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comparison scripts/special-matrix/gallery.m @ 20852:516bb87ea72e

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2015 Code Sprint: remove class of function from docstring for all m-files.
author Rik <rik@octave.org>
date Sat, 12 Dec 2015 07:31:00 -0800
parents c5a8eff5a05d
children 45a64a6c7273
comparison
equal deleted inserted replaced
20851:0828bf20d105 20852:516bb87ea72e
16 ## You should have received a copy of the GNU General Public License 16 ## You should have received a copy of the GNU General Public License
17 ## along with Octave; see the file COPYING. If not, see 17 ## along with Octave; see the file COPYING. If not, see
18 ## <http://www.gnu.org/licenses/>. 18 ## <http://www.gnu.org/licenses/>.
19 19
20 ## -*- texinfo -*- 20 ## -*- texinfo -*-
21 ## @deftypefn {Function File} {} gallery (@var{name}) 21 ## @deftypefn {} {} gallery (@var{name})
22 ## @deftypefnx {Function File} {} gallery (@var{name}, @var{args}) 22 ## @deftypefnx {} {} gallery (@var{name}, @var{args})
23 ## Create interesting matrices for testing. 23 ## Create interesting matrices for testing.
24 ## 24 ##
25 ## @end deftypefn 25 ## @end deftypefn
26 ## 26 ##
27 ## @deftypefn {Function File} {@var{c} =} gallery ("cauchy", @var{x}) 27 ## @deftypefn {} {@var{c} =} gallery ("cauchy", @var{x})
28 ## @deftypefnx {Function File} {@var{c} =} gallery ("cauchy", @var{x}, @var{y}) 28 ## @deftypefnx {} {@var{c} =} gallery ("cauchy", @var{x}, @var{y})
29 ## Create a Cauchy matrix. 29 ## Create a Cauchy matrix.
30 ## 30 ##
31 ## @end deftypefn 31 ## @end deftypefn
32 ## 32 ##
33 ## @deftypefn {Function File} {@var{c} =} gallery ("chebspec", @var{n}) 33 ## @deftypefn {} {@var{c} =} gallery ("chebspec", @var{n})
34 ## @deftypefnx {Function File} {@var{c} =} gallery ("chebspec", @var{n}, @var{k}) 34 ## @deftypefnx {} {@var{c} =} gallery ("chebspec", @var{n}, @var{k})
35 ## Create a Chebyshev spectral differentiation matrix. 35 ## Create a Chebyshev spectral differentiation matrix.
36 ## 36 ##
37 ## @end deftypefn 37 ## @end deftypefn
38 ## 38 ##
39 ## @deftypefn {Function File} {@var{c} =} gallery ("chebvand", @var{p}) 39 ## @deftypefn {} {@var{c} =} gallery ("chebvand", @var{p})
40 ## @deftypefnx {Function File} {@var{c} =} gallery ("chebvand", @var{m}, @var{p}) 40 ## @deftypefnx {} {@var{c} =} gallery ("chebvand", @var{m}, @var{p})
41 ## Create a Vandermonde-like matrix for the Chebyshev polynomials. 41 ## Create a Vandermonde-like matrix for the Chebyshev polynomials.
42 ## 42 ##
43 ## @end deftypefn 43 ## @end deftypefn
44 ## 44 ##
45 ## @deftypefn {Function File} {@var{a} =} gallery ("chow", @var{n}) 45 ## @deftypefn {} {@var{a} =} gallery ("chow", @var{n})
46 ## @deftypefnx {Function File} {@var{a} =} gallery ("chow", @var{n}, @var{alpha}) 46 ## @deftypefnx {} {@var{a} =} gallery ("chow", @var{n}, @var{alpha})
47 ## @deftypefnx {Function File} {@var{a} =} gallery ("chow", @var{n}, @var{alpha}, @var{delta}) 47 ## @deftypefnx {} {@var{a} =} gallery ("chow", @var{n}, @var{alpha}, @var{delta})
48 ## Create a Chow matrix -- a singular Toeplitz lower Hessenberg matrix. 48 ## Create a Chow matrix -- a singular Toeplitz lower Hessenberg matrix.
49 ## 49 ##
50 ## @end deftypefn 50 ## @end deftypefn
51 ## 51 ##
52 ## @deftypefn {Function File} {@var{c} =} gallery ("circul", @var{v}) 52 ## @deftypefn {} {@var{c} =} gallery ("circul", @var{v})
53 ## Create a circulant matrix. 53 ## Create a circulant matrix.
54 ## 54 ##
55 ## @end deftypefn 55 ## @end deftypefn
56 ## 56 ##
57 ## @deftypefn {Function File} {@var{a} =} gallery ("clement", @var{n}) 57 ## @deftypefn {} {@var{a} =} gallery ("clement", @var{n})
58 ## @deftypefnx {Function File} {@var{a} =} gallery ("clement", @var{n}, @var{k}) 58 ## @deftypefnx {} {@var{a} =} gallery ("clement", @var{n}, @var{k})
59 ## Create a tridiagonal matrix with zero diagonal entries. 59 ## Create a tridiagonal matrix with zero diagonal entries.
