MATLAB Function Reference Volume 1: A - E - Bad Request

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cholinc Examples Example 1. 2-250 gets rid of the symptoms of the problem, but it does not solve it. The preconditioner may not be singular, but it probably is not useful, and a warning message is printed. The Cholesky-Infinity factorization is meant to be used within interior-point methods. Otherwise, its use is not recommended. Start with a symmetric positive definite matrix, S. S = delsq(numgrid('C',15)); S is the two-dimensional, five-point discrete negative Lapacian on the grid generated by numgrid('C',15). Compute the Cholesky factorization and the incomplete Cholesky factorization of level 0 to compare the fill-in. Make S singular by zeroing out a diagonal entry and compute the (partial) incomplete Cholesky factorization of level 0. C = chol(S); R0 = cholinc(S,'0'); S2 = S; S2(101,101) = 0; [R,p] = cholinc(S2,'0'); Fill-in occurs within the bands of S in the complete Cholesky factor, but none in the incomplete Cholesky factor. The incomplete factorization of the singular S2 stopped at row p = 101 resulting in a 100-by-139 partial factor. D1 = (R0'*R0).*spones(S)-S; D2 = (R'*R).*spones(S2)-S2; D1 has elements of the order of eps, showing that R0'*R0 agrees with S over its sparsity pattern. D2 has elements of the order of eps over its first 100 rows and first 100 columns, D2(1:100,:) and D2(:,1:100).
0 20 40 60 80 100 120 140 0 50 nz = 643 100 0 20 40 60 80 100 120 140 0 50 nz = 391 100 S R0=cholinc(S,’0’) Example 2. 0 20 40 60 80 0 20 40 60 80 100 120 C= chol(S) 140 0 50 nz = 1557 100 Partial factor [R,p]=cholinc(S2,’0’) 100 0 50 100 nz = 290 cholinc The first subplot below shows that cholinc(S,0), the incomplete Cholesky factor with a drop tolerance of 0, is the same as the Cholesky factor of S. Increasing the drop tolerance increases the sparsity of the incomplete factors, as seen below. 0 20 40 60 80 100 120 cholinc(S,0) 140 0 50 100 nz = 1557 0 20 40 60 80 100 120 cholinc(S,1e−2) 140 0 50 100 nz = 671 0 20 40 60 80 100 120 cholinc(S,1e−3) 140 0 50 100 nz = 1211 0 20 40 60 80 100 120 cholinc(S,1e−1) 140 0 50 100 nz = 391 2-251
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MATLAB® MATLAB Function Reference
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1 Functions By Category Development
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Functions By Category 1
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Development Environment Development
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ls List directory on UNIX matlabroo
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Mathematics Mathematics Functions f
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Slash or right matrix divide ' Tran
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Matrix Analysis cond Condition numb
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atan, atanh Inverse tangent and inv
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Correlation corrcoef Correlation co
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Convex Hull convhull Convex hull co
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etainc Incomplete beta function bet
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Tree Operations etree Elimination t
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permute Rearrange dimensions of mul
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int8 Convert to signed 8-bit intege
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Array Manipulation : Specify range
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itxor Bit-wise XOR Relational Opera
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evalc Evaluate MATLAB expression wi
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methodsview Display information on
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open Open files of various types us
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Microsoft WAVE Sound Functions wavp
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gtext Place text on 2-D graph using
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tsearch Search for enclosing Delaun
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3-D Visualization 3-D Visualization
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• Selecting Region of Interest Co
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Creating Graphical User Interfaces
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Controlling Program Execution uires
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Alphabetical List of Functions 2
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axis . . . . . . . . . . . . . . .
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clear . . . . . . . . . . . . . . .
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dbup . . . . . . . . . . . . . . .
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expm . . . . . . . . . . . . . . .
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Arithmetic Operators + - * / \ ^ '
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See Also all, any, find, strcmp Rel
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Logical Operators & | ~ expression
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Special Characters [ ] ( ) {} = ' .
