Hi all, I am searching for a Matlab function that can do the non-parametric bootstrapping of multivariate data. For instance, I have a matrix of sample data (MxN) where M is the dimension of the random vector (multivariate data), and N is the number of observation. I want to generate (resample) bootstrap data from this initial multivariate data. Does anyone knows this function? Thank you very much for your help. Best regards, CT DO

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8/17/2010 5:59:05 AM

"CT " <cong-thanh.do@hotmail.fr> wrote in message <i4d8f9$n3a$1@fred.mathworks.com>... > Hi all, > > I am searching for a Matlab function that can do the non-parametric bootstrapping of multivariate data. For instance, I have a matrix of sample data (MxN) where M is the dimension of the random vector (multivariate data), and N is the number of observation. I want to generate (resample) bootstrap data from this initial multivariate data. Does anyone knows this function? > > Thank you very much for your help. > > Best regards, > CT DO matlab does not not have a pre-built function for multivariate data.However, in the file exhcnage you can find a code, the function is called 'bstrag'

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8/17/2010 6:33:42 AM

On 8/17/2010 1:59 AM, CT wrote: > I am searching for a Matlab function that can do the non-parametric > bootstrapping of multivariate data. For instance, I have a matrix of > sample data (MxN) where M is the dimension of the random vector > (multivariate data), and N is the number of observation. I want to > generate (resample) bootstrap data from this initial multivariate data. > Does anyone knows this function? If you have access to the Statistics Toolbox, the BOOTSTRP function does what you are asking. it is here: <http://www.mathworks.com/access/helpdesk/help/toolbox/stat /bootstrp.html>

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8/17/2010 12:34:34 PM

Peter Perkins <Peter.Perkins@MathRemoveThisWorks.com> wrote in message <i4dvkq$8ns$2@fred.mathworks.com>... > On 8/17/2010 1:59 AM, CT wrote: > > I am searching for a Matlab function that can do the non-parametric > > bootstrapping of multivariate data. For instance, I have a matrix of > > sample data (MxN) where M is the dimension of the random vector > > (multivariate data), and N is the number of observation. I want to > > generate (resample) bootstrap data from this initial multivariate data. > > Does anyone knows this function? > > If you have access to the Statistics Toolbox, the BOOTSTRP function does > what you are asking. it is here: > > <http://www.mathworks.com/access/helpdesk/help/toolbox/stat /bootstrp.html> Isn't this just: X(:,ceil(rand(1,N)*N)) where X is the sample matrix?

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8/17/2010 2:18:05 PM

Peter Perkins <Peter.Perkins@MathRemoveThisWorks.com> wrote in message <i4eikn$ndn$1@fred.mathworks.com>... > On 8/17/2010 10:18 AM, Simon Preston wrote: > >> <http://www.mathworks.com/access/helpdesk/help/toolbox/stat > >> /bootstrp.html> > > Sorry, for some reason that link was missing an "s" > <http://www.mathworks.com/access/helpdesk/help/toolbox/stats/bootstrp.html> > > > Isn't this just: > > > > X(:,ceil(rand(1,N)*N)) > > > > where X is the sample matrix? > > That's the basis of it, yes. But: > > 1) It's kind of tedious to write the same loop over and over, regardless > of how simple that loop is, > 1) There is a good deal of flexibility in the arguments you can pass to > BOOTSTRP, so a single matrix isn't the only case it handles for you, and > 2) (in recent MATLAB releases) There is support for parallelizing the > computations using PARFOR (if your installation supports that) > > Just as an aside, since 2008b you might find it easier to use RANDI to > generate random integers. Just one thing to point out, you said that M is the dimention of the data. I thought that you ment different groups or different experiments where the data was collected, after all thats why your data is not of dimenation N*M x 1, for instance. If the columns of the matrix represent different groups, for some or another reason, you cannot pool the series. As far as know 'bootstrp' does not distinguishes among different groups. If this last statement is incorrect, can someone send me the link to read about it. Thanks

