From bf2c69a0218fd549d835e44ff2f52d20252144be Mon Sep 17 00:00:00 2001 From: Luis Mendo Date: Sat, 26 Mar 2016 19:01:06 +0100 Subject: [PATCH] Various changes * `Yk` (closest value) now includes a third output with indices of selected values * `Z^` (Cartesian power) now allows inputs in reverse order if the second is an array of at least two elements * `m` (`ismember`) and `u` (`unique`) now accept numeric content in cell array input * `Z+` (2D convolution; see also `Y+`) now produces output the same size as the input * Bug corrected in `e` (`reshape`) for `logical` input * Modular indexing has been added, only for scalar indices (thanks to @Dennis for the suggestion) * Bug corrected in `ZA`. In addition, now it allows cell array input, and ignores non-recognized digits * `o` with cell input now allows specifying fill value and padding side * `Z}` (split array) now by default splits along the first non-singleton dimension * Added `W` function: 2 raised to input, element-wise * Updated the Fibonacci example in the documentation (1 byte fewer using `y`), and included the new features * `YS` (`circshift`) now allows second input to be a vector with third input specifying dimension when first input is a 2D array * `Xd` (`diag`) now includes `spdiags` functionality * `format` function has been integrated with `ZG` * `h` (horizontal concatenation) and `v` (vertical concatenation) now linearize their inputs if sizes don't match --- doc/MATL_spec.pdf | Bin 489436 -> 501190 bytes doc/function_table.pdf | Bin 72936 -> 73051 bytes funDef.mat | Bin 42911 -> 45856 bytes funDef.txt | 177 +++++++++++++++++++++++++++-------------- genHelp.m | 10 ++- help.mat | Bin 38612 -> 40327 bytes matl_compile.m | 29 ++++++- preLit.mat | Bin 3548 -> 3648 bytes preLit.txt | 10 ++- 9 files changed, 159 insertions(+), 67 deletions(-) diff --git a/doc/MATL_spec.pdf b/doc/MATL_spec.pdf index 64944bd04c0c5ee0861adce21370d964167179d7..818ce538f5953f64349dee21291c450159f2918d 100644 GIT binary patch delta 159107 zcmZUaV{j%+u&86(ww=7OZQHi(>>Foe+sVeZZQIty+L(LyJNMN6bAQcLS9jM;SIta4 z)7{&*grieL^#&-QTlsAvWm*3Yjb{*NBqp=ogqLQZh@Cl zzR^6$B2tTh2`L?hs%VD6(~a%s>S9lNGC94=;|s(*-5CtEZRcVXe`P zym<+VtN~m>q73#d7yUS^F&;zw@e$*=euzThx8RjxP3g@KpSy|1;f0XIi^yk10egwy zLcJZr-`|Q#;(ttoO8Is|s2PBV+?jc2H^W{%qD4DYY?;^9olMp|xK(u$Mm)ylYH6xg zi2(9#Eb$T&5KJ?13II!S=FfS2Vrl-Y9d1AH`wX%UEJCs*D~m@zK7z-lha);!;ru$i zZDlBQci9f&R#nqM2?MFh>}K1%Gv}P(jt!gNu-k2Dp5unvyiRZHg8Lpl=@Nr|yBJG0E1s)J!zJ{{EZ>DFyShxKZ)pN9(6xN}_>Q z)P=V2TAY`p2xsZ2X`dBX!(^j>FfNMYR`2z)xcZo8f|^=1jSa9aZCaSpjNnAqHUAbT zJrN}d_&M2R*#}k27Vj&82M{*k%Gz7q!yQ^6CUc- zg#6900D1aoGAIzJoaQt~b~p#vuiGoH;t_CnE5@bq>qi0OKkMB^AZiQ}RQqvxmFe(Q 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z%T#anJwPj_r)gHO`Tl>(bq~xCHXVvw@k6$iW@zWH7CS#Vc2F*Bl69-QO}(-D$TOD`bWCai=4;XwTq{$w~>JcQ7U3aYgo24-@|G9)X& zYfy8$eD9X6htICL9$vTJYkup7pP8;nhEI8G=D!#id{=Db-gK||j z`73;>?Y-Y<*xN8YDb)L;MeoS*17(?*F51+W2_LKZM(2|4x2cl|mYL3sDe}GyYHc|Q z3Qnumel(sz), sz = [ sz ones(1,Ni-numel(sz)) ]; end for n = 1:Ni if ~islogical(indices{n}) && ~all(real(indices{n}(:))) indices{n} = num2cell(real(indices{n})+(sz(n)+imag(indices{n})).*~real(indices{n})); @@ -98,7 +98,7 @@ Z' 0 1 0 1 1 1 true true true true if numel(in)==0, out{1} = now; current date a end out{1} = arrayDestination; % This code above was easy, after the code for ) had been done -% shiftdim is needed to preserve end-index shape (the colon operation gives a row vector both for say [1 0] and [1;0]). I realized this here, with assignment indexing. For referencing indexing and for curly-brace indexing it probably doesn't matter, but I also add the shiftdim operation there just case +% shiftdim is needed to preserve end-index shape (the colon operation gives a row vector both for say [1 0] and [1;0]). I realized this here, with assignment indexing. For referencing indexing and for curly-brace indexing it probably doesn't matter, but I also add the shiftdim operation there just in case % `data = []; x=[5 4 7]; x([1 3]) = data;` doesn't work. It has to be `data = []; x=[5 4 7]; x([1 3]) = [];`. In addition, for indexing with various indices, all of them except for one should be `:`. But MATL doesn't have `:`. So assignment with [] only works with one index X( 3 inf 3 1 1 1 true true true true if numel(in)==3, in{4} = 1; end; Ni = in{end}; assignment {} indexing assignment \matlab+{ }+ indexing indices = in(end-Ni:end-1); @@ -106,7 +106,7 @@ X( 3 inf 3 1 1 1 true true true true if numel(in)==3, in{4} = 1; end; Ni = in{en arrayDestination = in{1}; assert(iscell(arrayDestination), 'MATL:runtime', 'MATL run-time error: a cell array is needed as first input') sz = size(arrayDestination); - sz = [ sz(1:Ni-1) prod(sz(Ni:end)) ]; + if Ninumel(sz), sz = [ sz ones(1,Ni-numel(sz)) ]; end for n = 1:Ni if ~islogical(indices{n}) && ~all(real(indices{n}(:))) indices{n} = num2cell(real(indices{n})+(sz(n)+imag(indices{n})).