Class CommonOps_DDRM

java.lang.Object
org.ejml.dense.row.CommonOps_DDRM

public class CommonOps_DDRM
extends 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_DDRM.

See Also:
MatrixMatrixMult_DDRM, MatrixVectorMult_DDRM, SpecializedOps_DDRM, MatrixFeatures_DDRM
  • Constructor Summary

    Constructors
    Constructor Description
    CommonOps_DDRM()  
  • Method Summary

    Modifier and Type Method Description
    static void abs​(DMatrixD1 a)
    Performs absolute value of a matrix:

    a = abs(a)
    aij = abs(aij)
    static void abs​(DMatrixD1 a, DMatrixD1 c)
    Performs absolute value of a matrix:

    c = abs(a)
    cij = abs(aij)
    static <T extends DMatrixD1>
    T
    add​(double alpha, T a, double beta, T b, T output)
    Performs the following operation:

    c = α * a + β * b
    cij = α * aij + β * bij
    static <T extends DMatrixD1>
    T
    add​(double alpha, T a, T b, T output)
    Performs the following operation:

    c = α * a + b
    cij = α * aij + bij
    static void add​(DMatrixD1 a, double val)
    Performs an in-place scalar addition:

    a = a + val
    aij = aij + val
    static <T extends DMatrixD1>
    T
    add​(T a, double val, T output)
    Performs scalar addition:

    c = a + val
    cij = aij + val
    static <T extends DMatrixD1>
    T
    add​(T a, double beta, T b, T output)
    Performs the following operation:

    c = a + β * b
    cij = aij + β * bij
    static <T extends DMatrixD1>
    T
    add​(T a, T b, T output)
    Performs the following operation:

    c = a + b
    cij = aij + bij
    static void addEquals​(DMatrixD1 a, double beta, DMatrixD1 b)
    Performs the following operation:

    a = a + β * b
    aij = aij + β * bij
    static void addEquals​(DMatrixD1 a, DMatrixD1 b)
    Performs the following operation:

    a = a + b
    aij = aij + bij
    static DMatrixRMaj apply​(DMatrixRMaj input, DOperatorUnary func)  
    static DMatrixRMaj apply​(DMatrixRMaj input, DOperatorUnary func, @Nullable DMatrixRMaj output)
    This applies a given unary function on every value stored in the matrix
    static void changeSign​(DMatrixD1 a)
    Changes the sign of every element in the matrix.

    aij = -aij
    static <T extends DMatrixD1>
    T
    changeSign​(T input, T output)
    Changes the sign of every element in the matrix.

    outputij = -inputij
    static DMatrixRMaj[] columnsToVector​(DMatrixRMaj A, @Nullable DMatrixRMaj[] v)
    Converts the columns in a matrix into a set of vectors.
    static DMatrixRMaj concatColumns​(DMatrixRMaj a, DMatrixRMaj b, @Nullable DMatrixRMaj output)
    output = [a , b]
    static DMatrixRMaj concatColumnsMulti​(DMatrixRMaj... m)
    Concatinates all the matrices together along their columns.
    static void concatRows​(DMatrixRMaj a, DMatrixRMaj b, DMatrixRMaj output)
    output = [a ; b]
    static DMatrixRMaj concatRowsMulti​(DMatrixRMaj... m)
    Concatinates all the matrices together along their columns.
    static int countTrue​(BMatrixRMaj A)
    Counts the number of elements in A which are true
    static double det​(DMatrixRMaj mat)
    Returns the determinant of the matrix.
    static DMatrixRMaj 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
    static DMatrixRMaj diag​(@Nullable DMatrixRMaj ret, int width, double... diagEl)  
    static DMatrixRMaj 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
    static void divide​(double alpha, DMatrixD1 a)
    Performs an in-place element by element scalar division with the scalar on top.

    aij = α/aij
    static <T extends DMatrixD1>
    T
    divide​(double alpha, T input, T output)
    Performs an element by element scalar division with the scalar on top.

    bij = α/aij
    static void divide​(DMatrixD1 a, double alpha)
    Performs an in-place element by element scalar division with the scalar on bottom.

    aij = aij
    static <T extends DMatrixD1>
    T
    divide​(T input, double alpha, T output)
    Performs an element by element scalar division with the scalar on botton.