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8/17/2010 7:31:04 PM

I mean that I have N observations of the random vectors x, the vector x has M elements, these are the seed data. So each variable here is a vector (of M elements). Their probability density distribution (pdf) might be multivariate distribution, e.g. Gaussian mixture model (GMM). Since the bootstrap here is non-parametric, the N observations will be used instead of a concrete pdf. I have tried to used BOOTSTRP to perform the bootstrapping, but it is not easy, even unfeasible (tell me if I am wrong), since the manual of BOOTSTRP in Matlab is not clear in this case (I think). If the generated data is only X(:,ceil(rand(1,N)*N)), I don't see anything new that the bootstrap can bring. As I see, this is only a disorder of the initial data, we cannot expect anything different from the new data, I'm wrong? "Rogelio " <rogelioa@math.uio.no> wrote in message <i4eo1o$c8b$1@fred.mathworks.com>... > Peter Perkins <Peter.Perkins@MathRemoveThisWorks.com> wrote in message <i4eikn$ndn$1@fred.mathworks.com>... > > On 8/17/2010 10:18 AM, Simon Preston wrote: > > >> <http://www.mathworks.com/access/helpdesk/help/toolbox/stat > > >> /bootstrp.html> > > > > Sorry, for some reason that link was missing an "s" > > <http://www.mathworks.com/access/helpdesk/help/toolbox/stats/bootstrp.html> > > > > > Isn't this just: > > > > > > X(:,ceil(rand(1,N)*N)) > > > > > > where X is the sample matrix? > > > > That's the basis of it, yes. But: > > > > 1) It's kind of tedious to write the same loop over and over, regardless > > of how simple that loop is, > > 1) There is a good deal of flexibility in the arguments you can pass to > > BOOTSTRP, so a single matrix isn't the only case it handles for you, and > > 2) (in recent MATLAB releases) There is support for parallelizing the > > computations using PARFOR (if your installation supports that) > > > > Just as an aside, since 2008b you might find it easier to use RANDI to > > generate random integers. > > Just one thing to point out, you said that M is the dimention of the data. I thought that you ment different groups or different experiments where the data was collected, after all thats why your data is not of dimenation N*M x 1, for instance. If the columns of the matrix represent different groups, for some or another reason, you cannot pool the series. As far as know 'bootstrp' does not distinguishes among different groups. If this last statement is incorrect, can someone send me the link to read about it. > Thanks

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8/18/2010 6:17:24 AM

If you are saying or have a feeling that your data might come from a multivariate distribution, then as far as I know 'bootstrp' will pool your data together, assuming they come from the same pdf which might be an erronous assumption. > I have tried to used BOOTSTRP to perform the bootstrapping, but it is not easy, even unfeasible (tell me if I am wrong), since the manual of BOOTSTRP in Matlab is not clear in this case (I think)< Why? can you tell us what is the mistake or post the code >As I see, this is only a disorder of the initial data, we cannot expect anything different from the new data, I'm wrong?< What the bootstrapring does, roughly speaking, is to resample with replacement. We create pseudo random variables out from your original data. The empirical pdf will converge to the pdf, this is asymptotically. "CT " <cong-thanh.do@hotmail.fr> wrote in message <i4fttk$qpk$1@fred.mathworks.com>... > I mean that I have N observations of the random vectors x, the vector x has M elements, these are the seed data. So each variable here is a vector (of M elements). Their probability density distribution (pdf) might be multivariate distribution, e.g. Gaussian mixture model (GMM). Since the bootstrap here is non-parametric, the N observations will be used instead of a concrete pdf. > > I have tried to used BOOTSTRP to perform the bootstrapping, but it is not easy, even unfeasible (tell me if I am wrong), since the manual of BOOTSTRP in Matlab is not clear in this case (I think). > > If the generated data is only X(:,ceil(rand(1,N)*N)), I don't see anything new that the bootstrap can bring. As I see, this is only a disorder of the initial data, we cannot expect anything different from the new data, I'm wrong? > > "Rogelio " <rogelioa@math.uio.no> wrote in message <i4eo1o$c8b$1@fred.mathworks.com>... > > Peter Perkins <Peter.Perkins@MathRemoveThisWorks.com> wrote in message <i4eikn$ndn$1@fred.mathworks.com>... > > > On 8/17/2010 10:18 AM, Simon Preston wrote: > > > >> <http://www.mathworks.com/access/helpdesk/help/toolbox/stat > > > >> /bootstrp.html> > > > > > > Sorry, for some reason that link was missing an "s" > > > <http://www.mathworks.com/access/helpdesk/help/toolbox/stats/bootstrp.html> > > > > > > > Isn't this just: > > > > > > > > X(:,ceil(rand(1,N)*N)) > > > > > > > > where X is the sample matrix? > > > > > > That's the basis of it, yes. But: > > > > > > 1) It's kind of tedious to write the same loop over and over, regardless > > > of how simple that loop is, > > > 1) There is a good deal of flexibility in the arguments you can pass to > > > BOOTSTRP, so a single matrix isn't the only case it handles for you, and > > > 2) (in recent MATLAB releases) There is support for parallelizing the > > > computations using PARFOR (if your installation supports that) > > > > > > Just as an aside, since 2008b you might find it easier to use RANDI to > > > generate random integers. > > > > Just one thing to point out, you said that M is the dimention of the data. I thought that you ment different groups or different experiments where the data was collected, after all thats why your data is not of dimenation N*M x 1, for instance. If the columns of the matrix represent different groups, for some or another reason, you cannot pool the series. As far as know 'bootstrp' does not distinguishes among different groups. If this last statement is incorrect, can someone send me the link to read about it. > > Thanks

