Ipermute Inverse permute array dimensions.
A = IPERMUTE(B,ORDER) is the inverse of permute. IPERMUTE
rearranges the dimensions of B so that PERMUTE(A,ORDER) will
produce B. The array produced has the same values of A but the
order of the subscripts needed to access any particular element
are rearranged as specified by ORDER. For an N-D array A,
numel(ORDER)>=ndims(A). All the elements of ORDER must be unique.
PERMUTE and IPERMUTE are a generalization of transpose (.')
for N-D arrays.
Example
a = rand(1,2,3,4);
b = permute(a,[3 2 1 4]);
c = ipermute(b,[3 2 1 4]); % a and c are equal
See also permute,size.
Overloaded methods:
categorical/ipermute
uss/ipermute
umat/ipermute
ufrd/ipermute
Reference page in Help browser
doc ipermute
<shiftdim> - Shift dimensions.
SHIFTDIM Shift dimensions.
B = SHIFTDIM(X,N) shifts the dimensions of X by N. When N is
positive, SHIFTDIM shifts the dimensions to the left and wraps the
N leading dimensions to the end. When N is negative, SHIFTDIM
shifts the dimensions to the right and pads with singletons.
[B,NSHIFTS] = SHIFTDIM(X) returns the array B with the same
number of elements as X but with any leading singleton
dimensions removed. NSHIFTS returns the number of dimensions
that are removed. If X is a scalar, SHIFTDIM has no effect.
SHIFTDIM is handy for creating functions that, like SUM
or DIFF, work along the first non-singleton dimension.
Examples:
a = rand(1,1,3,1,2);
[b,n] = shiftdim(a); % b is 3-by-1-by-2 and n is 2.
c = shiftdim(b,-n); % c == a.
d = shiftdim(a,3); % d is 1-by-2-by-1-by-1-by-3.
See also circshift, reshape, squeeze.
Overloaded methods:
categorical/shiftdim
Reference page in Help browser
doc shiftdim
<circshift> - Shift array circularly.
CIRCSHIFT Shift array circularly.
B = CIRCSHIFT(A,SHIFTSIZE) circularly shifts the values in the array A
by SHIFTSIZE elements. SHIFTSIZE is a vector of integer scalars where
the N-th element specifies the shift amount for the N-th dimension of
array A. If an element in SHIFTSIZE is positive, the values of A are
shifted down (or to the right). If it is negative, the values of A
are shifted up (or to the left).
Examples:
A = [ 1 2 3;4 5 6; 7 8 9];
B = circshift(A,1) % circularly shifts first dimension values down by 1.
B = 7 8 9
1 2 3
4 5 6
B = circshift(A,[1 -1]) % circularly shifts first dimension values
% down by 1 and second dimension left by 1.
B = 8 9 7
2 3 1
5 6 4
See also fftshift, shiftdim, permute.
Overloaded methods:
categorical/circshift
Reference page in Help browser
doc circshift
<squeeze> - Remove singleton dimensions.
SQUEEZE Remove singleton dimensions.
B = SQUEEZE(A) returns an array B with the same elements as
A but with all the singleton dimensions removed. A singleton
is a dimension such that size(A,dim)==1. 2-D arrays are
unaffected by squeeze so that row vectors remain rows.
For example,
squeeze(rand(2,1,3))
is 2-by-3.
See also shiftdim.
Overloaded methods:
categorical/squeeze
uss/squeeze
umat/squeeze
ufrd/squeeze
ndlft/squeeze
Reference page in Help browser
doc squeeze
Array utility functions.
<isscalar> - True for scalar.
ISSCALAR True if input is a scalar.
ISSCALAR(S) returns logical true (1) if SIZE(S) returns [1 1] and
logical false (0) otherwise.
See also ISSVECTOR, isrow, iscolumn, ismatrix, isnumeric, islogical, ischar,
isempty, size.
Overloaded methods:
categorical/isscalar
cgvariable/isscalar
cgsymvalue/isscalar
dfilt.isscalar
Reference page in Help browser
doc isscalar
<isvector> - True for vector.
ISVECTOR True if input is a vector.
ISVECTOR(V) returns logical true (1) if SIZE(V) returns [1 n] or [n 1]
with a nonnegative integer value n, and logical false (0) otherwise.
See also isscalar, isrow, iscolumn, ismatrix, isnumeric, islogical, ischar,
isempty, size.
Overloaded methods:
categorical/isvector
Reference page in Help browser
doc isvector
<isrow> - True for row vector.
