CommonOps
org.ejml.ops

Class CommonOps



  • public class CommonOpsextends Object

    Common matrix operations are contained here. Which specific underlying algorithm is used is not specified just the out come of the operation. Nor should calls to these functions reply on the underlying implementation. Which algorithm is used can depend on the matrix being passed in.

    For more exotic and specialized generic operations see SpecializedOps.

    See Also:
    MatrixMatrixMult, MatrixVectorMult, SpecializedOps, MatrixFeatures
    • Constructor Detail

      • CommonOps

        public CommonOps()
    • Method Detail

      • mult

        public static void mult(RowD1Matrix64F a,        RowD1Matrix64F b,        RowD1Matrix64F c)

        Performs the following operation:

        c = a * b

        cij = ∑k=1:n { aik * bkj}

        Parameters:
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • mult

        public static void mult(double alpha,        RowD1Matrix64F a,        RowD1Matrix64F b,        RowD1Matrix64F c)

        Performs the following operation:

        c = α * a * b

        cij = α ∑k=1:n { * aik * bkj}

        Parameters:
        alpha - Scaling factor.
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multTransA

        public static void multTransA(RowD1Matrix64F a,              RowD1Matrix64F b,              RowD1Matrix64F c)

        Performs the following operation:

        c = aT * b

        cij = ∑k=1:n { aki * bkj}

        Parameters:
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multTransA

        public static void multTransA(double alpha,              RowD1Matrix64F a,              RowD1Matrix64F b,              RowD1Matrix64F c)

        Performs the following operation:

        c = α * aT * b

        cij = α ∑k=1:n { aki * bkj}

        Parameters:
        alpha - Scaling factor.
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multTransB

        public static void multTransB(RowD1Matrix64F a,              RowD1Matrix64F b,              RowD1Matrix64F c)

        Performs the following operation:

        c = a * bT
        cij = ∑k=1:n { aik * bjk}

        Parameters:
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multTransB

        public static void multTransB(double alpha,              RowD1Matrix64F a,              RowD1Matrix64F b,              RowD1Matrix64F c)

        Performs the following operation:

        c = α * a * bT
        cij = α ∑k=1:n { aik * bjk}

        Parameters:
        alpha - Scaling factor.
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multTransAB

        public static void multTransAB(RowD1Matrix64F a,               RowD1Matrix64F b,               RowD1Matrix64F c)

        Performs the following operation:

        c = aT * bT
        cij = ∑k=1:n { aki * bjk}

        Parameters:
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multTransAB

        public static void multTransAB(double alpha,               RowD1Matrix64F a,               RowD1Matrix64F b,               RowD1Matrix64F c)

        Performs the following operation:

        c = α * aT * bT
        cij = α ∑k=1:n { aki * bjk}

        Parameters:
        alpha - Scaling factor.
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multOuter

        public static void multOuter(RowD1Matrix64F a,             RowD1Matrix64F c)

        Computes the matrix multiplication outer product:

        c = a * aT

        cij = ∑k=1:m { aik * ajk}

        Is faster than using a generic matrix multiplication by taking advantage of symmetry.

        Parameters:
        a - The matrix being multiplied. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multAdd

        public static void multAdd(RowD1Matrix64F a,           RowD1Matrix64F b,           RowD1Matrix64F c)

        Performs the following operation:

        c = c + a * b
        cij = cij + ∑k=1:n { aik * bkj}

        Parameters:
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multAdd

        public static void multAdd(double alpha,           RowD1Matrix64F a,           RowD1Matrix64F b,           RowD1Matrix64F c)

        Performs the following operation:

        c = c + α * a * b
        cij = cij + α * ∑k=1:n { aik * bkj}

        Parameters:
        alpha - scaling factor.
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multAddTransA

        public static void multAddTransA(RowD1Matrix64F a,                 RowD1Matrix64F b,                 RowD1Matrix64F c)

        Performs the following operation:

        c = c + aT * b
        cij = cij + ∑k=1:n { aki * bkj}

        Parameters:
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multAddTransA

        public static void multAddTransA(double alpha,                 RowD1Matrix64F a,                 RowD1Matrix64F b,                 RowD1Matrix64F c)

