speed-up Interpolation Overview Construct new data points for as close as possible fit within range of a discrete set of known points (that were obtained via sampling, experimentation) Use Taylor Series Expansion of a function f(x) around a specific value for x Linear Interpolation http://en.wikipedia.org/wiki/Linear_interpolation C++: http://www.hamaluik.com/?p=289 Straight line between 2 points à concatenate interpolants between each pair of data points Bilinear Interpolation http://en.wikipedia.org/wiki/Bilinear_interpolation C++: http://supercomputingblog.com/graphics/coding-bilinear-interpolation/2/ Extension of the linear function for interpolating functions of 2 variables – perform linear interpolation first in 1 direction, then in another. Used in image processing – e.g. texture mapping filter. Uses 4 vertices to interpolate a value within a unit cell. Lagrange Interpolation http://en.wikipedia.org/wiki/Lagrange_polynomial C++: http://www.codecogs.com/code/maths/approximation/interpolation/lagrange.php For polynomials Requires recomputation for all terms for each distinct x value – can only be applied for small number of nodes Numerically unstable Barycentric Interpolation http://epubs.siam.org/doi/pdf/10.1137/S0036144502417715 C++: http://www.gamedev.net/topic/621445-barycentric-coordinates-c-code-check/ Rearrange the terms in the equation of the Legrange interpolation by defining weight functions that are independent of the interpolated value of x Newton Divided Difference Interpolation http://en.wikipedia.org/wiki/Newton_polynomial C++: http://jee-appy.blogspot.co.il/2011/12/newton-divided-difference-interpolation.html Hermite Divided Differences: Interpolation polynomial approximation for a given set of data points in the NR form - divided differences are used to approximately calculate the various differences. For a given set of 3 data points , fit a quadratic interpolant through the data Bracketed functions allow Newton divided differences to be calculated recursively Difference table Cubic Spline Interpolation http://en.wikipedia.org/wiki/Spline_interpolation C++: https://www.marcusbannerman.co.uk/index.php/home/latestarticles/42-articles/96-cubic-spline-class.html Spline is a piecewise polynomial Provides smoothness – for interpolations with significantly varying data Use weighted coefficients to bend the function to be smooth & its 1st & 2nd derivatives are continuous through the edge points in the interval Curve Fitting A generalization of interpolating whereby given data points may contain noise à the curve does not necessarily pass through all the points Least Squares Fit http://en.wikipedia.org/wiki/Least_squares C++: http://www.ccas.ru/mmes/educat/lab04k/02/least-squares.c Residual – difference between observed value & expected value Model function is often chosen as a linear combination of the specified functions Determines: A) The model instance in which the sum of squared residuals has the least value B) param values for which model best fits data Straight Line Fit Linear correlation between independent variable and dependent variable Linear Regression http://en.wikipedia.org/wiki/Linear_regression C++: http://www.oocities.org/david_swaim/cpp/linregc.htm Special case of statistically exact extrapolation Leverage least squares Given a basis function, the sum of the residuals is determined and the corresponding gradient equation is expressed as a set of normal linear equations in matrix form that can be solved (e.g. using LU Decomposition) Can be weighted - Drop the assumption that all errors have the same significance –-> confidence of accuracy is different for each data point. Fit the function closer to points with higher weights Polynomial Fit - use a polynomial basis function Moving Average http://en.wikipedia.org/wiki/Moving_average C++: http://www.codeproject.com/Articles/17860/A-Simple-Moving-Average-Algorithm Used for smoothing (cancel fluctuations to highlight longer-term trends & cycles), time series data analysis, signal processing filters Replace each data point with average of neighbors. Can be simple (SMA), weighted (WMA), exponential (EMA). Lags behind latest data points – extra weight can be given to more recent data points. Weights can decrease arithmetically or exponentially according to distance from point. Parameters: smoothing factor, period, weight basis Optimization Overview Given function with multiple variables, find Min (or max by minimizing –f(x)) Iterative approach Efficient, but not necessarily reliable Conditions: noisy data, constraints, non-linear models Detection via sign of first derivative - Derivative of saddle points will be 0 Local minima Bisection method Similar method for finding a root for a non-linear equation Start with an interval that contains a minimum Golden Search method http://en.wikipedia.org/wiki/Golden_section_search C++: http://www.codecogs.com/code/maths/optimization/golden.php Bisect intervals according to golden ratio 0.618.. Achieves reduction by evaluating a single function instead of 2 Newton-Raphson Method Brent method http://en.wikipedia.org/wiki/Brent's_method C++: http://people.sc.fsu.edu/~jburkardt/cpp_src/brent/brent.cpp Based on quadratic or parabolic interpolation – if the function is smooth & parabolic near to the minimum, then a parabola fitted through any 3 points should approximate the minima – fails when the 3 points are collinear , in which case the denominator is 0 Simplex Method http://en.wikipedia.org/wiki/Simplex_algorithm C++: http://www.codeguru.com/cpp/article.php/c17505/Simplex-Optimization-Algorithm-and-Implemetation-in-C-Programming.htm Find the global minima of any multi-variable function Direct search – no derivatives required At each step it maintains a non-degenerative simplex – a convex hull of n+1 vertices. Obtains the minimum for a function with n variables by evaluating the function at n-1 points, iteratively replacing the point of worst result with the point of best result, shrinking the multidimensional simplex around the best point. Point replacement involves expanding & contracting the simplex near the worst value point to determine a better replacement point Oscillation can be avoided by choosing the 2nd worst result Restart if it gets stuck Parameters: contraction & expansion factors Simulated Annealing http://en.wikipedia.org/wiki/Simulated_annealing C++: http://code.google.com/p/cppsimulatedannealing/ Analogy to heating & cooling metal to strengthen its structure Stochastic method – apply random permutation search for global minima - Avoid entrapment in local minima via hill climbing Heating schedule - Annealing schedule params: temperature, iterations at each temp, temperature delta Cooling schedule – can be linear, step-wise or exponential Differential Evolution http://en.wikipedia.org/wiki/Differential_evolution C++: http://www.amichel.com/de/doc/html/ More advanced stochastic methods analogous to biological processes: Genetic algorithms, evolution strategies Parallel direct search method against multiple discrete or continuous variables Initial population of variable vectors chosen randomly – if weighted difference vector of 2 vectors yields a lower objective function value then it replaces the comparison vector Many params: #parents, #variables, step size, crossover constant etc Convergence is slow – many more function evaluations than simulated annealing Numerical Differentiation Overview 2 approaches to finite difference methods: · A) approximate function via polynomial interpolation then differentiate · B) Taylor series approximation – additionally provides error estimate Finite Difference methods http://en.wikipedia.org/wiki/Finite_difference_method C++: http://www.wpi.edu/Pubs/ETD/Available/etd-051807-164436/unrestricted/EAMPADU.pdf Find differences between high order derivative values - Approximate differential equations by finite differences at evenly spaced data points Based on forward & backward Taylor