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2Colon : Purpose Create vectors, ar
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2abs Purpose Absolute value and com
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Algorithm acos and acosh use these
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Algorithm acot and acoth use these
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See Also csc, csch acsc, acsch 2-33
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actxcontrol Note There are two ways
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actxserver 2actxserver Purpose Crea
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fig=figure; set(fig,'DoubleBuffer',
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Verify that the files were added to
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[W,ierr] = airy(k,Z) also returns a
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2all Purpose Test to determine if a
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2allchild Purpose Find all children
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• 'rand' - set the AlphaData prop
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2alphamap Purpose Specify the figur
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2angle Purpose Phase angle Syntax P
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2any Purpose Test for any nonzeros
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2area Purpose Area fill of a two-di
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2asec, asech Purpose Inverse secant
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2asin, asinh Purpose Inverse sine a
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2assignin Purpose Assign a value to
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2atan, atanh Purpose Inverse tangen
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2atan2 Purpose Four-quadrant invers
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2audioplayer Purpose Create an audi
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Property Description Type Type Name
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Method Description audiorecorder is
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audiorecorder Examples Example 1 Us
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2auwrite Purpose Write NeXT/SUN (.a
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Parameter Value Default You can als
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2aviinfo Purpose Return information
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2aviread Purpose Read an Audio Vide
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While the basic purpose of an axes
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In this example, the first plot occ
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Property Name Property Description
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Axes Properties objects in the axes
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CameraView Angle [0 1 0] (positive
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Color {none} | ColorSpec Axes Prope
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X-, Y-, Z-Limits following table de
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Axes Properties FontName A name suc
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Axes Properties When a handle’s v
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Axes Properties • replacechildren
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Axes Properties define object handl
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Visible {on} | off Axes Properties
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XMinorGrid, YMinorGrid, ZMinorGrido
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2axis Purpose Axis scaling and appe
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Examples The statements axis off tu
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5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 axis(
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2balance Purpose Improve accuracy o
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Now the eigenvectors are well behav
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ar, barh distinct elements and show
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See Also bar3, ColorSpec, patch, st
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ar3, bar3h •'stacked' displays on
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See Also bar, LineSpec, patch 1 0.5
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2beep Purpose Produce a beep sound
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[H,ierr] = besselh(...) also return
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esseli, besselk and the other is a
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2besselj, bessely Purpose Bessel fu
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0.19602657795532 0.28670098806392 0
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1/168 1/252 1/360 1/495 1/660 In th
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Examples Example 1. bicg(afun,b,tol
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flag = relres = iter = 1 1 0 The va
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4559 This time U2 is nonsingular an
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time to precondition and converge t
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Example Example 1. bicgstab bicgsta
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icgstab flag2 is 0 because bicgstab
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2bin2dec Purpose Binary to decimal
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2bitcmp Purpose Complement bits Syn
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2bitmax Purpose Maximum floating-po
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2bitset Purpose Set bit Syntax C =
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2bitxor Purpose Bit-wise XOR Syntax
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2blkdiag Purpose Construct a block
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2break Purpose Terminate execution
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2builtin Purpose Execute builtin fu
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parameters Optional. A vector that
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function dydx = twoode(x,y) dydx =
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fprintf('The fourth eigenvalue is a
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2bvpget Purpose Extract properties
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solinit is a structure with the fol
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Property Value Description Vectoriz
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2calendar Purpose Calendar Syntax c
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camdolly Remarks camdolly sets the
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Examples This example creates a lig
