Construct a symmetric tridiagonal matrix from the given matrix.
Construct a symmetric tridiagonal matrix from the given matrix.
the matrix of values to assign
Construct a symmetric tridiagonal matrix with the given diagonal and sub-diagonal.
Construct a symmetric tridiagonal matrix with the given diagonal and sub-diagonal.
the diagonal vector
the sub-diagonal vector
the first/row dimension (symmetric => d2 = d1)
Multiply this matrix by scalar x.
Multiply this matrix by scalar x.
the scalar to multiply by
Multiply this matrix by vector u.
Multiply this matrix by vector u.
the vector to multiply by
Multiply this matrix by matrix b.
Multiply this matrix by matrix b. Requires b to have type SymTriMatrixN [T], but returns a more general type of matrix.
the matrix to multiply by
Multiply this matrix by matrix b.
Multiply this matrix by matrix b.
the matrix to multiply by
Multiply this matrix by vector u to produce another matrix (a_ij * u_j)
Multiply this matrix by vector u to produce another matrix (a_ij * u_j)
the vector to multiply by
Multiply in-place this matrix by vector u to produce another matrix (a_ij * u_j)
Multiply in-place this matrix by vector u to produce another matrix (a_ij * u_j)
the vector to multiply by
Multiply in-place this matrix by scalar x.
Multiply in-place this matrix by scalar x.
the scalar to multiply by
Multiply in-place this matrix by matrix b
Multiply in-place this matrix by matrix b
the matrix to multiply by
Add this matrix and scalar x.
Add this matrix and matrix b.
Add this matrix and matrix b.
the matrix to add (requires leDimensions)
Concatenate this matrix and vector u.
Concatenate this matrix and vector u.
the vector to be concatenated as the new last row in matrix
Add in-place this matrix and scalar x.
Add in-place this matrix and matrix b.
Add in-place this matrix and matrix b.
the matrix to add (requires leDimensions)
From this matrix subtract scalar x.
From this matrix subtract matrix b.
From this matrix subtract matrix b.
the matrix to subtract (requires leDimensions)
From this matrix subtract in-place scalar x.
From this matrix subtract in-place scalar x.
the scalar to subtract
From this matrix subtract in-place matrix b.
From this matrix subtract in-place matrix b.
the matrix to subtract (requires leDimensions)
Divide this matrix by scalar x.
Divide in-place this matrix by scalar x.
Divide in-place this matrix by scalar x.
the scalar to divide by
Numeric zero (0)
Numeric one (1)
Numeric minus one (-1)
Get a slice this matrix row-wise at index i and column-wise on range jr.
Get a slice this matrix row-wise at index i and column-wise on range jr. Ex: u = a(2, 3..5)
the row index
the column range
Get a slice this matrix row-wise on range ir and column-wise at index j.
Get a slice this matrix row-wise on range ir and column-wise at index j. Ex: u = a(2..4, 3)
the row range
the column index
Get a slice this matrix row-wise on range ir and column-wise on range jr.
Get a slice this matrix row-wise on range ir and column-wise on range jr. Ex: b = a(2..4, 3..5)
the row range
the column range
Get this matrix's vector at the i-th index position (i-th row).
Get this matrix's vector at the i-th index position (i-th row).
the row index
Get this matrix's element at the i,j-th index position.
Get this matrix's element at the i,j-th index position.
the row index
the column index
Get this matrix's element at the i,j-th index position, returning 0.
Get this matrix's element at the i,j-th index position, returning 0. if off tridiagonal.
the row index
the column index
Clean values in matrix at or below the threshold by setting them to zero.
Clean values in 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.
the cutoff threshold (a small value)
whether to use relative or absolute cutoff
Get column 'col' from the matrix, returning it as a vector.
Get column 'col' from the matrix, returning it as a vector.
the column to extract from the matrix
the position to start extracting from
the first/row dimension (symmetric => d2 = d1)
Compute the determinant of this matrix.
Compute the determinant of this matrix.
Get the diagonal of the matrix.