series expansion of f(x) about x plus or minus multiples of delta h. Forward / backward difference - the sums of the series contains even derivatives and the difference of the series contains odd derivatives – coupled equations that can be solved. Provide an approximation of the derivative within a O(h^2) accuracy There is also central difference & extended central difference which has a O(h^4) accuracy Richardson Extrapolation http://en.wikipedia.org/wiki/Richardson_extrapolation C++: http://mathscoding.blogspot.co.il/2012/02/introduction-richardson-extrapolation.html A sequence acceleration method applied to finite differences Fast convergence, high accuracy O(h^4) Derivatives via Interpolation Cannot apply Finite Difference method to discrete data points at uneven intervals – so need to approximate the derivative of f(x) using the derivative of the interpolant via 3 point Lagrange Interpolation Note: the higher the order of the derivative, the lower the approximation precision Numerical Integration Estimate finite & infinite integrals of functions More accurate procedure than numerical differentiation Use when it is not possible to obtain an integral of a function analytically or when the function is not given, only the data points are Newton Cotes Methods http://en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas C++: http://www.siafoo.net/snippet/324 For equally spaced data points Computationally easy – based on local interpolation of n rectangular strip areas that is piecewise fitted to a polynomial to get the sum total area Evaluate the integrand at n+1 evenly spaced points – approximate definite integral by Sum Weights are derived from Lagrange Basis polynomials Leverage Trapezoidal Rule for default 2nd formulas, Simpson 1/3 Rule for substituting 3 point formulas, Simpson 3/8 Rule for 4 point formulas. For 4 point formulas use Bodes Rule. Higher orders obtain more accurate results Trapezoidal Rule uses simple area, Simpsons Rule replaces the integrand f(x) with a quadratic polynomial p(x) that uses the same values as f(x) for its end points, but adds a midpoint Romberg Integration http://en.wikipedia.org/wiki/Romberg's_method C++: http://code.google.com/p/romberg-integration/downloads/detail?name=romberg.cpp&can=2&q= Combines trapezoidal rule with Richardson Extrapolation Evaluates the integrand at equally spaced points The integrand must have continuous derivatives Each R(n,m) extrapolation uses a higher order integrand polynomial replacement rule (zeroth starts with trapezoidal) à a lower triangular matrix set of equation coefficients where the bottom right term has the most accurate approximation. The process continues until the difference between 2 successive diagonal terms becomes sufficiently small. Gaussian Quadrature http://en.wikipedia.org/wiki/Gaussian_quadrature C++: http://www.alglib.net/integration/gaussianquadratures.php Data points are chosen to yield best possible accuracy – requires fewer evaluations Ability to handle singularities, functions that are difficult to evaluate The integrand can include a weighting function determined by a set of orthogonal polynomials. Points & weights are selected so that the integrand yields the exact integral if f(x) is a polynomial of degree <= 2n+1 Techniques (basically different weighting functions): · Gauss-Legendre Integration w(x)=1 · Gauss-Laguerre Integration w(x)=e^-x · Gauss-Hermite Integration w(x)=e^-x^2 · Gauss-Chebyshev Integration w(x)= 1 / Sqrt(1-x^2) Solving ODEs Use when high order differential equations cannot be solved analytically Evaluated under boundary conditions RK for systems – a high order differential equation can always be transformed into a coupled first order system of equations Euler method http://en.wikipedia.org/wiki/Euler_method C++: http://rosettacode.org/wiki/Euler_method First order Runge–Kutta method. Simple recursive method – given an initial value, calculate derivative deltas. Unstable & not very accurate (O(h) error) – not used in practice A first-order method - the local error (truncation error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size In evolving solution between data points xn & xn+1, only evaluates derivatives at beginning of interval xn à asymmetric at boundaries Higher order Runge Kutta http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods C++: http://www.dreamincode.net/code/snippet1441.htm 2nd & 4th order RK - Introduces parameterized midpoints for more symmetric solutions à accuracy at higher computational cost Adaptive RK – RK-Fehlberg – estimate the truncation at each integration step & automatically adjust the step size to keep error within prescribed limits. At each step 2 approximations are compared – if in disagreement to a specific accuracy, the step size is reduced Boundary Value Problems Where solution of differential equations are located at 2 different values of the independent variable x à more difficult, because cannot just start at point of initial value – there may not be enough starting conditions available at the end points to produce a unique solution An n-order equation will require n boundary conditions – need to determine the missing n-1 conditions which cause the given conditions at the other boundary to be satisfied Shooting Method http://en.wikipedia.org/wiki/Shooting_method C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-shooting-method-for-solving.html Iteratively guess the missing values for one end & integrate, then inspect the discrepancy with the boundary values of the other end to adjust the estimate Given the starting boundary values u1 & u2 which contain the root u, solve u given the false position method (solving the differential equation as an initial value problem via 4th order RK), then use u to solve the differential equations. Finite Difference Method For linear & non-linear systems Higher order derivatives require more computational steps – some combinations for boundary conditions may not work though Improve the accuracy by increasing the number of mesh points Solving EigenValue Problems An eigenvalue can substitute a matrix when doing matrix multiplication à convert matrix multiplication into a polynomial EigenValue For a given set of equations in matrix form, determine what are the solution eigenvalue & eigenvectors Similar Matrices - have same eigenvalues. Use orthogonal similarity transforms to reduce a matrix to diagonal form from which eigenvalue(s) & eigenvectors can be computed iteratively Jacobi method http://en.wikipedia.org/wiki/Jacobi_method C++: http://people.sc.fsu.edu/~jburkardt/classes/acs2_2008/openmp/jacobi/jacobi.html Robust but Computationally intense – use for small matrices < 10x10 Power Iteration http://en.wikipedia.org/wiki/Power_iteration For any given real symmetric matrix, generate the largest single eigenvalue & its eigenvectors Simplest method – does not compute matrix decomposition à suitable for large, sparse matrices Inverse Iteration Variation of power iteration method – generates the smallest eigenvalue from the inverse matrix Rayleigh Method http://en.wikipedia.org/wiki/Rayleigh's_method_of_dimensional_analysis Variation of power iteration method Rayleigh Quotient Method Variation of inverse iteration method Matrix Tri-diagonalization Method Use householder algorithm to reduce an NxN symmetric matrix to a tridiagonal real symmetric matrix vua N-2 orthogonal transforms     Whats Next Outside of Numerical Methods there are lots of different types of algorithms that I’ve learned over the decades: Data Mining – (I covered this briefly in a previous post: http://geekswithblogs.net/JoshReuben/archive/2007/12/31/ssas-dm-algorithms.aspx ) Search & Sort Routing Problem Solving Logical Theorem Proving Planning Probabilistic Reasoning Machine Learning Solvers (eg MIP) Bioinformatics (Sequence Alignment, Protein Folding) Quant Finance (I read Wilmott’s books – interesting) Sooner or later, I’ll cover the above topics as well.