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8/18/2010 6:55:23 AM

By the way ...... what is the statistc that you are bootstraping? it will be nice if you post the code. "Rogelio " <rogelioa@math.uio.no> wrote in message <i4g04r$fa8$1@fred.mathworks.com>... > If you are saying or have a feeling that your data might come from a multivariate distribution, then as far as I know 'bootstrp' will pool your data together, assuming they come from the same pdf which might be an erronous assumption. > > I have tried to used BOOTSTRP to perform the bootstrapping, but it is not easy, even unfeasible (tell me if I am wrong), since the manual of BOOTSTRP in Matlab is not clear in this case (I think)< > Why? can you tell us what is the mistake or post the code > >As I see, this is only a disorder of the initial data, we cannot expect anything different from the new data, I'm wrong?< > What the bootstrapring does, roughly speaking, is to resample with replacement. We create pseudo random variables out from your original data. The empirical pdf will converge to the pdf, this is asymptotically. > > > "CT " <cong-thanh.do@hotmail.fr> wrote in message <i4fttk$qpk$1@fred.mathworks.com>... > > I mean that I have N observations of the random vectors x, the vector x has M elements, these are the seed data. So each variable here is a vector (of M elements). Their probability density distribution (pdf) might be multivariate distribution, e.g. Gaussian mixture model (GMM). Since the bootstrap here is non-parametric, the N observations will be used instead of a concrete pdf. > > > > I have tried to used BOOTSTRP to perform the bootstrapping, but it is not easy, even unfeasible (tell me if I am wrong), since the manual of BOOTSTRP in Matlab is not clear in this case (I think). > > > > If the generated data is only X(:,ceil(rand(1,N)*N)), I don't see anything new that the bootstrap can bring. As I see, this is only a disorder of the initial data, we cannot expect anything different from the new data, I'm wrong? > > > > "Rogelio " <rogelioa@math.uio.no> wrote in message <i4eo1o$c8b$1@fred.mathworks.com>... > > > Peter Perkins <Peter.Perkins@MathRemoveThisWorks.com> wrote in message <i4eikn$ndn$1@fred.mathworks.com>... > > > > On 8/17/2010 10:18 AM, Simon Preston wrote: > > > > >> <http://www.mathworks.com/access/helpdesk/help/toolbox/stat > > > > >> /bootstrp.html> > > > > > > > > Sorry, for some reason that link was missing an "s" > > > > <http://www.mathworks.com/access/helpdesk/help/toolbox/stats/bootstrp.html> > > > > > > > > > Isn't this just: > > > > > > > > > > X(:,ceil(rand(1,N)*N)) > > > > > > > > > > where X is the sample matrix? > > > > > > > > That's the basis of it, yes. But: > > > > > > > > 1) It's kind of tedious to write the same loop over and over, regardless > > > > of how simple that loop is, > > > > 1) There is a good deal of flexibility in the arguments you can pass to > > > > BOOTSTRP, so a single matrix isn't the only case it handles for you, and > > > > 2) (in recent MATLAB releases) There is support for parallelizing the > > > > computations using PARFOR (if your installation supports that) > > > > > > > > Just as an aside, since 2008b you might find it easier to use RANDI to > > > > generate random integers. > > > > > > Just one thing to point out, you said that M is the dimention of the data. I thought that you ment different groups or different experiments where the data was collected, after all thats why your data is not of dimenation N*M x 1, for instance. If the columns of the matrix represent different groups, for some or another reason, you cannot pool the series. As far as know 'bootstrp' does not distinguishes among different groups. If this last statement is incorrect, can someone send me the link to read about it. > > > Thanks