60 ## 60 ##
61 ## @end deftypefn 61 ## @end deftypefn
62 ## 62 ##
63 ## @deftypefn {Function File} {@var{c} =} gallery ("compar", @var{a}) 63 ## @deftypefn {} {@var{c} =} gallery ("compar", @var{a})
64 ## @deftypefnx {Function File} {@var{c} =} gallery ("compar", @var{a}, @var{k}) 64 ## @deftypefnx {} {@var{c} =} gallery ("compar", @var{a}, @var{k})
65 ## Create a comparison matrix. 65 ## Create a comparison matrix.
66 ## 66 ##
67 ## @end deftypefn 67 ## @end deftypefn
68 ## 68 ##
69 ## @deftypefn {Function File} {@var{a} =} gallery ("condex", @var{n}) 69 ## @deftypefn {} {@var{a} =} gallery ("condex", @var{n})
70 ## @deftypefnx {Function File} {@var{a} =} gallery ("condex", @var{n}, @var{k}) 70 ## @deftypefnx {} {@var{a} =} gallery ("condex", @var{n}, @var{k})
71 ## @deftypefnx {Function File} {@var{a} =} gallery ("condex", @var{n}, @var{k}, @var{theta}) 71 ## @deftypefnx {} {@var{a} =} gallery ("condex", @var{n}, @var{k}, @var{theta})
72 ## Create a `counterexample' matrix to a condition estimator. 72 ## Create a `counterexample' matrix to a condition estimator.
73 ## 73 ##
74 ## @end deftypefn 74 ## @end deftypefn
75 ## 75 ##
76 ## @deftypefn {Function File} {@var{a} =} gallery ("cycol", [@var{m} @var{n}]) 76 ## @deftypefn {} {@var{a} =} gallery ("cycol", [@var{m} @var{n}])
77 ## @deftypefnx {Function File} {@var{a} =} gallery ("cycol", @var{n}) 77 ## @deftypefnx {} {@var{a} =} gallery ("cycol", @var{n})
78 ## @deftypefnx {Function File} {@var{a} =} gallery (@dots{}, @var{k}) 78 ## @deftypefnx {} {@var{a} =} gallery (@dots{}, @var{k})
79 ## Create a matrix whose columns repeat cyclically. 79 ## Create a matrix whose columns repeat cyclically.
80 ## 80 ##
81 ## @end deftypefn 81 ## @end deftypefn
82 ## 82 ##
83 ## @deftypefn {Function File} {[@var{c}, @var{d}, @var{e}] =} gallery ("dorr", @var{n}) 83 ## @deftypefn {} {[@var{c}, @var{d}, @var{e}] =} gallery ("dorr", @var{n})
84 ## @deftypefnx {Function File} {[@var{c}, @var{d}, @var{e}] =} gallery ("dorr", @var{n}, @var{theta}) 84 ## @deftypefnx {} {[@var{c}, @var{d}, @var{e}] =} gallery ("dorr", @var{n}, @var{theta})
85 ## @deftypefnx {Function File} {@var{a} =} gallery ("dorr", @dots{}) 85 ## @deftypefnx {} {@var{a} =} gallery ("dorr", @dots{})
86 ## Create a diagonally dominant, ill-conditioned, tridiagonal matrix. 86 ## Create a diagonally dominant, ill-conditioned, tridiagonal matrix.
87 ## 87 ##
88 ## @end deftypefn 88 ## @end deftypefn
89 ## 89 ##
90 ## @deftypefn {Function File} {@var{a} =} gallery ("dramadah", @var{n}) 90 ## @deftypefn {} {@var{a} =} gallery ("dramadah", @var{n})
91 ## @deftypefnx {Function File} {@var{a} =} gallery ("dramadah", @var{n}, @var{k}) 91 ## @deftypefnx {} {@var{a} =} gallery ("dramadah", @var{n}, @var{k})
92 ## Create a (0, 1) matrix whose inverse has large integer entries. 92 ## Create a (0, 1) matrix whose inverse has large integer entries.
93 ## 93 ##
94 ## @end deftypefn 94 ## @end deftypefn
95 ## 95 ##
96 ## @deftypefn {Function File} {@var{a} =} gallery ("fiedler", @var{c}) 96 ## @deftypefn {} {@var{a} =} gallery ("fiedler", @var{c})
97 ## Create a symmetric @nospell{Fiedler} matrix. 97 ## Create a symmetric @nospell{Fiedler} matrix.
98 ## 98 ##
99 ## @end deftypefn 99 ## @end deftypefn
100 ## 100 ##
101 ## @deftypefn {Function File} {@var{a} =} gallery ("forsythe", @var{n}) 101 ## @deftypefn {} {@var{a} =} gallery ("forsythe", @var{n})
102 ## @deftypefnx {Function File} {@var{a} =} gallery ("forsythe", @var{n}, @var{alpha}) 102 ## @deftypefnx {} {@var{a} =} gallery ("forsythe", @var{n}, @var{alpha})
103 ## @deftypefnx {Function File} {@var{a} =} gallery ("forsythe", @var{n}, @var{alpha}, @var{lambda}) 103 ## @deftypefnx {} {@var{a} =} gallery ("forsythe", @var{n}, @var{alpha}, @var{lambda})
104 ## Create a @nospell{Forsythe} matrix (a perturbed Jordan block). 104 ## Create a @nospell{Forsythe} matrix (a perturbed Jordan block).
