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  • How to solve linear recurrences involving two functions?

    - by Aditya Bahuguna
    Actually I came across a question in Dynamic Programming where we need to find the number of ways to tile a 2 X N area with tiles of given dimensions.. Here is the problem statement Now after a bit of recurrence solving I came out with these. F(n) = F(n-1) + F(n-2) + 2G(n-1), and G(n) = G(n-1) + F(n-1) I know how to solve LR model where one function is there.For large N as is the case in the above problem we can do the matrix exponentiation and achieve O(k^3log(N)) time where k is the minimum number such that for all km F(n) does not depend on F(n-k). The method of solving linear recurrence with matrix exponentiation as it is given in that blog. Now for the LR involving two functions can anyone suggest an approach feasible enough for large N.

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  • How to manually detect deadlocks

    - by Dawson
    I understand the concepts of deadlock well enough, but when I'm given a problem like the one below I'm not sure how to go about solving it. I can draw a resource allocation graph, but I'm not sure how to solve it from there. Is there a better more formal way of solving this? Consider a system with five processes, P1 through P5, and five resources, R1 through R5. Resource ownership is as follows. • P1 holds R1 and wants R3 • P2 holds R2 and wants R1 • P3 holds R3 and wants R5 • P4 holds R5 and wants R2 • P5 holds R4 and wants R2 Is this system deadlocked? Justify your answer. If the system is deadlocked, list the involved processes.

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  • What is the best way to learn C# programming? [closed]

    - by MSU
    My case I want to get the capability of doing anything in C# from building applications to solving problems. I searched for and tried to read books. Then one of the experts said that reading books will not make any good and that to learn, you have to solve real world problems in C#, and he gave me some problems which I previously solved in C++. The thing is that while I know the internal logic of solving the problem, I don't know how to implement it using C# efficiently. I know the message to pass but not the exact way to pass it. I did a program to solve a problem, then find out there are much easier ways of doing it wherever I was doing it in tougher way. What I need to get hold of the language and get the ability to code in C# proficiently?

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  • easiest to code algorithm for rubik's cube

    - by kokokok
    edit : I should rephrase this,what would be a relatively easy algorithm to code in java for solving a rubik's cube. Efficiency is also important but a secondary consideration. orig : what is the easiest algorithm to code for solving a rubik's cube? it could be the least efficient but I am looking for something easy to code right now

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  • NSCFString Memory Leak

    - by Lakshmie
    Hello, I have been solving a lot of memory leaks but have been unsuccessful in solving this one. There are tons of NSCF memory leaks coming due to [NSCFString substringWithRange:]. I have been checking all the String allocations and have released all of them at appropriate places. The responsible library: Foundation. Has anyone encountered this problem before? Can anyone suggest me as how I should takle this issue? Thanks, Lakshmie

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  • Travelling Salesman Problem

    - by Arjun Vasudevan
    I'm trying to solve the travelling salesman problem using the following algorithms - DFS, Hill Climbing and A*. I could write up a code for solving it using DFS. Can I have some help in solving it using the other 2 algorithms? I searched for it a lot, on the web.

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  • Reverse-projection 2D points into 3D

    - by ehsan baghaki
    Suppose we have a 3d Space with a plane on it with an arbitary equation : ax+by+cz+d=0 now suppose that we pick 3 random points on that plane: (x0,y0,z0) (x1,y1,z1) (x1,y1,z1) now i have a different point of view(camera) for this plane. i mean i have a different camera that will look at this plane from a different point of view. From that camera point of view these points have different locations. for example (x0,y0,z0) will be (x0',y0') and (x1,y1,z1) will be (x1',y1') and (x2,y2,z2) will be (x2',y2') from the new camera point of view. So here is my a little hard question! I want to pick a point for example (X,Y) from the new camera point of view and tell where it will be on that plane. All i know is that 3 points and their locations on 3d space and their projection locations on the new camera view. Do you know the coefficients of the plane-equation and the camera positions (along with the projection), or do you only have the six points? - Nils i know the location of first 3 points. therefore we can calculate the coefficients of the plane. so we know exactly where the plane is from (0,0,0) point of view. and then we have the camera that can only see the points! So the only thing that camera sees is 3 points and also it knows their locations in 3d space (and for sure their locations on 2d camera view plane). and after all i want to look at camera view, pick a point (for example (x1,y1)) and tell where is that point on that plane. (for sure this (X,Y,Z) point should fit on the plane equation). Also i know nothing about the camera location.