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8/18/2010 7:08:05 AM

On 8/18/2010 2:55 AM, Rogelio wrote: > If you are saying or have a feeling that your data might come from a > multivariate distribution, then as far as I know 'bootstrp' will pool > your data together, assuming they come from the same pdf which might be > an erronous assumption. Rogelio, your definition of "multivariate" seems to mean "grouped" or "stratified" or "from a mixture distribution". The usual way to define "multivariate" is simply that there are multiple variables. You are correct that BOOTSTRP does not resample with stratification, but it's not clear that that is what the OP was asking about.

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8/18/2010 12:22:25 PM

For instance, I have a matrix X(M,N) = X(3,500) of initial data. There are thus N = 500 observations of random vector tri-variate random vector x following the multivariate normal distribution. These data can be generated by the code: mu = [1 -1 -2]; Sigma = [2 -1 1; -1 2 -1; 1 -1 2]; X = mvnrnd(mu, Sigma, 500); I don't know if I can use 'bootstrp' to generate the data of the same nature, i.e. they follow (asymptotically) the multivariate normal distribution that I have used to generate X: [bootstat, bootsamp] = bootstrp(10, [], X); (I don't care about the stats of the data at the moment, I want to have the resampled data only). However, 'bootstrp' returns the matrix bootsamp of dimension 500x10, so 'bootstrp' has done only for one dimensional variable? And I don't know if 'bootstrp' can return the stats for multivariate distribution or not? (here are the mean vector and covariance matrix) "Rogelio " <rogelioa@math.uio.no> wrote in message <i4g0sl$a6k$1@fred.mathworks.com>... > By the way ...... what is the statistc that you are bootstraping? it will be nice if you post the code. > > "Rogelio " <rogelioa@math.uio.no> wrote in message <i4g04r$fa8$1@fred.mathworks.com>... > > If you are saying or have a feeling that your data might come from a multivariate distribution, then as far as I know 'bootstrp' will pool your data together, assuming they come from the same pdf which might be an erronous assumption. > > > I have tried to used BOOTSTRP to perform the bootstrapping, but it is not easy, even unfeasible (tell me if I am wrong), since the manual of BOOTSTRP in Matlab is not clear in this case (I think)< > > Why? can you tell us what is the mistake or post the code > > >As I see, this is only a disorder of the initial data, we cannot expect anything different from the new data, I'm wrong?< > > What the bootstrapring does, roughly speaking, is to resample with replacement. We create pseudo random variables out from your original data. The empirical pdf will converge to the pdf, this is asymptotically. > > > > > > "CT " <cong-thanh.do@hotmail.fr> wrote in message <i4fttk$qpk$1@fred.mathworks.com>... > > > I mean that I have N observations of the random vectors x, the vector x has M elements, these are the seed data. So each variable here is a vector (of M elements). Their probability density distribution (pdf) might be multivariate distribution, e.g. Gaussian mixture model (GMM). Since the bootstrap here is non-parametric, the N observations will be used instead of a concrete pdf. > > > > > > I have tried to used BOOTSTRP to perform the bootstrapping, but it is not easy, even unfeasible (tell me if I am wrong), since the manual of BOOTSTRP in Matlab is not clear in this case (I think). > > > > > > If the generated data is only X(:,ceil(rand(1,N)*N)), I don't see anything new that the bootstrap can bring. As I see, this is only a disorder of the initial data, we cannot expect anything different from the new data, I'm wrong? > > > > > > "Rogelio " <rogelioa@math.uio.no> wrote in message <i4eo1o$c8b$1@fred.mathworks.com>... > > > > Peter Perkins <Peter.Perkins@MathRemoveThisWorks.com> wrote in message <i4eikn$ndn$1@fred.mathworks.com>... > > > > > On 8/17/2010 10:18 AM, Simon Preston wrote: > > > > > >> <http://www.mathworks.com/access/helpdesk/help/toolbox/stat > > > > > >> /bootstrp.html> > > > > > > > > > > Sorry, for some reason that link was missing an "s" > > > > > <http://www.mathworks.com/access/helpdesk/help/toolbox/stats/bootstrp.html> > > > > > > > > > > > Isn't this just: > > > > > > > > > > > > X(:,ceil(rand(1,N)*N)) > > > > > > > > > > > > where X is the sample matrix? > > > > > > > > > > That's the basis of it, yes. But: > > > > > > > > > > 1) It's kind of tedious to write the same loop over and over, regardless > > > > > of how simple that loop is, > > > > > 1) There is a good deal of flexibility in the arguments you can pass to > > > > > BOOTSTRP, so a single matrix isn't the only case it handles for you, and > > > > > 2) (in recent MATLAB releases) There is support for parallelizing the > > > > > computations using PARFOR (if your installation supports that) > > > > > > > > > > Just as an aside, since 2008b you might find it easier to use RANDI to > > > > > generate random integers. > > > > > > > > Just one thing to point out, you said that M is the dimention of the data. I thought that you ment different groups or different experiments where the data was collected, after all thats why your data is not of dimenation N*M x 1, for instance. If the columns of the matrix represent different groups, for some or another reason, you cannot pool the series. As far as know 'bootstrp' does not distinguishes among different groups. If this last statement is incorrect, can someone send me the link to read about it. > > > > Thanks