    bij = aij
    static void divideCols​(DMatrixRMaj A, double[] values)
    Divides every element in column i by value[i].
    static void divideRows​(double[] values, DMatrixRMaj A)
    Divides every element in row i by value[i].
    static void divideRowsCols​(double[] diagA, int offsetA, DMatrixRMaj B, double[] diagC, int offsetC)
    Equivalent to multiplying a matrix B by the inverse of two diagonal matrices.
    static double dot​(DMatrixD1 a, DMatrixD1 b)
    Computes the dot product or inner product between two vectors.
    static void elementDiv​(DMatrixD1 A, DMatrixD1 B)
    Performs the an element by element division operation:

    aij = aij / bij
    static <T extends DMatrixD1>
    T
    elementDiv​(T A, T B, T output)
    Performs the an element by element division operation:

    cij = aij / bij
    static <T extends DMatrixD1>
    T
    elementExp​(T A, T output)
    Element-wise exp operation
    cij = Math.exp(aij)
    static BMatrixRMaj elementLessThan​(DMatrixRMaj A, double value, BMatrixRMaj output)
    Applies the > operator to each element in A.
    static BMatrixRMaj elementLessThan​(DMatrixRMaj A, DMatrixRMaj B, BMatrixRMaj output)
    Applies the < operator to each element in A.
    static BMatrixRMaj elementLessThanOrEqual​(DMatrixRMaj A, double value, BMatrixRMaj output)
    Applies the ≥ operator to each element in A.
    static BMatrixRMaj elementLessThanOrEqual​(DMatrixRMaj A, DMatrixRMaj B, BMatrixRMaj output)
    Applies the A ≤ B operator to each element.
    static <T extends DMatrixD1>
    T
    elementLog​(T A, T output)
    Element-wise log operation
    cij = Math.log(aij)
    static double elementMax​(DMatrixD1 a)
    Returns the value of the element in the matrix that has the largest value.

    Max{ aij } for all i and j
    static double elementMax​(DMatrixD1 a, ElementLocation loc)
    Returns the value of the element in the matrix that has the largest value.

    Max{ aij } for all i and j
    static double elementMaxAbs​(DMatrixD1 a)
    Returns the absolute value of the element in the matrix that has the largest absolute value.

    Max{ |aij| } for all i and j
    static double elementMaxAbs​(DMatrixD1 a, ElementLocation loc)
    Returns the absolute value of the element in the matrix that has the largest absolute value.

    Max{ |aij| } for all i and j
    static double elementMin​(DMatrixD1 a)
    Returns the value of the element in the matrix that has the minimum value.

    Min{ aij } for all i and j
    static double elementMin​(DMatrixD1 a, ElementLocation loc)
    Returns the value of the element in the matrix that has the minimum value.

    Min{ aij } for all i and j
    static double elementMinAbs​(DMatrixD1 a)
    Returns the absolute value of the element in the matrix that has the smallest absolute value.

    Min{ |aij| } for all i and j
    static double elementMinAbs​(DMatrixD1 a, ElementLocation loc)
    Returns the absolute value of the element in the matrix that has the smallest absolute value.

    Min{ |aij| } for all i and j
    static BMatrixRMaj elementMoreThan​(DMatrixRMaj A, double value, BMatrixRMaj output)
    Applies the > operator to each element in A.
    static BMatrixRMaj elementMoreThanOrEqual​(DMatrixRMaj A, double value, BMatrixRMaj output)
    Applies the ≥ operator to each element in A.
    static void elementMult​(DMatrixD1 A, DMatrixD1 B)
    Performs the an element by element multiplication operation:

    aij = aij * bij
    static <T extends DMatrixD1>
    T
    elementMult​(T A, T B, T output)
    Performs the an element by element multiplication operation:

    cij = aij * bij
    static <T extends DMatrixD1>
    T
    elementPower​(double a, T B, T output)
    Element-wise power operation
    cij = a ^ bij
    static <T extends DMatrixD1>
    T
    elementPower​(T A, double b, T output)
    Element-wise power operation
    cij = aij ^ b
    static <T extends DMatrixD1>
    T
    elementPower​(T A, T B, T output)
    Element-wise power operation
    cij = aij ^ bij
    static DMatrixRMaj elements​(DMatrixRMaj A, BMatrixRMaj marked, @Nullable DMatrixRMaj output)
    Returns a row matrix which contains all the elements in A which are flagged as true in 'marked'
    static double elementSum​(DMatrixD1 mat)
    Computes the sum of all the elements in the matrix:

    sum(i=1:m , j=1:n ; aij)
    static double elementSumAbs​(DMatrixD1 mat)
    Computes the sum of the absolute value all the elements in the matrix:

    sum(i=1:m , j=1:n ; |aij|)
    static void extract​(DMatrix src, int srcY0, int srcY1, int srcX0, int srcX1, DMatrix dst)
    Extract where the destination is reshaped to match the extracted region
    static void extract​(DMatrix src, int srcY0, int srcY1, int srcX0, int srcX1, DMatrix dst, int dstY0, int dstX0)
    Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.
    static void extract​(DMatrix src, int srcY0, int srcX0, DMatrix dst)
    Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.
    static DMatrixRMaj extract​(DMatrixRMaj src, int[] rows, int rowsSize, int[] cols, int colsSize, @Nullable DMatrixRMaj dst)
    Extracts out a matrix from source given a sub matrix with arbitrary rows and columns specified in two array lists
    static DMatrixRMaj extract​(DMatrixRMaj src, int[] indexes, int length, @Nullable DMatrixRMaj dst)
    Extracts the elements from the source matrix by their 1D index.
    static DMatrixRMaj extract​(DMatrixRMaj src, int srcY0, int srcY1, int srcX0, int srcX1)
    Creates a new matrix which is the specified submatrix of 'src'
    static DMatrixRMaj extractColumn​(DMatrixRMaj a, int column, @Nullable DMatrixRMaj out)
    Extracts the column from a matrix.
    static DMatrixRMaj extractDiag​(DMatrixRMaj src, @Nullable DMatrixRMaj dst)
    Extracts the diagonal elements 'src' write it to the 'dst' vector.
    static DMatrixRMaj extractRow​(DMatrixRMaj a, int row, @Nullable DMatrixRMaj out)
    Extracts the row from a matrix.
    static void fill​(DMatrixD1 a, double value)
    Sets every element in the matrix to the specified value.

    aij = value
    static DMatrixRMaj identity​(int width)
    Creates an identity matrix of the specified size.

    aij = 0 if i ≠ j
    aij = 1 if i = j
    static DMatrixRMaj identity​(int numRows, int numCols)
    Creates a rectangular matrix which is zero except along the diagonals.
    static void insert​(DMatrixRMaj src, DMatrixRMaj dst, int[] rows, int rowsSize, int[] cols, int colsSize)
    Inserts into the specified elements of dst the source matrix.
    static void insert​(DMatrix src, DMatrix dest, int destY0, int destX0)
    Inserts matrix 'src' into matrix 'dest' with the (0,0) of src at (row,col) in dest.
    static boolean invert​(DMatrixRMaj mat)
    Performs a matrix inversion operation on the specified matrix and stores the results in the same matrix.

    a = a-1
    static boolean invert​(DMatrixRMaj mat, DMatrixRMaj result)
    Performs a matrix inversion operation that does not modify the original and stores the results in another matrix.
    static boolean invertSPD​(DMatrixRMaj mat, DMatrixRMaj result)
    Matrix inverse for symmetric positive definite matrices.
    static DMatrixRMaj kron​(DMatrixRMaj A, DMatrixRMaj B, @Nullable DMatrixRMaj 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.
    static DMatrixRMaj maxCols​(DMatrixRMaj input, @Nullable DMatrixRMaj output)
    Finds the element with the minimum value along column in the input matrix and returns the results in a vector:

    bj = min(i=1:m ; aij)
    static DMatrixRMaj maxRows​(DMatrixRMaj input, @Nullable DMatrixRMaj output)
    Finds the element with the maximum value along each row in the input matrix and returns the results in a vector:

    bj = max(i=1:n ; aji)
    static DMatrixRMaj minCols​(DMatrixRMaj input, @Nullable DMatrixRMaj output)
    Finds the element with the minimum value along column in the input matrix and returns the results in a vector:

    bj = min(i=1:m ; aij)
    static DMatrixRMaj minRows​(DMatrixRMaj input, @Nullable DMatrixRMaj output)
    Finds the element with the minimum value along each row in the input matrix and returns the results in a vector:

    bj = min(i=1:n ; aji)
    static <T extends DMatrix1Row>
    T
    mult​(double alpha, T a, T b, T output)
    Performs the following operation:

    c = α * a * b

    cij = α ∑k=1:n { * aik * bkj}
    static <T extends DMatrix1Row>
    T
    mult​(T a, T b, T output)
    Performs the following operation:

    c = a * b

    cij = ∑k=1:n { aik * bkj}
    static void multAdd​(double alpha, DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)
    Performs the following operation:

    c = c + α * a * b
    cij = cij + α * ∑k=1:n { aik * bkj}
    static void multAdd​(DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)
    Performs the following operation:

    c = c + a * b
    cij = cij + ∑k=1:n { aik * bkj}
    static void multAddTransA​(double alpha, DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)
    Performs the following operation:

    c = c + α * aT * b
    cij =cij + α * ∑k=1:n { aki * bkj}
    static void multAddTransA​(DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)
    Performs the following operation:

    c = c + aT * b
    cij = cij + ∑k=1:n { aki * bkj}
    static void multAddTransAB​(double alpha, DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)
    Performs the following operation:

    c = c + α * aT * bT
    cij = cij + α * ∑k=1:n { aki * bjk}
    static void multAddTransAB​(DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)
    Performs the following operation:

    c = c + aT * bT
    cij = cij + ∑k=1:n { aki * bjk}
    static void multAddTransB​(double alpha, DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)
    Performs the following operation:

    c = c + α * a * bT
    cij = cij + α * ∑k=1:n { aik * bjk}
    static void multAddTransB​(DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)
    Performs the following operation:

    c = c + a * bT
    cij = cij + ∑k=1:n { aik * bjk}
    static void multCols​(DMatrixRMaj A, double[] values)
    Multiplies every element in column i by value[i].
    static <T extends DMatrix1Row>
    T
    multInner​(T a, T output)
    Computes the matrix multiplication inner product:

    c = aT * a

    cij = ∑k=1:n { aki * akj}
    static <T extends DMatrix1Row>
    T
    multOuter​(T a, T output)
    Computes the matrix multiplication outer product:

    c = a * aT

    cij = ∑k=1:m { aik * ajk}
    static void multRows​(double[] values, DMatrixRMaj A)
    Multiplies every element in row i by value[i].
    static <T extends DMatrix1Row>
    T
    multTransA​(double alpha, T a, T b, T output)
    Performs the following operation:

    c = α * aT * b

    cij = α ∑k=1:n { aki * bkj}
    static <T extends DMatrix1Row>
    T
    multTransA​(T a, T b, T output)
    Performs the following operation:

    c = aT * b

    cij = ∑k=1:n { aki * bkj}
    static <T extends DMatrix1Row>
    T
    multTransAB​(double alpha, T a, T b, T output)
    Performs the following operation:

    c = α * aT * bT
    cij = α ∑k=1:n { aki * bjk}
    static <T extends DMatrix1Row>
    T
    multTransAB​(T a, T b, T output)
    Performs the following operation:

    c = aT * bT
    cij = ∑k=1:n { aki * bjk}
    static <T extends DMatrix1Row>
    T
    multTransB​(double alpha, T a, T b, T output)
    Performs the following operation:

    c = α * a * bT
    cij = α ∑k=1:n { aik * bjk}
    static <T extends DMatrix1Row>
    T
    multTransB​(T a, T b, T output)
    Performs the following operation:

    c = a * bT
    cij = ∑k=1:n { aik * bjk}
    static DMatrixRMaj permuteRowInv​(int[] pinv, DMatrixRMaj input, DMatrixRMaj output)
    Applies the row permutation specified by the vector to the input matrix and save the results in the output matrix.
    static void pinv​(DMatrixRMaj A, DMatrixRMaj invA)
    Computes the Moore-Penrose pseudo-inverse:

    pinv(A) = (ATA)-1 AT
    or
    pinv(A) = AT(AAT)-1
    static void removeColumns​(DMatrixRMaj A, int col0, int col1)
    Removes columns from the matrix.
    static DMatrixRMaj[] rowsToVector​(DMatrixRMaj A, @Nullable DMatrixRMaj[] v)
    Converts the rows in a matrix into a set of vectors.
    static DMatrixRMaj rref​(DMatrixRMaj A, int numUnknowns, @Nullable DMatrixRMaj reduced)
    Puts the augmented system matrix into reduced row echelon form (RREF) using Gauss-Jordan elimination with row (partial) pivots.
    static void scale​(double alpha, DMatrixD1 a)
    Performs an in-place element by element scalar multiplication.

    aij = α*aij
    static void scale​(double alpha, DMatrixD1 a, DMatrixD1 b)
    Performs an element by element scalar multiplication.

    bij = α*aij
    static void scaleCol​(double alpha, DMatrixRMaj A, int col)
    In-place scaling of a column in A
    static void scaleRow​(double alpha, DMatrixRMaj A, int row)
    In-place scaling of a row in A
    static void setIdentity​(DMatrix1Row mat)
    Sets all the diagonal elements equal to one and everything else equal to zero.
    static boolean solve​(DMatrixRMaj a, DMatrixRMaj b, DMatrixRMaj x)
    Solves for x in the following equation:

    A*x = b
    static boolean solveSPD​(DMatrixRMaj A, DMatrixRMaj b, DMatrixRMaj x)
    Linear solver for systems which are symmetric positive definite.
    A*x = b
    static <T extends DMatrixD1>
    T
    subtract​(double val, T a, T output)
    Performs matrix scalar subtraction:

    c = val - a
    cij = val - aij
    static <T extends DMatrixD1>
    T
    subtract​(T a, double val, T output)
    Performs matrix scalar subtraction:

    c = a - val
    cij = aij - val
    static <T extends DMatrixD1>
    T
    subtract​(T a, T b, T output)
    Performs the following subtraction operation:

    c = a - b
    cij = aij - bij
    static void subtractEquals​(DMatrixD1 a, DMatrixD1 b)
    Performs the following subtraction operation:

    a = a - b
    aij = aij - bij
    static DMatrixRMaj sumCols​(DMatrixRMaj input, @Nullable DMatrixRMaj output)
    Computes the sum of each column in the input matrix and returns the results in a vector:

    bj = sum(i=1:m ; aij)
    static DMatrixRMaj sumRows​(DMatrixRMaj input, @Nullable DMatrixRMaj output)
    Computes the sum of each row in the input matrix and returns the results in a vector:

    bj = sum(i=1:n ; aji)
    static void symmLowerToFull​(DMatrixRMaj A)
    Given a symmetric matrix which is represented by a lower triangular matrix convert it back into a full symmetric matrix.
    static void symmUpperToFull​(DMatrixRMaj A)
    Given a symmetric matrix which is represented by a lower triangular matrix convert it back into a full symmetric matrix.
    static double trace​(DMatrix1Row a)
    This computes the trace of the matrix:

    trace = ∑i=1:n { aii }
    where n = min(numRows,numCols)
    static void transpose​(DMatrixRMaj mat)
    Performs an "in-place" transpose.
    static DMatrixRMaj transpose​(DMatrixRMaj A, @Nullable DMatrixRMaj A_tran)
    Transposes matrix 'a' and stores the results in 'b':

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

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
  • Constructor Details

    • CommonOps_DDRM

      public CommonOps_DDRM()
  • Method Details

    • mult

      public static <T extends DMatrix1Row> T mult​(T a, T b, @Nullable T output)

      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.
      output - Where the results of the operation are stored. Modified.
    • mult

      public static <T extends DMatrix1Row> T mult​(double alpha, T a, T b, @Nullable T output)

      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.
      output - Where the results of the operation are stored. Modified.
    • multTransA

      public static <T extends DMatrix1Row> T multTransA​(T a, T b, @Nullable T output)

      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.
      output - Where the results of the operation are stored. Modified.
    • multTransA

      public static <T extends DMatrix1Row> T multTransA​(double alpha, T a, T b, @Nullable T output)

      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.
      output - Where the results of the operation are stored. Modified.
    • multTransB

      public static <T extends DMatrix1Row> T multTransB​(T a, T b, @Nullable T output)

      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.
      output - Where the results of the operation are stored. Modified.
    • multTransB

      public static <T extends DMatrix1Row> T multTransB​(double alpha, T a, T b, @Nullable T output)

      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.
      output - Where the results of the operation are stored. Modified.
    • multTransAB

      public static <T extends DMatrix1Row> T multTransAB​(T a, T b, @Nullable T output)

      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.
      output - Where the results of the operation are stored. Modified.
    • multTransAB

      public static <T extends DMatrix1Row> T multTransAB​(double alpha, T a, T b, @Nullable T output)

      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.
      output - Where the results of the operation are stored. Modified.
    • dot

      public static double dot​(DMatrixD1 a, DMatrixD1 b)

      Computes the dot product or inner product between two vectors. If the two vectors are columns vectors then it is defined as:
      dot(a,b) = a<sup>T</sup> * b
      If the vectors are column or row or both is ignored by this function.

      Parameters:
      a - Vector
      b - Vector
      Returns:
      Dot product of the two vectors
    • multInner

      public static <T extends DMatrix1Row> T multInner​(T a, @Nullable T output)

      Computes the matrix multiplication inner product:

      c = aT * a

      cij = ∑k=1:n { aki * akj}

      Is faster than using a generic matrix multiplication by taking advantage of symmetry. For vectors there is an even faster option, see VectorVectorMult_DDRM.innerProd(DMatrixD1, DMatrixD1)

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

      public static <T extends DMatrix1Row> T multOuter​(T a, @Nullable T output)

      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.
      output - Where the results of the operation are stored. Modified.
    • multAdd

      public static void multAdd​(DMatrix1Row a, DMatrix1Row b, DMatrix1Row 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, DMatrix1Row a, DMatrix1Row b, DMatrix1Row 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​(DMatrix1Row a, DMatrix1Row b, DMatrix1Row 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, DMatrix1Row a, DMatrix1Row b, DMatrix1Row 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​(DMatrix1Row a, DMatrix1Row b, DMatrix1Row 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, DMatrix1Row a, DMatrix1Row b, DMatrix1Row 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​(DMatrix1Row a, DMatrix1Row b, DMatrix1Row 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, DMatrix1Row a, DMatrix1Row b, DMatrix1Row 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​(DMatrixRMaj a, DMatrixRMaj b, DMatrixRMaj 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_DDRM instead.