105 ## 105 ##
106 ## @end deftypefn 106 ## @end deftypefn
107 ## 107 ##
108 ## @deftypefn {Function File} {@var{f} =} gallery ("frank", @var{n}) 108 ## @deftypefn {} {@var{f} =} gallery ("frank", @var{n})
109 ## @deftypefnx {Function File} {@var{f} =} gallery ("frank", @var{n}, @var{k}) 109 ## @deftypefnx {} {@var{f} =} gallery ("frank", @var{n}, @var{k})
110 ## Create a Frank matrix (ill-conditioned eigenvalues). 110 ## Create a Frank matrix (ill-conditioned eigenvalues).
111 ## 111 ##
112 ## @end deftypefn 112 ## @end deftypefn
113 ## 113 ##
114 ## @deftypefn {Function File} {@var{c} =} gallery ("gcdmat", @var{n}) 114 ## @deftypefn {} {@var{c} =} gallery ("gcdmat", @var{n})
115 ## Create a greatest common divisor matrix. 115 ## Create a greatest common divisor matrix.
116 ## 116 ##
117 ## @var{c} is an @var{n}-by-@var{n} matrix whose values correspond to the 117 ## @var{c} is an @var{n}-by-@var{n} matrix whose values correspond to the
118 ## greatest common divisor of its coordinate values, i.e., @var{c}(i,j) 118 ## greatest common divisor of its coordinate values, i.e., @var{c}(i,j)
119 ## correspond @code{gcd (i, j)}. 119 ## correspond @code{gcd (i, j)}.
120 ## @end deftypefn 120 ## @end deftypefn
121 ## 121 ##
122 ## @deftypefn {Function File} {@var{a} =} gallery ("gearmat", @var{n}) 122 ## @deftypefn {} {@var{a} =} gallery ("gearmat", @var{n})
123 ## @deftypefnx {Function File} {@var{a} =} gallery ("gearmat", @var{n}, @var{i}) 123 ## @deftypefnx {} {@var{a} =} gallery ("gearmat", @var{n}, @var{i})
124 ## @deftypefnx {Function File} {@var{a} =} gallery ("gearmat", @var{n}, @var{i}, @var{j}) 124 ## @deftypefnx {} {@var{a} =} gallery ("gearmat", @var{n}, @var{i}, @var{j})
125 ## Create a Gear matrix. 125 ## Create a Gear matrix.
126 ## 126 ##
127 ## @end deftypefn 127 ## @end deftypefn
128 ## 128 ##
129 ## @deftypefn {Function File} {@var{g} =} gallery ("grcar", @var{n}) 129 ## @deftypefn {} {@var{g} =} gallery ("grcar", @var{n})
130 ## @deftypefnx {Function File} {@var{g} =} gallery ("grcar", @var{n}, @var{k}) 130 ## @deftypefnx {} {@var{g} =} gallery ("grcar", @var{n}, @var{k})
131 ## Create a Toeplitz matrix with sensitive eigenvalues. 131 ## Create a Toeplitz matrix with sensitive eigenvalues.
132 ## 132 ##
133 ## @end deftypefn 133 ## @end deftypefn
134 ## 134 ##
135 ## @deftypefn {Function File} {@var{a} =} gallery ("hanowa", @var{n}) 135 ## @deftypefn {} {@var{a} =} gallery ("hanowa", @var{n})
136 ## @deftypefnx {Function File} {@var{a} =} gallery ("hanowa", @var{n}, @var{d}) 136 ## @deftypefnx {} {@var{a} =} gallery ("hanowa", @var{n}, @var{d})
137 ## Create a matrix whose eigenvalues lie on a vertical line in the complex 137 ## Create a matrix whose eigenvalues lie on a vertical line in the complex
138 ## plane. 138 ## plane.
139 ## 139 ##
140 ## @end deftypefn 140 ## @end deftypefn
141 ## 141 ##
142 ## @deftypefn {Function File} {@var{v} =} gallery ("house", @var{x}) 142 ## @deftypefn {} {@var{v} =} gallery ("house", @var{x})
143 ## @deftypefnx {Function File} {[@var{v}, @var{beta}] =} gallery ("house", @var{x}) 143 ## @deftypefnx {} {[@var{v}, @var{beta}] =} gallery ("house", @var{x})
144 ## Create a householder matrix. 144 ## Create a householder matrix.
145 ## 145 ##
146 ## @end deftypefn 146 ## @end deftypefn
147 ## 147 ##
148 ## @deftypefn {Function File} {@var{a} =} gallery ("integerdata", @var{imax}, [@var{M} @var{N} @dots{}], @var{j}) 148 ## @deftypefn {} {@var{a} =} gallery ("integerdata", @var{imax}, [@var{M} @var{N} @dots{}], @var{j})
149 ## @deftypefnx {Function File} {@var{a} =} gallery ("integerdata", @var{imax}, @var{M}, @var{N}, @dots{}, @var{j}) 149 ## @deftypefnx {} {@var{a} =} gallery ("integerdata", @var{imax}, @var{M}, @var{N}, @dots{}, @var{j})
150 ## @deftypefnx {Function File} {@var{a} =} gallery ("integerdata", [@var{imin}, @var{imax}], [@var{M} @var{N} @dots{}], @var{j}) 150 ## @deftypefnx {} {@var{a} =} gallery ("integerdata", [@var{imin}, @var{imax}], [@var{M} @var{N} @dots{}], @var{j})
151 ## @deftypefnx {Function File} {@var{a} =} gallery ("integerdata", [@var{imin}, @var{imax}], @var{M}, @var{N}, @dots{}, @var{j}) 151 ## @deftypefnx {} {@var{a} =} gallery ("integerdata", [@var{imin}, @var{imax}], @var{M}, @var{N}, @dots{}, @var{j})
152 ## @deftypefnx {Function File} {@var{a} =} gallery ("integerdata", @dots{}, "@var{class}") 152 ## @deftypefnx {} {@var{a} =} gallery ("integerdata", @dots{}, "@var{class}")
153 ## Create a matrix with random integers in the range [1, @var{imax}]. 153 ## Create a matrix with random integers in the range [1, @var{imax}].