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  • Finding X on Excel scatter plot/trend line

    - by Wilka
    If I have some data in an scatter plot in Excel, e.g. X Y 1 10 2 20 3 30 4 40 5 50 and I want to find the Y value for X = 10, or X=3.5, or whatever (obviously this is a simplified example) I've been doing the following: Add a trend-line to the scatter plot data Format the trend-line to one that fits the data (linear in this case) Display the equation for the trend-line on the chart Type the equation into an empty cell, replacing x with a cell reference. E.g. "=10*A1" then put my X value into the cell A1 Is there a better way of doing this with Excel? It's quite a few steps, and fairly repetitive. Or maybe Excel is just a poor choice of application for doing this? (I'm using Excel 2007)

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  • Guidance in naming awkward objects?

    - by GlenH7
    I'm modeling a chemical system, and I'm having problems with naming my objects within an enum. I'm not sure if I should use: the atomic formula the chemical name an abbreviated chemical name. For example, sulfuric acid is H2SO4 and hydrochloric acid is HCl. With those two, I would probably just use the atomic formula as they are reasonably common. However, I have others like sodium hexafluorosilicate which is Na2SiF6. In that example, the atomic formula isn't as obvious (to me) but the chemical name is hideously long: myEnum.SodiumHexaFluoroSilicate. I'm not sure how I would be able to safely come up with an abbreviated chemical name that would have a consistent naming pattern. From a maintenance point of view, which of the options would you prefer to see and why? Audience for the code will be just programmers, not chemists. If that guides the particulars: I'm using C#; I'm starting with 10 - 20 compounds and would have at most 100 compounds. The enum is to facilitate common calculations - the equation is the same for all compounds but you insert a property of the compound to complete the equation.

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  • Guidance in naming awkward domain-specific objects?

    - by GlenH7
    I'm modeling a chemical system, and I'm having problems with naming my objects within an enum. I'm not sure if I should use: the atomic formula the chemical name an abbreviated chemical name. For example, sulfuric acid is H2SO4 and hydrochloric acid is HCl. With those two, I would probably just use the atomic formula as they are reasonably common. However, I have others like sodium hexafluorosilicate which is Na2SiF6. In that example, the atomic formula isn't as obvious (to me) but the chemical name is hideously long: myEnum.SodiumHexaFluoroSilicate. I'm not sure how I would be able to safely come up with an abbreviated chemical name that would have a consistent naming pattern. From a maintenance point of view, which of the options would you prefer to see and why? Some details from comments on this question: Audience for the code will be just programmers, not chemists. I'm using C#, but I think this question is more interesting when ignoring the implementation language I'm starting with 10 - 20 compounds and would have at most 100 compounds. The enum is to facilitate common calculations - the equation is the same for all compounds but you insert a property of the compound to complete the equation. For example, Molar mass (in g/mol) is used when calculating the number of moles from a mass (in grams) of the compound. Another example of a common calculation is the Ideal Gas Law and its use of the Specific Gas Constant

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  • What is the simplest way to interpolate and lookup in an x,y table in excel?

    - by dassouki
    I would like to do a lookup and interpolation based on x, y data for the following table. I'd like the equation to be as simple as possible to reduce the amount of possible errors. The full table is about 50 rows x 30 columns. I have about 20 of those tables. Here is an extract from one: A B C D 1 0.1 0.2 0.3 2 2.4 450 300 50 3 2.3 500 375 52 4 2.1 550 475 55 5 1.8 600 600 60 For example, the equation should find the value for x = 2.27 and y = 0.15

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  • HTML5 Canvas Converting between cartesian and isometric coordinates