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8/18/2010 3:55:28 PM

Here's some very basic code that might illustrate what's' going on %% Generate your original data set mu = [1 -1 -2]; Sigma = [2 -1 1; -1 2 -1; 1 -1 2]; X = mvnrnd(mu, Sigma, 500); %% Sampling with replacement to create a new data set % Generate an index boot_index = randsample(1:length(X),length(X), 'true')' % Use the index to create a new dataset Boot_dataset = X(bootindex,:) A bootstrap is simply repeating this same operation nboot times and then calculating something interesting using this set of new data sets. Jumping back to the whole "multivariate" discussion. Each time you're drawing from X, you're extracting an entire row. All of the elements of this row are related in that they are a single output from your original multivariate normal distribution. All of this assumes that you need to perform a nonparametric bootstrap. If you have prior knowledge that your population is described by a multivariate normal distribution with mu = [1 -1 -2] and Sigma = [2 -1 1; -1 2 -1; 1 -1 2]; then its often entirely appropriate to use parametric bootstrap and generate your new dataset using mvnrnd.

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8/18/2010 4:56:17 PM

Just a correction, the covariance matrix that I have used is only an example to illustrate the generation of multivariate data. A matrix like that might have no sense. Thank you for the discussions.

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8/19/2010 4:13:58 PM

I made ahuge load script in SQL Server 2000 as i load data from many tables(select some of each one collumns) into one single table and i want to test the loaded data against the selected data to make sure that the loaded data is the same the selected data is there a code or tool to make this test or monitoring ?? please urgent .... tamatem wrote: > I made ahuge load script in SQL Server 2000 as i load data from many > tables(select some of each one collumns) into one single table and i > want to test the loaded data against the selected data to make sure > that the loaded data ...

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This is a multi-part message in MIME format. --------------080106000404020703000908 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Your customer "bootstraptech1@gmail.com" has been asked not to violate our charter and spam us and to adhere to their Terms of Service with you on multiple occasions. They have continued to spam us repeatedly including 6 spam posts between 5:16 and 5:18am. Here is the information you need to kill their account. From: bootstraptech1@gmail.com Date: 5:16 AM Newsgroups: comp.databases.oracle.server Path: news....

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Hi, I have a problem I don't even know where to start from to solve it. I have two computers, say A and B. A wants to send a raw file to B (let's say "data.csv"). B wants to receive this file in a Matlab Session, and store the contents of this file in cell-array "data". B uses the cell-array "data" to perform some operation and obtains a solution cell-array he wants to send back to A as a Raw file, say "solution.csv". Do you have any idea? I thought I could use a TCP/IP connection setting a listening port, but practically I don't know h...