154 ## If @var{imin} is given then the integers are in the range 154 ## If @var{imin} is given then the integers are in the range
155 ## [@var{imin}, @var{imax}]. 155 ## [@var{imin}, @var{imax}].
156 ## 156 ##
157 ## The second input is a matrix of dimensions describing the size of the output. 157 ## The second input is a matrix of dimensions describing the size of the output.
166 ## @qcode{"uint32"}, @qcode{"int8"}, @qcode{"int16"}, int32", @qcode{"single"}, 166 ## @qcode{"uint32"}, @qcode{"int8"}, @qcode{"int16"}, int32", @qcode{"single"},
167 ## @qcode{"double"}. The default is @qcode{"double"}. 167 ## @qcode{"double"}. The default is @qcode{"double"}.
168 ## 168 ##
169 ## @end deftypefn 169 ## @end deftypefn
170 ## 170 ##
171 ## @deftypefn {Function File} {@var{a} =} gallery ("invhess", @var{x}) 171 ## @deftypefn {} {@var{a} =} gallery ("invhess", @var{x})
172 ## @deftypefnx {Function File} {@var{a} =} gallery ("invhess", @var{x}, @var{y}) 172 ## @deftypefnx {} {@var{a} =} gallery ("invhess", @var{x}, @var{y})
173 ## Create the inverse of an upper Hessenberg matrix. 173 ## Create the inverse of an upper Hessenberg matrix.
174 ## 174 ##
175 ## @end deftypefn 175 ## @end deftypefn
176 ## 176 ##
177 ## @deftypefn {Function File} {@var{a} =} gallery ("invol", @var{n}) 177 ## @deftypefn {} {@var{a} =} gallery ("invol", @var{n})
178 ## Create an involutory matrix. 178 ## Create an involutory matrix.
179 ## 179 ##
180 ## @end deftypefn 180 ## @end deftypefn
181 ## 181 ##
182 ## @deftypefn {Function File} {@var{a} =} gallery ("ipjfact", @var{n}) 182 ## @deftypefn {} {@var{a} =} gallery ("ipjfact", @var{n})
183 ## @deftypefnx {Function File} {@var{a} =} gallery ("ipjfact", @var{n}, @var{k}) 183 ## @deftypefnx {} {@var{a} =} gallery ("ipjfact", @var{n}, @var{k})
184 ## Create a Hankel matrix with factorial elements. 184 ## Create a Hankel matrix with factorial elements.
185 ## 185 ##
186 ## @end deftypefn 186 ## @end deftypefn
187 ## 187 ##
188 ## @deftypefn {Function File} {@var{a} =} gallery ("jordbloc", @var{n}) 188 ## @deftypefn {} {@var{a} =} gallery ("jordbloc", @var{n})
189 ## @deftypefnx {Function File} {@var{a} =} gallery ("jordbloc", @var{n}, @var{lambda}) 189 ## @deftypefnx {} {@var{a} =} gallery ("jordbloc", @var{n}, @var{lambda})
190 ## Create a Jordan block. 190 ## Create a Jordan block.
191 ## 191 ##
192 ## @end deftypefn 192 ## @end deftypefn
193 ## 193 ##
194 ## @deftypefn {Function File} {@var{u} =} gallery ("kahan", @var{n}) 194 ## @deftypefn {} {@var{u} =} gallery ("kahan", @var{n})
195 ## @deftypefnx {Function File} {@var{u} =} gallery ("kahan", @var{n}, @var{theta}) 195 ## @deftypefnx {} {@var{u} =} gallery ("kahan", @var{n}, @var{theta})
196 ## @deftypefnx {Function File} {@var{u} =} gallery ("kahan", @var{n}, @var{theta}, @var{pert}) 196 ## @deftypefnx {} {@var{u} =} gallery ("kahan", @var{n}, @var{theta}, @var{pert})
197 ## Create a @nospell{Kahan} matrix (upper trapezoidal). 197 ## Create a @nospell{Kahan} matrix (upper trapezoidal).
198 ## 198 ##
199 ## @end deftypefn 199 ## @end deftypefn
200 ## 200 ##
201 ## @deftypefn {Function File} {@var{a} =} gallery ("kms", @var{n}) 201 ## @deftypefn {} {@var{a} =} gallery ("kms", @var{n})
202 ## @deftypefnx {Function File} {@var{a} =} gallery ("kms", @var{n}, @var{rho}) 202 ## @deftypefnx {} {@var{a} =} gallery ("kms", @var{n}, @var{rho})
203 ## Create a @nospell{Kac-Murdock-Szego} Toeplitz matrix. 203 ## Create a @nospell{Kac-Murdock-Szego} Toeplitz matrix.