Set the diagonal of the matrix.
Set the diagonal of the matrix.
the vector to assign to the diagonal
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.
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.
the size of identity matrix Ip
the size of identity matrix Iq
Dimension 1
Dimension 1
Dimension 2
Dimension 2
Show the flaw by printing the error message.
Show the flaw by printing the error message.
the method where the error occurred
the error message
Iterate over the matrix row by row.
Get the kth diagonal of this matrix.
Get the kth diagonal of this matrix. Assumes dim2 >= dim1.
how far above the main diagonal, e.g., (-1, 0, 1) for (sub, main, super)
Invert this matrix (requires a squareMatrix) using partial pivoting.
Invert this matrix (requires a squareMatrix) using partial pivoting.
Invert in-place this matrix (requires a squareMatrix) using partial pivoting.
Invert in-place this matrix (requires a squareMatrix) using partial pivoting.
Invert this matrix (requires a squareMatrix) not using partial pivoting.
Invert this matrix (requires a squareMatrix) not using partial pivoting.
Check whether this matrix is nonnegative (has no negative elements).
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 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 square (same row and column dimensions).
Check whether this matrix is symmetric.
Check whether this matrix is symmetric.
Check whether this matrix dimensions are less than or equal to (le) those of the other Matrix.
Check whether this matrix dimensions are less than or equal to (le) those of the other Matrix.
the other matrix
Decompose this matrix into the product of lower and upper triangular matrices (l, u) using the LU Decomposition algorithm.
Decompose this matrix into the product of lower and upper triangular matrices (l, u) using the LU Decomposition algorithm. This version uses partial pivoting.
Decompose in-place this matrix into the product of lower and upper triangular matrices (l, u) using the LU Decomposition algorithm.
Decompose in-place this matrix into the product of lower and upper triangular matrices (l, u) using the LU Decomposition algorithm. This version uses partial pivoting.
Find the magnitude of this matrix, the element value farthest from zero.
Find the magnitude of this matrix, the element value farthest from zero.
Find the maximum element in this matrix.
Find the maximum element in this matrix.
the ending row index (exclusive) for the search
Find the minimum element in this matrix.
Find the minimum element in this matrix.
the ending row index (exclusive) for the search
Compute the 1-norm of this matrix, i.
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
Import Numeric evidence (gets nu val from superclass)
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.
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. The nullspace of matrix a is "this vector v times any scalar s", i.e., a*(v*s) = 0. The left nullspace of matrix a is the same as the right nullspace of a.t (a transpose).
Compute the (right) nullspace in-place 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.
Compute the (right) nullspace in-place 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. The nullspace of matrix a is "this vector v times any scalar s", i.e., a*(v*s) = 0. The left nullspace of matrix a is the same as the right nullspace of a.t (a transpose).
Range for the storage array on dimension 1 (rows)
Range for the storage array on dimension 1 (rows)
Range for the storage array on dimension 2 (columns)
Range for the storage array on dimension 2 (columns)
Determine the rank of this m by n matrix by taking the upper triangular matrix from the LU Decomposition and counting the number of non-zero diagonal elements.
Determine the rank of this m by n matrix by taking the upper triangular matrix from the LU Decomposition and counting the number of non-zero diagonal elements. FIX: should implement in implementing classes.
Use Gauss-Jordan reduction on this matrix to make the left part embed an identity matrix.
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.
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 have the same cross dimensions.
Check whether this matrix and the other matrix have the same cross dimensions.
the other matrix
Check whether this matrix and the other Matrix have the same dimensions.
Check whether this matrix and the other Matrix have the same dimensions.
the other matrix
Get the sub-diagonal of the matrix.
Set the sub-diagonal of the matrix.
Set the sub-diagonal of the matrix.
the vector to assign to the sub-diagonal
Select columns from this matrix according to the given index/basis.
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.
the column index positions (e.g., (0, 2, 5))
Select rows from this matrix according to the given index/basis.