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

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

      public static boolean solveSPD​(DMatrixRMaj A, DMatrixRMaj b, DMatrixRMaj x)

      Linear solver for systems which are symmetric positive definite.
      A*x = b

      Parameters:
      A - A matrix that is n by n and SPD. Not modified.
      b - A matrix that is n by k. Not modified.
      x - A matrix that is n by k. Modified.
      Returns:
      true if it could invert the matrix false if it could not.
      See Also:
      UnrolledCholesky_DDRM, LinearSolverFactory_DDRM
    • transpose

      public static void transpose​(DMatrixRMaj mat)

      Performs an "in-place" transpose.

      For square matrices the transpose is truly in-place and does not require additional memory. For non-square matrices, internally a temporary matrix is declared and transpose(DMatrixRMaj, DMatrixRMaj) is invoked.

      Parameters:
      mat - The matrix that is to be transposed. Modified.
    • transpose

      public static DMatrixRMaj transpose​(DMatrixRMaj A, @Nullable @Nullable DMatrixRMaj 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​(DMatrix1Row a)

      This computes the trace of the matrix:

      trace = ∑i=1:n { aii }
      where n = min(numRows,numCols)

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

      public static double det​(DMatrixRMaj mat)
      Returns the determinant of the matrix. If the inverse of the matrix is also needed, then using LUDecomposition_F64 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​(DMatrixRMaj 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​(DMatrixRMaj mat, DMatrixRMaj 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_DDRM 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.
    • invertSPD

      public static boolean invertSPD​(DMatrixRMaj mat, DMatrixRMaj result)
      Matrix inverse for symmetric positive definite matrices. For small matrices an unrolled cholesky is used. Otherwise a standard decomposition.
      Parameters:
      mat - (Input) SPD matrix
      result - (Output) Inverted matrix.
      Returns:
      true if it could invert the matrix false if it could not.
      See Also:
      UnrolledCholesky_DDRM, LinearSolverFactory_DDRM.chol(int)
    • pinv

      public static void pinv​(DMatrixRMaj A, DMatrixRMaj invA)

      Computes the Moore-Penrose pseudo-inverse:

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

      Internally it uses SolvePseudoInverseSvd_DDRM 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 DMatrixRMaj[] columnsToVector​(DMatrixRMaj A, @Nullable @Nullable DMatrixRMaj[] v)
      Converts the columns in a matrix into a set of vectors.
      Parameters:
      A - Matrix. Not modified.
      Returns:
      An array of vectors.
    • rowsToVector

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

      public static void setIdentity​(DMatrix1Row 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 DMatrixRMaj 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 DMatrixRMaj 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 DMatrixRMaj 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...)
    • diag

      public static DMatrixRMaj diag​(@Nullable @Nullable DMatrixRMaj ret, int width, double... diagEl)
      See Also:
      diag(double...)
    • diagR

      public static DMatrixRMaj 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 DMatrixRMaj kron​(DMatrixRMaj A, DMatrixRMaj B, @Nullable @Nullable DMatrixRMaj 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. Nullable. Modified.
    • extract

      public static void extract​(DMatrix src, int srcY0, int srcY1, int srcX0, int srcX1, DMatrix 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 void extract​(DMatrix src, int srcY0, int srcY1, int srcX0, int srcX1, DMatrix dst)
      Extract where the destination is reshaped to match the extracted region
      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.
    • extract

      public static void extract​(DMatrix src, int srcY0, int srcX0, DMatrix dst)

      Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'. Uses the shape of dst to determine the size of the matrix extracted.

      Parameters:
      src - The original matrix which is to be copied. Not modified.
      srcY0 - Start row in src.
      srcX0 - Start column in src.
      dst - Where the matrix is extracted into.
    • extract

      public static DMatrixRMaj extract​(DMatrixRMaj 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.
    • extract

      public static DMatrixRMaj extract​(DMatrixRMaj src, int[] rows, int rowsSize, int[] cols, int colsSize, @Nullable @Nullable DMatrixRMaj dst)
      Extracts out a matrix from source given a sub matrix with arbitrary rows and columns specified in two array lists
      Parameters:
      src - Source matrix. Not modified.
      rows - array of row indexes
      rowsSize - maximum element in row array
      cols - array of column indexes
      colsSize - maximum element in column array
      dst - output matrix. Must be correct shape.
    • extract

      public static DMatrixRMaj extract​(DMatrixRMaj src, int[] indexes, int length, @Nullable @Nullable DMatrixRMaj dst)
      Extracts the elements from the source matrix by their 1D index.
      Parameters:
      src - Source matrix. Not modified.
      indexes - array of row indexes
      length - maximum element in row array
      dst - output matrix. Must be a vector of the correct length.
    • insert

      public static void insert​(DMatrixRMaj src, DMatrixRMaj dst, int[] rows, int rowsSize, int[] cols, int colsSize)
      Inserts into the specified elements of dst the source matrix.
       for i in len(rows):
         for j in len(cols):
            dst(rows[i],cols[j]) = src(i,j)
       