*~real(indices{n})); @@ -120,13 +120,13 @@ X( 3 inf 3 1 1 1 true true true true if numel(in)==3, in{4} = 1; end; Ni = in{en % This code above was based on that for (. % An added difficulty is that `[arrayDestination{indices{:}}] = deal(data{:})` doesn't work (but explicitly writing the indices does work!: [arrayDestination{1:2, 3:4}] = deal(data{:}) ). So I had to use () indexing on the LHS and reshape on the RHS % nnz works for numeric, logical or char indices -Y( 2 inf 3 1 1 1 true true true true arrayDestination = in{1}; assignment ( ) indexing with final colon assignment \matlab+(..., :)+ indexing. Null assignment (\matlab+x(..., :) = []+) can only be done with a single index (in addition to the colon) +Y( 2 inf 3 1 1 1 true true true true arrayDestination = in{1}; assignment ( ) indexing with final colon assignment \matlab+(..., :)+ indexing. Null assignment (\matlab+x(..., :) = []+) can only be done with a single index (in addition to the implicit colon) arrayData = in{2}; indices = [in(3:end) {':'}]; Ni = numel(indices); sz = size(arrayDestination); - sz = [ sz(1:Ni-1) prod(sz(Ni:end)) ]; - for n = 1:Ni + if Ninumel(sz), sz = [ sz ones(1,Ni-numel(sz)) ]; end + for n = 1:Ni-1 if ~islogical(indices{n}) && ~all(real(indices{n}(:))) indices{n} = num2cell(real(indices{n})+(sz(n)+imag(indices{n})).*~real(indices{n})); if numel(indices{n})==1, indices{n} = indices{n}{1}; else shape = find(size(indices{n})>1,1); indices{n} = colon(indices{n}{:}); indices{n} = shiftdim(indices{n}(:),1-shape); end @@ -137,13 +137,13 @@ Y( 2 inf 3 1 1 1 true true true true arrayDestination = in{1}; assignment ( ) in end out{1} = arrayDestination; % The code for Y( is the same as for ( except fot the `indices = ...` line -Z( 2 inf 3 1 1 1 true true true true arrayDestination = in{1}; assignment ( ) indexing with initial colon assignment \matlab+(:, ...)+ indexing. Null assignment (\matlab+x(:, ...) = []+) can only be done with a single index (in addition to the colon) +Z( 2 inf 3 1 1 1 true true true true arrayDestination = in{1}; assignment ( ) indexing with initial colon assignment \matlab+(:, ...)+ indexing. Null assignment (\matlab+x(:, ...) = []+) can only be done with a single index (in addition to the implicit colon) arrayData = in{2}; indices = [{':'} in(3:end)]; Ni = numel(indices); sz = size(arrayDestination); - sz = [ sz(1:Ni-1) prod(sz(Ni:end)) ]; - for n = 1:Ni + if Ninumel(sz), sz = [ sz ones(1,Ni-numel(sz)) ]; end + for n = 2:Ni if ~islogical(indices{n}) && ~all(real(indices{n}(:))) indices{n} = num2cell(real(indices{n})+(sz(n)+imag(indices{n})).*~real(indices{n})); if numel(indices{n})==1, indices{n} = indices{n}{1}; else shape = find(size(indices{n})>1,1); indices{n} = colon(indices{n}{:}); indices{n} = shiftdim(indices{n}(:),1-shape); end @@ -158,38 +158,45 @@ Z( 2 inf 3 1 1 1 true true true true arrayDestination = in{1}; assignment ( ) in indices = in(2:end); Ni = numel(indices); sz = size(array); - sz = [ sz(1:Ni-1) prod(sz(Ni:end)) ]; + if Ninumel(sz), sz = [ sz ones(1,Ni-numel(sz)) ]; end for n = 1:Ni if ~islogical(indices{n}) && ~all(real(indices{n}(:))) indices{n} = num2cell(real(indices{n})+(sz(n)+imag(indices{n})).*~real(indices{n})); if numel(indices{n})==1, indices{n} = indices{n}{1}; else shape = find(size(indices{n})>1,1); indices{n} = colon(indices{n}{:}); indices{n} = shiftdim(indices{n}(:),1-shape); end + elseif ~islogical(indices{n}) && ~ischar(indices{n}) && numel(indices{n})==1 && (indices{n}<=0 || indices{n}>sz(n)) + indices{n} = mod(indices{n}-1,sz(n))+1; end end out{1} = array(indices{:}); if nout>1, y = array; y(indices{:}) = []; out{2} = y; end -% This code above for ) indexing has been a little difficult. It had to correctly handle an arbitrary number of indices, possibly with partially linear indexing; and end-based indexing -X) 2 inf 2 1 1 1 true true true true array = in{1}; reference {} indexing reference \matlab+{ }+ indexing +% This code above for ) indexing has been a little difficult. It had to correctly handle an arbitrary number of indices, possibly with partially linear indexing; and end-based indexing. Then I added modular indexing (for scalar indices) +X) 2 inf 2 0 inf -1 true true true true array = in{1}; reference {} indexing reference \matlab+{ }+ indexing assert(iscell(array), 'MATL:runtime', 'MATL run-time error: a cell array is needed as first input') indices = in(2:end); Ni = numel(indices); sz = size(array); - sz = [ sz(1:Ni-1) prod(sz(Ni:end)) ]; + if Ninumel(sz), sz = [ sz ones(1,Ni-numel(sz)) ]; end for n = 1:Ni if ~islogical(indices{n}) && ~all(real(indices{n}(:))) indices{n} = num2cell(real(indices{n})+(sz(n)+imag(indices{n})).*~real(indices{n})); if numel(indices{n})==1, indices{n} = indices{n}{1}; else shape = find(size(indices{n})>1,1); indices{n} = colon(indices{n}{:}); indices{n} = shiftdim(indices{n}(:),1-shape); end + elseif ~islogical(indices{n}) && ~ischar(indices{n}) && numel(indices{n})==1 && (indices{n}<=0 || indices{n}>sz(n)) + indices{n} = mod(indices{n}-1,sz(n))+1; end end out = reshape(array(indices{:}),1,[]); + if nout>=0, out = out(1:nout); end Y) 1 inf 2 1 2 1 true true true true array = in{1}; reference ( ) indexing with final colon reference \matlab+(..., :)+ indexing. If $2$ outputs: only one input index can be used. The second output produces the "complementary" array \matlab+y=x; y(ind,:)=[]+, where \matlab+y+ and \matlab+ind+ are the inputs indices = [in(2:end) {':'}]; Ni = numel(indices); sz = size(array); - sz = [ sz(1:Ni-1) prod(sz(Ni:end)) ]; - for n = 1:Ni + if Ninumel(sz), sz = [ sz ones(1,Ni-numel(sz)) ]; end + for n = 1:Ni-1 if ~islogical(indices{n}) && ~all(real(indices{n}(:))) indices{n} = num2cell(real(indices{n})+(sz(n)+imag(indices{n})).