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See Also campos, camtarget camlooka
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end camorbit Rotation in the camera
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2campos Purpose Set or query the ca
Page 253 and 254: 2camproj Purpose Set or query the p
Page 255 and 256: 2camtarget Purpose Set or query the
Page 257 and 258: 2camup Purpose Set or query the cam
Page 259 and 260: 2camva Purpose Set or query the cam
Page 261 and 262: 2camzoom Purpose Zoom in and out on
Page 263 and 264: 2cart2pol Purpose Transform Cartesi
Page 265 and 266: 2case Purpose Case switch Descripti
Page 267 and 268: 2catch Purpose Begin catch block De
Page 269 and 270: each time they render. CData values
Page 271 and 272: The blue color of the ocean is the
Page 273 and 274: 2cdf2rdf Purpose Convert complex di
Page 275 and 276: 2cdfinfo Purpose Return details abo
Page 277 and 278: Column 5 - Record and Dimension Var
Page 279 and 280: Examples Read all of the data from
Page 281 and 282: 2cell Purpose Create cell array Syn
Page 283 and 284: 2cell2struct Purpose Convert cell a
Page 285 and 286: 2cellfun Purpose Apply a function t
Page 287 and 288: 2cellplot Purpose Graphically displ
Page 289 and 290: 2cgs Purpose Conjugate Gradients Sq
Page 291 and 292: Alternatively, use this matrix-vect
Page 293 and 294: 2char Purpose Create character arra
Page 295 and 296: 2checkin Purpose Check file into so
Page 297 and 298: 2checkout Purpose Check file out of
Page 299 and 300: Example 2 - Check out Multiple File
Page 301 and 302: Destroy the positive definiteness (
Page 303: cholinc michol stands for modified
Page 307 and 308: cholinc For hilb(20), the Cholesky
Page 309 and 310: 2cholupdate Purpose Rank 1 update t
Page 311 and 312: Compare chol with cholupdate: R1 =
Page 313 and 314: 2clabel Purpose Contour plot elevat
Page 315 and 316: 2class Purpose Create object or ret
Page 317 and 318: 2clc Purpose Clear Command Window G
Page 319 and 320: clear keyword clears the items indi
Page 321 and 322: To clear all compiled M- and MEX-fu
Page 323 and 324: 2clf Purpose Clear current figure w
Page 325 and 326: 2clock Purpose Current time as a da
Page 327 and 328: See Also delete, figure, gcf must s
Page 329 and 330: 2closereq Purpose Default figure cl
Page 331 and 332: 2colamd Purpose Column approximate
Page 333 and 334: 2colmmd Purpose Sparse column minim
Page 335 and 336: See Also colamd, colperm, lu, sppar
Page 337 and 338: colorbar See Also colormap 10 8 6 4
Page 339 and 340: 2colormap Purpose Set and get the c
Page 341 and 342: The rgbplot function plots colormap
Page 343 and 344: 2ColorSpec Purpose Color specificat
Page 345 and 346: 2colperm Purpose Sparse column perm
Page 347 and 348: 2comet3 Purpose Three-dimensional c
Page 349 and 350: 2compass Purpose Plot arrows emanat
Page 351 and 352: 2complex Purpose Construct complex
Page 353 and 354: 2computer Purpose Identify informat
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2cond Purpose Condition number with
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2condest Purpose 1-norm condition n
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coneplot(...,'method') specifies th
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3. Add the Slice Planes coneplot
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2conj Purpose Complex conjugate Syn
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2contour Purpose Two-dimensional co
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3 2.5 2 1.5 1 0.5 0 −0.5 −1 −
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2contour3 Purpose Three-dimensional
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2contourc Purpose Low-level contour
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2contourf Purpose Filled two-dimens
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2contourslice Purpose Draw contours
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3 2 1 0 −1 −2 −3 3 2 1 0 −1
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2conv Purpose Convolution and polyn
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In practice however, conv2 computes
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4 2 0 −2 −4 15 This figure comb
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2convhull Purpose Convex hull Synta
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2convhulln Purpose n-D convex hull
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2convn Purpose N-dimensional convol
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2copyobj Purpose Copy graphics obje
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2corrcoef Purpose Correlation coeff
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Algorithm cos and cosh use these al
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Algorithm cot and coth use these al
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2cplxpair Purpose Sort complex numb
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2cross Purpose Vector cross product
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Algorithm csc and csch use these al
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5 10 15 20 25 30 7 14 21 28 35 42 1
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2cumprod Purpose Cumulative product
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2cumtrapz Purpose Cumulative trapez
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2curl Purpose Computes the curl and
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See Also streamribbon, divergence c
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2cylinder Purpose Generate cylinder
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See Also sphere, surf 1 0.8 0.6 0.4
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daspect the window). This means set
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2date Purpose Current date string S
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Examples Convert a date string to a
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dateform (number) dateform (string)
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2datetick Purpose Label tick lines
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datetick('x',11) % Replace x-axis t
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ans = See Also clock, datenum, date
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See Also dbcont, dbdown, dbquit, db
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2dbdown Purpose Change local worksp
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dblquad The integrnd function integ
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2dbquit Purpose Quit debug mode Gra
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2dbstatus Purpose List all breakpoi
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2dbstop Purpose Set breakpoints in
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Examples The file buggy, used in th
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2dbtype Purpose List M-file with li
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2ddeadv Purpose Set up advisory lin