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  • Microsoft Excel 2007 constantly calculating sheets

    - by acseven
    I believe this happening for two weeks now: Excel 2007 (on Windows XP) is acting funny on my computer; any medium sized sheet with some formulas in it takes a significant amount of time recalculating. I can see this because the "calculating: 2 processors xx%" message was almost unseen before and now it appears on most operations like calculating a formula (on one cell), saving, previewing, etc. If the sheet is complex (lots of formulas) I have to disable automatic calculations because excel renders as unusable - it hangs for a really long time, measureable in minutes. Any idea on what may be causing this? ps: this is a Core2 Duo computer with 2 Gb of RAM

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  • VBA + Polymorphism: Override worksheet functions from 3rd party

    - by phi
    my company makes extensive use of a data provider using a (closed source) VBA plugin. In principal, every query follows follows a certain structure: Fill one cell with a formula, where arguments to the formula specify the query the range of that formula is extended (not an arrray formula!) and cells below/right are filled with data For this to work, however, a user has to have a terminal program installed on the machine, as well as a com-plugin referenced in VBA/Excel. My Problem These Excelsheets are used and extended by multiple users, and not all of them have access to the data provider. While they can open the sheet, it will recalculate and the data will be gone. However, frequent recalculation is required. I would like every user to be able to use the sheets, without executing a very specific set of formulas. Attempts remove the reference on those computers where I do not have terminal access. This generates a NAME error i the cell containing the query (acceptable), but this query overrides parts of the data (not acceptable) If you allow the program to refresh, all data will be gone after a failed query Replace all formulas with the plain-text result in the respective cells (press a button and loop over every cell...). Obviously destroys any refresh-capabilities the querys offer for all subsequent users, so pretty bad, too. A theoretical idea, and I'm not sure how to implement it: Replace the functions offered by the plugin with something that will be called either first (and relay the query through to the original function, if thats available) or instead of the original function (by only deploying the solution on non-terminal machines), which just returns the original value. More specifically, if my query function is used like this: =GETALLDATA(Startdate, Enddate, Stockticker, etc) I would like to transparently swap the function behind the call. Do you see any hope, or am I lost? I appreciate your help. PS: Of course I'm talking about Bloomberg... Some additional points to clarify issues raise by Frank: The formula in the sheets may not be changed. This is mission-critical software, and its way too complex for any sane person to try and touch it. Only excel and VBA may be used (which is the reason for the previous point...) It would be sufficient to prevent execution of these few specific formulas/functions on a specific machine for all excel sheets to come This looks more and more like a problem for stackoverflow ;-)

