Multiply 'this' matrix by matrix 'b'.

Multiply 'this' matrix by scalar 'x'.

Multiply 'this' matrix by (column) vector 'u'

Multiply 'this' matrix by vector 'u' to produce another matrix 'a_ij * u_j'. E.g., multiply a matrix by a diagonal matrix represented as a vector.

Multiply 'this' matrix by matrix 'b' elementwise (Hadamard product).

Multiply vector 'u' by 'this' matrix to produce another matrix 'u_i * a_ij'. E.g., multiply a diagonal matrix represented as a vector by a matrix. This operator is right associative.

Multiply in-place 'this' matrix by vector 'u' to produce another matrix 'a_ij * u_j'.

Multiply (row) vector 'u' by 'this' matrix. Note '*:' is right associative. vector = vector *: matrix

Multiply in-place 'this' matrix by matrix 'b'

Multiply in-place 'this' matrix by matrix 'x'

Add 'this' matrix and vector 'u'.

Add 'this' matrix and scalar 'x'.

Add 'this' matrix and matrix 'b'.

Concatenate (row-wise) 'this' matrix and matrix 'b'. FIX

Concatenate (column-wise) 'this' matrix and matrix 'b'.

Concatenate (row) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.

Add in-place 'this' matrix and matrix 'b'.

Add in-place 'this' matrix and vector 'u'.

Add in-place 'this' matrix and scalar 'x'.

Concatenate (column) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.

From 'this' matrix subtract matrix 'b'.

From 'this' matrix subtract vector 'u'.

From 'this' matrix subtract scalar 'x'.

From 'this' matrix subtract in-place matrix 'b'.

From 'this' matrix subtract in-place vector 'u'.

From 'this' matrix subtract in-place scalar 'x'.

Divide 'this' matrix by scalar 'x'.

Divide in-place 'this' matrix by scalar 'x'.

Concatenate 'this' matrix and (row) vector 'u', i.e., append 'u' to 'this'.

Concatenate 'this' matrix and (column) vector 'u', i.e., append 'u' to 'this'.

Get a slice 'this' matrix row-wise on range 'ir' and column-wise on range 'jr'. Ex: b = a(2..4, 3..5)

Get 'this' matrix's vector at the 'i'-th index position ('i'-th row).

Get 'this' matrix's element at the 'i, j'-th index position.

Get the rows indicated by the index vector 'iv' FIX - implement in all implementing classes

Get a slice 'this' matrix row-wise at index 'i' and column-wise on range 'jr'. Ex: u = a(2, 3..5)

Get a slice 'this' matrix row-wise on range 'ir' and column-wise at index j. Ex: u = a(2..4, 3)

Solve for 'x' using back substitution in the equation 'u*x = y' where 'this' matrix ('u') is upper triangular (see 'lud_npp' above).

Clean values in 'this' matrix at or below the threshold 'thres' by setting them to zero. Iterative algorithms give approximate values and if very close to zero, may throw off other calculations, e.g., in computing eigenvectors.

Get column 'col' from the matrix, returning it as a vector.

Get column 'col' from the matrix, returning it as a vector.

Create an exact copy of 'this' m-by-n matrix.

Compute the determinant of 'this' matrix. The value of the determinant indicates, among other things, whether there is a unique solution to a system of linear equations (a nonzero determinant).

Combine 'this' matrix with matrix 'b', placing them along the diagonal and filling in the bottom left and top right regions with zeros; '[this, b]'.

Form a matrix '[Ip, this, Iq]' where Ir is a 'r-by-r' identity matrix, by positioning the three matrices 'Ip', 'this' and 'Iq' along the diagonal. Fill the rest of matrix with zeros.

Dimension 1

Dimension 2

Compute the dot product of 'this' matrix and matrix 'b'. Results in a Vector.

Compute the dot product of 'this' matrix and matrix 'b'. Results in a Vector.

Compute the dot product of 'this' matrix and vector 'b', by first transposing 'this' matrix and then multiplying by 'b' (i.e., 'a dot u = a.t * b').