        Performs the following operation:

        c = c + α * aT * b
        cij =cij + α * ∑k=1:n { aki * bkj}

        Parameters:
        alpha - scaling factor
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multAddTransB

        public static void multAddTransB(RowD1Matrix64F a,                 RowD1Matrix64F b,                 RowD1Matrix64F c)

        Performs the following operation:

        c = c + a * bT
        cij = cij + ∑k=1:n { aik * bjk}

        Parameters:
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multAddTransB

        public static void multAddTransB(double alpha,                 RowD1Matrix64F a,                 RowD1Matrix64F b,                 RowD1Matrix64F c)

        Performs the following operation:

        c = c + α * a * bT
        cij = cij + α * ∑k=1:n { aik * bjk}

        Parameters:
        alpha - Scaling factor.
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • multAddTransAB

        public static void multAddTransAB(RowD1Matrix64F a,                  RowD1Matrix64F b,                  RowD1Matrix64F c)

        Performs the following operation:

        c = c + aT * bT
        cij = cij + ∑k=1:n { aki * bjk}

        Parameters:
        a - The left matrix in the multiplication operation. Not Modified.
        b - The right matrix in the multiplication operation. Not Modified.
        c - Where the results of the operation are stored. Modified.
      • multAddTransAB

        public static void multAddTransAB(double alpha,                  RowD1Matrix64F a,                  RowD1Matrix64F b,                  RowD1Matrix64F c)

        Performs the following operation:

        c = c + α * aT * bT
        cij = cij + α * ∑k=1:n { aki * bjk}

        Parameters:
        alpha - Scaling factor.
        a - The left matrix in the multiplication operation. Not Modified.
        b - The right matrix in the multiplication operation. Not Modified.
        c - Where the results of the operation are stored. Modified.
      • solve

        public static boolean solve(DenseMatrix64F a,            DenseMatrix64F b,            DenseMatrix64F x)

        Solves for x in the following equation:

        A*x = b

        If the system could not be solved then false is returned. If it returns true that just means the algorithm finished operating, but the results could still be bad because 'A' is singular or nearly singular.

        If repeat calls to solve are being made then one should consider using LinearSolverFactory instead.

        It is ok for 'b' and 'x' to be the same matrix.

        Parameters:
        a - A matrix that is m by m. Not modified.
        b - A matrix that is m by n. Not modified.
        x - A matrix that is m by n. Modified.
        Returns:
        true if it could invert the matrix false if it could not.
      • transpose

        public static void transpose(DenseMatrix64F mat)
        Performs an in-place transpose. This algorithm is only efficient for square matrices.
        Parameters:
        mat - The matrix that is to be transposed. Modified.
      • transpose

        public static DenseMatrix64F transpose(DenseMatrix64F A,                       DenseMatrix64F A_tran)

        Transposes matrix 'a' and stores the results in 'b':

        bij = aji
        where 'b' is the transpose of 'a'.

        Parameters:
        A - The original matrix. Not modified.
        A_tran - Where the transpose is stored. If null a new matrix is created. Modified.
        Returns:
        The transposed matrix.
      • trace

        public static double trace(RowD1Matrix64F a)

        This computes the trace of the matrix:

        trace = ∑i=1:n { aii }

        The trace is only defined for square matrices.

        Parameters:
        a - A square matrix. Not modified.
      • det

        public static double det(DenseMatrix64F mat)
        Returns the determinant of the matrix. If the inverse of the matrix is also needed, then using LUDecompositionAlt directly (or any similar algorithm) can be more efficient.
        Parameters:
        mat - The matrix whose determinant is to be computed. Not modified.
        Returns:
        The determinant.
      • invert

        public static boolean invert(DenseMatrix64F mat)

        Performs a matrix inversion operation on the specified matrix and stores the results in the same matrix.

        a = a-1

        If the algorithm could not invert the matrix then false is returned. If it returns true that just means the algorithm finished. The results could still be bad because the matrix is singular or nearly singular.