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  • How can I make results of a formula values that can be filtered or use vlookup with Excel

    - by Burt
    I am having an issue in that I am using various formulas to move, split data, etc from various sources. The problem is when my final results post to the final destination that I want, I still need to either run advanced filters, or a vlookup with the results. I can’t do this because as an example if cell A1 shows a value of: A127 the actual cell content is: =RIGHT(A2,FIND(" ",A2&" ")-2) Everything I read said to copy and paste special values, but this doesn’t work for me as the idea is to have the formulas/macros run everything and eliminating cutting and pasting. In the case above I have a formula that pulls that info from a spreadsheet that is saved every week. Once it is pulled part of it is cut out in another column. I then need to run a vlookup on those results for data already contained on another tab.

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  • Showing name of row instead of excel cell name

    - by Kare
    I am having extremely long formulas over an extremely big sheet. At the moment I am tracking the formulas with the Formula Auditing Tool. However, my idea would be to just replace for example in a formula like this: =IF(AND(ROUND($GX19-SUM(0)/$M$12;2)<=0;$AK$7=1);0;$M$12*$M$22/$K$62 My idea would be to replace the excel cell names with the table row names they are in. Like: =IF(AND(ROUND( "Income" -SUM(0)/ "Debt" ;2)<=0; "Percentage" =1);0; "Investment" * "Debt of house" / "Investment costs" Is there any way to achive sth. like that in excel? I appreciate your inputs!!!

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  • Searching Excel sheet for errors

    - by Graphth
    Imagine a huge worksheet with tens of thousands of formulas. I want to be able to quickly find all the errors to correct them. I have found that using the normal search procedure I can type in things like #DIV/0! or #NAME? and it will find them, but I would have to type in all the various types of errors separately and that is somewhat time consuming. Is there a way to simply search for any error? One solution we seem to use at work is to put most formulas inside =if(iserror()) or now =iferror() and to just have it output "error" if it is an error. Is this necessary? Or, is there a way to find all the errors without it?

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  • Can I insert rows next to a locked column in Excel?

    - by Tom
    If I lock cells A1:A3000, is there a way to insert rows in columns B-Z? I highlight them and I don't get the option to insert even though it is selected in the lock options. (Bottom line is that I need column A static, not to move.) Any ideas? Is it even possible? Better yet, is there any way to have formulas in column A static, as I insert rows in column B? Column A formulas change cell location when I do so.

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  • Developing a Configurable Pricing Program

    - by Ben DeMott
    The organization I work at has some interesting requirements when it comes to pricing for online commerce. Currently the developers write different 'pricing rules' and those rules can be applied to our items based on attributes of the items. For Example: INPUTS: [cost, sug_retail, discontinued, warehouse_qty, orderable_qty, brand, type, days_available, shipping_rate, weight, map_protected, map_discount] MATCH: brand=x, warehouse_qty 1, discontinued=True, map_protected=False SET: retail_price = (sug_retail * 0.95), offer_price1 = (cost * 1.25 + shipping_rate) I am looking to allow the merchandising team to have more control over the pricing and formulas - they are afterall technical enough to write excel formulas. I've been looking at writing a desktop application that uses something like numexpr http://code.google.com/p/numexpr/ or http://sympy.org/en/index.html to allow non-programmers to integrate their own logic into our pricing backend. We have multiple price-tiers we have to set, for multiple markets, so an elegant solution is needed. It's getting frustrating for the dev team to continually tweak/manage all of the pricing rules (we sell over 200 brands in 3 markets). My question is; does this seem like a decent approach? Can you think of a better way to parse string-mathematical-grammer? Can you think of a different way for users to provide formula's to integrate into a automated pricing system? Does anyone know of any examples of existing applications that do this? Excel, and Access are out of the question - the volume of data we manipulate has already proven the need to automate it - now we just need some visibility into that automation.

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  • Basket Analysis with #dax in #powerpivot and #ssas #tabular

    - by Marco Russo (SQLBI)
    A few days ago I published a new article on DAX Patterns web site describing how to implement Basket Analysis in DAX. This topic is a very classical one and is also covered in the many-to-many revolution white paper. It has been also discussed in several blog posts, listed here in historical order: Simple Basket Analysis in DAX by Chris Webb PowerPivot, basket analysis and the hidden many to many by Alberto Ferrari Applied Basket Analysis in Power Pivot using DAX by Gerhard Brueckl As usual, in DAX Patterns we try to present the required DAX formulas in a way that is easy to adapt to specific models. We also try to show a good implementation from a performance point of view. Further optimizations are always possible in DAX. However, in order to keep the model simple to adapt in different scenarios, we avoid presenting optimizations that would require particular assumptions or restrictions on the data model. I hope you will find the Basket Analysis pattern useful. Even if you do not need it today, reading the DAX formula is a good exercise to check your knowledge of evaluation contexts in DAX. For example, describing how does it work the following expression is not a trivial task! [Orders with Both Products] := CALCULATE (     DISTINCTCOUNT ( Sales[SalesOrderNumber] ),     CALCULATETABLE (         SUMMARIZE ( Sales, Sales[SalesOrderNumber] ),         ALL ( Product ),         USERELATIONSHIP ( Sales[ProductCode], 'Filter Product'[Filter ProductCode] )     ) ) The good news is that you can use the patterns even if you do not really understand all the details of the DAX formulas you are using! Any feedback on this new pattern is very welcome.

