Returns the matrix product of matrices a and b. If a is a vector it is treated as a row vector; if b is a vector it is treated as a column vector.
Returns the element of ARRAY specified by SUBSCRIPTS.
Returns a list whose elements are the dimensions of ARRAY
Returns a list whose elements are the dimensions of ARRAY
Returns T if SUBSCRIPTS are valid subscripts for ARRAY; NIL otherwise.
Returns the number of dimensions of ARRAY.
Returns the index into the data vector of ARRAY for the element of ARRAY specified by SUBSCRIPTS.
Returns the total number of elements of ARRAY.
Returns T if X is an array; NIL otherwise.
The ARGS can be matrices, vectors, or lists. Arguments are bound into a matrix along their columns. Example: (bind-columns #2a((1 2)(3 4)) #(5 6)) returns #2a((1 2 5)(3 4 6))
The ARGS can be matrices, vectors, or lists. Arguments are bound into a matrix along their rows. Example: (bind-rows #2a((1 2)(3 4)) #(5 6)) returns #2a((1 2)(3 4)(5 6))
Modified Cholesky decomposition.
A
should be a square, symmetric
matrix. Computes lower triangular matrix
L
such that
where
D
is a diagonal matrix. If
A
is strictly positive definite
D
will be zero. Otherwise
D
is as small as possible to make
A + D
numerically strictly positive definite. Returns a list
.
Returns a list of the columns of M as vectors
Returns a copy of ARRAY with elements eq to the elements of ARRAY.
Returns a new copy of LIST.
Returns a copy of VECTOR with elements eq to the elements of VECTOR
Returns the number of its arguments. Vector reducing
If X is a matrix returns (matmult (transpose X) X). If X is a vector returns (inner-product X X).
Returns the determinant of the square matrix M.
If X is a matrix, returns the diagonal of X. If X is a sequence, returns a diagonal matrix of rank (length X) with diagonal elements eq to the elements of X.
Returns the identity matrix of rank N.
Returns inner product of sequences X and Y.
Returns the inverse of the the square matrix M; signals an error if M is ill conditioned or singular
A is a square matrix of numbers (real or complex). Computes the LU decomposition of A and returns a list of the form (LU IV D FLAG), where LU is a matrix with the L part in the lower triangle, the U part in the upper triangle (the diagonal entries of L are taken to be 1), IV is a vector describing the row permutation used, D is 1 if the number of permutations is odd, -1 if even, and FLAG is T if A is numerically singular, NIL otherwise. Used bu LU-SOLVE.
LU is the result of (LU-DECOMP A) for a square matrix A, B is a sequence. Returns the solution to the equation Ax = B. Signals an error if A is singular.
Creates and returns a list containing SIZE elements, each of which is initialized to INITIAL-ELEMENT.
X is a matrix, Y and WEIGHTS are sequences. Returns the sweep matrix for the (possibly weighted) regression of Y on X.
FUNCTION must take as many arguments as there are DATA arguments supplied. DATA arguments must either all be sequences or all be arrays of the same shape. The result is of the same type and shape as the first DATA argument, with elements the result of applying FUNCTION elementwise to the DATA arguments
Returns the matrix product of matrices a and b. If a is a vector it is treated as a row vector; if b is a vector it is treated as a column vector.
returns a matrix of dimensions DIM initialized using sequence DATA in row major order.
Returns T if M is a matrix, NIL otherwise.
Returns the generalized outer product of x and y, using fcn. That is, the result is a matrix of dimension ((length x) (length y)) and the (i j) element of the result is computed as (apply fcn (aref x i) (aref y j)).
Returns a copy of the array A permuted according to the permutation P.
A is a matrix of real numbers with at least as many rows as columns. Computes the QR factorization of A and returns the result in a list of the form (Q R).
Returns an estimate of the reciprocal of the L1 condition number of an upper triangular matrix a.
Returns a list of the rows of M as vectors
Solves A x = B using LU decomposition and backsolving. B can be a sequence or a matrix.
Returns a list of COLS lists of equal length of the elements of LIST. Example: (split-list '(1 2 3 4 5 6) 2) returns ((1 2 3) (4 5 6))
Returns the sum of all the elements of its arguments. Returns 0 if there are no arguments. Vector reducing.
A is a matrix of real numbers with at least as many rows as columns. Computes the singular value decomposition of A and returns a list of the form (U W V FLAG) where U and V are matrices whose columns are the left and right singular vectors of A and W is the sequence of singular values of A. FLAG is T if the algorithm converged, NIL otherwise.
A is a matrix, INDICES a sequence of the column indices to be swept. Returns a list of the swept result and the list of the columns actually swept. (See MULTREG documentation.) If supplied, TOLERANCES should be a list of real numbers the same length as INDICES. An index will only be swept if its pivot element is larger than the corresponding element of TOLERANCES.
Returns the transpose of the matrix M.
Returns T if M is a vector, NIL otherwise.
Anthony Rossini