        Parameters:
        mat - The matrix that is to be inverted. Results are stored here. Modified.
        Returns:
        true if it could invert the matrix false if it could not.
      • invert

        public static boolean invert(DenseMatrix64F mat,             DenseMatrix64F result)

        Performs a matrix inversion operation that does not modify the original and stores the results in another matrix. The two matrices must have the same dimension.

        b = a-1

        If the algorithm could not invert the matrix then false is returned. If it returns true that just means the algorithm finished. The results could still be bad because the matrix is singular or nearly singular.

        For medium to large matrices there might be a slight performance boost to using LinearSolverFactory instead.

        Parameters:
        mat - The matrix that is to be inverted. Not modified.
        result - Where the inverse matrix is stored. Modified.
        Returns:
        true if it could invert the matrix false if it could not.
      • pinv

        public static void pinv(DenseMatrix64F A,        DenseMatrix64F invA)

        Computes the Moore-Penrose pseudo-inverse:

        pinv(A) = (ATA)-1 AT
        or
        pinv(A) = AT(AAT)-1

        Internally it uses SolvePseudoInverseSvd to compute the inverse. For performance reasons, this should only be used when a matrix is singular or nearly singular.

        Parameters:
        A - A m by n Matrix. Not modified.
        invA - Where the computed pseudo inverse is stored. n by m. Modified.
      • columnsToVector

        public static DenseMatrix64F[] columnsToVector(DenseMatrix64F A,                               DenseMatrix64F[] v)
        Converts the columns in a matrix into a set of vectors.
        Parameters:
        A - Matrix. Not modified.
        v -
        Returns:
        An array of vectors.
      • rowsToVector

        public static DenseMatrix64F[] rowsToVector(DenseMatrix64F A,                            DenseMatrix64F[] v)
        Converts the rows in a matrix into a set of vectors.
        Parameters:
        A - Matrix. Not modified.
        v -
        Returns:
        An array of vectors.
      • setIdentity

        public static void setIdentity(RowD1Matrix64F mat)
        Sets all the diagonal elements equal to one and everything else equal to zero. If this is a square matrix then it will be an identity matrix.
        Parameters:
        mat - A square matrix.
        See Also:
        identity(int)
      • identity

        public static DenseMatrix64F identity(int width)

        Creates an identity matrix of the specified size.

        aij = 0 if i ≠ j
        aij = 1 if i = j

        Parameters:
        width - The width and height of the identity matrix.
        Returns:
        A new instance of an identity matrix.
      • identity

        public static DenseMatrix64F identity(int numRows,                      int numCols)
        Creates a rectangular matrix which is zero except along the diagonals.
        Parameters:
        numRows - Number of rows in the matrix.
        numCols - NUmber of columns in the matrix.
        Returns:
        A matrix with diagonal elements equal to one.
      • diag

        public static DenseMatrix64F diag(double... diagEl)

        Creates a new square matrix whose diagonal elements are specified by diagEl and all the other elements are zero.

        aij = 0 if i ≤ j
        aij = diag[i] if i = j

        Parameters:
        diagEl - Contains the values of the diagonal elements of the resulting matrix.
        Returns:
        A new matrix.
        See Also:
        diagR(int, int, double...)
      • diagR

        public static DenseMatrix64F diagR(int numRows,                   int numCols,                   double... diagEl)

        Creates a new rectangular matrix whose diagonal elements are specified by diagEl and all the other elements are zero.

        aij = 0 if i ≤ j
        aij = diag[i] if i = j

        Parameters:
        numRows - Number of rows in the matrix.
        numCols - Number of columns in the matrix.
        diagEl - Contains the values of the diagonal elements of the resulting matrix.
        Returns:
        A new matrix.
        See Also:
        diag(double...)
      • kron

        public static void kron(DenseMatrix64F A,        DenseMatrix64F B,        DenseMatrix64F C)

        The Kronecker product of two matrices is defined as:
        Cij = aijB
        where Cij is a sub matrix inside of C ∈ ℜ m*k × n*l, A ∈ ℜ m × n, and B ∈ ℜ k × l.