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  • Defining formula through user interface in user form

    - by BriskLabs Pakistan
    I am a student and developing a simple assignment - windows form application in visual studio 2010. The application is suppose to construct formulas as per user requirement. The process: It has to pick data from columns of Microsoft Access database and the user should be able to pick the data by column name like we do in a drop down menu. and create reusable formulas in it ( configure it once and can change it again). followings are column titles from database that can be picked for example. e.g Col -1 : Marks in Maths Col -2 : Total Marks in Maths Col -3 : Marks in science Col -4 : Total marks in science Finally we should be able to construct any formula in the UI like (Col 1 + Col 3 ) / ( col 2 + col 4) = Formula 1 once this is formula is set saved and a name is assigned to it by user. he/she can use the formula and results shall appear in a window below. i.e He would be able to calculate his desired figures (formula) by only manipulating underlying data on the UI layer....choose the data for a period and apply the formula and get the answer Problem: It looks like I have to create an app where rules are set through UI....... this means no stored procedures are required in SQL.... please suggest the right approach.

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  • Why is math taught "backwards"? [closed]

    - by Yorirou
    A friend of mine showed me a pretty practical Java example. It was a riddle. I got excited and quickly solved the problem. After it, he showed me the mathematical explanation of my solution (he proved why is it good), and it was completely clear for me. This seems like natural approach for me: solve problems, and generalize. This is very familiar to me, I do it all the time when I am programming: I write a function. When I have to write a similar function, I generalize the problem, grab the generic parts, and refactor them to a function, and solve the original problems as a specialization of the general function. At the university (or at least where I study), things work backwards. The professors shows just the highest possible level of the solutions ("cryptic" mathematical formulas). My problem is that this is too abstract for me. There is no connection of my previous knowledge (== reality in my sense), so even if I can understand it, I can't really learn it properly. Others are learning these formulas word-by-word, and get good grades, since they can write exactly the same to the test, but this is not an option for me. I am a curious person, I can learn interesting things, but I can't learn just text. My brain is for storing toughts, not strings. There are proofs for the theories, but they are also really hard to understand because of this, and in most of the cases they are omitted. What is the reason for this? I don't understand why is it a good idea to show the really high level of abstraction and then leave the practical connections (or some important ideas / practical motivations) out?

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  • Difference between LASTDATE and MAX for semi-additive measures in #DAX

    - by Marco Russo (SQLBI)
    I recently wrote an article on SQLBI about the semi-additive measures in DAX. I included the formulas common calculations and there is an interesting point that worth a longer digression: the difference between LASTDATE and MAX (which is similar to FIRSTDATE and MIN – I just describe the former, for the latter just replace the correspondent names). LASTDATE is a dax function that receives an argument that has to be a date column and returns the last date active in the current filter context. Apparently, it is the same value returned by MAX, which returns the maximum value of the argument in the current filter context. Of course, MAX can receive any numeric type (including date), whereas LASTDATE only accepts a column of type date. But overall, they seems identical in the result. However, the difference is a semantic one. In fact, this expression: LASTDATE ( 'Date'[Date] ) could be also rewritten as: FILTER ( VALUES ( 'Date'[Date] ), 'Date'[Date] = MAX ( 'Date'[Date] ) ) LASTDATE is a function that returns a table with a single column and one row, whereas MAX returns a scalar value. In DAX, any expression with one row and one column can be automatically converted into the corresponding scalar value of the single cell returned. The opposite is not true. So you can use LASTDATE in any expression where a table or a scalar is required, but MAX can be used only where a scalar expression is expected. Since LASTDATE returns a table, you can use it in any expression that expects a table as an argument, such as COUNTROWS. In fact, you can write this expression: COUNTROWS ( LASTDATE ( 'Date'[Date] ) ) which will always return 1 or BLANK (if there are no dates active in the current filter context). You cannot pass MAX as an argument of COUNTROWS. You can pass to LASTDATE a reference to a column or any table expression that returns a column. The following two syntaxes are semantically identical: LASTDATE ( 'Date'[Date] ) LASTDATE ( VALUES ( 'Date'[Date] ) ) The result is the same and the use of VALUES is not required because it is implicit in the first syntax, unless you have a row context active. In that case, be careful that using in a row context the LASTDATE function with a direct column reference will produce a context transition (the row context is transformed into a filter context) that hides the external filter context, whereas using VALUES in the argument preserve the existing filter context without applying the context transition of the row context (see the columns LastDate and Values in the following query and result). You can use any other table expressions (including a FILTER) as LASTDATE argument. For example, the following expression will always return the last date available in the Date table, regardless of the current filter context: LASTDATE ( ALL ( 'Date'[Date] ) ) The following query recap the result produced by the different syntaxes described. EVALUATE     CALCULATETABLE(         ADDCOLUMNS(              VALUES ('Date'[Date] ),             "LastDate", LASTDATE( 'Date'[Date] ),             "Values", LASTDATE( VALUES ( 'Date'[Date] ) ),             "Filter", LASTDATE( FILTER ( VALUES ( 'Date'[Date] ), 'Date'[Date] = MAX ( 'Date'[Date] ) ) ),             "All", LASTDATE( ALL ( 'Date'[Date] ) ),             "Max", MAX( 'Date'[Date] )         ),         'Date'[Calendar Year] = 2008     ) ORDER BY 'Date'[Date] The LastDate columns repeat the current date, because the context transition happens within the ADDCOLUMNS. The Values column preserve the existing filter context from being replaced by the context transition, so the result corresponds to the last day in year 2008 (which is filtered in the external CALCULATETABLE). The Filter column works like the Values one, even if we use the FILTER instead of the LASTDATE approach. The All column shows the result of LASTDATE ( ALL ( ‘Date’[Date] ) ) that ignores the filter on Calendar Year (in fact the date returned is in year 2010). Finally, the Max column shows the result of the MAX formula, which is the easiest to use and only don’t return a table if you need it (like in a filter argument of CALCULATE or CALCULATETABLE, where using LASTDATE is shorter). I know that using LASTDATE in complex expressions might create some issue. In my experience, the fact that a context transition happens automatically in presence of a row context is the main reason of confusion and unexpected results in DAX formulas using this function. For a reference of DAX formulas using MAX and LASTDATE, read my article about semi-additive measures in DAX.