ISROW True if input is a row vector.
ISROW(V) returns logical true (1) if SIZE(V) returns [1 n]
with a nonnegative integer value n, and logical false (0) otherwise.
See also isscalar, isvector, iscolumn, ismatrix, isnumeric, islogical, ischar,
isempty, size.
Reference page in Help browser
doc isrow
<iscolumn> - True for column vector.
ISCOLUMN True if input is a column vector.
ISCOLUMN(V) returns logical true (1) if SIZE(V) returns [n 1]
with a nonnegative integer value n, and logical false (0) otherwise.
See also isscalar, isvector, isrow, ismatrix, isnumeric, islogical, ischar,
isempty, size.
Reference page in Help browser
doc iscolumn
<ismatrix> - True for matrix.
ISMATRIX True if input is a matrix.
ISMATRIX(M) returns logical true (1) if SIZE(M) returns [m n]
with nonnegative integer values m and n, and logical false (0) otherwise.
See also isscalar, isvector, isrow, iscolumn, isnumeric, islogical, ischar,
isempty, size.
Reference page in Help browser
doc ismatrix
Special variables and constants.
<eps> - Floating point relative accuracy.
EPS Spacing of floating point numbers.
D = EPS(X), is the positive distance from ABS(X) to the next larger in
magnitude floating point number of the same precision as X.
X may be either double precision or single precision.
For all X, EPS(X) is equal to EPS(ABS(X)).
EPS, with no arguments, is the distance from 1.0 to the next larger double
precision number, that is EPS with no arguments returns 2^(-52).
EPS('double') is the same as EPS, or EPS(1.0).
EPS('single') is the same as EPS(single(1.0)), or single(2^-23).
Except for numbers whose absolute value is smaller than REALMIN,
if 2^E <= ABS(X) < 2^(E+1), then
EPS(X) returns 2^(E-23) if ISA(X,'single')
EPS(X) returns 2^(E-52) if ISA(X,'double')
For all X of class double such that ABS(X) <= REALMIN, EPS(X)
returns 2^(-1074). Similarly, for all X of class single such that
ABS(X) <= REALMIN('single'), EPS(X) returns 2^(-149).
Replace expressions of the form
if Y < EPS * ABS(X)
with
if Y < EPS(X)
Example return values from calling EPS with various inputs are
presented in the table below:
Expression Return Value
===========================================
eps(1/2) 2^(-53)
eps(1) 2^(-52)
eps(2) 2^(-51)
eps(realmax) 2^971
eps(0) 2^(-1074)
eps(realmin/2) 2^(-1074)
eps(realmin/16) 2^(-1074)
eps(Inf) NaN
eps(NaN) NaN
-------------------------------------------
eps(single(1/2)) 2^(-24)
eps(single(1)) 2^(-23)
eps(single(2)) 2^(-22)
eps(realmax('single')) 2^104
eps(single(0)) 2^(-149)
eps(realmin('single')/2) 2^(-149)
eps(realmin('single')/16) 2^(-149)
eps(single(Inf)) single(NaN)
eps(single(NaN)) single(NaN)
See also realmax, realmin.
Overloaded methods:
codistributed/eps
qfft/eps
Reference page in Help browser
doc eps
<realmax> - Largest positive floating point number.
REALMAX Largest positive floating point number.
x = realmax is the largest double precision floating point number
representable on this computer. Anything larger overflows.
REALMAX('double') is the same as REALMAX with no arguments.
REALMAX('single') is the largest single precision floating point number
representable on this computer. Anything larger overflows to single(Inf).
See also eps, realmin, intmax.
Reference page in Help browser
doc realmax
<realmin> - Smallest positive floating point number.
REALMIN Smallest positive normalized floating point number.
x = realmin is the smallest positive normalized double precision floating
point number on this computer. Anything smaller underflows or is an IEEE
"denormal".
REALMIN('double') is the same as REALMIN with no arguments.
REALMIN('single') is the smallest positive normalized single precision
floating point number on this computer.
See also eps, realmax, intmin.
Reference page in Help browser
doc realmin
<intmax> - Largest positive integer value.
INTMAX Largest positive integer value.
X = INTMAX is the largest positive value representable in an int32.
Any value that is larger than INTMAX will saturate to INTMAX when
cast to int32.
INTMAX('int32') is the same as INTMAX with no arguments.