        Parameters:
        A - The left matrix in the operation. Not modified.
        B - The right matrix in the operation. Not modified.
        C - Where the results of the operation are stored. Modified.
      • extract

        public static void extract(Matrix64F src,           int srcY0,           int srcY1,           int srcX0,           int srcX1,           Matrix64F dst,           int dstY0,           int dstX0)

        Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.

        si-y0 , j-x0 = oij for all y0 ≤ i < y1 and x0 ≤ j < x1

        where 'sij' is an element in the submatrix and 'oij' is an element in the original matrix.

        Parameters:
        src - The original matrix which is to be copied. Not modified.
        srcX0 - Start column.
        srcX1 - Stop column+1.
        srcY0 - Start row.
        srcY1 - Stop row+1.
        dst - Where the submatrix are stored. Modified.
        dstY0 - Start row in dst.
        dstX0 - start column in dst.
      • extract

        public static DenseMatrix64F extract(DenseMatrix64F src,                     int srcY0,                     int srcY1,                     int srcX0,                     int srcX1)

        Creates a new matrix which is the specified submatrix of 'src'

        si-y0 , j-x0 = oij for all y0 ≤ i < y1 and x0 ≤ j < x1

        where 'sij' is an element in the submatrix and 'oij' is an element in the original matrix.

        Parameters:
        src - The original matrix which is to be copied. Not modified.
        srcX0 - Start column.
        srcX1 - Stop column+1.
        srcY0 - Start row.
        srcY1 - Stop row+1.
        Returns:
        Extracted submatrix.
      • extractDiag

        public static void extractDiag(DenseMatrix64F src,               DenseMatrix64F dst)

        Extracts the diagonal elements 'src' write it to the 'dst' vector. 'dst' can either be a row or column vector.

        Parameters:
        src - Matrix whose diagonal elements are being extracted. Not modified.
        dst - A vector the results will be written into. Modified.
      • insert

        public static void insert(Matrix64F src,          Matrix64F dest,          int destY0,          int destX0)
        Inserts matrix 'src' into matrix 'dest' with the (0,0) of src at (row,col) in dest. This is equivalent to calling extract(src,0,src.numRows,0,src.numCols,dest,destY0,destX0).
        Parameters:
        src - matrix that is being copied into dest. Not modified.
        dest - Where src is being copied into. Modified.
        destY0 - Start row for the copy into dest.
        destX0 - Start column for the copy into dest.
      • elementMax

        public static double elementMax(D1Matrix64F a)

        Returns the value of the element in the matrix that has the largest value.

        Max{ aij } for all i and j

        Parameters:
        a - A matrix.
        Returns:
        The max element value of the matrix.
      • elementMaxAbs

        public static double elementMaxAbs(D1Matrix64F a)

        Returns the absolute value of the element in the matrix that has the largest absolute value.

        Max{ |aij| } for all i and j

        Parameters:
        a - A matrix.
        Returns:
        The max element value of the matrix.
      • elementMin

        public static double elementMin(D1Matrix64F a)

        Returns the value of the element in the matrix that has the minimum value.

        Min{ aij } for all i and j

        Parameters:
        a - A matrix.
        Returns:
        The value of element in the matrix with the minimum value.
      • elementMinAbs

        public static double elementMinAbs(D1Matrix64F a)

        Returns the absolute value of the element in the matrix that has the smallest absolute value.

        Min{ |aij| } for all i and j

        Parameters:
        a - A matrix.
        Returns:
        The max element value of the matrix.
      • elementMult

        public static void elementMult(D1Matrix64F a,               D1Matrix64F b)

        Performs the an element by element multiplication operation:

        aij = aij * bij

        Parameters:
        a - The left matrix in the multiplication operation. Modified.
        b - The right matrix in the multiplication operation. Not modified.
      • elementMult

        public static void elementMult(D1Matrix64F a,               D1Matrix64F b,               D1Matrix64F c)

