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How To Fix Error In Orthogonal Basis
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Symptoms & Summary
Error In Orthogonal Basis and other critical errors can occur when your Windows operating system becomes corrupted. Opening programs will be slower and response times will lag. When you have multiple applications running, you may experience crashes and freezes. There can be numerous causes of this error including excessive startup entries, registry errors, hardware/RAM decline, fragmented files, unnecessary or redundant program installations and so on.
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File Size 746 KB
Compatible Windows XP, Vista, 7 (32/64 bit), 8 (32/64 bit), 8.1 (32/64 bit) Windows 10 (32/64 bit)
to CCL by: Guilherme Menegon Arantes [dinamica~!~webcable.com.br] Hi there list, Any tip about the following error seen in Gaussian 03 (B.04) on how to find orthogonal basis a SGI Altix running SUSE LINUX Enterprise Server 9 (ia64), kernel
2.6.5-7.201-rtgfx: (Enter /usr/local/g03/l302.exe) NPDir=0 NMtPBC= 1 NCelOv= 1 NCel= 1 NClECP= 1 NCelD= 1 NCelK= 1 NCelE2= 1 orthogonal basis functions NClLst= 1 CellRange= 0.0. One-electron integrals computed using PRISM. Error in orthogonal basis= 4.77D+01 with 295 functions, increasing threshold to 2.00D-06. Error in orthogonal basis= 9.49D+01 with 295 functions,
increasing threshold to 4.00D-06. ... Error in orthogonal basis= 9.49D+01 with 295 functions, increasing threshold to 5.24D-01. Error in orthogonal basis= 9.49D+01 with 288 functions, increasing threshold to 1.05D+00. Error in orthogonal basis= 2.27D+01 with 145 functions, increasing threshold to 2.10D+00. Error in orthogonal basis= 2.22D+01 with 30 functions, increasing threshold to 4.19D+00. Error in orthogonal basis= 2.13D+00 with orthogonal basis calculator 1 functions, increasing threshold to 8.39D+00. Bad length for file. FileIO: IOper= 1 IFilNo(1)= -685 Len= 0 IPos= 0 Q= 1142739344 dumping /fiocom/, unit = 1 NFiles = 46 SizExt = 524288 WInBlk = 2048 defal = T LstWrd = 9723904 FType=2 FMxFil=10000 ... Base 20480 End 65536 End1 65536 Wr Pntr 20480 Rd Pntr 20480 Length 45056 Error termination in NtrErr: NtrErr Called from FileIO. --------------------------------------------------------- This job route session: %nosave %mem=97440512 %chk=temp/oi.chk #p mp2/6-311+G(df,p) maxdisk=1920mw scan counterpoise=2 --------------------------------------------------------- What puzzles me is that this looks like a disk/scratch file error, but there is plenty of space and the files never get bigger than 1GB (not at this stage of the calculation!). This "Error in orthogonal basis" appears to be caused by a linear dependence in the basis set (not seen in G98 for the same job). If I tunr off this lin. dep. check (using iop(3/32=2)), the SCF does not converge. I googled around and also looked in the Gaussian web site, but no help. Thanks for your attention, Guilherme Menegon Arantes Sao
från GoogleLogga inDolda fältBöckerbooks.google.se - Models of dynamical systems are of great importance in almost all fields of science and engineering and specifically in control, signal processing and
information science. A model is always only an approximation of
a real phenomenon so that having an approximation theory which allows for the analysis...https://books.google.se/books/about/Modelling_and_Identification_with_Ration.html?hl=sv&id=QVb5K1wI29QC&utm_source=gb-gplus-shareModelling and orthogonal basis matlab Identification with Rational Orthogonal Basis FunctionsMitt bibliotekHjälpAvancerad boksökningKöp e-bok – 1 517,10 krSkaffa ett tryckt exemplar av den här bokenSpringer ShopAmazon.co.ukAdlibrisAkademibokandelnBokus.seHitta boken i ett bibliotekAlla försäljare»Modelling and http://www.ccl.net/chemistry/resources/messages/2006/04/04.009-dir/ Identification with Rational Orthogonal Basis FunctionsPeter S.C. Heuberger, Paul M.J. van den Hof, Bo WahlbergSpringer Science & Business Media, 6 dec. 2005 - 397 sidor 0 Recensionerhttps://books.google.se/books/about/Modelling_and_Identification_with_Ration.html?hl=sv&id=QVb5K1wI29QCModels of dynamical systems are of great importance in almost all fields of science and engineering and specifically in control, signal processing and information science. https://books.google.com/books?id=QVb5K1wI29QC&pg=PA121&lpg=PA121&dq=error+in+orthogonal+basis&source=bl&ots=CZEz4G-uo6&sig=uP0bWpO-N2nFyS_aX3BkQiqR6qw&hl=en&sa=X&ved=0ahUKEwi1l7HU1MzPAhUT3WMKHdgUBzkQ6AEIKjAC A model is always only an approximation of a real phenomenon so that having an approximation theory which allows for the analysis of model quality is a substantial concern. The use of rational orthogonal basis functions to represent dynamical systems and stochastic signals can provide such a theory and underpin advanced analysis and efficient modelling. It also has the potential to extend beyond these areas to deal with many problems in circuit theory, telecommunications, systems, control theory and signal processing. Nine international experts have contributed to this work to produce thirteen chapters that can be read independently or as a comprehensive whole with a logical line of reasoning: Construction and analysis of generalized orthogonal basis function model structure; System Identification in a time domain setting and related issues of variance, numerics, and uncertainty bounding; System identification in the frequency domain; Design issues and optimal basis selection; Transformation and realization theory. Modelli