INTMAX(CLASSNAME) is the largest positive value in the integer class
CLASSNAME. Valid values of CLASSNAME are 'int8', 'uint8', 'int16',
'uint16', 'int32', 'uint32', 'int64' and 'uint64'.
See also intmin, realmax.
Reference page in Help browser
doc intmax
<intmin> - Smallest integer value.
INTMIN Smallest integer value.
X = INTMIN is the smallest value representable in an int32.
Any value that is smaller than INTMIN will saturate to INTMIN when
cast to int32.
INTMIN('int32') is the same as INTMIN with no arguments.
INTMIN(CLASSNAME) is the smallest value in the integer class CLASSNAME.
Valid values of CLASSNAME are 'int8', 'uint8', 'int16', 'uint16',
'int32', 'uint32', 'int64' and 'uint64'.
See also intmax, realmin.
Reference page in Help browser
doc intmin
<pi> - 3.1415926535897....
PI 3.1415926535897....
PI = 4*atan(1) = imag(log(-1)) = 3.1415926535897....
Reference page in Help browser
doc pi
<i> - Imaginary unit.
I Imaginary unit.
As the basic imaginary unit SQRT(-1), i and j are used to enter
complex numbers. For example, the expressions 3+2i, 3+2*i, 3+2j,
3+2*j and 3+2*sqrt(-1) all have the same value.
Since both i and j are functions, they can be overridden and used
as a variable. This permits you to use i or j as an index in FOR
loops, etc.
See also j.
Reference page in Help browser
doc i
<inf> - Infinity.
INF Infinity.
INF returns the IEEE arithmetic representation for positive
infinity. Infinity is also produced by operations like dividing by
zero, eg. 1.0/0.0, or from overflow, eg. exp(1000).
INF('double') is the same as INF with no inputs.
INF('single') is the single precision representation of INF.
INF(N) is an N-by-N matrix of INFs.
INF(M,N) or INF([M,N]) is an M-by-N matrix of INFs.
INF(M,N,P,...) or INF([M,N,P,...]) is an M-by-N-by-P-by-... array of INFs.
INF(...,CLASSNAME) is an array of INFs of class specified by CLASSNAME.
CLASSNAME must be either 'single' or 'double'.
Note: The size inputs M, N, and P... should be nonnegative integers.
Negative integers are treated as 0.
See also nan, isinf, isfinite, isfloat.
Overloaded methods:
distributed/inf
codistributor2dbc/inf
codistributor1d/inf
codistributed/inf
Reference page in Help browser
doc inf
<nan> - Not-a-Number.
NaN Not-a-Number.
NaN is the IEEE arithmetic representation for Not-a-Number.
A NaN is obtained as a result of mathematically undefined
operations like 0.0/0.0 and inf-inf.
NaN('double') is the same as NaN with no inputs.
NaN('single') is the single precision representation of NaN.
NaN(N) is an N-by-N matrix of NaNs.
NaN(M,N) or NaN([M,N]) is an M-by-N matrix of NaNs.
NaN(M,N,P,...) or NaN([M,N,P,...]) is an M-by-N-by-P-by-... array of NaNs.
NaN(...,CLASSNAME) is an array of NaNs of class specified by CLASSNAME.
CLASSNAME must be either 'single' or 'double'.
Note: The size inputs M, N, and P... should be nonnegative integers.
Negative integers are treated as 0.
See also inf, isnan, isfinite, isfloat.
Overloaded methods:
distributed/nan
codistributor2dbc/nan
codistributor1d/nan
codistributed/nan
Reference page in Help browser
doc nan
<isnan> - True for Not-a-Number.
ISNAN True for Not-a-Number.
ISNAN(X) returns an array that contains 1's where
the elements of X are NaN's and 0's where they are not.
For example, ISNAN([pi NaN Inf -Inf]) is [0 1 0 0].
See also isfinite, isinf.
Overloaded methods:
codistributed/isnan
idmodel/isnan
iddata/isnan
idnlmodel/isnan
idnlgrey/isnan
Reference page in Help browser
doc isnan
<isinf> - True for infinite elements.
ISINF True for infinite elements.
ISINF(X) returns an array that contains 1's where the
elements of X are +Inf or -Inf and 0's where they are not.
For example, ISINF([pi NaN Inf -Inf]) is [0 0 1 1].
See also isfinite, isnan.
Overloaded methods:
codistributed/isinf
iddata/isinf
Reference page in Help browser
doc isinf
<isfinite> - True for finite elements.
ISFINITE True for finite elements.
ISFINITE(X) returns an array that contains 1's where
the elements of X are finite and 0's where they are not.