*~real(indices{n})); if numel(indices{n})==1, indices{n} = indices{n}{1}; else shape = find(size(indices{n})>1,1); indices{n} = colon(indices{n}{:}); indices{n} = shiftdim(indices{n}(:),1-shape); end + elseif ~islogical(indices{n}) && ~ischar(indices{n}) && numel(indices{n})==1 && (indices{n}<=0 || indices{n}>sz(n)) + indices{n} = mod(indices{n}-1,sz(n))+1; end end out{1} = array(indices{:}); @@ -199,11 +206,13 @@ Z) 1 inf 2 1 2 1 true true true true array = in{1}; reference ( ) indexing with indices = [{':'} in(2:end)]; Ni = numel(indices); sz = size(array); - sz = [ sz(1:Ni-1) prod(sz(Ni:end)) ]; - for n = 1:Ni + if Ninumel(sz), sz = [ sz ones(1,Ni-numel(sz)) ]; end + for n = 2:Ni if ~islogical(indices{n}) && ~all(real(indices{n}(:))) indices{n} = num2cell(real(indices{n})+(sz(n)+imag(indices{n})).*~real(indices{n})); if numel(indices{n})==1, indices{n} = indices{n}{1}; else shape = find(size(indices{n})>1,1); indices{n} = colon(indices{n}{:}); indices{n} = shiftdim(indices{n}(:),1-shape); end + elseif ~islogical(indices{n}) && ~ischar(indices{n}) && numel(indices{n})==1 && (indices{n}<=0 || indices{n}>sz(n)) + indices{n} = mod(indices{n}-1,sz(n))+1; end end out{1} = array(indices{:}); @@ -219,7 +228,7 @@ Z* 1 inf 2 1 1 1 true true true true n = numel(in); combs = cell(1,n); Cartesian + 1 inf 2 1 1 1 true true true true y = in{1}; for n=2:numel(in), y = bsxfun(@plus, y, in{n}); end; out{1} = y; clear y n; addition (element-wise, singleton expansion) \matlab|+| (\matlab+plus+), element-wise with singleton expansion X+ 2 3 2 1 1 1 true true true true out{1} = conv(double(in{1}), double(in{2}), in{3:end}); convolution \matlab+conv+. Converts first two inputs to \matlab+double+. \sa \matl|Y+|, \matl|Z+| Y+ 2 4 2 1 1 1 true true true true out{1} = conv2(double(in{1}), double(in{2}), in{3:end}); two-dimensional convolution \matlab+conv2+. Converts first two inputs to \matlab+double+. \sa \matl|X+|, \matl|Z+| -Z+ 2 3 2 1 1 1 true true true true out{1} = conv2(double(in{1}), double(in{2}), in{3:end}, 'valid'); two-dimensional convolution; part without zero-padded edges \matlab+conv2(..., 'valid')+. Converts first two inputs to \matlab+double+. \sa \matl|X+|, \matl|Y+| +Z+ 2 3 2 1 1 1 true true true true out{1} = conv2(double(in{1}), double(in{2}), in{3:end}, 'same'); two-dimensional convolution; maintains size \matlab+conv2(..., 'same')+. Converts first two inputs to \matlab+double+. \sa \matl|X+|, \matl|Y+| , X, 1 1 1 1 1 1 true true true true out{1} = cos(in{1}); cosine (radians) \matlab+cos+ Y, 1 1 1 1 1 1 true true true true out{1} = sin(in{1}); sine (radians) \matlab+sin+ @@ -292,7 +301,9 @@ Z5 X6 1 1 1 1 1 1 true true true true fn = 'X6'; k = find(preLit.(fn).key==in{1}, 1); predefined literal predefined literal depending on input assert(~isempty(k), 'MATL:runtime', 'MATL run-time error: input not allowed in function %s', fn); out{1} = preLit.(fn).val{k}; -Y6 +Y6 1 1 1 1 1 1 true true true true fn = 'Y6'; k = find(preLit.(fn).key==in{1}, 1); predefined literal predefined literal depending on input + assert(~isempty(k), 'MATL:runtime', 'MATL run-time error: input not allowed in function %s', fn); + out{1} = preLit.(fn).val{k}; Z6 7 X7 1 1 1 1 1 1 true true true true fn = 'X7'; k = find(preLit.(fn).key==in{1}, 1); predefined literal predefined literal depending on input @@ -364,19 +375,16 @@ YA 2 4 2 1 1 1 true true true true if numel(in{2})==1, out{1} = dec2base(in{:}); clear d n b s end % Adapted from dec2base -ZA 2 2 2 1 1 1 true true true true if numel(in{2})==1, out{1} = base2dec(in{:}); convert string in given base to decimal integer \matlab+base2dec+. If second input has more than one element: it defines the symbols, which can be characters (case-sensitive) or numbers. The number of symbols defines the base, which can exceed $36$ - else h = char(in{1}); symbols = double(in{2}); b = numel(symbols); - if ~isempty(find(h==' ' | h==0,1)), - h = strjust(h); h(h==' ' | h==0) = '0'; end - [m,n] = size(h); - bArr = [ones(m,1) cumprod(b(ones(m,n-1)),2)]; - values = -1*ones(256,1); - values(symbols) = 0:b-1; - if any(any(values(h) >= b | values(h) < 0)) - error(message('MATLAB:base2dec:NumberOutsideRange', h,b)); - end - a = fliplr(reshape(values(abs(h)),size(h))); - out{1} = sum((bArr .* a),2); end +ZA 2 2 2 1 1 1 true true true true x = in{1}; convert string in given base to decimal integer (i) \matlab+base2dec+. (ii) If second input has more than one element: it defines the symbols, which can be characters (case-sensitive) or numbers. The number of symbols defines the base, which can exceed $36$. In (i) and (ii), non-recognized digits are ignored + a = in{2}; if numel(a)==1; b = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'; a=b(1:a); x = upper(x); end + if ~iscell(x), x = mat2cell(x, ones(size(x,1),1), size(x,2)); end + y = NaN(numel(x),1); + for n = 1:numel(x) + [tf, ind] = ismember(x{n}, a); + ind = ind(tf); + y(n) = polyval(ind-1, numel(a)); + end + out{1} = y; clear tf ind x y B 1 2 1 1 1 1 true true true true out{1} = logical(dec2bin(in{:})-'0'); convert from decimal to binary. Produces a logical vector \matlab|logical(dec2bin(...)-'0')|. \sa \matl|YB| XB 1 1 1 1 1 1 true true true true if ~iscell(in{1}) convert from binary to decimal \matlab|bin2dec(char(logical(...)+'0'))|. Works also for cell array input. \sa \matl|ZB| out{1} = bin2dec(char(logical(in{1})+'0')); @@ -425,7 +433,7 @@ YE ZE F XF -YF 0 1 1 0 0 0 true true true true format(in{:}) set output format \matlab+format+ +YF ZF G 0 1 double(numel(CB_G)>1) 0 inf 1+(numel(CB_G)-1)*(numel(in)==0) true true false true if numel(in)==0, out = CB_G(1:nout); else out = CB_G(real(in{1}) + (numel(CB_G)+imag(in{1})).