      Parameters:
      src - Source matrix. Not modified.
      dst - output matrix. Must be correct shape.
      rows - array of row indexes.
      rowsSize - maximum element in row array
      cols - array of column indexes
      colsSize - maximum element in column array
    • extractDiag

      public static DMatrixRMaj extractDiag​(DMatrixRMaj src, @Nullable @Nullable DMatrixRMaj 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.
    • extractRow

      public static DMatrixRMaj extractRow​(DMatrixRMaj a, int row, @Nullable @Nullable DMatrixRMaj out)
      Extracts the row from a matrix.
      Parameters:
      a - Input matrix
      row - Which row is to be extracted
      out - output. Storage for the extracted row. If null then a new vector will be returned.
      Returns:
      The extracted row.
    • extractColumn

      public static DMatrixRMaj extractColumn​(DMatrixRMaj a, int column, @Nullable @Nullable DMatrixRMaj out)
      Extracts the column from a matrix.
      Parameters:
      a - Input matrix
      column - Which column is to be extracted
      out - output. Storage for the extracted column. If null then a new vector will be returned.
      Returns:
      The extracted column.
    • removeColumns

      public static void removeColumns​(DMatrixRMaj A, int col0, int col1)
      Removes columns from the matrix.
      Parameters:
      A - Matrix. Modified
      col0 - First column
      col1 - Last column, inclusive.
    • insert

      public static void insert​(DMatrix src, DMatrix 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​(DMatrixD1 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. Not modified.
      Returns:
      The max element value of the matrix.
    • elementMax

      public static double elementMax​(DMatrixD1 a, ElementLocation loc)

      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. Not modified.
      loc - (Output) Location of selected element.
      Returns:
      The max element value of the matrix.
    • elementMaxAbs

      public static double elementMaxAbs​(DMatrixD1 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. Not modified.
      Returns:
      The max abs element value of the matrix.
    • elementMaxAbs

      public static double elementMaxAbs​(DMatrixD1 a, ElementLocation loc)

      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. Not modified.
      loc - (Output) Location of element element.
      Returns:
      The max abs element value of the matrix.
    • elementMin

      public static double elementMin​(DMatrixD1 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. Not modified.
      Returns:
      The value of element in the matrix with the minimum value.
    • elementMin

      public static double elementMin​(DMatrixD1 a, ElementLocation loc)

      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. Not modified.
      loc - (Output) Location of selected element.
      Returns:
      The value of element in the matrix with the minimum value.
    • elementMinAbs

      public static double elementMinAbs​(DMatrixD1 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. Not modified.
      Returns:
      The max element value of the matrix.
    • elementMinAbs

      public static double elementMinAbs​(DMatrixD1 a, ElementLocation loc)

      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 - (Input) A matrix. Not modified.
      loc - (Output) Location of selected element.
      Returns:
      The max element value of the matrix.
    • elementMult

      public static void elementMult​(DMatrixD1 A, DMatrixD1 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 <T extends DMatrixD1> T elementMult​(T A, T B, @Nullable T output)

      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.
      output - Where the results of the operation are stored. Modified.
    • elementDiv

      public static void elementDiv​(DMatrixD1 A, DMatrixD1 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 <T extends DMatrixD1> T elementDiv​(T A, T B, @Nullable T output)

      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.
      output - Where the results of the operation are stored. Modified.
    • elementSum

      public static double elementSum​(DMatrixD1 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​(DMatrixD1 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.
    • elementPower

      public static <T extends DMatrixD1> T elementPower​(T A, T B, @Nullable T output)

      Element-wise power operation
      cij = aij ^ bij

      Parameters:
      A - left side
      B - right side
      output - output (modified)
    • elementPower

      public static <T extends DMatrixD1> T elementPower​(double a, T B, @Nullable T output)

      Element-wise power operation
      cij = a ^ bij

      Parameters:
      a - left scalar
      B - right side
      output - output (modified)
    • elementPower

      public static <T extends DMatrixD1> T elementPower​(T A, double b, @Nullable T output)

      Element-wise power operation
      cij = aij ^ b

      Parameters:
      A - left side
      b - right scalar
      output - output (modified)
    • elementLog

      public static <T extends DMatrixD1> T elementLog​(T A, @Nullable T output)

      Element-wise log operation
      cij = Math.log(aij)

      Parameters:
      A - (input) A matrix
      output - (input/output) Storage for results. can be null. (modified)
      Returns:
      The results
    • elementExp

      public static <T extends DMatrixD1> T elementExp​(T A, @Nullable T output)

      Element-wise exp operation
      cij = Math.exp(aij)