For example, ISFINITE([pi NaN Inf -Inf]) is [1 0 0 0].
For any X, exactly one of ISFINITE(X), ISINF(X), or ISNAN(X)
is 1 for each element.
See also isnan, isinf.
Overloaded methods:
codistributed/isfinite
sweepset/isfinite
Reference page in Help browser
doc isfinite
< j > - Imaginary unit.
J Imaginary unit.
As the basic imaginary unit SQRT(-1), i and j are used to enter
complex numbers. For example, the expressions 3+2i, 3+2*i, 3+2j,
3+2*j and 3+2*sqrt(-1) all have the same value.
Since both i and j are functions, they can be overridden and used
as a variable. This permits you to use i or j as an index in FOR
loops, subscripts, etc.
See also i.
Reference page in Help browser
doc j
<why> - Succinct answer.
WHY Provides succinct answers to almost any question.
WHY, by itself, provides a random answer.
WHY(N) provides the N-th answer.
Please embellish or modify this function to suit your own tastes.
Specialized matrices.
<compan> - Companion matrix.
COMPAN Companion matrix.
COMPAN(P) is a companion matrix of the polynomial
with coefficients P.
Class support for input P:
float: double, single
Reference page in Help browser
doc compan
<gallery> - Test matrices.
GALLERY Higham test matrices.
[out1,out2,...] = GALLERY(matname, param1, param2, ...)
takes matname, a string that is the name of a matrix family, and
the family's input parameters. See the listing below for available
matrix families. Most of the functions take an input argument
that specifies the order of the matrix, and unless otherwise
stated, return a single output.
GALLERY(matname,param1, param2, ..., CLASSNAME) produces a matrix
of class CLASSNAME, which must be either 'single' or 'double' (unless
matname is 'integerdata', in which case 'int8', 'int16', 'int32',
'uint8', 'uint16', and 'uint32' are also allowed.)
If CLASSNAME is not specified then the class of the matrix is
determined from those arguments among param 1, param2, ..., that do
not specify dimensions or select an option:
if any of these arguments is of class single then the matrix is
single; otherwise the matrix is double.
For additional information, type "help private/matname", where matname
is the name of the matrix family.
binomial Binomial matrix -- multiple of involutory matrix.
cauchy Cauchy matrix.
chebspec Chebyshev spectral differentiation matrix.
chebvand Vandermonde-like matrix for the Chebyshev polynomials.
chow Chow matrix -- a singular Toeplitz lower Hessenberg matrix.
circul Circulant matrix.
clement Clement matrix -- tridiagonal with zero diagonal entries.
compar Comparison matrices.
condex Counter-examples to matrix condition number estimators.
cycol Matrix whose columns repeat cyclically.
dorr Dorr matrix -- diagonally dominant, ill-conditioned, tridiagonal.
(One or three output arguments, sparse)
dramadah Matrix of ones and zeroes whose inverse has large integer entries.
fiedler Fiedler matrix -- symmetric.
forsythe Forsythe matrix -- a perturbed Jordan block.
frank Frank matrix -- ill-conditioned eigenvalues.
gcdmat GCD matrix.
gearmat Gear matrix.
grcar Grcar matrix -- a Toeplitz matrix with sensitive eigenvalues.
hanowa Matrix whose eigenvalues lie on a vertical line in the complex
plane.
house Householder matrix. (Three output arguments)
integerdata Array of arbitrary data from uniform distribution on
specified range of integers
invhess Inverse of an upper Hessenberg matrix.
invol Involutory matrix.
ipjfact Hankel matrix with factorial elements. (Two output arguments)
jordbloc Jordan block matrix.
kahan Kahan matrix -- upper trapezoidal.
kms Kac-Murdock-Szego Toeplitz matrix.
krylov Krylov matrix.
lauchli Lauchli matrix -- rectangular.
lehmer Lehmer matrix -- symmetric positive definite.
leslie Leslie matrix.
lesp Tridiagonal matrix with real, sensitive eigenvalues.
lotkin Lotkin matrix.
minij Symmetric positive definite matrix MIN(i,j).
moler Moler matrix -- symmetric positive definite.
neumann Singular matrix from the discrete Neumann problem (sparse).
normaldata Array of arbitrary data from standard normal distribution
orthog Orthogonal and nearly orthogonal matrices.
parter Parter matrix -- a Toeplitz matrix with singular values near PI.
pei Pei matrix.