    - by Amir
    I'm having issues wrapping my head around the Cartesian to Isometric coordinate conversion in HTML5 canvas. As I understand it, the process is two fold: (1) Scale down the y-axis by 0.5, i.e. ctx.scale(1,0.5); or ctx.setTransform(1,0,0,0.5,0,0); This supposedly produces the following matrix: [x; y] x [1, 0; 0, 0.5] (2) Rotate the context by 45 degrees, i.e. ctx.rotate(Math.PI/4); This should produce the following matrix: [x; y] x [cos(45), -sin(45); sin(45), cos(45)] This (somehow) results in the final matrix of ctx.setTransform(2,-1,1,0.5,0,0); which I cannot seem to understand... How is this matrix derived? I cannot seem to produce this matrix by multiplying the scaling and rotation matrices produced earlier... Also, if I write out the equation for the final transformation matrix, I get: newX = 2x + y newY = -x + y/2 But this doesn't seem to be correct. For example, the following code draws an isometric tile at cartesian coordinates (500, 100). ctx.setTransform(2,-1,1,0.5,0,0); ctx.fillRect(500, 100, width*2, height); When I check the result on the screen, the actual coordinates are (285, 215) which do not satisfy the equations I produced earlier... So what is going on here? I would be very grateful if you could: (1) Help me understand how the final isometric transformation matrix is derived; (2) Help me produce the correct equation for finding the on-screen coordinates of an isometric projection. Many thanks and kind regards

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  • Three Key Tenets of Optimal Social Collaboration

    - by kellsey.ruppel
    Today's blog post comes to us from John Bruswick! This post is an abridged version of John’s white paper in which he discusses three principals to optimize social collaboration within an enterprise.   By [email protected], Oracle Principal Sales Consultant Effective social collaboration is actionable, deeply contextual and inherently derives its value from business entities outside of itself. How does an organization begin the journey from traditional, siloed collaboration to natural, business entity based social collaboration? Successful enablement of enterprise social collaboration requires that organizations embrace the following tenets and understand that traditional collaborative functionality has inherent limits - it is innovation and integration in accordance with the following tenets that will provide net-new efficiency benefits. Key Tenets of Optimal Social Collaboration Leverage a Ubiquitous Social Fabric - Collaborative activities should be supported through a ubiquitous social fabric, providing a personalized experience, broadcasting key business events and connecting people and business processes.  This supports education of participants working in and around a specific business entity that will benefit from an implicit capture of tacit knowledge and provide continuity between participants.  In the absence of this ubiquitous platform activities can still occur but are essentially siloed causing frequent duplication of effort across similar tasks, with critical tacit knowledge eluding capture. Supply Continuous Context to Support Decision Making and Problem Solving - People generally engage in collaborative behavior to obtain a decision or the resolution for a specific issue.  The time to achieve resolution is referred to as "Solve Time".  Users have traditionally been forced to switch or "alt-tab" between business systems and synthesize their own context across disparate systems and processes.  The constant loss of context forces end users to exert a large amount of effort that could be spent on higher value problem solving. Extend the Collaborative Lifecycle into Back Office - Beyond the solve time from decision making efforts, additional time is expended formalizing the resolution that was generated from collaboration in a system of record.  Extending collaboration to result in the capture of an explicit decision maximizes efficiencies, creating a closed circuit for a particular thread.  This type of structured action may exist today within your organization's customer support system around opening, solving and closing support issues, but generally does not extend to Sales focused collaborative activities. Excelling in the Unstructured Future We will always have to deal with unstructured collaborative processes within our organizations.  Regardless of the participants and nature of the collaborate process, two things are certain – the origination and end points are generally known and relate to a business entity, perhaps a customer, opportunity, order, shipping location, product or otherwise. Imagine the benefits if an organization's key business systems supported a social fabric, provided continuous context and extended the lifecycle around the collaborative decision making to include output into back office systems of record.   The technical hurdle to embracing optimal social collaboration would fall away, leaving the company with an opportunity to focus on and refine how processes were approached.  Time and resources previously required could then be reallocated to focusing on innovation to support competitive differentiation unique to your business. How can you achieve optimal social collaboration? Oracle Social Network enables business users to collaborate with each other using a broad range of collaboration styles and integrates data from a variety of sources and business applications -- allowing you to achieve optimal social collaboration. Looking to learn more? Read John's white paper, where he discusses in further detail the three principals to optimize social collaboration within an enterprise. 

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  • Homework with allocate subnet IP address

    - by Don Lun
    I'm having difficulty solving a subnet allocation homework problem. Assume that a university has an address block 128.205.224.0/19. It has to allocate addresses for 2 departments' networks, each of size 1800, and for 4 offices, of sizes 550, 600, 650, and 750 nodes respectively. Assuming that the university network allocates addresses sequentially from the beginning of the allocated allocated address space, what are the prefix allocations for these subnetworks? I first thought in this way: There should be 6 subnets in the network. So I need 3 bits for the subnets. So 3 + 19 = 22 bits should be the network bits. Then there are only 10 bits left. 2^10 = 1024 < 1800, so this cannot work. Could you guys give me a hint or some thoughts for solving this problem?

