Construct a matrix and assign values from matrix u.
Construct a matrix and assign values from matrix u.
the matrix of values to assign
Construct a matrix and assign values from array of vectors u.
Construct a matrix and assign values from array of vectors u.
the 2D array of values to assign
Construct a matrix from repeated real values.
Construct a matrix from repeated real values.
the (row, column) dimensions
the first value (necessary due to type erasure)
the rest of the repeated values
Construct a matrix from repeated values.
Construct a matrix from repeated values.
the (row, column) dimensions
the repeated values
Construct a matrix and assign values from array of arrays u.
Construct a matrix and assign values from array of arrays u.
the 2D array of values to assign
Construct a dim1 by dim1 square matrix with x assigned on the diagonal and y assigned off the diagonal.
Construct a dim1 by dim1 square matrix with x assigned on the diagonal and y assigned off the diagonal. To obtain an identity matrix, let x = 1 and y = 0.
the row and column dimension
the scalar value to assign on the diagonal
the scalar value to assign off the diagonal
Construct a dim1 by dim2 matrix and assign each element the value x.
Construct a dim1 by dim2 matrix and assign each element the value x.
the row dimension
the column dimesion
the scalar value to assign
Construct a dim1 by dim1 square matrix.
Construct a dim1 by dim1 square matrix.
the row and column dimension
the first/row dimension
the second/column dimension
the 2D array used to store matrix elements
Multiply this matrix by scalar x.
Multiply this matrix by vector u (efficient solution).
Multiply this matrix by matrix b (efficient solution).
Multiply this matrix by matrix b (efficient solution).
the matrix to multiply by (requires sameCrossDimensions)
Multiply this matrix by vector u to produce another matrix (a_ij * b_j)
Multiply in-place this matrix by vector u to produce another matrix (a_ij * b_j)
Multiply in-place this matrix by scalar x.
Multiply in-place this matrix by matrix b.
Multiply in-place this matrix by matrix b. If b and this reference the same matrix (b == this), a copy of the this matrix is made.
the matrix to multiply by (requires square and sameCrossDimensions)
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.
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 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.
Get a slice this matrix row-wise at index i and column-wise on range jr.
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 on range jr.
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.
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 as a rational number)
whether to use relative or absolute cutoff
Get column 'col' from the matrix, returning it as a vector.
the first/row dimension
the second/column dimension
Compute the determinant of this 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.
Combine this matrix with matrix b, placing them along the diagonal and filling in the bottom left and top right regions with zeroes; [this, b].
Combine this matrix with matrix b, placing them along the diagonal and filling in the bottom left and top right regions with zeroes; [this, b].
the matrix to combine with this matrix
Dimension 1
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.
Invert this matrix (requires a squareMatrix) and use partial pivoting.
Invert in-place this matrix (requires a squareMatrix) and uses partial pivoting.
Invert this matrix (requires a squareMatrix) and does not use partial pivoting.
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 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 in-place 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 upper and lower triangular matrices (l, u) using the LU Decomposition algorithm.
Decompose this matrix into the product of upper and lower triangular matrices (l, u) using the LU Decomposition algorithm. This version uses no 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 minimum element in this matrix.
Compute the 1-norm of this matrix, i.
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).
Return 1 if the condition is true else 0
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.
Use Gauss-Jordan reduction 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.
Get row 'r' from the matrix, returning it as a vector.
Get row 'r' from the matrix, returning it as a vector.
the row to extract from the matrix
the position to start extracting from
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
Select columns from this matrix according to the given index/basis.
Select rows from this matrix according to the given index/basis.
Set this matrix's ith row starting at column j to the vector u.
Set all the values in this matrix as copies of the values in 2D array u.
Set all the elements in this matrix to the scalar x.
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 the main diagonal of this matrix to the scalar x.
Set the kth diagonal of this matrix to the vector u.
Set all the lower triangular elements in this matrix to the scalar x.
Set all the lower triangular elements in this matrix to the scalar x.
the scalar value to assign
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 excluding the given row and column.
Solve for x in the equation a*x = b where a is this matrix (see lud above).
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).
Compute the sum of this matrix, i.
Compute the abs sum of this matrix, i.
Compute the sum of the lower triangular region of this matrix.
Transpose this matrix (rows => columns).
Convert this matrix to a string.
Convert this matrix to a string.
Compute the trace of this matrix, i.
Set a slice this matrix row-wise at index i and column-wise on range jr.
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 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 element at the i,j-th index position to the scalar x.
Raise this matrix to the pth power (for some integer p >= 2).
The MatrixR class stores and operates on Numeric Matrices of type Rational. This class follows the MatrixN framework and is provided for efficieny.