poisson Block tridiagonal matrix from Poisson's equation (sparse).
prolate Prolate matrix -- symmetric, ill-conditioned Toeplitz matrix.
qmult Pre-multiply matrix by random orthogonal matrix.
randcolu Random matrix with normalized cols and specified singular values.
randcorr Random correlation matrix with specified eigenvalues.
randhess Random, orthogonal upper Hessenberg matrix.
randjorth Random J-orthogonal (hyperbolic, pseudo-orthogonal) matrix.
rando Random matrix with elements -1, 0 or 1.
randsvd Random matrix with pre-assigned singular values and specified
bandwidth.
redheff Matrix of 0s and 1s of Redheffer.
riemann Matrix associated with the Riemann hypothesis.
ris Ris matrix -- a symmetric Hankel matrix.
sampling Nonsymmetric matrix with integer, ill conditioned eigenvalues.
smoke Smoke matrix -- complex, with a "smoke ring" pseudospectrum.
toeppd Symmetric positive definite Toeplitz matrix.
toeppen Pentadiagonal Toeplitz matrix (sparse).
tridiag Tridiagonal matrix (sparse).
triw Upper triangular matrix discussed by Wilkinson and others.
uniformdata Array of arbitrary data from standard uniform distribution
wathen Wathen matrix -- a finite element matrix (sparse, random entries).
wilk Various specific matrices devised/discussed by Wilkinson.
(Two output arguments)
GALLERY(3) is a badly conditioned 3-by-3 matrix.
GALLERY(5) is an interesting eigenvalue problem. Try to find
its EXACT eigenvalues and eigenvectors.
See also magic, hilb, invhilb, hadamard, pascal, rosser, vander, wilkinson.
Reference page in Help browser
doc gallery
<hadamard> - Hadamard matrix.
HADAMARD Hadamard matrix.
HADAMARD(N) is a Hadamard matrix of order N, that is,
a matrix H with elements 1 or -1 such that H'*H = N*EYE(N).
An N-by-N Hadamard matrix with N > 2 exists only if REM(N,4)=0.
This function handles only the cases where N, N/12 or N/20
is a power of 2.
HADAMARD(N,CLASSNAME) produces a matrix of class CLASSNAME.
CLASSNAME must be either 'single' or 'double' (the default).
Reference page in Help browser
doc hadamard
<hankel> - Hankel matrix.
HANKEL Hankel matrix.
HANKEL(C) is a square Hankel matrix whose first column is C and
whose elements are zero below the first anti-diagonal.
HANKEL(C,R) is a Hankel matrix whose first column is C and whose
last row is R.
Hankel matrices are symmetric, constant across the anti-diagonals,
and have elements H(i,j) = P(i+j-1) where P = [C R(2:END)]
completely determines the Hankel matrix.
Class support for inputs C,R:
double, single, int8, int16, int32, uint8, uint16, uint32
See also toeplitz.
Reference page in Help browser
doc hankel
<hilb> - Hilbert matrix.
HILB Hilbert matrix.
HILB(N) is the N by N matrix with elements 1/(i+j-1),
which is a famous example of a badly conditioned matrix.
See INVHILB for the exact inverse.
HILB(N,CLASSNAME) produces a matrix of class CLASSNAME.
CLASSNAME must be either 'single' or 'double' (the default).
This is also a good example of efficient MATLAB programming
style where conventional FOR or DO loops are replaced by
vectorized statements. This approach is faster, but uses
more storage.
See also invhilb.
Reference page in Help browser
doc hilb
<invhilb> - Inverse Hilbert matrix.
INVHILB Inverse Hilbert matrix.
INVHILB(N) is the inverse of the N by N matrix with elements
1/(i+j-1), which is a famous example of a badly conditioned
matrix. The result is exact for N less than about 15.
INVHILB(N,CLASSNAME) produces a matrix of class CLASSNAME.
CLASSNAME must be either 'single' or 'double' (the default).
See also hilb.
Reference page in Help browser
doc invhilb
<magic> - Magic square.
MAGIC Magic square.
MAGIC(N) is an N-by-N matrix constructed from the integers
1 through N^2 with equal row, column, and diagonal sums.
Produces valid magic squares for all N > 0 except N = 2.
Reference page in Help browser
doc magic
< pascal> - Pascal matrix.
PASCAL Pascal matrix.
PASCAL(N) is the Pascal matrix of order N: a symmetric positive
definite matrix with integer entries, made up from Pascal's
triangle. Its inverse has integer entries.