Override equals to determine whether 'this' vector equals vector 'b'.

Format string used for printing vector values (change using 'setFormat')

Flatten 'this' matrix in row-major fashion, returning a vector containing all the elements from the matrix.

Show the flaw by printing the error message.

Iterate over 'this' matrix row by row applying method 'f'.

Get the 'k'th diagonal of 'this' matrix.

Must also override hashCode for 'this' vector to be compatible with equals.

Invert 'this' matrix (requires a square matrix) and use partial pivoting.

Invert in-place 'this' matrix (requires a square matrix) and uses partial pivoting. Note: this method turns the original matrix into the identity matrix. The inverse is returned and is captured by assignment.

Check whether 'this' matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal). The method may be overriding for efficiency.

Check whether 'this' matrix is nonnegative (has no negative elements).

Check whether 'this' matrix is rectangular (all rows have the same number of columns).

Check whether 'this' matrix is square (same row and column dimensions).

Check whether 'this' matrix is symmetric.

Check whether 'this' matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal). The method may be overriding for efficiency.

Check whether 'this' matrix dimensions are less than or equal to 'le' those of the other matrix 'b'.

Return the lower triangular of 'this' matrix (rest are zero).

Factor in-place 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using an 'LU' Factorization algorithm. FIX - check for 0 pivots (divide by zero).

Factor 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using an 'LU' Factorization algorithm. FIX - check for 0 pivots (divide by zero).

Find the magnitude of 'this' matrix, the element value farthest from zero.

Map the elements of 'this' matrix by applying the mapping function 'f'. FIX - remove ??? and implement in all implementing classes

Find the maximum element in 'this' matrix.

Compute the matrix dot product of 'this' matrix and matrix 'b'.

Compute the matrix dot product of 'this' matrix and matrix 'b'.

Compute the column means of 'this' matrix.

Compute the column means of 'this' matrix ignoring zero elements (e.g., a zero may indicate a missing value as in recommender systems).

Compute the row means of 'this' matrix.

Compute the row means of 'this' matrix ignoring zero elements (e.g., a zero may indicate a missing value as in recommender systems).

Find the minimum element in 'this' matrix.

Multiply 'this' matrix by (column) vector 'u'

Compute the 1-norm of 'this' matrix, i.e., the maximum 1-norm of the column vectors. This is useful for comparing matrices '(a - b).norm1'.

Compute the Frobenius-norm of 'this' matrix, i.e., the square root of the sum of the squared values over all the elements (sqrt (sse)). FIX: for MatriC should take absolute values, first.

Compute the sqaure of the Frobenius-norm of 'this' matrix, i.e., the sum of the squared values over all the elements (sse). FIX: for MatriC should take absolute values, first.

Compute the (infinity) INF-norm of 'this' matrix, i.e., the maximum 1-norm of the row vectors.

Compute the (right) nullspace of 'this' 'm-by-n' matrix (requires 'n = m+1') by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.

nullspace (a) = set of orthogonal vectors v s.t. a * v = 0

The left nullspace of matrix 'a' is the same as the right nullspace of 'a.t'. FIX: need a more robust algorithm for computing nullspace (@see Fac_QR.scala). FIX: remove the 'n = m+1' restriction.

Compute in-place the (right) nullspace of 'this' 'm-by-n' matrix (requires 'n = m+1') by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.

nullspace (a) = set of orthogonal vectors v s.t. a * v = 0

The left nullspace of matrix 'a' is the same as the right nullspace of 'a.t'. FIX: need a more robust algorithm for computing nullspace (@see Fac_QR.scala). FIX: remove the 'n = m+1' restriction.

Range for the storage array on dimension 1 (rows)

Range for the storage array on dimension 2 (columns)

Use Gauss-Jordan reduction on 'this' matrix to make the left part embed an identity matrix. A constraint on this 'm-by-n' matrix is that 'n >= m'. It can be used to solve 'a * x = b': augment 'a' with 'b' and call reduce. Takes '[a | b]' to '[I | x]'.