Matlab and Octave have a function orth() which will compute an orthonormal basis for a space given any set of vectors which span the space. In Matlab, e.g., we have the following help info: >> help orth ORTH Orthogonalization. Q = orth(A) is an orthonormal basis for the range of A. Q'*Q = I, the columns of Q span the same space as https://www.dsprelated.com/freebooks/mdft/Orthogonal_Basis_Computation.html the columns of A and the number of columns of Q is the rank of A. See also QR, http://www.mathworks.com/matlabcentral/mlc-downloads/downloads/submissions/9554/versions/5/previews/numerical-tour/coding_approximation/index.html NULL. Below is an example of using orth() to orthonormalize a linearly independent basis set for : % Demonstration of the orth() function. v1 = [1; 2; 3]; % our first basis vector (a column vector) v2 = [1; -2; 3]; % a second, linearly independent vector v1' * v2 % show that v1 is not orthogonal to v2 ans = 6 V = [v1,v2] % Each column of V is one of our vectors V orthogonal basis = 1 1 2 -2 3 3 W = orth(V) % Find an orthonormal basis for the same space W = 0.2673 0.1690 0.5345 -0.8452 0.8018 0.5071 w1 = W(:,1) % Break out the returned vectors w1 = 0.2673 0.5345 0.8018 w2 = W(:,2) w2 = 0.1690 -0.8452 0.5071 w1' * w2 % Check that w1 is orthogonal to w2 ans = 2.5723e-17 w1' * w1 % Also check that the new vectors are unit length ans = 1 w2' * w2 ans = 1 W' * W % faster way to do the above checks error in orthogonal ans = 1 0 0 1 % Construct some vector x in the space spanned by v1 and v2: x = 2 * v1 - 3 * v2 x = -1 10 -3 % Show that x is also some linear combination of w1 and w2: c1 = x' * w1 % Coefficient of projection of x onto w1 c1 = 2.6726 c2 = x' * w2 % Coefficient of projection of x onto w2 c2 = -10.1419 xw = c1 * w1 + c2 * w2 % Can we make x using w1 and w2? xw = -1 10 -3 error = x - xw error = 1.0e-14 * 0.1332 0 0 norm(error) % typical way to summarize a vector error ans = 1.3323e-15 % It works! (to working precision, of course) % Construct a vector x NOT in the space spanned by v1 and v2: y = [1; 0; 0]; % Almost anything we guess in 3D will work % Try to express y as a linear combination of w1 and w2: c1 = y' * w1; % Coefficient of projection of y onto w1 c2 = y' * w2; % Coefficient of projection of y onto w2 yw = c1 * w1 + c2 * w2 % Can we make y using w1 and w2? yw = 0.1 0.0 0.3 yerror = y - yw yerror = 0.9 0.0 -0.3 norm(yerror) ans = 0.9487 While the error is not zero, it is the smallest possible error in the least squares sense. That is, yw is the optimal least-squares approximation to y in the space spanned by v1 and v2 (w1 and w2). In other words, norm(yerror) is less than or equal to norm(y-yw
Wavelet Transform of an Image Comparison of the Orthogonal Bases Comparison of Wavelet Approximations of Several Images Installing toolboxes and setting up the path. You need to download the general purpose toolbox and the signal toolbox. You need to unzip these toolboxes in your working directory, so that you have toolbox_general/ and toolbox_signal/ in your directory. For Scilab user: you must replace the Matlab comment '%' by its Scilab counterpart '//'. Recommandation: You should create a text file named for instance numericaltour.sce (in Scilab) or numericaltour.m (in Matlab) to write all the Scilab/Matlab commands you want to execute. Then, simply run exec('numericaltour.sce'); (in Scilab) or numericaltour; (in Matlab) to run the commands. Execute this line only if you are using Matlab.getd = @(p)path(path,p); % scilab users must *not* execute this Then you can add these toolboxes to the path.% Add some directories to the path getd('toolbox_signal/'); getd('toolbox_general/'); Fourier Approximation Approximation with Fourier basis is not efficient because it is too global, and also it treats the boundary of the image using periodic condition. First we load an image.n = 256; M = rescale( load_image('lena', n) ); Compute the Fourier transform using the FFT algorithm.MF = fft2(M); Display its magnitude. We use the function fftshift to put the low frequency in the center. clf; imageplot(M, 'Original image', 1,2,1); imageplot(log(1e-5+abs(fftshift(MF))), 'log(FFT)', 1,2,2); Exercice 1: (the solution is exo1.m) Compute a best m-term approximation in the Fourier basis of M (use a well chosen hard thresholding). You can use several m values, for instance m=.02*n^2 and m=.1*n^2. Use the function ifft2 to recover an image from the coefficients. exo1; Best m-term approximation error err_fft(m) by summing the v(i+1:end) where v is the vector of decreasing ordered squared coefficients. v = sort(abs(MF(:)).^2); if v(n^2)
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