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

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eig 2-470 [V,D] = eig(A,B) produces a diagonal matrix D of generalized eigenvalues and a full matrix V whose columns are the corresponding eigenvectors so that A*V = B*V*D. [V,D] = eig(A,B,flag) specifies the algorithm used to compute eigenvalues and eigenvectors. flag can be: 'chol' Computes the generalized eigenvalues of A and B using the Cholesky factorization of B. This is the default for symmetric (Hermitian) A and symmetric (Hermitian) positive definite B. 'qz' Ignores the symmetry, if any, and uses the QZ algorithm as it would for nonsymmetric (non-Hermitian) A and B. Remarks The eigenvalue problem is to determine the nontrivial solutions of the equation Ax = λx where A is an n-by-n matrix, x is a length n column vector, and λ is a scalar. The n values of λ that satisfy the equation are the eigenvalues, and the corresponding values of x are the right eigenvectors. In <strong>MATLAB</strong>, the function eig solves for the eigenvalues λ , and optionally the eigenvectors x . The generalized eigenvalue problem is to determine the nontrivial solutions of the equation Ax = λBx where both A and B are n-by-n matrices and λ is a scalar. The values of λ that satisfy the equation are the generalized eigenvalues and the corresponding values of x are the generalized right eigenvectors. If B is nonsingular, the problem could be solved by reducing it to a standard eigenvalue problem B 1 – Ax = λx Because B can be singular, an alternative algorithm, called the QZ method, is necessary. When a matrix has no repeated eigenvalues, the eigenvectors are always independent and the eigenvector matrix V diagonalizes the original matrix A if applied as a similarity transformation. However, if a matrix has repeated
Examples The matrix eigenvalues, it is not similar to a diagonal matrix unless it has a full (independent) set of eigenvectors. If the eigenvectors are not independent then the original matrix is said to be defective. Even if a matrix is defective, the solution from eig satisfies A*X = X*D. B = [ 3 -2 -.9 2*eps -2 4 1 -eps -eps/4 eps/2 -1 0 -.5 -.5 .1 1 ]; has elements on the order of roundoff error. It is an example for which the nobalance option is necessary to compute the eigenvectors correctly. Try the statements [VB,DB] = eig(B) B*VB - VB*DB [VN,DN] = eig(B,'nobalance') B*VN - VN*DN Algorithm <strong>MATLAB</strong> uses LAPACK routines to compute eigenvalues and eigenvectors: Case Routine Real symmetric A DSYEV Real nonsymmetric A: • With preliminary balance step DGEEV (with SCLFAC = 2 instead of 8 in DGEBAL) • d = eig(A,'nobalance') DGEHRD, DHSEQR • [V,D] = eig(A,'nobalance') DGEHRD, DORGHR, DHSEQR, DTREVC Hermitian A ZHEEV eig 2-471
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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
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2camproj Purpose Set or query the p
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2camtarget Purpose Set or query the
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2camup Purpose Set or query the cam
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2camva Purpose Set or query the cam
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2camzoom Purpose Zoom in and out on
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2cart2pol Purpose Transform Cartesi
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2case Purpose Case switch Descripti
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2catch Purpose Begin catch block De
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each time they render. CData values
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The blue color of the ocean is the
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2cdf2rdf Purpose Convert complex di
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2cdfinfo Purpose Return details abo
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Column 5 - Record and Dimension Var
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Examples Read all of the data from
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2cell Purpose Create cell array Syn
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2cell2struct Purpose Convert cell a
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2cellfun Purpose Apply a function t
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2cellplot Purpose Graphically displ
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2cgs Purpose Conjugate Gradients Sq
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Alternatively, use this matrix-vect
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2char Purpose Create character arra
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2checkin Purpose Check file into so
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2checkout Purpose Check file out of
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Example 2 - Check out Multiple File
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Destroy the positive definiteness (