        Performs the an element by element multiplication operation:

        cij = aij * bij

        Parameters:
        a - The left matrix in the multiplication operation. Not modified.
        b - The right matrix in the multiplication operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • elementDiv

        public static void elementDiv(D1Matrix64F a,              D1Matrix64F b)

        Performs the an element by element division operation:

        aij = aij / bij

        Parameters:
        a - The left matrix in the division operation. Modified.
        b - The right matrix in the division operation. Not modified.
      • elementDiv

        public static void elementDiv(D1Matrix64F a,              D1Matrix64F b,              D1Matrix64F c)

        Performs the an element by element division operation:

        cij = aij / bij

        Parameters:
        a - The left matrix in the division operation. Not modified.
        b - The right matrix in the division operation. Not modified.
        c - Where the results of the operation are stored. Modified.
      • elementSum

        public static double elementSum(D1Matrix64F mat)

        Computes the sum of all the elements in the matrix:

        sum(i=1:m , j=1:n ; aij)

        Parameters:
        mat - An m by n matrix. Not modified.
        Returns:
        The sum of the elements.
      • elementSumAbs

        public static double elementSumAbs(D1Matrix64F mat)

        Computes the sum of the absolute value all the elements in the matrix:

        sum(i=1:m , j=1:n ; |aij|)

        Parameters:
        mat - An m by n matrix. Not modified.
        Returns:
        The sum of the absolute value of each element.
      • sumRows

        public static DenseMatrix64F sumRows(DenseMatrix64F input,                     DenseMatrix64F output)

        Computes the sum of each row in the input matrix and returns the results in a vector:

        bj = sum(i=1:n ; |aji|)

        Parameters:
        input - INput matrix whose rows are summed.
        output - Optional storage for output. Must be a vector. If null a row vector is returned. Modified.
        Returns:
        Vector containing the sum of each row in the input.
      • sumCols

        public static DenseMatrix64F sumCols(DenseMatrix64F input,                     DenseMatrix64F output)

        Computes the sum of each column in the input matrix and returns the results in a vector:

        bj = sum(i=1:m ; |aij|)

        Parameters:
        input - INput matrix whose rows are summed.
        output - Optional storage for output. Must be a vector. If null a column vector is returned. Modified.
        Returns:
        Vector containing the sum of each row in the input.
      • addEquals

        public static void addEquals(D1Matrix64F a,             D1Matrix64F b)

        Performs the following operation:

        a = a + b
        aij = aij + bij

        Parameters:
        a - A Matrix. Modified.
        b - A Matrix. Not modified.
      • addEquals

        public static void addEquals(D1Matrix64F a,             double beta,             D1Matrix64F b)

        Performs the following operation:

        a = a + β * b
        aij = aij + β * bij

        Parameters:
        beta - The number that matrix 'b' is multiplied by.
        a - A Matrix. Modified.
        b - A Matrix. Not modified.
      • add

        public static void add(D1Matrix64F a,       D1Matrix64F b,       D1Matrix64F c)

        Performs the following operation:

        c = a + b
        cij = aij + bij

        Matrix C can be the same instance as Matrix A and/or B.

        Parameters:
        a - A Matrix. Not modified.
        b - A Matrix. Not modified.
        c - A Matrix where the results are stored. Modified.
      • add

        public static void add(D1Matrix64F a,       double beta,       D1Matrix64F b,       D1Matrix64F c)

        Performs the following operation:

        c = a + β * b
        cij = aij + β * bij

        Matrix C can be the same instance as Matrix A and/or B.

        Parameters:
        a - A Matrix. Not modified.
        beta - Scaling factor for matrix b.
        b - A Matrix. Not modified.
        c - A Matrix where the results are stored. Modified.
      • add

        public static void add(double alpha,       D1Matrix64F a,       double beta,       D1Matrix64F b,       D1Matrix64F c)

        Performs the following operation:

        c = α * a + β * b
        cij = α * aij + β * bij

        Matrix C can be the same instance as Matrix A and/or B.