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  • Using VLOOKUP in Excel

    - by Mark Virtue
    VLOOKUP is one of Excel’s most useful functions, and it’s also one of the least understood.  In this article, we demystify VLOOKUP by way of a real-life example.  We’ll create a usable Invoice Template for a fictitious company. So what is VLOOKUP?  Well, of course it’s an Excel function.  This article will assume that the reader already has a passing understanding of Excel functions, and can use basic functions such as SUM, AVERAGE, and TODAY.  In its most common usage, VLOOKUP is a database function, meaning that it works with database tables – or more simply, lists of things in an Excel worksheet.  What sort of things?   Well, any sort of thing.  You may have a worksheet that contains a list of employees, or products, or customers, or CDs in your CD collection, or stars in the night sky.  It doesn’t really matter. Here’s an example of a list, or database.  In this case it’s a list of products that our fictitious company sells: Usually lists like this have some sort of unique identifier for each item in the list.  In this case, the unique identifier is in the “Item Code” column.  Note:  For the VLOOKUP function to work with a database/list, that list must have a column containing the unique identifier (or “key”, or “ID”), and that column must be the first column in the table.  Our sample database above satisfies this criterion. The hardest part of using VLOOKUP is understanding exactly what it’s for.  So let’s see if we can get that clear first: VLOOKUP retrieves information from a database/list based on a supplied instance of the unique identifier. Put another way, if you put the VLOOKUP function into a cell and pass it one of the unique identifiers from your database, it will return you one of the pieces of information associated with that unique identifier.  In the example above, you would pass VLOOKUP an item code, and it would return to you either the corresponding item’s description, its price, or its availability (its “In stock” quantity).  Which of these pieces of information will it pass you back?  Well, you get to decide this when you’re creating the formula. If all you need is one piece of information from the database, it would be a lot of trouble to go to to construct a formula with a VLOOKUP function in it.  Typically you would use this sort of functionality in a reusable spreadsheet, such as a template.  Each time someone enters a valid item code, the system would retrieve all the necessary information about the corresponding item. Let’s create an example of this:  An Invoice Template that we can reuse over and over in our fictitious company. First we start Excel… …and we create ourselves a blank invoice: This is how it’s going to work:  The person using the invoice template will fill in a series of item codes in column “A”, and the system will retrieve each item’s description and price, which will be used to calculate the line total for each item (assuming we enter a valid quantity). For the purposes of keeping this example simple, we will locate the product database on a separate sheet in the same workbook: In reality, it’s more likely that the product database would be located in a separate workbook.  It makes little difference to the VLOOKUP function, which doesn’t really care if the database is located on the same sheet, a different sheet, or a completely different workbook. In order to test the VLOOKUP formula we’re about to write, we first enter a valid item code into cell A11: Next, we move the active cell to the cell in which we want information retrieved from the database by VLOOKUP to be stored.  Interestingly, this is the step that most people get wrong.  To explain further:  We are about to create a VLOOKUP formula that will retrieve the description that corresponds to the item code in cell A11.  Where do we want this description put when we get it?  In cell B11, of course.  So that’s where we write the VLOOKUP formula – in cell B11. Select cell B11: We need to locate the list of all available functions that Excel has to offer, so that we can choose VLOOKUP and get some assistance in completing the formula.  This is found by first clicking the Formulas tab, and then clicking Insert Function:   A box appears that allows us to select any of the functions available in Excel.  To find the one we’re looking for, we could type a search term like “lookup” (because the function we’re interested in is a lookup function).  The system would return us a list of all lookup-related functions in Excel.  VLOOKUP is the second one in the list.  Select it an click OK… The Function Arguments box appears, prompting us for all the arguments (or parameters) needed in order to complete the VLOOKUP function.  You can think of this box as the function is asking us the following questions: What unique identifier are you looking up in the database? Where is the database? Which piece of information from the database, associated with the unique identifier, do you wish to have retrieved for you? The first three arguments are shown in bold, indicating that they are mandatory arguments (the VLOOKUP function is incomplete without them and will not return a valid value).  The fourth argument is not bold, meaning that it’s optional:   We will complete the arguments in order, top to bottom. The first argument we need to complete is the Lookup_value argument.  The function needs us to tell it where to find the unique identifier (the item code in this case) that it should be retuning the description of.  We must select the item code we entered earlier (in A11). Click on the selector icon to the right of the first argument: Then click once on the cell containing the item code (A11), and press Enter: The value of “A11” is inserted into the first argument. Now we need to enter a value for the Table_array argument.  In other words, we need to tell VLOOKUP where to find the database/list.  Click on the selector icon next to the second argument: Now locate the database/list and select the entire list – not including the header line.  The database is located on a separate worksheet, so we first click on that worksheet tab: Next we select the entire database, not including the header line: …and press Enter.  The range of cells that represents the database (in this case “’Product Database’!A2:D7”) is entered automatically for us into the second argument. Now we need to enter the third argument, Col_index_num.  