*~real(in{1})); end paste from user-input clipboard G paste from user-input clipboard. With 0 input arguments: addresses all levels. With 1 input argument: addresses level specified by the input XG 1 inf 1 0 0 0 true true true true plot(in{:}); drawnow plot \matlab+plot+. Calls \matlab+drawnow+ to update figure immediately @@ -440,7 +448,8 @@ YG 2 inf 2 0 0 0 true true true true if isnumeric(in{end})&&numel(in{end})~=1, i end end drawnow -ZG 1 inf 2 0 1 0 true true true true switch in{end} control appearance of graphics Depending on numeric last input, calls a graphic function with the remaining inputs. $1$: \matlab+axis+. $2$: \matlab+colormap+. With $0$ outputs, calls \matlab+drawnow+ to update figure immediately. $3$: \matlab+hold+ +ZG 1 inf 2 0 1 0 true true true true switch in{end} control appearance of graphics / format Depending on numeric last input, calls a graphic function or \matlab+format+ with the remaining inputs. $0$: \matlab+format+. $1$: \matlab+axis+. $2$: \matlab+colormap+. With $0$ outputs, calls \matlab+drawnow+ to update figure immediately. $3$: \matlab+hold+ + case 0, format(in{1:end-1}); case 1, axis(in{1:end-1}); case 2, [out{:}] = colormap(in{1:end-1}); if isempty(out), drawnow, end case 3, hold(in{1:end-1}) @@ -483,7 +492,7 @@ XM 1 2 1 1 3 1 true true true true [out{:}] = mode(in{:}); mode (most frequent v YM ZM N 0 0 0 1 1 1 true true false true out{1} = numel(STACK); number of elements in the stack number of elements in the stack -XN 2 2 2 1 1 1 true true true true if numel(in{1})0) all combinations \matlab+nchoosek+. This interprets first input as an array (even if it is a single number). For inputs \matlab+x+ and \matlab+k+, if \matlab+x+ has less than \matlab+k+ elements or if \matlab+k+ is non-positive the result is an empty array +XN 2 2 2 1 1 1 true true true true if numel(in{1})0) all combinations \matlab+nchoosek+. This interprets first input as an array (even if it is a single number). For inputs \matlab+x+ and \matlab+k+, if \matlab+x+ has less than \matlab+k+ elements or if \matlab+k+ is non-positive the result is an empty array. \sa \matl|Xn| out{1} = []; else out{1} = nchoosek(in{:}); end @@ -507,7 +516,7 @@ R 1 2 1 1 1 1 true true true true out{1} = triu(in{:}); upper triangular part \m XR 1 1 1 1 1 1 true true true true out{1} = triu(in{1},1); upper triangular part, above diagonal \matlab+triu(..., 1)+. \sa \matl+R+. YR 1 2 1 1 1 1 true true true true out{1} = tril(in{:}); lower triangular part \matlab+tril+. \sa \matl+ZR+. ZR 1 1 1 1 1 1 true true true true out{1} = tril(in{1},-1); lower triangular part, below diagonal \matlab+tril(..., -1)+. \sa \matl+YR+. -S 1 3 1 1 2 1 true true true true if numel(in)>1 && ~ischar(in{2}) && numel(in{2})>1 && isvector(in{2}) && isequal(numel(in{1}),numel(in{2})) sort sort an array (\matlab+sort+) / sort an array based on another. (i) Single-array mode works like Matlab's \matlab+sort+. If $2$ inputs, a negative value of the second input corresponds to descending order. If first input is a cell array and the first cell contains a char array, the rest of the cells' contents are converted to char. (ii) If the first input is a cell array and the first cell contains a numeric array, single-array numeric mode is used. The first input is linearized if it's not a vector, and its contents are linearized for the purposes of sorting. The first input is then sorted in lexicographic order, ignoring other inputs. (iii) In two-array mode, this function takes as first $2$ inputs an array and a vector array which is not char. If the first array is not a vector it is linearized. The second vector is sorted and its order is applied to the first. An optional third input specifies direction as a string, or as a negative number in the non-singleton dimension of the second vector. The outputs are the two sorted arrays. (In two-array mode, if the two input arrays are scalar the result is the same as if the second input is interpreted as dimension, corresponding to single array mode) +S 1 3 1 1 2 1 true true true true if numel(in)>1 && ~ischar(in{2}) && numel(in{2})>1 && isvector(in{2}) && isequal(numel(in{1}),numel(in{2})) sort sort an array (\matlab+sort+) / sort an array based on another. (i) Single-array mode works like Matlab's \matlab+sort+. If $2$ inputs, a negative value of the second input corresponds to descending order. If first input is a cell array and the first cell contains a char array, the rest of the cells' contents are converted to char. (ii) If the first input is a cell array and the first cell contains a numeric array, single-array numeric mode is used. The first input is linearized if it's not a vector, and its contents are linearized for the purposes of sorting. The first input is then sorted in lexicographic order, ignoring other inputs. (iii) In two-array mode, this function takes as first $2$ inputs an array and a vector array which is not char. If the first array is not a vector it is linearized. The second vector is sorted and its order is applied to the first. An optional third input specifies direction as a string, or as a negative number in the non-singleton dimension of the second vector. The outputs are the two sorted arrays. (In two-array mode, if the two input arrays are scalar the result is the same as if the second input is