        Parameters:
        alpha - A scaling factor for matrix a.
        a - A Matrix. Not modified.
        beta - A scaling factor for matrix b.
        b - A Matrix. Not modified.
        c - A Matrix where the results are stored. Modified.
      • add

        public static void add(double alpha,       D1Matrix64F a,       D1Matrix64F b,       D1Matrix64F c)

        Performs the following operation:

        c = α * a + b
        cij = α * aij + bij

        Matrix C can be the same instance as Matrix A and/or B.

        Parameters:
        alpha - A scaling factor for matrix a.
        a - A Matrix. Not modified.
        b - A Matrix. Not modified.
        c - A Matrix where the results are stored. Modified.
      • add

        public static void add(D1Matrix64F a,       double val)

        Performs an in-place scalar addition:

        a = a + val
        aij = aij + val

        Parameters:
        a - A matrix. Modified.
        val - The value that's added to each element.
      • add

        public static void add(D1Matrix64F a,       double val,       D1Matrix64F c)

        Performs scalar addition:

        c = a + val
        cij = aij + val

        Parameters:
        a - A matrix. Not modified.
        c - A matrix. Modified.
        val - The value that's added to each element.
      • subEquals

        public static void subEquals(D1Matrix64F a,             D1Matrix64F b)

        Performs the following subtraction operation:

        a = a - b
        aij = aij - bij

        Parameters:
        a - A Matrix. Modified.
        b - A Matrix. Not modified.
      • sub

        public static void sub(D1Matrix64F a,       D1Matrix64F b,       D1Matrix64F c)

        Performs the following subtraction operation:

        c = a - b
        cij = aij - bij

        Matrix C can be the same instance as Matrix A and/or B.

        Parameters:
        a - A Matrix. Not modified.
        b - A Matrix. Not modified.
        c - A Matrix. Modified.
      • scale

        public static void scale(double alpha,         D1Matrix64F a)

        Performs an in-place element by element scalar multiplication.

        aij = α*aij

        Parameters:
        a - The matrix that is to be scaled. Modified.
        alpha - the amount each element is multiplied by.
      • scale

        public static void scale(double alpha,         D1Matrix64F a,         D1Matrix64F b)

        Performs an element by element scalar multiplication.

        bij = α*aij

        Parameters:
        a - The matrix that is to be scaled. Modified.
        alpha - the amount each element is multiplied by.
      • divide

        public static void divide(double alpha,          D1Matrix64F a)

        Performs an in-place element by element scalar division.

        aij = aij

        Parameters:
        a - The matrix whose elements are to be divided. Modified.
        alpha - the amount each element is divided by.
      • divide

        public static void divide(double alpha,          D1Matrix64F a,          D1Matrix64F b)

        Performs an element by element scalar division.

        bij = *aij

        Parameters:
        a - The matrix whose elements are to be divided. Modified.
        alpha - the amount each element is divided by.
      • changeSign

        public static void changeSign(D1Matrix64F a)

        Changes the sign of every element in the matrix.

        aij = -aij

        Parameters:
        a - A matrix. Modified.
      • fill

        public static void fill(D1Matrix64F a,        double value)

        Sets every element in the matrix to the specified value.

        aij = value

        Parameters:
        a - A matrix whose elements are about to be set. Modified.
        value - The value each element will have.
      • rref

        public static DenseMatrix64F rref(DenseMatrix64F A,                  int numUnknowns,                  DenseMatrix64F reduced)

        Puts the augmented system matrix into reduced row echelon form (RREF). A matrix is said to be in RREF is the following conditions are true:

        1. If a row has non-zero entries, then the first non-zero entry is 1. This is known as the leading one.
        2. If a column contains a leading one then all other entries in that column are zero.
        3. If a row contains a leading 1, then each row above contains a leading 1 further to the left.

        [1] Page 19 in, Otter Bretscherm "Linear Algebra with Applications" Prentice-Hall Inc, 1997

        Parameters:
        A - Input matrix. Unmodified.
        numUnknowns - Number of unknowns/columns that are reduced. Set to -1 to default to Math.min(A.numRows,A.numCols), which works for most systems.
        reduced - Storage for reduced echelon matrix. If null then a new matrix is returned. Modified.
        Returns:
        Reduced echelon form of A

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