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cholinc michol stands for modified
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0 20 40 60 80 100 120 140 0 50 nz =
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cholinc For hilb(20), the Cholesky
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2cholupdate Purpose Rank 1 update t
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Compare chol with cholupdate: R1 =
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2clabel Purpose Contour plot elevat
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2class Purpose Create object or ret
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2clc Purpose Clear Command Window G
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clear keyword clears the items indi
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To clear all compiled M- and MEX-fu
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2clf Purpose Clear current figure w
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2clock Purpose Current time as a da
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See Also delete, figure, gcf must s
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2closereq Purpose Default figure cl
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2colamd Purpose Column approximate
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2colmmd Purpose Sparse column minim
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See Also colamd, colperm, lu, sppar
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colorbar See Also colormap 10 8 6 4
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2colormap Purpose Set and get the c
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The rgbplot function plots colormap
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2ColorSpec Purpose Color specificat
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2colperm Purpose Sparse column perm
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2comet3 Purpose Three-dimensional c
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2compass Purpose Plot arrows emanat
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2complex Purpose Construct complex
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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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Page 475 and 476: 2delaunay3 Purpose 3-D Delaunay tes
Page 477 and 478: delaunay3 [2] National Science and
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Page 481 and 482: 2delete Purpose Delete files or gra
Page 483 and 484: 2delete (serial) Purpose Remove a s
Page 485 and 486: 2depfun Purpose List the dependent
Page 487 and 488: depfun not examine the files on whi
Page 489 and 490: 2det Purpose Matrix determinant Syn
Page 491 and 492: y = -0.0000 1.0000 -2.0000 1.0000 0
Page 493 and 494: 2diag Purpose Diagonal matrices and
Page 495 and 496: 2dialog Purpose Create and display
Page 497 and 498: 2diff Purpose Differences and appro
Page 499 and 500: 2dir Purpose Display directory list
Page 501 and 502: 2disp Purpose Display text or array
Page 503 and 504: 2display Purpose Overloaded method
Page 505 and 506: 2divergence Purpose Computes the di
Page 507 and 508: 2dlmread Purpose Read an ASCII deli
Page 509 and 510: 2dmperm Purpose Dulmage-Mendelsohn
Page 511 and 512: 2docopt Purpose Display location of
Page 513 and 514: To open the notepad editor and retu
Page 515 and 516: 2double Purpose Convert to double-p
Page 517 and 518: 2drawnow Purpose Complete pending d
Page 519 and 520: 2dsearchn Purpose n-D nearest point
Page 521 and 522: 2edit Purpose Edit or create M-file
Page 523: 2eig Purpose Find eigenvalues and e
Page 527 and 528: 2eigs Purpose Find a few eigenvalue
Page 529 and 530: eigs(A,K,sigma,opts) and eigs(A,B,k
Page 531 and 532: [dum,ind] = sort(abs(d)); plot(dlm,
Page 533 and 534: (lambda - 4.0), where lambda is an
Page 535 and 536: 2ellipj Purpose Jacobi elliptic fun
Page 537 and 538: 2ellipke Purpose Complete elliptic
Page 539 and 540: 2ellipsoid Purpose Generate ellipso
Page 541 and 542: 2elseif Purpose Conditionally execu
Page 543 and 544: 2end Purpose Terminate for, while,
Page 545 and 546: 2eomday Purpose End of month Syntax
Page 547 and 548: 2erf, erfc, erfcx, erfinv, erfcinv
Page 549 and 550: 2error Purpose Display error messag
Page 551 and 552: errorbar(X,Y,E) 1.4 See Also LineSp
Page 553 and 554: displays this dialog box on a UNIX
Page 555 and 556: 2etree Purpose Elimination tree Syn
Page 557 and 558: 2eval Purpose Execute a string cont
Page 559 and 560: 2evalc Purpose Evaluate MATLAB expr
Page 561 and 562: Limitation evalin cannot be used re
Page 563 and 564: If item is a Java class, then exist
Page 565 and 566: 2exit Purpose Terminate MATLAB (sam
Page 567 and 568: 2expint Purpose Exponential integra
Page 569 and 570: expm Notice that the diagonal eleme
Page 571 and 572: 2ezcontour Purpose Easy to use cont
Page 573 and 574: 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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