Use Gauss-Jordan reduction in-place on 'this' matrix to make the left part embed an identity matrix. A constraint on this 'm-by-n' matrix is that 'n >= m'. It can be used to solve 'a * x = b': augment 'a' with 'b' and call reduce. Takes '[a | b]' to '[I | x]'.

Check whether 'this' matrix and the other matrix 'b' have the same cross dimensions.

Check whether 'this' matrix and the other matrix 'b' have the same dimensions.

Select columns from 'this' matrix according to the given index/basis. Ex: Can be used to divide a matrix into a basis and a non-basis.

Select rows from 'this' matrix according to the given index/basis.

Select rows from 'this' matrix according to the given index/basis 'rowIndex'.

Select all rows from 'this' matrix excluding the rows from the given 'rowIndex'.

Select all rows from 'this' matrix excluding the rows from the given 'rowIndex'.

Set the values in 'this' matrix as copies of the values in matrix 'u'.

Set all the values in 'this' matrix as copies of the values in 2D array 'u'.

Set 'this' matrix's 'i'-th row starting at column 'j' to the vector 'u'.

Set all the elements in 'this' matrix to the scalar 'x'.

Set column 'col' of the matrix to a vector.

Set the 'k'th diagonal of 'this' matrix to the vector 'u'. Assumes 'dim2 >= dim1'.

Set the main diagonal of 'this' matrix to the scalar 'x'.

Set the format to the 'newFormat'.

Slice 'this' matrix row-wise 'r_from' to 'r_end' and column-wise 'c_from' to 'c_end'.

Slice 'this' matrix row-wise 'from' to 'end'.

Slice 'this' matrix row-wise over the given range 'rg'.

Slice 'this' matrix column-wise 'from' to 'end'.

Slice 'this' matrix excluding the given row and/or column.

Slice 'this' matrix row-wise excluding the given range 'rg'.

Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' matrix.

Solve for 'x' in the equation 'l*u*x = b'

Solve for 'x' in the equation 'l*u*x = b' (see 'lud' above).

Split the rows from 'this' matrix to form two matrices, one from the rows in 'rowIndex' and the other from rows not in 'rowIndex'.

Split the rows from 'this' matrix to form two matrices, one from the rows in 'rowIndex' and the other from rows not in 'rowIndex'.

Compute the sum of 'this' matrix, i.e., the sum of its elements.

Compute the 'abs' sum of 'this' matrix, i.e., the sum of the absolute value of its elements. This is useful for comparing matrices '(a - b).sumAbs'.

Compute the sum of the lower triangular region of 'this' matrix.

Swap the elements in rows 'i' and 'k' starting from column 'col'.

Swap the elements in columns 'j' and 'l' starting from row 'row'.

Transpose 'this' matrix (columns => rows).

Convert 'this' matrix to a dense matrix.

Convert 'this' RleMatrixI into a dense double matrix MatrixD.

Convert 'this' RleMatrixI into a dense integer matrix MatrixI.

Convert 'this' real (Int precision) matrix to a string.

Compute the trace of 'this' matrix, i.e., the sum of the elements on the main diagonal. Should also equal the sum of the eigenvalues.

Set a slice 'this' matrix row-wise on range ir and column-wise on range 'jr'. Ex: a(2..4, 3..5) = b

Set 'this' matrix's row at the 'i'-th index position to the vector 'u'.

Set 'this' matrix's element at the 'i, j'-th index position to the scalar 'x'.

Set a slice of 'this' matrix row-wise at index 'i' and column-wise on range 'jr' to vector 'u'. Ex: a(2, 3..5) = u

Set a slice of 'this' matrix row-wise on range 'ir' and column-wise at index 'j' to vector 'u'. Ex: a(2..4, 3) = u

Return the upper triangular of 'this' matrix (rest are zero).

Write 'this' matrix to a CSV-formatted text file with name 'fileName'.

Create an m-by-n matrix with all elements intialized to zero.

Raise 'this' matrix to the 'p'th power (for some integer 'p' >= 2). FIX - make compatible with imple in BldMatrix