interpreted as dimension, corresponding to single array mode). \sa \matl|XS| if numel(in)==3 && isnumeric(in{3}) && in{3}<0, in{3}=-in{3}; in{4} = 'descend'; end if ~isvector(in{1}), in{1} = in{1}(:); end [y2, ind] = sort(in{2:end}); y1 = in{1}(ind); out = {y1, y2}; out = out(1:nout); clear y1 y2 @@ -524,14 +533,23 @@ S 1 3 1 1 2 1 true true true true if numel(in)>1 && ~ischar(in{2}) && numel(in{2 [out{:}] = sort(in{:}); end end -XS 1 2 1 1 2 1 true true true true [out{:}] = sortrows(in{:}); sort rows \matlab+sortrows+ -YS 2 3 2 1 1 1 true true true true if numel(in{2})==1 && numel(in)==2 circular shift \matlab+circshift+. If second input is a scalar and there's no third input, the shift is applied along the first non-singleton dimension +XS 1 2 1 1 2 1 true true true true [out{:}] = sortrows(in{:}); sort rows \matlab+sortrows+. \sa \matl|S| +YS 2 3 2 1 1 1 true true true true if numel(in)==3 && numel(in{2})>1 && ndims(in{1})==2 && in{3}<=2 circular shift \matlab+circshift+. If second input is a scalar and there's no third input, the shift is applied along the first non-singleton dimension. This function also allows first input a 2D array; third input a scalar specifying dimension; and second input a vector or array specifying the shift for each position in the other dimension + x = in{1}; + if in{3}==2, x = x.'; end + ind = bsxfun(@plus, 0:size(x,1):numel(x)-1, mod(bsxfun(@plus, (1:size(x,1)).', -in{2}(:).'-1), size(x,1))+1); + x(:) = x(ind); + if in{3}==2, x = x.'; end + out{1} = x; clear x ind + else + if numel(in{2})==1 && numel(in)==2 d = find(size(in{1})>1,1); if isempty(d), d = 1; end y = circshift(in{:}, d); else y = circshift(in{:}); end - out{1} = y; + out{1} = y; clear d y + end ZS 1 1 1 1 1 1 true true true true out{1} = sign(in{:}); sign function \matlab+sign+ T XT @@ -547,7 +565,7 @@ V 1 2 1 1 1 1 true true true true out{1} = num2str(in{:}); convert numbers to a XV YV ZV -W +W 1 1 1 1 1 1 true true true true out{1} = 2.^in{1}; 2 raised to array, element-wise \matlab+2.^(...)+ XW YW ZW @@ -582,7 +600,8 @@ Z] ^ 2 2 2 1 1 1 true true true true out{1} = bsxfun(@power, in{1}, in{2}); array power (element-wise, singleton expansion) \matlab+.^+ (\matlab+power+), element-wise with singleton expansion X^ 1 1 1 1 1 1 true true true true out{1} = sqrt(in{:}); square root \matlab+sqrt+ Y^ 2 2 2 1 1 1 true true true true out{1} = in{1}^in{2}; matrix power \matlab+^+ (\matlab+mpower+) -Z^ 2 2 2 1 1 1 true true true true n = in{2}; combs = cell(1,n); Cartesian power Cartesian power. Given an array and a number $n$, computes the Cartesian power of the array times itself $n$ times. \sa \matl+Z*+ +Z^ 2 2 2 1 1 1 true true true true if numel(in{1})==1 && numel(in{2})>1, in([1 2]) = in([2 1]); end Cartesian power (i) Given an array and a number $n$, computes the Cartesian power of the array times itself $n$ times. (ii) If the first input is a number and the second input is an array of at least two elements, the inputs are interpreted in reverse order. When using this mode, caution is needed in case the second input (array) may become a scalar, because then mode (i) will be used. \sa \matl+Z*+ + n = in{2}; combs = cell(1,n); [combs{end:-1:1}] = ndgrid(in{1}); combs = cat(n+1, combs{:}); combs = reshape(combs,[],n); out{1} = combs; clear combs n @@ -661,7 +680,13 @@ Zc 1 2 1 1 1 1 true true true true if ischar(in{1}{1}) join cell array of string out{1} = y; clear y singledelim delim end d 1 3 1 1 1 1 true true true true out{1} = diff(in{:}); difference \matlab+diff+ -Xd 1 2 1 1 1 1 true true true true out{1} = diag(in{:}); diagonal matrices and diagonals of a matrix \matlab+diag+ +Xd 1 4 2 1 2 1 true true true true if numel(in)==1 && numel(out)==1, out{1} = diag(in{:}); diagonal matrices and diagonals of a matrix If $1$ input and $1$ output: \matlab+diag+. Otherwise: \matlab+spdiags+ + elseif numel(in)==2 && numel(out)==1 && isrow(in{1}) + y = zeros(size(in{2})); mask = (in{2}>=0) & (in{2}<=numel(in{1})-1); y(mask) = in{1}(in{2}(mask)+1); out{1} = y; clear y + elseif numel(in)==2 && numel(out)==1 && iscolumn(in{1}) + y = zeros(size(in{2})); mask = (in{2}<=0) & (in{2}>=1-numel(in{1})); y(mask) = in{1}(1-in{2}(mask)); out{1} = y; clear y + else, [out{:}] = spdiags(in{:}); + end Yd 1 inf 2 1 1 1 true true true true out{1} = blkdiag(in{:}); block diagonal concatenation \matlab+blkdiag+ Zd 1 2 2 1 3 1 true true true true if numel(in)==1 && numel(out)==1, x=in{1}(1); for t=in{1}(:).', x=gcd(x,t); end; out{1}=x; greatest common divisor (element-wise, singleton expansion) \matlab+gcd+, element-wise with singleton expansion. With $1$ input and $1$ output, computes the greatest common divisor of all elements of the input else @@ -679,18 +704,21 @@ e 1 inf 2 1 1 1 true true true true if numel(in)>1 reshape array / remove single if numel(in)==2 && isscalar(in{2}), in{3} = []; end if ~any(cellfun(@isempty, in(2:end))) && prod([in{2:end}])>numel(in{1}) if isnumeric(in{1}), in{1} = in{1}(:); in{1}(prod([in{2:end}])) = 0; + elseif islogical(in{1}), in{1} = in{1}(:); in{1}(end+prod([in{2:end}])-mod(numel(in{1}),prod([in{2:end}]))) = false; elseif ischar(in{1}), in{1} = in{1}(:); in{1}(prod([in{2:end}])) = ' '; elseif iscell(in{1}), in{1} = in{1}(:); in{1}(prod([in{2:end}])) = {[]}; else error('MATL:runtime', 'MATL run-time error: unrecognized type of first input'); end, end if ~any(cellfun(@isempty, in(2:end))) && prod([in{2:end}])1 