Multiply 'this' bidiagonal matrix by scalar 'x'.

Multiply 'this' bidiagonal matrix by vector 'u'.

Multiply 'this' bidiagonal matrix by matrix 'b'. Requires 'b' to have type BidMatrixR, but returns a more general type of matrix.

Multiply 'this' bidiagonal matrix by matrix 'b'.

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

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

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

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

Multiply in-place 'this' bidiagonal matrix by scalar 'x'.

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

Add 'this' bidiagonal matrix and scalar 'x'.

Add 'this' bidiagonal matrix and (row) vector u.

Add 'this' bidiagonal matrix and matrix 'b'.

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

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' bidiagonal matrix and scalar 'x'.

Add in-place 'this' bidiagonal matrix and (row) vector 'u'.

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

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

From 'this' bidiagonal matrix subtract scalar 'x'.

From 'this' bidiagonal matrix subtract (row) vector 'u'.

From 'this' bidiagonal matrix subtract matrix 'b'.

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

From 'this' bidiagonal matrix subtract in-place (row) vector 'u'.

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

Divide 'this' bidiagonal matrix by scalar 'x'.

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

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

Get 'this' bidiagonal 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)

Get 'this' bidiagonal matrix's element at the 'i,j'-th index position, returning 0, if off bidiagonal.

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

Clean values in 'this' bidiagonal matrix at or below the threshold 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 'this' bidiagonal matrix, returning it as a vector.

Create a clone of 'this' m-by-n matrix.

Compute the determinant of 'this' bidiagonal matrix.

Set the diagonal of 'this' bidiagonal matrix.

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.

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

Dimension 1

Dimension 2

Compute the dot product of 'this' matrix with matrix 'b' to produce a vector.

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

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' bidiagonal matrix. Assumes 'dim2 >= dim1'.

Invert 'this' bidiagonal matrix.

Invert in-place 'this' matrix (requires a 'squareMatrix') and use partial pivoting.

Check whether 'this' matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal).

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

Check whether 'this' bidiagonal 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).

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 the 'LU' Decomposition algorithm.

Factor 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.

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' bidiagonal matrix.

Compute the matrix dot product of 'this' matrix with matrix 'b' to produce a matrix.

Compute the matrix dot product of 'this' matrix with matrix 'b' to produce a matrix.

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' bidiagonal matrix.

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.

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.

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.

Set the sup-diagonal of 'this' bidiagonal matrix.

Select columns from 'this' bidiagonal 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' bidiagonal 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 'this' bidiagonal matrix's 'i'th row starting at column 'j' to the vector 'u'.

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

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

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

Set column 'col' of 'this' bidiagonal matrix to a vector.

Set the main diagonal of 'this' bidiagonal matrix to the scalar 'x'. Assumes 'dim2 >= dim1'.

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

Set the format to the 'newFormat'.

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

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

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

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

Slice 'this' bidiagonal matrix excluding the given 'row' and 'col'umn.

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

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

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

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' bidiagonal matrix, i.e., the sum of its elements.

Compute the 'abs' sum of 'this' bidiagonal 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' bidiagonal 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' bidiagonal matrix (rows => columns).

Convert 'this' tridiagonal matrix to a dense matrix.

Convert 'this' BidMatrixR into a double matrix BidMatrixD.

Convert 'this' BidMatrixR into an integer matrix BidMatrixI.

Convert 'this' bidiagonal matrix to a string showing the diagonal vector followed by the sup-diagonal vector.

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

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

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

Set 'this' bidiagonal 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 initialized to zero.

Raise 'this' bidiagonal matrix to the 'p'th power (for some integer 'p' >= 2).