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

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

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

Multiply 'this' tridiagonal matrix by matrix 'b'.

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

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

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

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

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

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

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

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

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

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

From 'this' tridiagonal matrix subtract matrix 'b'.

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

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

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

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

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

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

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

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' tridiagonal 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' tridiagonal matrix, returning it as a vector.

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

Compute the determinant of 'this' tridiagonal matrix.

Set the diagonal of 'this' tridiagonal 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' tridiagonal 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 with matrix 'b' to produce a vector.

Compute the dot product of 'this' tridiagonal matrix and vector 'u', by first transposing 'this' tridiagonal matrix and then multiplying by 'u' (i.e., 'a dot u = a.t * u'). Since 'this' is symmetric, the result is the same as 'a * 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' tridiagonal matrix. Assumes 'dim2 >= dim1'.

Invert 'this' tridiagonal 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). The method may be overriding for efficiency.

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

Check whether 'this' tridiagonal 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' tridiagonal matrix is symmetric.

Check whether 'this' tridiagonal 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 the 'LU' Decomposition algorithm.

Factor 'this' tridiagonal matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Factorization algorithm. 'l' is lower bidiagonal and 'u' is upper bidiagonal. FIX: would be more efficient to use tridiagonal matrices than dense matrices.

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' tridiagonal 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' tridiagonal 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 sub-diagonal of 'this' tridiagonal matrix.

Select columns from 'this' tridiagonal 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' tridiagonal 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' tridiagonal 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' tridiagonal matrix as copies of the values in 2D array 'u'. Ignore parts of array not corresponding to tridiagonal.

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

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

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

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

Set the format to the 'newFormat'.

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

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

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

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

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

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

Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' tridiagonal matrix, using the Thomas Algorithm. Caveat: Stability vs. diagonal dominance. This method is more efficient, since a 'lud_npp' creates dense matrices.

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

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

Compute the 'abs' sum of 'this' tridiagonal 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' tridiagonal 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' tridiagonal matrix (rows => columns). Note, since the matrix is symmetric, it returns itself.

Convert 'this' tridiagonal matrix to a dense matrix.

Convert 'this' SymTriMatrixI into a double matrix SymTriMatrixD.

Convert 'this' SymTriMatrixI into an integer matrix SymTriMatrixI.

Convert 'this' tridiagonal matrix to a string showing the diagonal vector followed by the sub-diagonal vector.

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

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

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

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

Create an m-by-n symmetric tridiagonal matrix with all elements initialized to zero.

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