204 ## 204 ##
205 ## @end deftypefn 205 ## @end deftypefn
206 ## 206 ##
207 ## @deftypefn {Function File} {@var{b} =} gallery ("krylov", @var{a}) 207 ## @deftypefn {} {@var{b} =} gallery ("krylov", @var{a})
208 ## @deftypefnx {Function File} {@var{b} =} gallery ("krylov", @var{a}, @var{x}) 208 ## @deftypefnx {} {@var{b} =} gallery ("krylov", @var{a}, @var{x})
209 ## @deftypefnx {Function File} {@var{b} =} gallery ("krylov", @var{a}, @var{x}, @var{j}) 209 ## @deftypefnx {} {@var{b} =} gallery ("krylov", @var{a}, @var{x}, @var{j})
210 ## Create a Krylov matrix. 210 ## Create a Krylov matrix.
211 ## 211 ##
212 ## @end deftypefn 212 ## @end deftypefn
213 ## 213 ##
214 ## @deftypefn {Function File} {@var{a} =} gallery ("lauchli", @var{n}) 214 ## @deftypefn {} {@var{a} =} gallery ("lauchli", @var{n})
215 ## @deftypefnx {Function File} {@var{a} =} gallery ("lauchli", @var{n}, @var{mu}) 215 ## @deftypefnx {} {@var{a} =} gallery ("lauchli", @var{n}, @var{mu})
216 ## Create a @nospell{Lauchli} matrix (rectangular). 216 ## Create a @nospell{Lauchli} matrix (rectangular).
217 ## 217 ##
218 ## @end deftypefn 218 ## @end deftypefn
219 ## 219 ##
220 ## @deftypefn {Function File} {@var{a} =} gallery ("lehmer", @var{n}) 220 ## @deftypefn {} {@var{a} =} gallery ("lehmer", @var{n})
221 ## Create a @nospell{Lehmer} matrix (symmetric positive definite). 221 ## Create a @nospell{Lehmer} matrix (symmetric positive definite).
222 ## 222 ##
223 ## @end deftypefn 223 ## @end deftypefn
224 ## 224 ##
225 ## @deftypefn {Function File} {@var{t} =} gallery ("lesp", @var{n}) 225 ## @deftypefn {} {@var{t} =} gallery ("lesp", @var{n})
226 ## Create a tridiagonal matrix with real, sensitive eigenvalues. 226 ## Create a tridiagonal matrix with real, sensitive eigenvalues.
227 ## 227 ##
228 ## @end deftypefn 228 ## @end deftypefn
229 ## 229 ##
230 ## @deftypefn {Function File} {@var{a} =} gallery ("lotkin", @var{n}) 230 ## @deftypefn {} {@var{a} =} gallery ("lotkin", @var{n})
231 ## Create a @nospell{Lotkin} matrix. 231 ## Create a @nospell{Lotkin} matrix.
232 ## 232 ##
233 ## @end deftypefn 233 ## @end deftypefn
234 ## 234 ##
235 ## @deftypefn {Function File} {@var{a} =} gallery ("minij", @var{n}) 235 ## @deftypefn {} {@var{a} =} gallery ("minij", @var{n})
236 ## Create a symmetric positive definite matrix MIN(i,j). 236 ## Create a symmetric positive definite matrix MIN(i,j).
237 ## 237 ##
238 ## @end deftypefn 238 ## @end deftypefn
239 ## 239 ##
240 ## @deftypefn {Function File} {@var{a} =} gallery ("moler", @var{n}) 240 ## @deftypefn {} {@var{a} =} gallery ("moler", @var{n})
241 ## @deftypefnx {Function File} {@var{a} =} gallery ("moler", @var{n}, @var{alpha}) 241 ## @deftypefnx {} {@var{a} =} gallery ("moler", @var{n}, @var{alpha})
242 ## Create a @nospell{Moler} matrix (symmetric positive definite). 242 ## Create a @nospell{Moler} matrix (symmetric positive definite).
243 ## 243 ##
244 ## @end deftypefn 244 ## @end deftypefn
245 ## 245 ##
246 ## @deftypefn {Function File} {[@var{a}, @var{t}] =} gallery ("neumann", @var{n}) 246 ## @deftypefn {} {[@var{a}, @var{t}] =} gallery ("neumann", @var{n})
247 ## Create a singular matrix from the discrete Neumann problem (sparse). 247 ## Create a singular matrix from the discrete Neumann problem (sparse).
248 ## 248 ##
249 ## @end deftypefn 249 ## @end deftypefn
250 ## 250 ##
251 ## @deftypefn {Function File} {@var{a} =} gallery ("normaldata", [@var{M} @var{N} @dots{}], @var{j}) 251 ## @deftypefn {} {@var{a} =} gallery ("normaldata", [@var{M} @var{N} @dots{}], @var{j})
252 ## @deftypefnx {Function File} {@var{a} =} gallery ("normaldata", @var{M}, @var{N}, @dots{}, @var{j}) 252 ## @deftypefnx {} {@var{a} =} gallery ("normaldata", @var{M}, @var{N}, @dots{}, @var{j})
253 ## @deftypefnx {Function File} {@var{a} =} gallery ("normaldata", @dots{}, "@var{class}") 253 ## @deftypefnx {} {@var{a} =} gallery ("normaldata", @dots{}, "@var{class}")
254 ## Create a matrix with random samples from the standard normal distribution 254 ## Create a matrix with random samples from the standard normal distribution
255 ## (mean = 0, std = 1). 255 ## (mean = 0, std = 1).