We use this argument to specify to VLOOKUP which piece of information from the database, associate with our item code in A11, we wish to have returned to us.  In this particular example, we wish to have the item’s description returned to us.  If you look on the database worksheet, you’ll notice that the “Description” column is the second column in the database.  This means that we must enter a value of “2” into the Col_index_num box: It is important to note that that we are not entering a “2” here because the “Description” column is in the B column on that worksheet.  If the database happened to start in column K of the worksheet, we would still enter a “2” in this field. Finally, we need to decide whether to enter a value into the final VLOOKUP argument, Range_lookup.  This argument requires either a true or false value, or it should be left blank.  When using VLOOKUP with databases (as is true 90% of the time), then the way to decide what to put in this argument can be thought of as follows: If the first column of the database (the column that contains the unique identifiers) is sorted alphabetically/numerically in ascending order, then it’s possible to enter a value of true into this argument, or leave it blank. If the first column of the database is not sorted, or it’s sorted in descending order, then you must enter a value of false into this argument As the first column of our database is not sorted, we enter false into this argument: That’s it!  We’ve entered all the information required for VLOOKUP to return the value we need.  Click the OK button and notice that the description corresponding to item code “R99245” has been correctly entered into cell B11: The formula that was created for us looks like this: If we enter a different item code into cell A11, we will begin to see the power of the VLOOKUP function:  The description cell changes to match the new item code: We can perform a similar set of steps to get the item’s price returned into cell E11.  Note that the new formula must be created in cell E11.  The result will look like this: …and the formula will look like this: Note that the only difference between the two formulae is the third argument (Col_index_num) has changed from a “2” to a “3” (because we want data retrieved from the 3rd column in the database). If we decided to buy 2 of these items, we would enter a “2” into cell D11.  We would then enter a simple formula into cell F11 to get the line total: =D11*E11 …which looks like this… Completing the Invoice Template We’ve learned a lot about VLOOKUP so far.  In fact, we’ve learned all we’re going to learn in this article.  It’s important to note that VLOOKUP can be used in other circumstances besides databases.  This is less common, and may be covered in future How-To Geek articles. Our invoice template is not yet complete.  In order to complete it, we would do the following: We would remove the sample item code from cell A11 and the “2” from cell D11.  This will cause our newly created VLOOKUP formulae to display error messages: We can remedy this by judicious use of Excel’s IF() and ISBLANK() functions.  We change our formula from this…       =VLOOKUP(A11,’Product Database’!A2:D7,2,FALSE) …to this…       =IF(ISBLANK(A11),”",VLOOKUP(A11,’Product Database’!A2:D7,2,FALSE)) We would copy the formulas in cells B11, E11 and F11 down to the remainder of the item rows of the invoice.  Note that if we do this, the resulting formulas will no longer correctly refer to the database table.  We could fix this by changing the cell references for the database to absolute cell references.  Alternatively – and even better – we could create a range name for the entire product database (such as “Products”), and use this range name instead of the cell references.  The formula would change from this…       =IF(ISBLANK(A11),”",VLOOKUP(A11,’Product Database’!A2:D7,2,FALSE)) …to this…       =IF(ISBLANK(A11),”",VLOOKUP(A11,Products,2,FALSE)) …and then copy the formulas down to the rest of the invoice item rows. We would probably “lock” the cells that contain our formulae (or rather unlock the other cells), and then protect the worksheet, in order to ensure that our carefully constructed formulae are not accidentally overwritten when someone comes to fill in the invoice. We would save the file as a template, so that it could be reused by everyone in our company If we were feeling really clever, we would create a database of all our customers in another worksheet, and then use the customer ID entered in cell F5 to automatically fill in the customer’s name and address in cells B6, B7 and B8. If you would like to practice with VLOOKUP, or simply see our resulting Invoice Template, it can be downloaded from here. Similar Articles Productive Geek Tips Make Excel 2007 Print Gridlines In Workbook FileMake Excel 2007 Always Save in Excel 2003 FormatConvert Older Excel Documents to Excel 2007 FormatImport Microsoft Access Data Into ExcelChange the Default Font in Excel 2007 TouchFreeze Alternative in AutoHotkey The Icy Undertow Desktop Windows Home Server – Backup to LAN The Clear & Clean Desktop Use This Bookmarklet to Easily Get Albums Use AutoHotkey to Assign a Hotkey to a Specific Window Latest Software Reviews Tinyhacker Random Tips DVDFab 6 Revo Uninstaller Pro Registry Mechanic 9 for Windows PC Tools Internet Security Suite 2010 Classic Cinema Online offers 100’s of OnDemand Movies OutSync will Sync Photos of your Friends on Facebook and Outlook Windows 7 Easter Theme YoWindoW, a real time weather screensaver Optimize your computer the Microsoft way Stormpulse provides slick, real time weather data

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  • Finding the Formula for a Curve

    - by Mystagogue
    Is there a program that will take "response curve" values from me, and provide a formula that approximates the response curve? It would be cool if such a program would take a numeric "percent correct" (perhaps with a standard deviation) so that it returns simplified formulas when laxity is permissable, and more precise (viz. complex) formulas when the curve needs to be approximated closely. My interest is to play with the response curve values and "laxity" factor, until such a tool spits out a curve-fit formula simple enough that I know it will be high performance during machine computations.