PASCAL(N).^r is symmetric positive semidefinite for all
nonnegative r.
PASCAL(N,1) is the lower triangular Cholesky factor (up to signs
of columns) of the Pascal matrix. It is involutory (is its own
inverse).
PASCAL(N,2) is a rotated version of PASCAL(N,1), with sign flipped
if N is even, which is a cube root of the identity.
PASCAL(N,CLASSNAME) or PASCAL(N,K,CLASSNAME) produces a matrix of
class CLASSNAME. CLASSNAME must be either 'single' or 'double'
(the default).
Reference page in Help browser
doc pascal
<peaks> - A sample function of two variables.
PEAKS A sample function of two variables.
PEAKS is a function of two variables, obtained by translating and
scaling Gaussian distributions, which is useful for demonstrating
MESH, SURF, PCOLOR, CONTOUR, etc.
There are several variants of the calling sequence:
Z = PEAKS;
Z = PEAKS(N);
Z = PEAKS(V);
Z = PEAKS(X,Y);
PEAKS;
PEAKS(N);
PEAKS(V);
PEAKS(X,Y);
[X,Y,Z] = PEAKS;
[X,Y,Z] = PEAKS(N);
[X,Y,Z] = PEAKS(V);
The first variant produces a 49-by-49 matrix.
The second variant produces an N-by-N matrix.
The third variant produces an N-by-N matrix where N = length(V).
The fourth variant evaluates the function at the given X and Y,
which must be the same size. The resulting Z is also that size.
The next four variants, with no output arguments, do a SURF
plot of the result.
The last three variants also produce two matrices, X and Y, for
use in commands such as PCOLOR(X,Y,Z) or SURF(X,Y,Z,DEL2(Z)).
If not given as input, the underlying matrices X and Y are
[X,Y] = MESHGRID(V,V)
where V is a given vector, or V is a vector of length N with
elements equally spaced from -3 to 3. If no input argument is
given, the default N is 49.
Reference page in Help browser
doc peaks
<rosser> - Classic symmetric eigenvalue test problem.
ROSSER Classic symmetric eigenvalue test problem.
This matrix was a challenge for many matrix eigenvalue algorithms.
But LAPACK's DSYEV routine used in MATLAB has no trouble with it.
The matrix is 8-by-8 with integer elements.
It has:
* A double eigenvalue.
* Three nearly equal eigenvalues.
* Dominant eigenvalues of opposite sign.
* A zero eigenvalue.
* A small, nonzero eigenvalue.
ROSSER(CLASSNAME) produces a matrix of class CLASSNAME.
CLASSNAME must be either 'single' or 'double' (the default).
Reference page in Help browser
doc rosser
<toeplitz> - Toeplitz matrix.
TOEPLITZ Toeplitz matrix.
TOEPLITZ(C,R) is a non-symmetric Toeplitz matrix having C as its
first column and R as its first row.
TOEPLITZ(R) is a symmetric Toeplitz matrix for real R.
For a complex vector R with a real first element, T = toeplitz(r)
returns the Hermitian Toeplitz matrix formed from R. When the
first element of R is not real, the resulting matrix is Hermitian
off the main diagonal, i.e., T_{i,j} = conj(T_{j,i}) for i ~= j.
Class support for inputs C,R:
float: double, single
See also hankel.
Reference page in Help browser
doc toeplitz
<vander> - Vandermonde matrix.
VANDER Vandermonde matrix.
A = VANDER(V) returns the Vandermonde matrix whose columns
are powers of the vector V, that is A(i,j) = v(i)^(n-j).
Class support for input V:
float: double, single
Reference page in Help browser
doc vander
< wilkinson> - Wilkinson's eigenvalue test matrix
WILKINSON Wilkinson's eigenvalue test matrix.
WILKINSON(n) is J. H. Wilkinson's eigenvalue test matrix, Wn+.
It is a symmetric, tridiagonal matrix with pairs of nearly,
but not exactly, equal eigenvalues.
The most frequently used case is WILKINSON(21).
For example, WILKINSON(7) is
3 1 0 0 0 0 0
1 2 1 0 0 0 0
0 1 1 1 0 0 0
0 0 1 0 1 0 0
0 0 0 1 1 1 0
0 0 0 0 1 2 1
0 0 0 0 0 1 3
WILKINSON(CLASSNAME) produces a matrix of class CLASSNAME.
CLASSNAME must be either 'single' or 'double' (the default).
Reference page in Help browser
doc wilkinson