256 ## 256 ##
257 ## The first input is a matrix of dimensions describing the size of the output. 257 ## The first input is a matrix of dimensions describing the size of the output.
258 ## The dimensions can also be input as comma-separated arguments. 258 ## The dimensions can also be input as comma-separated arguments.
265 ## Possible values for @var{class}: @qcode{"single"}, @qcode{"double"}. 265 ## Possible values for @var{class}: @qcode{"single"}, @qcode{"double"}.
266 ## The default is @qcode{"double"}. 266 ## The default is @qcode{"double"}.
267 ## 267 ##
268 ## @end deftypefn 268 ## @end deftypefn
269 ## 269 ##
270 ## @deftypefn {Function File} {@var{q} =} gallery ("orthog", @var{n}) 270 ## @deftypefn {} {@var{q} =} gallery ("orthog", @var{n})
271 ## @deftypefnx {Function File} {@var{q} =} gallery ("orthog", @var{n}, @var{k}) 271 ## @deftypefnx {} {@var{q} =} gallery ("orthog", @var{n}, @var{k})
272 ## Create orthogonal and nearly orthogonal matrices. 272 ## Create orthogonal and nearly orthogonal matrices.
273 ## 273 ##
274 ## @end deftypefn 274 ## @end deftypefn
275 ## 275 ##
276 ## @deftypefn {Function File} {@var{a} =} gallery ("parter", @var{n}) 276 ## @deftypefn {} {@var{a} =} gallery ("parter", @var{n})
277 ## Create a @nospell{Parter} matrix (a Toeplitz matrix with singular values 277 ## Create a @nospell{Parter} matrix (a Toeplitz matrix with singular values
278 ## near pi). 278 ## near pi).
279 ## 279 ##
280 ## @end deftypefn 280 ## @end deftypefn
281 ## 281 ##
282 ## @deftypefn {Function File} {@var{p} =} gallery ("pei", @var{n}) 282 ## @deftypefn {} {@var{p} =} gallery ("pei", @var{n})
283 ## @deftypefnx {Function File} {@var{p} =} gallery ("pei", @var{n}, @var{alpha}) 283 ## @deftypefnx {} {@var{p} =} gallery ("pei", @var{n}, @var{alpha})
284 ## Create a Pei matrix. 284 ## Create a Pei matrix.
285 ## 285 ##
286 ## @end deftypefn 286 ## @end deftypefn
287 ## 287 ##
288 ## @deftypefn {Function File} {@var{a} =} gallery ("Poisson", @var{n}) 288 ## @deftypefn {} {@var{a} =} gallery ("Poisson", @var{n})
289 ## Create a block tridiagonal matrix from Poisson's equation (sparse). 289 ## Create a block tridiagonal matrix from Poisson's equation (sparse).
290 ## 290 ##
291 ## @end deftypefn 291 ## @end deftypefn
292 ## 292 ##
293 ## @deftypefn {Function File} {@var{a} =} gallery ("prolate", @var{n}) 293 ## @deftypefn {} {@var{a} =} gallery ("prolate", @var{n})
294 ## @deftypefnx {Function File} {@var{a} =} gallery ("prolate", @var{n}, @var{w}) 294 ## @deftypefnx {} {@var{a} =} gallery ("prolate", @var{n}, @var{w})
295 ## Create a prolate matrix (symmetric, ill-conditioned Toeplitz matrix). 295 ## Create a prolate matrix (symmetric, ill-conditioned Toeplitz matrix).
296 ## 296 ##
297 ## @end deftypefn 297 ## @end deftypefn
298 ## 298 ##
299 ## @deftypefn {Function File} {@var{h} =} gallery ("randhess", @var{x}) 299 ## @deftypefn {} {@var{h} =} gallery ("randhess", @var{x})
300 ## Create a random, orthogonal upper Hessenberg matrix. 300 ## Create a random, orthogonal upper Hessenberg matrix.
301 ## 301 ##
302 ## @end deftypefn 302 ## @end deftypefn
303 ## 303 ##
304 ## @deftypefn {Function File} {@var{a} =} gallery ("rando", @var{n}) 304 ## @deftypefn {} {@var{a} =} gallery ("rando", @var{n})
305 ## @deftypefnx {Function File} {@var{a} =} gallery ("rando", @var{n}, @var{k}) 305 ## @deftypefnx {} {@var{a} =} gallery ("rando", @var{n}, @var{k})
306 ## Create a random matrix with elements -1, 0 or 1. 306 ## Create a random matrix with elements -1, 0 or 1.
307 ## 307 ##
308 ## @end deftypefn 308 ## @end deftypefn
309 ## 309 ##
310 ## @deftypefn {Function File} {@var{a} =} gallery ("randsvd", @var{n}) 310 ## @deftypefn {} {@var{a} =} gallery ("randsvd", @var{n})
311 ## @deftypefnx {Function File} {@var{a} =} gallery ("randsvd", @var{n}, @var{kappa}) 311 ## @deftypefnx {} {@var{a} =} gallery ("randsvd", @var{n}, @var{kappa})
312 ## @deftypefnx {Function File} {@var{a} =} gallery ("randsvd", @var{n}, @var{kappa}, @var{mode}) 312 ## @deftypefnx {} {@var{a} =} gallery ("randsvd", @var{n}, @var{kappa}, @var{mode})
313 ## @deftypefnx {Function File} {@var{a} =} gallery ("randsvd", @var{n}, @var{kappa}, @var{mode}, @var{kl}) 313 ## @deftypefnx {} {@var{a} =} gallery ("randsvd", @var{n}, @var{kappa}, @var{mode}, @var{kl})
314 ## @deftypefnx {Function File} {@var{a} =} gallery ("randsvd", @var{n}, @var{kappa}, @var{mode}, @var{kl}, @var{ku}) 314 ## @deftypefnx {} {@var{a} =} gallery ("randsvd", @var{n}, @var{kappa}, @var{mode}, @var{kl}, @var{ku})
315 ## Create a random matrix with pre-assigned singular values. 315 ## Create a random matrix with pre-assigned singular values.