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  • Using Sandy 3D AS3, fill the viewport (exact fit) with multiple 3D objects.

    - by Andrew Mullins
    I'm stitching together an image using multiple instances of the sandy.primitive.Box. Each box is 96x91 while the viewport is 960x273 which should make for an exact fit if I layout the boxes in a perfect grid of 10x3. However, I can't seem to get the exact camera fieldOfView. I've tried a couple formulas (one for adjusting the "focal length" and one for adjusting the fov, directly). Both of these formulas produce a fov angle that is too narrow. // focal length (stage.stageHeight/2) / Math.tan(cam.fov / 2 * Math.PI / 180) // field of view 2 * Math.atan2( (stage.stageHeight/2), -cam.z ) * (180 / Math.PI) Another question about the same project: I need to adjust the perspective of each cube so that the image appears to be in 2D space (flat)... Any ideas on the best method for calculating such a "correction"?

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  • Ruby: Parse, replace, and evaluate a string formula

    - by Swartz
    I'm creating a simple Ruby on Rails survey application for a friend's psychological survey project. So we have surveys, each survey has a bunch of questions, and each question has one of the options participants can choose from. Nothing exciting. One of the interesting aspects is that each answer option has a score value associated with it. And so for each survey a total score needs to be calculated based on these values. Now my idea is instead of hard-coding calculations is to allow user add a formula by which the total survey score will be calculated. Example formulas: "Q1 + Q2 + Q3" "(Q1 + Q2 + Q3) / 3" "(10 - Q1) + Q2 + (Q3 * 2)" So just basic math (with some extra parenthesis for clarity). The idea is to keep the formulas very simple such that anyone with basic math can enter them without resolving to some fancy syntax. My idea is to take any given formula and replace placeholders such as Q1, Q2, etc with the score values based on what the participant chooses. And then eval() the newly formed string. Something like this: f = "(Q1 + Q2 + Q3) / 2" # some crazy formula for this survey values = {:Q1 => 1, :Q2 => 2, :Q3 => 2} # values for substitution result = f.gsub(/(Q\d+)/) {|m| values[$1.to_sym] } # string to be eval()-ed eval(result) So my questions are: Is there a better way to do this? I'm open to any suggestions. How to handle formulas where not all placeholders were successfully replaced (e.g. one question wasn't answered)? Ex: {:Q3 = 2} wasn't in values hash? My idea is to rescue eval()... any thoughts? How to get proper result? Should be 2.5, but due to integer arithmetic, it will truncate to 2. I can't expect people who provide the correct formula (e.g. / 2.0 ) to understand this nuance. I do not expect this, but how to best protect eval() from abuse (e.g. bad formula, manipulated values coming in)? Thank you!

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  • syntax to express mathematical formula concisely in your language of choice

    - by aaa
    hello. I am developing functional domain specific embedded language within C++ to translate formulas into working code as concisely and accurately as possible. Right now my language looks something like this: // implies two nested loops j=0:N, i=0,j (range(i) < j < N)[T(i,j) = (T(i,j) - T(j,i))/e(i+j)]; // implies summation over above expression sum(range(i) < j < N))[(T(i,j) - T(j,i))/e(i+j)]; I am looking for possible syntax improvements/extensions or just different ideas about expressing mathematical formulas as clearly and precisely as possible. Can you give me some syntax examples relating to my question which can be accomplished in your language of choice which consider useful. In particular, if you have some ideas about how to translate the above code segments, I would be happy to hear them Thank you

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  • How to setup Math program

    - by Miles
    I'm needing to write a program (C#) that will allow the user to create generic formulas with variables and numbers. For example: D = A + (A - C / X)(7.8 - 6.6) F = E + (E - C / X)(7.8 - 6.6) FinalResult = (A + D)(0.9) + (E + F)(0.32) + B(0.1) + .023 where all variables would mean for me to go to a database and look something up based on values and return a number in its place. So A would be 2.12 for example (and the same for C and E) Whats the best way to structure this program? How would I make my program read these formulas? I've seen a little bit of the MathML but not sure how to get that started (or an example of it)

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  • VBA - Prevent Excel 2007 from showing a defined names message box?

    - by John M
    I am working on a Excel 2007 workbook that will contain a macro to save the current sheet (a template) as a PDF file (no problem) a Excel 97-2003 file (problem) When saving the Excel file a messagebox appears asking about "Defined names of formulas in this workbook may display different values when they are recalculated...Do you want Excel to recalculate all formulas when this workbook is opened?". The user can then select Yes/No and then the file will save. How do I disable the messagebox from appearing? The default answer would be 'No'. My code for saving: Sub saveAs_97_2003_Workbook(tempFilePath As String, tempFileName As String) Dim Destwb As Workbook Dim SaveFormat As Long 'Remember the users setting SaveFormat = Application.DefaultSaveFormat 'Set it to the 97-2003 file format Application.DefaultSaveFormat = 56 ActiveSheet.Copy Set Destwb = ActiveWorkbook Destwb.CheckCompatibility = False With Destwb .SaveAs tempFilePath & tempFileName & ".xls", FileFormat:=56 .Close SaveChanges:=False End With 'Set DefaultSaveFormat back to the users setting Application.DefaultSaveFormat = SaveFormat End Sub

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