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  • Per-vertex animation with VBOs: VBO per character or VBO per animation?

    - by charstar
    Goal To leverage the richness of well vetted animation tools such as Blender to do the heavy lifting for a small but rich set of animations. I am aware of additive pose blending like that from Naughty Dog and similar techniques but I would prefer to expend a little RAM/VRAM to avoid implementing a thesis-ready pose solver. I would also like to avoid implementing a key-frame + interpolation curve solver (reinventing Blender vertex groups and IPOs), if possible. Scenario Meshes are animated using either skeletons (skinned animation) or some form of morph targets (i.e. per-vertex key frames). However, in either case, the animations are known in full at load-time, that is, there is no physics, IK solving, or any other form of in-game pose solving. The number of character actions (animations) will be limited but rich (hand-animated). There may be multiple characters using a each mesh and its animations simultaneously in-game (they will likely be at different frames of the same animation at the same time). Assume color and texture coordinate buffers are static. Current Considerations Much like a non-shader-powered pose solver, create a VBO for each character and copy vertex and normal data to each VBO on each frame (VBO in STREAMING). Create one VBO for each animation where each frame (interleaved vertex and normal data) is concatenated onto the VBO. Then each character simply has a buffer pointer offset based on its current animation frame (e.g. pointer offset = (numVertices+numNormals)*frameNumber). (VBO in STATIC) Known Trade-Offs In 1 above: Each VBO would be small but there would be many VBOs and therefore lots of buffer binding and vertex copying each frame. Both client and pipeline intensive. In 2 above: There would be few VBOs therefore insignificant buffer binding and no vertex data getting jammed down the pipe each frame, but each VBO would be quite large. Are there any pitfalls to number 2 (aside from finite memory)? I've found a lot of information on what you can do, but no real best practices. Are there other considerations or methods that I am missing?

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  • Oracle SOA Suite, the Most Capable Tool for Every Possible Integration Challenge

    - by Demed L'Her
    session ID: CON8601 - when: Monday, Oct. 1, 10:45am-11:45am - where: Moscone South 102 "Oracle SOA Suite, the Most Capable Tool for Every Possible Integration Challenge" is the name of the session I will be delivering at Oracle OpenWorld this year. I'm usually going for more subdued titles but decided to remove the gloves this year, at the risk of sounding arrogant! While we have a number of worthy competitors in various areas of integration no one can really compete with the breadth and reliability of Oracle SOA Suite. This session is primarily intended for people who are not yet familiar with Oracle SOA Suite (i.e. if you are an existing customer your time might be better spent at some of the other sessions we have on the topic). I will provide an overview of Oracle SOA Suite, the customers using it and the types of challenges they are solving with it: from integrating Oracle Applications (E-Business Suite, Siebel, PeopleSoft, RightNow, Taleo etc.) to third-party applications (did you know that over a third of our customers actually use us to integrate SAP?), mainframes and a variety of technologies. We will talk about some emerging trends and problems that our users are solving with the product: cloud integration, B2B consolidation and mobile-enablement. I will also briefly touch upon the exciting projects we are doing with Oracle Event Processing, in the domain of "Fast Data" and "Big Data". Last but not least, I will be joined on stage by Venktesh Maudgalya, Director at Electronic Arts. Venktesh will bring his customer perspective and explain how EA leveraged Oracle SOA Suite to implement iHub, the massive integration hub that interconnects all their applications (E-BusinessSuite, Hyperion, Demantra, Peoplesoft, Salesforce.com, Kronos, Teradata, GXS etc.) and carries 3/4 of their revenue flows. I just picked up my badge and will be kicking off the festivities tomorrow talking to partners in a pre-OOW briefing at the Oracle Headquarters - see you next week! PS: if you're going to tweet about Oracle SOA Suite next week please make sure to use the #oraclesoa and #oow hashtags so that we can track and amplify your tweets!