316 ## 316 ##
317 ## @end deftypefn 317 ## @end deftypefn
318 ## 318 ##
319 ## @deftypefn {Function File} {@var{a} =} gallery ("redheff", @var{n}) 319 ## @deftypefn {} {@var{a} =} gallery ("redheff", @var{n})
320 ## Create a zero and ones matrix of @nospell{Redheffer} associated with the 320 ## Create a zero and ones matrix of @nospell{Redheffer} associated with the
321 ## Riemann hypothesis. 321 ## Riemann hypothesis.
322 ## 322 ##
323 ## @end deftypefn 323 ## @end deftypefn
324 ## 324 ##
325 ## @deftypefn {Function File} {@var{a} =} gallery ("riemann", @var{n}) 325 ## @deftypefn {} {@var{a} =} gallery ("riemann", @var{n})
326 ## Create a matrix associated with the Riemann hypothesis. 326 ## Create a matrix associated with the Riemann hypothesis.
327 ## 327 ##
328 ## @end deftypefn 328 ## @end deftypefn
329 ## 329 ##
330 ## @deftypefn {Function File} {@var{a} =} gallery ("ris", @var{n}) 330 ## @deftypefn {} {@var{a} =} gallery ("ris", @var{n})
331 ## Create a symmetric Hankel matrix. 331 ## Create a symmetric Hankel matrix.
332 ## 332 ##
333 ## @end deftypefn 333 ## @end deftypefn
334 ## 334 ##
335 ## @deftypefn {Function File} {@var{a} =} gallery ("smoke", @var{n}) 335 ## @deftypefn {} {@var{a} =} gallery ("smoke", @var{n})
336 ## @deftypefnx {Function File} {@var{a} =} gallery ("smoke", @var{n}, @var{k}) 336 ## @deftypefnx {} {@var{a} =} gallery ("smoke", @var{n}, @var{k})
337 ## Create a complex matrix, with a `smoke ring' pseudospectrum. 337 ## Create a complex matrix, with a `smoke ring' pseudospectrum.
338 ## 338 ##
339 ## @end deftypefn 339 ## @end deftypefn
340 ## 340 ##
341 ## @deftypefn {Function File} {@var{t} =} gallery ("toeppd", @var{n}) 341 ## @deftypefn {} {@var{t} =} gallery ("toeppd", @var{n})
342 ## @deftypefnx {Function File} {@var{t} =} gallery ("toeppd", @var{n}, @var{m}) 342 ## @deftypefnx {} {@var{t} =} gallery ("toeppd", @var{n}, @var{m})
343 ## @deftypefnx {Function File} {@var{t} =} gallery ("toeppd", @var{n}, @var{m}, @var{w}) 343 ## @deftypefnx {} {@var{t} =} gallery ("toeppd", @var{n}, @var{m}, @var{w})
344 ## @deftypefnx {Function File} {@var{t} =} gallery ("toeppd", @var{n}, @var{m}, @var{w}, @var{theta}) 344 ## @deftypefnx {} {@var{t} =} gallery ("toeppd", @var{n}, @var{m}, @var{w}, @var{theta})
345 ## Create a symmetric positive definite Toeplitz matrix. 345 ## Create a symmetric positive definite Toeplitz matrix.
346 ## 346 ##
347 ## @end deftypefn 347 ## @end deftypefn
348 ## 348 ##
349 ## @deftypefn {Function File} {@var{p} =} gallery ("toeppen", @var{n}) 349 ## @deftypefn {} {@var{p} =} gallery ("toeppen", @var{n})
350 ## @deftypefnx {Function File} {@var{p} =} gallery ("toeppen", @var{n}, @var{a}) 350 ## @deftypefnx {} {@var{p} =} gallery ("toeppen", @var{n}, @var{a})
351 ## @deftypefnx {Function File} {@var{p} =} gallery ("toeppen", @var{n}, @var{a}, @var{b}) 351 ## @deftypefnx {} {@var{p} =} gallery ("toeppen", @var{n}, @var{a}, @var{b})
352 ## @deftypefnx {Function File} {@var{p} =} gallery ("toeppen", @var{n}, @var{a}, @var{b}, @var{c}) 352 ## @deftypefnx {} {@var{p} =} gallery ("toeppen", @var{n}, @var{a}, @var{b}, @var{c})
353 ## @deftypefnx {Function File} {@var{p} =} gallery ("toeppen", @var{n}, @var{a}, @var{b}, @var{c}, @var{d}) 353 ## @deftypefnx {} {@var{p} =} gallery ("toeppen", @var{n}, @var{a}, @var{b}, @var{c}, @var{d})
354 ## @deftypefnx {Function File} {@var{p} =} gallery ("toeppen", @var{n}, @var{a}, @var{b}, @var{c}, @var{d}, @var{e}) 354 ## @deftypefnx {} {@var{p} =} gallery ("toeppen", @var{n}, @var{a}, @var{b}, @var{c}, @var{d}, @var{e})
355 ## Create a pentadiagonal Toeplitz matrix (sparse). 355 ## Create a pentadiagonal Toeplitz matrix (sparse).