Select rows from this matrix according to the given index/basis.
the row index positions (e.g., (0, 2, 5))
Set this matrix's ith row starting at column j to the vector u.
Set this matrix's ith row starting at column j to the vector u.
the row index
the vector value to assign
the starting column index
Set all the values in this matrix as copies of the values in 2D array u.
Set all the values in this matrix as copies of the values in 2D array u.
the 2D array of values to assign
Set all the elements in this matrix to the scalar x.
Set all the elements in this matrix to the scalar x.
the scalar value to assign
Set column 'col' of the matrix to a vector.
Set column 'col' of the matrix to a vector.
the column to set
the vector to assign to the column
Set the main diagonal of this matrix to the scalar x.
Set the main diagonal of this matrix to the scalar x. Assumes dim2 >= dim1.
the scalar to set the diagonal to
Set the kth diagonal of this matrix to the vector u.
Set the kth diagonal of this matrix to the vector u. Assumes dim2 >= dim1.
the vector to set the diagonal to
how far above the main diagonal, e.g., (-1, 0, 1) for (sub, main, super)
Slice this matrix row-wise r_from to r_end and column-wise c_from to c_end.
Slice this matrix row-wise r_from to r_end and column-wise c_from to c_end.
the start of the row slice
the end of the row slice
the start of the column slice
the end of the column slice
Slice this matrix row-wise from to end.
Slice this matrix row-wise from to end.
the start row of the slice (inclusive)
the end row of the slice (exclusive)
Slice this matrix excluding the given row and column.
Slice this matrix excluding the given row and column.
the row to exclude
the column to exclude
Solve for x in the equation l*u*x = b (see lud above).
Solve for x in the equation l*u*x = b (see lud above).
the lower and upper triangular matrices
the constant vector
Solve for x in the equation l*u*x = b (see lud above).
Solve for x in the equation l*u*x = b (see lud above).
the lower triangular matrix
the upper triangular matrix
the constant vector
Solve for x in the equation a*x = d where a is this matrix.
Solve for x in the equation a*x = d where a is this matrix.
the constant vector.
Compute the sum of this matrix, i.
Compute the sum of this matrix, i.e., the sum of its elements.
Compute the abs sum of this matrix, i.
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.
Compute the sum of the lower triangular region of this matrix.
Transpose this matrix (rows => columns).
Transpose this matrix (rows => columns). Note, since the matrix is symmetric, it returns itself.
Convert this symmetric tridiagonal matrix to a string showing the diagonal vector followed by the sub-diagonal vector.
Convert this symmetric tridiagonal matrix to a string showing the diagonal vector followed by the sub-diagonal vector.
Compute the trace of this matrix, i.
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.
Eigen.scala
Set a slice this matrix row-wise at index i and column-wise on range jr.
Set a slice this matrix row-wise at index i and column-wise on range jr. Ex: a(2, 3..5) = u
the row index
the column range
the vector to assign
Set a slice this matrix row-wise on range ir and column-wise at index j.
Set a slice this matrix row-wise on range ir and column-wise at index j. Ex: a(2..4, 3) = u
the row range
the column index
the vector to assign
Set a slice this matrix row-wise on range ir and column-wise on range jr.
Set a slice this matrix row-wise on range ir and column-wise on range jr. Ex: a(2..4, 3..5) = b
the row range
the column range
the matrix to assign
Set this matrix's row at the i-th index position to the vector u.
Set this matrix's row at the i-th index position to the vector u.
the row index
the vector value to assign
Set this matrix's element at the i,j-th index position to the scalar x.
Set this matrix's element at the i,j-th index position to the scalar x. Only store x if it is non-zero.
the row index
the column index
the scalar value to assign
Raise this matrix to the pth power (for some integer p >= 2).
Raise this matrix to the pth power (for some integer p >= 2).
the power to raise this matrix to
The
SymTriMatrixNclass stores and operates on symmetric tridiagonal matrices. The elements are of type of T. A matrix is stored as two vectors: the diagonal vector and the sub-diagonal vector.