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  • Is it common for a development position to be extremely mundane and not challenging at all? [closed]

    - by Kim Jong Woo
    Hi guys so I am working at this company as a web developer but after 1 week of working here, I realize the stuff I am doing seem to be very easy stuff compared to what my peers who have been around for longer are doing. I am way ahead of my schedule and finish my projects early but it's because the work is not at all hard or problem solving involved. So I am puzzled why I would be thanked over doing such menial tasks. Is this normal? This is driving me nuts, I ask to be given more work and I do get it and still finish it quickly and accurately. Now I am having this paranoia that they are just conspiring to use me for a short period of time and terminate me. Am I going too far with this? I keep losing sleep over this. On days when I have a full load of work to complete, this uneasiness goes away but so far I feel like I am not being allowed to pursue what I thought I would do like solving and designing solutions. A lot of it doesn't require any thinking, just cleaning up other people's code and closing bug tickets.

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  • What is the Best way to learn c# programming and capability to do anything with C#?

    - by MSU
    I browsed all the answers given in Stackoverflow,i couldn't find my answer that's why i am writing this, so please don't mark this a duplicate. My case i want to get the capability of doing anything in C# from building applications to solving problems. I searched for and tried to read books. Then one of the experts said, reading books will not make any good for you, for learning you have to solve problems i.e. real world problems in C#, he gave me some sample problems, which i previously did in C++, i started doing, but the thing is that i know the internal logic of solving the problem or the algorithm to solve. But i don't know how to imepelement them using C# efficiently. so, the gap is, i can't think in C#, I know the message to passed but don't the exact way to pass it. I did a program to solve a problem, then find out there are much easier ways of doing it wherever i was doing it in tougher way. So, can you guys(C# experts) please enlighten me, what i need to get hold of the language and get the ability to code in C# proficiently?

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  • Per-vertex animation with VBOs: Stream each frame or use index offset per frame?

    - by charstar
    Scenario Meshes are animated using either skeletons (skinned animation) or some form of morph targets (i.e. per-vertex key frames). However, in either case, the animations are known in full at load-time, that is, there is no physics, IK solving, or any other form of in-game pose solving. The number of character actions (animations) will be limited but rich (hand-animated). There may be multiple characters using a each mesh and its animations simultaneously in-game (they will be at different poses/keyframes at the same time). Assume color and texture coordinate buffers are static. Goal To leverage the richness of well vetted animation tools such as Blender to do the heavy lifting for a small but rich set of animations. I am aware of additive pose blending like that from Naughty Dog and similar techniques but I would prefer to expend a little RAM/VRAM to avoid implementing a thesis-ready pose solver. I would also like to avoid implementing a key-frame + interpolation curve solver (reinventing Blender vertex groups and IPOs). Current Considerations Much like a non-shader-powered pose solver, create a VBO for each character and copy vertex and normal data to each VBO on each frame (VBO in STREAMING). Create one VBO for each animation where each frame (interleaved vertex and normal data) is concatenated onto the VBO. Then each character simply has a buffer pointer offset based on its current animation frame (e.g. pointer offset = (numVertices+numNormals)*frameNumber). (VBO in STATIC) Known Trade-Offs In 1 above: Each VBO would be small but there would be many VBOs and therefore lots of buffer binding and vertex copying each frame. Both client and pipeline intensive. In 2 above: There would be few VBOs therefore insignificant buffer binding and no vertex data getting jammed down the pipe each frame, but each VBO would be quite large. Are there any pitfalls to number 2 (aside from finite memory)? Are there other methods that I am missing?

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  • Developing wheel reinventing tendencies into a skill as opposed to reluctantly learning wheel-finding skills? [duplicate]

    - by Korey Hinton
    This question already has an answer here: Is reinventing the wheel really all that bad? 20 answers I am more of a high-level wheel reinventor. I definitely prefer to make use of existing API features built into a language and popular third-party frameworks that I know can solve the problem, however when I have a particular problem that I feel capable of solving within a reasonable time I am very reluctant to find someone else's solution. Here are a few reasons why I reinvent: It takes time to learn a new API API restrictions might exist that I don't know about Avoiding re-work of unfamiliar code I am conflicted between doing what I know and shifting to a new technique I don't feel comfortable with. On one hand I feel like following my instincts and getting really good at solving problems, especially ones that I would never challenge myself with if all I did was try to find answers. And on the other hand I feel like I might be missing out on important skills like saving time by finding the right framework and expanding my knowledge by learning how to use a new framework. I guess my question comes down to this: My current attitude is to stick to the built-in API and APIs I know well* and to not spend my time searching github for a solution to a problem I know I can solve myself within a reasonable amount of time. Is that a reasonable balance for a successful programmer? *Obviously I will still look around for new frameworks that save time and solve/simplify difficult problems.