reshape array / remove single else out{1} = squeeze(in{:}); end -Xe +Xe 1 4 1 1 2 1 true true true true if numel(in)==1 && numel(out)==1, in{2} = 1-size(in{1},1):size(in{1},2)-1; end (sparse) matrix formed by digaonals \matlab+spdiags+. With $1$ input and $1$ output, extracts all diagonals from the input + [out{:}] = spdiags(in{:}); Ye Ze 1 1 1 1 1 1 true true true true out{1} = exp(in{:}); exponential \matlab+exp+ f 1 3 1 1 3 1 true true true true [out{:}] = find(in{:}); find \matlab+find+ @@ -734,7 +763,10 @@ g 1 1 1 1 1 1 true true true true out{1} = logical(in{1}); convert to logical va Xg 1 inf 2 1 inf numel(in) true true true true [out{:}] = ndgrid(in{:}); rectangular grid in N-D space \matlab+ndgrid+ Yg Zg 1 1 1 1 1 1 true true true true out{1} = gammaln(in{:}); logarithm of gamma function \matlab+gammaln+ -h 0 inf 2 1 1 1 true true true true out{1} = horzcat(in{:}); horizontal concatenation \matlab+horzcat+ +h 0 inf 2 1 1 1 true true true true if any(diff(cellfun(@(x) size(x,1), in))) horizontal concatenation \matlab+horzcat+. If inputs are matrices with non-matching sizes they are linearized + in = cellfun(@(x) reshape(x,1,[]), in, 'uniformoutput', false); + end + out{1} = horzcat(in{:}); Xh 0 inf numel(STACK) 1 1 1 true true true true out{1} = in; concatenate into cell array concatenate into cell array (\matlab+{..., ...}+) Yh 1 2 2 1 1 1 true true true true out{1} = hankel(in{:}); Hankel matrix \matlab+hankel+ Zh 3 3 3 1 1 1 true true true true y = hypergeom(in{:}); if any(cellfun(@ischar,in)), y = char(y); end; out{1} = y; hypergeometric function \matlab+hypergeom+. If any input is of type char: returns char output @@ -755,14 +787,28 @@ Yj 1 1 1 1 1 1 true true true true out{1} = imag(in{:}); imaginary part \matlab+ Zj 1 1 1 1 1 1 true true true true out{1} = conj(in{:}); complex conjugate \matlab+conj+ k 1 1 1 1 1 1 true true true true if isnumeric(in{1}), out{1} = floor(in{1}); else, out{1} = lower(in{1}); end convert string to lowercase / round towards minus infinity \matlab+lower+ for strings or cell arrays of strings; \matlab+floor+ for numerical arrays Xk 1 1 1 1 1 1 true true true true if isnumeric(in{1}), out{1} = ceil(in{1}); else, out{1} = upper(in{1}); end convert string to uppercase / round towards infinity \matlab+upper+ for strings or cell arrays of strings; \matlab+ceil+ for numerical arrays -Yk 2 2 2 1 2 1 true true true true x = in{1}(:).'; y = in{2}(:); [dmin, ind] = min(abs(bsxfun(@minus, x, y)),[],1); closest value closest value in second input to each value in first input, in terms of absolute difference. For equidistant values it picks the one that appears first (in linear order) in the second input. Second output gives resulting absolute differences - out{1} = reshape(y(ind), size(in{1})); if nout>=2, out{2} = reshape(dmin, size(in{1})); end; clear x y ind dmin +Yk 2 2 2 1 3 1 true true true true x = in{1}(:).'; y = in{2}(:); [dmin, ind] = min(abs(bsxfun(@minus, x, y)),[],1); closest value closest value in second input to each value in first input, in terms of absolute difference. For equidistant values it picks the one that appears first (in linear order) in the second input. Second output gives resulting absolute differences. Third output gives linear indices of selected elements + out{1} = reshape(y(ind), size(in{1})); + if nout>=2, out{2} = reshape(dmin, size(in{1})); end; + if nout>=3, out{3} = reshape(ind, size(in{1})); end; + clear x y ind dmin Zk l 0 inf 0 1 1 1 true true true true out{1} = ones(in{:}); array of ones \matlab+ones+ (if $0$ inputs: produces output $1$) Xl Yl 1 2 1 1 1 1 true true true true if numel(in)==1, out{1} = log(in{1}); else out{1} = log(in{1})/log(in{2}); end logarithm \matlab+log+. If $2$ inputs: second input specifies logarithm base Zl 1 1 1 1 2 1 true true true true [out{:}] = log2(in{:}); base 2 logarithm \matlab+log2+ -m 2 4 2 1 2 1 true true true true [out{:}] = ismember(in{:}); true for set member \matlab+ismember+. \sa \matl+Xm+ +m 2 4 2 1 2 1 true true true true if (iscell(in{1}) && (nnz(~cellfun(@ischar, in{1})) || isnumeric(in{2}))) || (iscell(in{2}) && (nnz(~cellfun(@ischar, in{2})) || isnumeric(in{1}))) true for set member \matlab+ismember+. It also works for cell arrays with numeric content, or with mixed char/numeric content. \sa \matl+Xm+ + if ~iscell(in{1}), in{1} = in(1); end; if ~iscell(in{2}), in{2} = in(2); end + [i2, i1] = ndgrid(1:numel(in{2}), 1:numel(in{1})); + in1 = reshape(in{1}(i1), size(i1)); in2 = reshape(in{2}(i2), size(i2)); + e = cellfun(@isequal, in1, in2); + [tf, ind] = max(e, [], 1); ind = ind.*tf; + tf = reshape(tf, size(in{1})); ind = reshape(ind, size(in{1})); + out{1} = tf; if nout>=2, out{2} = ind; end + clear in1 in2 i1 i2 e tf ind + else + [out{:}] = ismember(in{:}); + end Xm 2 3 2 1 2 1 true true true true [out{:}] = ismember(in{1},in{2},'rows',in{3:end}); true for set member, row-wise \matlab+ismember(..., 'rows', ...)