356 ## 356 ##
357 ## @end deftypefn 357 ## @end deftypefn
358 ## 358 ##
359 ## @deftypefn {Function File} {@var{a} =} gallery ("tridiag", @var{x}, @var{y}, @var{z}) 359 ## @deftypefn {} {@var{a} =} gallery ("tridiag", @var{x}, @var{y}, @var{z})
360 ## @deftypefnx {Function File} {@var{a} =} gallery ("tridiag", @var{n}) 360 ## @deftypefnx {} {@var{a} =} gallery ("tridiag", @var{n})
361 ## @deftypefnx {Function File} {@var{a} =} gallery ("tridiag", @var{n}, @var{c}, @var{d}, @var{e}) 361 ## @deftypefnx {} {@var{a} =} gallery ("tridiag", @var{n}, @var{c}, @var{d}, @var{e})
362 ## Create a tridiagonal matrix (sparse). 362 ## Create a tridiagonal matrix (sparse).
363 ## 363 ##
364 ## @end deftypefn 364 ## @end deftypefn
365 ## 365 ##
366 ## @deftypefn {Function File} {@var{t} =} gallery ("triw", @var{n}) 366 ## @deftypefn {} {@var{t} =} gallery ("triw", @var{n})
367 ## @deftypefnx {Function File} {@var{t} =} gallery ("triw", @var{n}, @var{alpha}) 367 ## @deftypefnx {} {@var{t} =} gallery ("triw", @var{n}, @var{alpha})
368 ## @deftypefnx {Function File} {@var{t} =} gallery ("triw", @var{n}, @var{alpha}, @var{k}) 368 ## @deftypefnx {} {@var{t} =} gallery ("triw", @var{n}, @var{alpha}, @var{k})
369 ## Create an upper triangular matrix discussed by 369 ## Create an upper triangular matrix discussed by
370 ## @nospell{Kahan, Golub, and Wilkinson}. 370 ## @nospell{Kahan, Golub, and Wilkinson}.
371 ## 371 ##
372 ## @end deftypefn 372 ## @end deftypefn
373 ## 373 ##
374 ## @deftypefn {Function File} {@var{a} =} gallery ("uniformdata", [@var{M} @var{N} @dots{}], @var{j}) 374 ## @deftypefn {} {@var{a} =} gallery ("uniformdata", [@var{M} @var{N} @dots{}], @var{j})
375 ## @deftypefnx {Function File} {@var{a} =} gallery ("uniformdata", @var{M}, @var{N}, @dots{}, @var{j}) 375 ## @deftypefnx {} {@var{a} =} gallery ("uniformdata", @var{M}, @var{N}, @dots{}, @var{j})
376 ## @deftypefnx {Function File} {@var{a} =} gallery ("uniformdata", @dots{}, "@var{class}") 376 ## @deftypefnx {} {@var{a} =} gallery ("uniformdata", @dots{}, "@var{class}")
377 ## Create a matrix with random samples from the standard uniform distribution 377 ## Create a matrix with random samples from the standard uniform distribution
378 ## (range [0,1]). 378 ## (range [0,1]).
379 ## 379 ##
380 ## The first input is a matrix of dimensions describing the size of the output. 380 ## The first input is a matrix of dimensions describing the size of the output.
381 ## The dimensions can also be input as comma-separated arguments. 381 ## The dimensions can also be input as comma-separated arguments.
388 ## Possible values for @var{class}: @qcode{"single"}, @qcode{"double"}. 388 ## Possible values for @var{class}: @qcode{"single"}, @qcode{"double"}.
389 ## The default is @qcode{"double"}. 389 ## The default is @qcode{"double"}.
390 ## 390 ##
391 ## @end deftypefn 391 ## @end deftypefn
392 ## 392 ##
393 ## @deftypefn {Function File} {@var{a} =} gallery ("wathen", @var{nx}, @var{ny}) 393 ## @deftypefn {} {@var{a} =} gallery ("wathen", @var{nx}, @var{ny})
394 ## @deftypefnx {Function File} {@var{a} =} gallery ("wathen", @var{nx}, @var{ny}, @var{k}) 394 ## @deftypefnx {} {@var{a} =} gallery ("wathen", @var{nx}, @var{ny}, @var{k})
395 ## Create the @nospell{Wathen} matrix. 395 ## Create the @nospell{Wathen} matrix.
396 ## 396 ##
397 ## @end deftypefn 397 ## @end deftypefn
398 ## 398 ##
399 ## @deftypefn {Function File} {[@var{a}, @var{b}] =} gallery ("wilk", @var{n}) 399 ## @deftypefn {} {[@var{a}, @var{b}] =} gallery ("wilk", @var{n})
400 ## Create various specific matrices devised/discussed by Wilkinson. 400 ## Create various specific matrices devised/discussed by Wilkinson.
401 ## 401 ##
402 ## @end deftypefn 402 ## @end deftypefn
403 403
404 ## Code for most of the individual matrices (except binomial, gcdmat, 404 ## Code for most of the individual matrices (except binomial, gcdmat,