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  • Natural talent vs experience [on hold]

    - by Tord Johansson Munk
    Hi i have a question for you guys if you had a choice of hiring one of two programmers. One of them is a natural born programming talent, he has been programming since he was 14 year old and he has been programming all sorts of things by him self, 3d renders,games,his own frameworks, he is really good at algorithms and problem solving. He is now about 25 years old and is looking for a job after some unchallenged years of college the only experience he has is working on his own/university stuff and some open source project. This guy spends all his free time programming and has several pet projects at home. The other person is a 37 year old career programmer. He has been programming since he graduated from university at the age of 26 and have been working since then. He did not have an interest in programming before university. During his studies he discovered that programming was fun and challenging but it never was a "passion". During his career he mainly worked with "enterprise" platforms such as .net or javaEE. He mainly have done database business applications and thus is lacking skills of the young talent like abstract problem solving or algorithms. But he know the tools he has been using during the years and is reliable and almost always makes his boss happy. He keeps him self updated in the platform and tools he has and is using. But outside the office walls he don't touch any code at all. Witch one would you hire? Would you favor one of them in certain projects? Do you think that if the young talent learns his tools he will be a better programmer than the older one? Would your decision be different if both of them where lacking a degree? or if only one of them was lacking a degree be the old and experienced or the young genius.

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  • I can write code...but can't design well. Any suggestions?

    - by user396089
    I feel that I am good at writing code in bits and pieces, but my designs really suck. The question is how do I improve my designs (in order to become a better designer). I think schools and colleges do a good job of teaching people as to how to become good at mathematical problem solving, but lets admit the fact that most programs taught at school are generally around 1000 - 2000 lines long, which means that it is mostly an academic exercise and no way reflects the complexity of real world software (a few hundred thousand to millions of lines of code). This is where I believe that even projects like topcoder/project euler also won't be of much help, they might sharpen your mathematical problem solving ability - but you might become a theoretician programmer; someone who is more interested in the nice, clean stuff, and someone who is utterly un-interested in the day to day mundane and hairy stuff that most application programmers deal with. So my question is how do I improve my design skills? That is the ability to design small/medium scale applications that will go into a few thousand of lines of code? How can I learn design skills that would help me build a better html editor kit, or some graphics program like gimp?

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  • How do I force ode45 to take steps of exactly 0.01 on the T axis?

    - by Gravitas
    I'm using Matlab to solve a differential equation. I want to force ode45 to take constant steps, so it always increments 0.01 on the T axis while solving the equation. How do I do this? ode45 is consistently taking optimized, random steps, and I can't seem to work out how to make it take consistent, small steps of 0.01. Here is the code: options= odeset('Reltol',0.001,'Stats','on'); %figure(1); %clf; init=[xo yo zo]'; tspan=[to tf]; %tspan = t0:0.01:tf; [T,Y]=ode45(name,tspan,init,options);

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  • Convert latitude and longitude into northings and eastings

    - by Rippo
    Hi I have the following UK postcode dy8 3xt and know that the latitude and longitude is:- 54.452772 -2.156082 I also know that the Eastings, Northings for the postcode is:- 389490 283880 However I am struggling to find the equation that converts lat/long to northings and Eastings, I would prefer to have the equation in both in jScript and c# (I am being greedy)! Can anyone help? EDIT Thanks for your help so far guys, I am starting to learn something here esp. the terminology... Some more info, if you click on this link you can see the results I am looking for. The postcode I entered projects to lat/lng using WG S84 and the grid ref projects to OSGB. So my question is how is this done? WHAT I LEARNT Thanks to all that answered, I finally got led to here which I can confirm works great

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  • Matlab: how do I force ode45 to take steps of exactly 0.01 on the T axis?

    - by Gravitas
    I'm using Matlab to solve a differential equation. I want to force ode45 to take constant steps, so it always increments 0.01 on the T axis while solving the equation. How do I do this? ode45 is consistently taking optimized, random steps, and I can't seem to work out how to make it take consistent, small steps of 0.01. Here is the code: options= odeset('Reltol',0.001,'Stats','on'); %figure(1); %clf; init=[xo yo zo]'; tspan=[to tf]; %tspan = t0:0.01:tf; [T,Y]=ode45(name,tspan,init,options);

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