+. \sa \matl+m+ Ym 1 4 1 1 1 1 true true true true out{1} = mean(in{:}); mean value \matlab+mean+ Zm 1 2 2 1 1 1 true true true true if numel(in)==1, x=1; for t=in{1}(:).', x=lcm(x,t); end; out{1}=x; least common multiple (element-wise, singleton expansion) \matlab+lcm+, element-wise with singleton expansion. With $1$ input, computes the least common multiple of all elements of the input @@ -778,7 +824,7 @@ Zm 1 2 2 1 1 1 true true true true if numel(in)==1, x=1; for t=in{1}(:).', x=lcm end end n 1 1 1 1 1 1 true true true true out{1} = numel(in{:}); number of elements in array \matlab+numel+ -Xn 2 2 2 1 1 1 true true true true nd = max(ndims(in{1}), ndims(in{2})); sz1 = arrayfun(@(n)size(in{1},n), 1:nd); sz2 = arrayfun(@(n)size(in{2},n), 1:nd); binomial coefficient \matlab+nchoosek+. This interprets first input as number(s). If the inputs are arrays, the function is computed element-wise with singleton expansion. For values \matlab+n+ and \matlab+k+ in first and second inputs, if \matlab+n+ is less than \matlab+k+ the result \matlab+0+. +Xn 2 2 2 1 1 1 true true true true nd = max(ndims(in{1}), ndims(in{2})); sz1 = arrayfun(@(n)size(in{1},n), 1:nd); sz2 = arrayfun(@(n)size(in{2},n), 1:nd); binomial coefficient (number of combinations) \matlab+nchoosek+. This interprets first input as number(s). If the inputs are arrays, the function is computed element-wise with singleton expansion. For values \matlab+n+ and \matlab+k+ in first and second inputs, if \matlab+n+ is less than \matlab+k+ the result \matlab+0+. \sa \matl|XN| assert(all(sz1==sz2 | sz1==1 | sz2==1), 'MATL:runtime', 'MATL run-time error: inputs have incompatible sizes') rm1 = ones(1,nd); rm1(sz1==1) = sz2(sz1==1); rm2 = ones(1,nd); rm2(sz2==1) = sz1(sz2==1); insx1 = repmat(in{1}, rm1); insx2 = repmat(in{2}, rm2); @@ -787,13 +833,18 @@ Xn 2 2 2 1 1 1 true true true true nd = max(ndims(in{1}), ndims(in{2})); sz1 = a % The code for implementing singleton expanstion (through repmat) is taken from the code for the bitand function Yn 1 5 2 1 1 1 true true true true out{1} = interp1(in{:}); interpolation (table lookup) \matlab+interp1+. \matlab+'pp'+ option not supported Zn 1 2 1 1 1 1 true true true true out{1} = norm(in{:}); matrix or vector norm \matlab+norm+ -o 1 1 1 1 1 1 true true true true if ~iscell(in{1}) convert to double precision \matlab+double+. For cell array input behaves analogously to \matlab+char+: linearizes cell array, converts cell contents to double, and concatenates vertically padding with zeros if needed +o 1 3 1 1 1 1 true true true true if ~iscell(in{1}) convert to double precision \matlab+double+. For cell array input behaves analogously to \matlab+char+: linearizes cell array, converts cell contents to double and concatenates vertically, padding if needed. By default, padding is with zeros on the right. Second input specifies fill value, and third indicates fill side: 0 indicated left, 1 indicates right out{1} = double(in{1}); else in{1} = in{1}(:); n = max(cellfun(@(c) size(c,2), in{1})); - for k = 1:numel(in{1}), in{1}{k} = [double(in{1}{k}) zeros(size(in{1}{k},1), n-size(in{1}{k},2))]; end - out{1} = vertcat(in{1}{:}); + if numel(in)>=2, fill = in{2}; else, fill = 0; end + if numel(in)>=3, lr = in{3}; else, lr = 1; end + for k = 1:numel(in{1}) + if lr in{1}{k} = [double(in{1}{k}) repmat(fill, size(in{1}{k},1), n-size(in{1}{k},2))]; + else in{1}{k} = [repmat(fill, size(in{1}{k},1), n-size(in{1}{k},2)) double(in{1}{k})]; end + end + out{1} = vertcat(in{1}{:}); clear n fill lr end Xo 1 1 1 1 1 1 true true true true out{1} = int64(in{1}); convert to signed 64-bit integer \matlab+int64+ Yo 1 3 1 1 1 1 true true true true out{1} = round(in{:}); round towards nearest decimal or integer \matlab+round+ @@ -873,11 +924,22 @@ Zt 3 3 3 1 1 1 true true true true if ~isnumeric(in{1}) replace substring with a if ischar(in{3}), y = char(y); end out{1} = y; end -u 1 4 1 1 3 1 true true true true [out{:}] = unique(in{:}); unique \matlab+unique+. \sa \matl+Xu+. +u 1 4 1 1 3 1 true true true true if iscell(in{1}) && ~ischar(in{1}{1}) unique \matlab+unique+. It also allows cell array input with numeric content, or mixed char/numeric content. In this case it only works with a single input and single output, in stable mode. \sa \matl+Xu+ + [ii, jj] = ndgrid(1:numel(in{1})); + ind = ~any(triu(cellfun(@isequal, in{1}(ii), in{1}(jj)),1),1); + y = in{1}(ind); y = y(:); + if ndims(in{1})==2 && size(in{1},1)==1, y = y.'; end + out{1} = y; out = out(1:nout); clear y ii jj + else + [out{:}] = unique(in{:}); + end Xu 1 3 1 1 3 1 true true true true [out{:}] = unique(in{1},'rows',in{2:end}); unique rows \matlab+unique(..., 'rows', ...)+. \sa \matl+u+. Yu Zu 1 2 1 1 1 1 true true true true out{1} = strjust(in{:}); justify character array \matlab+strjust+ -v 0 inf numel(STACK) 1 1 1 true true true true out{1} = vertcat(in{:}); vertical concatenation \matlab+vertcat+ +v 0 inf numel(STACK) 1 1 1 true true true true if any(diff(cellfun(@(x) size(x,2), in))) vertical concatenation \matlab+vertcat+. If inputs are matrices with non-matching sizes they are linearized + in = cellfun(@(x) reshape(x,[],1), in, 'uniformoutput', false); + end + out{1} = vertcat(in{:}); Xv 1 1 1 1 1 1 true true true true if isnumeric(in{1}), in{1}=char(in{1}); end; out{1} = regexprep(in{1}, '\s', ''); remove space remove space from input string or cell array strings. If input is a numeric array, it is converted to char Yv 1 1 1 1 1 1 true true true true out{1} = strtrim(in{:}); remove insignificant whitespace \matlab+strtrim+ Zv 1 1 1 1 1 1 true true true true out{1} = deblank(in{:}); remove trailing blanks \matlab+deblank+ @@ -920,12 +982,9 @@ Z| 2 3 2 1 1 1 true true true true if ischar(in{1}), in{1} = double(in{1}); end } X} Y} 1 1 1 1 1 1 true true true true out{1} = cell2mat(in{:}); convert contents of cell array into single array \matlab+cell2mat+ -Z} 1 2 1 0 inf prod(size(in{:})) true true true true if numel(in)==1, outall = mat2cell(in{1}(:), ones(1,numel(in{1}))).'; split array split array into elements in linear order. With $2$ inputs: split into subarrays along the dimension indicated by the second input - elseif numel(in)==2, d = num2cell(size(in{1})); d{in{2}} = ones(1,size(in{1},in{2})); outall = mat2cell(in{1}, d{:}); outall = outall(:).'; clear d - else error('MATL:runtime', 'MATL run-time error: too many inputs'); end - out = outall(1:nout); -% The default nout, prod(size(in{:})), is either numel(in{1}) o size(in{1}, in{2}) -% I considered defining Z} such that with 1 input it split along the first non-singleton dimension. But that gave me trouble. : The default nout should have been the size along the first non-singleton dimension or along the dimension indicated by the first output. : I didn't see how to define the default nout in a single statement. I tried size(in{1}, (numel(in)>1)*in{end} + (numel(in)==1)*[find(size(in{1})-1,1) repmat(1,1,numel(in{1})==1)]); but it didn't work when the first input was a cell array and there was not second input: in that case in{end} was not a number +Z} 1 2 1 0 inf -2 true true true true if numel(in)==1, sz = size(in{1}); [~, d] = max(sz>1); in{2} = d; end; split array split array into subarrays along the first non-singleton dimension. With $2$ inputs: split into subarrays along the dimension indicated by the second input + d = num2cell(size(in{1})); d{in{2}} = ones(1,size(in{1},in{2})); out = mat2cell(in{1}, d{:}); out = out(:).'; clear d + if nout>=0, out = out(1:nout); end ~ 1 1 1 1 1 1 true true true true out{1} = ~in{1}; logical 'not' (element-wise) \matlab+~+ (\matlab+not+) X~ 2 4 2 1 3 1 true true true true if ischar(in{1}) && isnumeric(in{2}), in{2} = char(in{2}); end set exclusive-or \matlab+setxor+. Uses the \matlab+'stable'+ flag by default. If one input is char and the other is numeric, the latter is converted to char. if ischar(in{2}) && isnumeric(in{1}), in{1} = char(in{1}); end diff --git a/genHelp.m b/genHelp.m index df9db5d..6b93298 100644 --- a/genHelp.m +++ b/genHelp.m @@ -162,8 +162,8 @@ inFormatted{n} = sprintf('%i', defIn); end - % Format output spec. Changes done here should be done in MATL_spec.tex too - if isnan(defOut) && ~isempty(F(n).defOut) % F(n).defOut contains a string that couldn't be converted to a number + % Format output spec. Changes done here should also be done in genFunDefTableLatex.m and in MATL_spec.tex + if (isnan(defOut) || defOut<0) && ~isempty(F(n).defOut) % F(n).defOut contains a string that couldn't be converted to a number, or a negative number switch F(n).defOut case {'numel(CB_H)' 'numel(CB_I)' 'numel(CB_J)' 'numel(CB_K)'} defOutStr = 'number of elements in clipboard'; @@ -181,6 +181,10 @@ defOutStr = 'according to specified keywords'; case 'numel(in)' defOutStr = 'number of inputs'; + case '-1' + defOutStr = 'number of elements that will be produced'; + case '-2' + defOutStr = 'number of subarrays that will be produced'; otherwise error('Unrecognized default number of outputs') end @@ -198,7 +202,7 @@ end else if maxOut ~= defOut - error('Incorrect specification of number of inputs') + error('Incorrect specification of number of outputs') end outFormatted{n} = sprintf('%i', defOut); end diff --git a/help.mat b/help.mat index 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output specification''), end', minOut, maxOut) ... sprintf('elseif islogical(S_OUT), if numel(S_OUT) < %s || numel(S_OUT) > %s, error(''MATL:runner'', ''MATL run-time error: incorrect output specification''), end', minOut, maxOut) ... 'else error(''MATL:runner'', ''MATL run-time error: output specification not recognized''), end' ... sprintf('if isnumeric(S_OUT) && S_OUT > %s, S_OUT = [false(1,S_OUT-(%s+1)) true]; end', maxOut, maxOut) ... 'if isnumeric(S_OUT), nout = S_OUT; else nout = numel(S_OUT); end' ... - 'out = cell(1,nout);' }]; + 'if nout>=0, out = cell(1,nout); end' }]; % 2*(...) because a number in maxOut+1:2*maxOut corresponds to a logical vector with a single true value % For logical S_IN we use nnz (the inputs are picked from the stack), but % for logical S_OUT we use numel (the function is called with that many outputs) diff --git a/preLit.mat b/preLit.mat index 5157b5f2df3e94522330e9ab56e3d7a6afc50363..b1d30d91f06fd8d6bf7a15c56ca31f49d50928d3 100644 GIT binary patch delta 3416 zcmV-e4X5(l8^9cpG#FHMWgtyqav(A?ATTgGGC4XjF(5K9F*cD=BavVQk#rD$xD5aR zc$~yp%WfMt6s1Rx#4km8HvNLx#?Lsrz)6Y*Z~`L;+EI7(3^gJ|kpm7#k-O?=T||K68R0IHu}EpJ>s8{n*b zy$d?^YX|a)UVvy1MEf8*0MQ|Th>k#X45F7HIswruFnR$-dtkH=Mh9SY2u4R>bX?&N zLI3X*fY62c2%OzqP%yyR_%;V2QJ_0!O|7 zMEl&X;r%+!u$IGIzzc#xcYVeMO04wzEqx`2oPEhdJNu3L1m>dFf4xF~f3u~(S$;m6 zBc7vB^P>|^g7O&AM8{cmo_j4EC5L0o)q$Mt7&HC_^0n+R#+9HH#+UAS0V{VX{bBcR 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z1$L~oGRb4hpdwOnpG>=y^^iak7_bZaP#-TNi xQlT=({@04{i)jh(%xO_GG@Bw4)R{SOMhWdyT~*M|TA diff --git a/preLit.txt b/preLit.txt index 11a3084..2b8e413 100644 --- a/preLit.txt +++ b/preLit.txt @@ -345,4 +345,12 @@ Y5 3 'both' 4 'circular' 5 'replicate' -6 'symmetric' \ No newline at end of file +6 'symmetric' + + +Y6 + +1 [false true false; true false true; false true false] +2 [false true false; true true true; false true false] +3 [true true true; true false true; true true true] +4 [true true true; true true true; true true true] \ No newline at end of file