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2ddeexec Purpose Send string for ex
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2ddepoke Purpose Send data to appli
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2ddereq Purpose Request data from a
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2ddeterm Purpose Terminate DDE conv
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2deal Purpose Deal inputs to output
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2deblank Purpose Strip trailing bla
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2dec2bin Purpose Decimal to binary
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2deconv Purpose Deconvolution and p
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2del2 Purpose Discrete Laplacian Sy
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See Also diff, gradient V = 4*del2(
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Visualization Use one of these func
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1 0.5 0 −0.5 −1 15 delaunay Nex
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2delaunay3 Purpose 3-D Delaunay tes
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delaunay3 [2] National Science and
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3 9 1 5 2 9 1 6 2 3 9 4 2 3 9 1 7 9
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2delete Purpose Delete files or gra
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2delete (serial) Purpose Remove a s
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2depfun Purpose List the dependent
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depfun not examine the files on whi
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2det Purpose Matrix determinant Syn
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y = -0.0000 1.0000 -2.0000 1.0000 0
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2diag Purpose Diagonal matrices and
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2dialog Purpose Create and display
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2diff Purpose Differences and appro
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2dir Purpose Display directory list
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2disp Purpose Display text or array
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2display Purpose Overloaded method
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2divergence Purpose Computes the di
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2dlmread Purpose Read an ASCII deli
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2dmperm Purpose Dulmage-Mendelsohn
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2docopt Purpose Display location of
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To open the notepad editor and retu
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2double Purpose Convert to double-p
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2drawnow Purpose Complete pending d
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2dsearchn Purpose n-D nearest point
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2edit Purpose Edit or create M-file
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2eig Purpose Find eigenvalues and e
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Examples The matrix eigenvalues, it
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2eigs Purpose Find a few eigenvalue
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eigs(A,K,sigma,opts) and eigs(A,B,k
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[dum,ind] = sort(abs(d)); plot(dlm,
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(lambda - 4.0), where lambda is an
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2ellipj Purpose Jacobi elliptic fun
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2ellipke Purpose Complete elliptic
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2ellipsoid Purpose Generate ellipso
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2elseif Purpose Conditionally execu
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2end Purpose Terminate for, while,
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2eomday Purpose End of month Syntax
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2erf, erfc, erfcx, erfinv, erfcinv
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2error Purpose Display error messag
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errorbar(X,Y,E) 1.4 See Also LineSp
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displays this dialog box on a UNIX
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2etree Purpose Elimination tree Syn
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2eval Purpose Execute a string cont
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2evalc Purpose Evaluate MATLAB expr
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Limitation evalin cannot be used re
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If item is a Java class, then exist
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2exit Purpose Terminate MATLAB (sam
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2expint Purpose Exponential integra
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expm Notice that the diagonal eleme
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2ezcontour Purpose Easy to use cont
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ezcontour See Also contour, ezconto
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f( x, y) 31 ( - x) 2e x2 - ( y + 1)
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2ezmesh Purpose Easy to use 3-D mes
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2ezmeshc Purpose Easy to use combin
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2ezplot Purpose Easy to use functio
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2ezplot3 Purpose Easy to use 3-D pa
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2ezpolar Purpose Easy to use polar
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sqrt(x.^2 + y.^2); is written as: e
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2ezsurfc Purpose Easy to use combin
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See Also ezcontour, ezcontourf, ezm
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Symbols ! 2-22 - 2-10 % 2-22 & 2-20
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eta function (defined) 2-144 incomp
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colamd 2-277 colmmd 2-279 Color Axe
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dbclear 2-378 dbcont 2-380 dbdown 2
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ellipj 2-481 ellipke 2-483 elliptic
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help files, location for UNIX 2-457
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mldivide (M-file function equivalen
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sound files reading 2-76 writing 2-
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ZGrid, Axes property 2-114 ZLim, Ax
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