Hi I am having some data in 6 channels. I need to group them (2 groups each of 3 channels). After grouping them i need to find mean of each roup. How can i do the grouping? VYBH Hi VYBH, build two arrays out of your six channels. Use the "Add Array Elements" function and divide it with the number of elements.Mike Hi VYBH, There are many ways to do this depending on the format of the data you have. Here are two examples of manipulating arrays. <img src="http://forums.ni.com/attachments/ni/170/332879/1/arrays.JPG...

The company I work for is currently trying to redeploy Maximo (CMMS software). We are trying to figure out the value of using the Standard Modifiers Dictionary. I was wondering if anyone has used Standard Modifiers Dictionary and what the impact has been for your company.Thank you, Steve ...

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Hi, I would like to extract data from the table attached. Could someone help me to create the regular expression to grab that informations? TABLE: <table border=1 cellpadding=4 cellspacing=0 width=100%><tr bgcolor='#dcdcdc'><td align=center><b>Data</b></td><td align=center><b>Apertura</b></td><td align=center><b>Massimo</b></td><td align=center><b>Minimo</b></td><td align=center><b>Chiusura</b></td><td align=center><b>Volumi</b></td&...

I think there is a profound misunderstanding about the nature of informats when I see a statement like this: "Now to be accurate, as the more informed members of SAS-L have said, informats read character data and transform it to either numeric or character." I would argue that there are a number of informats that read NUMERIC data. Firstly I will make it clear that I regard the main purpose of informats are to read raw data. True, I use them as others do within data steps, to map values to a numeric field that I will use for sorting but I would avoid doing data conversion within a ...

Hi, my questions are simple. 1.) Which ist the fastes way to transfer data (numeric, boolean) from and to a working FPGA on a RT-PXI-system. I've got a deterministic rt-loop and i have to write and to read data to and from a FPGA. FPGA-DMA-FIFO or FPGA-Read/Write-"Control" or Global Var. or ...? The transfer have to be in nano/microseconds! 2.)What is the fastest way to transfer data between a rt-loop and a lower priority loop (network communication)? RT-FIFO (1 element) or Notifier or Global Var. or Func. Var (LV2 Var.) or ...? The trans...

Hi All, =A0 I want to generate bootstrap samples based on the following original sampli= ng: =A0 =A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0= =A0=A0=A0=A0=A0=A0 =A0 =A0 =A0=A0=A0=A0=A0=A0Testing Results at Instrument = 1=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 Testing Results at Instrument 2 Sample ID=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 SITE1=A0=A0=A0=A0=A0=A0=A0=A0=A0= =A0=A0 SITE2=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 SITE3=A0=A0 SITE4=A0=A0=A0=A0= =A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 =A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 SITE1=A0= =A0=20 =A0 1=A0=A0=A0=A0=A0=A0=A0=A0=A0 =A0=A0=A0=A0=...

TOPIC: Data stack "frame" superior I am quite surprised that no one has commented on my timing studies in which I demonstrated that for the calculation of y = a * x ** + b * x + c in the unoptimal way the use of PICK with cleanup of the input parameters was faster than the normal use of the return stack. This started with the misrepresentation of NSI (named stack items) representing it as producing the following: (net time on a 486DX ) ( 163.52 ) : bar-roll-full 3 ROLL OVER * OVER * -ROT 3 ROLL * + + ; Of course this painted NSI in a bad light. Even the use of pick...

*********************************************************************** Bear Stearns is not responsible for any recommendation, solicitation, offer or agreement or any information about any transaction, customer account or account activity contained in this communication. *********************************************************************** say again!! On Mon, 23 Aug 2004, Braten, Michael Exchange wrote: > *********************************************************************** > Bear Stearns is not responsible for any recommendation, solicitation, > offer or agreement or any in...

US-TX-Austin: Database Architect/Admin, Data Modeling, SQL, UMS, Model 204; 3M (45283738500) ============================================================================================ Position: Database Architect/Admin Reference: SMC01140 Location: Austin TX Duration: 1Y Skills: Experience designing and developing enterprise-wide database systems. Skilled in the use of queries and analysis tools to interface with legacy data in support of both internal and external customers. BS in Computer Science o...