lattice parameters (needed only for periodic systems).Cartesian coordinates or Z-matrix input to specify the locations of the atoms and centers.keywords on the first line of the directive (to specify such optional input as the geometry name, input units, and print level for the output).The three main parts of the GEOMETRY directive are: The directive therefore appears to be rather long and complicated when presented in its general form, as follows: The directive allows the user to specify the geometry with a relatively small amount of input, but there are a large number of optional keywords and additional subordinate directives that the user can specify, if needed. The GEOMETRY directive is a compound directive that allows the user to define the geometry to be used for a given calculation. 1.8 SYSTEM - Lattice parameters for periodic systems.1.7 Applying constraints in geometry optimizations.1.6 ZCOORD - Forcing internal coordinates.1.2.1.6 Hexagonal space groups (group numbers: 168-194).1.2.1.4 Tetragonal space groups (group numbers: 75-142).1.2.1.3 Orthorhombic space groups (group numbers: 16-74).1.2.1.2 Monoclinic space groups (group numbers: 3-15).1.2.1.1 Triclinic space groups (group numbers: 1-2).1.2.1 Names of 3-dimensional space groups.vander(,8) produces an array of powers of 4, which in the (matrix multiplication) gets dot-producted with each binary vector, producing a similar s (transposed differently), and the rest is similar. It is passed to mat ("Interpret the input as a matrix"), which in particular makes it 2-dimensional, while also changing its type to uint8, which is necessary for the next function unpackbits, which breaks the numbers down into their binary representations, across the added dimension. c_ makes a vertical version of that sequence, which is doubled and added to the original sequence, which (by broadcasting) produces a table of sums, which is the required result. The matrix product ( is equivalent to taking the dot product of each broken-down number with b this squares each nonzero bit, changing powers of 2 into powers of 4, and adds them back up, producing a horizontal sequence 0, 1, 4, 5, 16, 17, 20, 21. The bitwise AND, with broadcasting, produces a table of values, splitting the numbers into their constituent bits. r_ produces 0 (inc.) to n (exc.), horizontally, and the left shift makes the corresponding powers of 2, saved in b. Python 3 with numpy, 91 87 74 70 69 67 bytes lambda numpy import*Ĭ_ produces an array of the numbers 0 (inclusive) to 2 n (exclusive), vertically. " - zip (rows of M) with (rows of that) and apply: number of times: chain's left argument -> n Ġ - group indices (of implicit ) by value -> ] (our initial M) Ġ "FL+ƊZƊ⁸¡⁺ - Link: non-negative integer, n ![]() Starts with ] and repeatedly applies a function that creates the required new entries to the right (and then below, via the transposed matrix) by adding the number of current elements to each element. Try it online! (Footer formats as a Python list for clarity.) How? ![]() 1 thanks to caird coinheringaahing (we can use 1-based values) Ġ "FL+ƊZƊ⁸¡⁺Ī monadic Link that accepts a non-negative integer and yields the matrix (using the 1-based values option). (Still no clue for the 6 byte code though!) Ḅ4 - convert from base four -> first 2^n terms of the Moser–De Bruijn sequence Ṗ - Cartesian power (n) -> binary representations of Makes a table under \$x+2y\$ where both \$x\$ and \$y\$ are a prefix of the Moser–De Bruijn sequence. (This should work on v7 or later from what I can tell, but in the testing setup I'm using (similar to here), it gives 'instruction not supported' errors on versions lower than v8.4, which doesn't seem right.) ![]() Divide the matrix into four quadrants of size \$2^, ! Place the result into memory, advancing the pointer.Given a non-negative integer \$n\$, create a 2D array of size \$2^n × 2^n\$ which is generated in the following manner: Originally from a CMC I proposed for the last BMG event Challenge
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