      Parameters:
      A - (input) A matrix
      output - (input/output) Storage for results. can be null. (modified)
      Returns:
      The results
    • multRows

      public static void multRows​(double[] values, DMatrixRMaj A)
      Multiplies every element in row i by value[i].
      Parameters:
      values - array. Not modified.
      A - Matrix. Modified.
    • divideRows

      public static void divideRows​(double[] values, DMatrixRMaj A)
      Divides every element in row i by value[i].
      Parameters:
      values - array. Not modified.
      A - Matrix. Modified.
    • multCols

      public static void multCols​(DMatrixRMaj A, double[] values)
      Multiplies every element in column i by value[i].
      Parameters:
      A - Matrix. Modified.
      values - array. Not modified.
    • divideCols

      public static void divideCols​(DMatrixRMaj A, double[] values)
      Divides every element in column i by value[i].
      Parameters:
      A - Matrix. Modified.
      values - array. Not modified.
    • divideRowsCols

      public static void divideRowsCols​(double[] diagA, int offsetA, DMatrixRMaj B, double[] diagC, int offsetC)
      Equivalent to multiplying a matrix B by the inverse of two diagonal matrices. B = inv(A)*B*inv(C), where A=diag(a) and C=diag(c).
      Parameters:
      diagA - Array of length offsteA + B.numRows
      offsetA - First index in A
      B - Rectangular matrix
      diagC - Array of length indexC + B.numCols
      offsetC - First index in C
    • sumRows

      public static DMatrixRMaj sumRows​(DMatrixRMaj input, @Nullable @Nullable DMatrixRMaj 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. Reshaped into a column. Modified.
      Returns:
      Vector containing the sum of each row in the input.
    • minRows

      public static DMatrixRMaj minRows​(DMatrixRMaj input, @Nullable @Nullable DMatrixRMaj output)

      Finds the element with the minimum value along each row in the input matrix and returns the results in a vector:

      bj = min(i=1:n ; aji)

      Parameters:
      input - Input matrix
      output - Optional storage for output. Reshaped into a column. Modified.
      Returns:
      Vector containing the sum of each row in the input.
    • maxRows

      public static DMatrixRMaj maxRows​(DMatrixRMaj input, @Nullable @Nullable DMatrixRMaj output)

      Finds the element with the maximum value along each row in the input matrix and returns the results in a vector:

      bj = max(i=1:n ; aji)

      Parameters:
      input - Input matrix
      output - Optional storage for output. Reshaped into a column. Modified.
      Returns:
      Vector containing the sum of each row in the input.
    • sumCols

      public static DMatrixRMaj sumCols​(DMatrixRMaj input, @Nullable @Nullable DMatrixRMaj 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
      output - Optional storage for output. Reshaped into a row vector. Modified.
      Returns:
      Vector containing the sum of each column
    • minCols

      public static DMatrixRMaj minCols​(DMatrixRMaj input, @Nullable @Nullable DMatrixRMaj output)

      Finds the element with the minimum value along column in the input matrix and returns the results in a vector:

      bj = min(i=1:m ; aij)

      Parameters:
      input - Input matrix
      output - Optional storage for output. Reshaped into a row vector. Modified.
      Returns:
      Vector containing the minimum of each column
    • maxCols

      public static DMatrixRMaj maxCols​(DMatrixRMaj input, @Nullable @Nullable DMatrixRMaj output)

      Finds the element with the minimum value along column in the input matrix and returns the results in a vector:

      bj = min(i=1:m ; aij)

      Parameters:
      input - Input matrix
      output - Optional storage for output. Reshaped into a row vector. Modified.
      Returns:
      Vector containing the maximum of each column
    • addEquals

      public static void addEquals​(DMatrixD1 a, DMatrixD1 b)

      Performs the following operation:

      a = a + b
      aij = aij + bij

      Parameters:
      a - (input/output) A Matrix. Modified.
      b - (input) A Matrix. Not modified.
    • addEquals

      public static void addEquals​(DMatrixD1 a, double beta, DMatrixD1 b)

      Performs the following operation:

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

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

      public static <T extends DMatrixD1> T add​(T a, T b, @Nullable T output)

      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.
      output - (output) A Matrix where the results are stored. Can be null. Modified.
      Returns:
      The results.
    • add

      public static <T extends DMatrixD1> T add​(T a, double beta, T b, @Nullable T output)

      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.
      output - (output) A Matrix where the results are stored. Can be null. Modified.
      Returns:
      The results.
    • add

      public static <T extends DMatrixD1> T add​(double alpha, T a, double beta, T b, @Nullable T output)

      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.
      output - (output) A Matrix where the results are stored. Can be null. Modified.
      Returns:
      The results.
    • add

      public static <T extends DMatrixD1> T add​(double alpha, T a, T b, T output)

      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.
      output - (output) A Matrix where the results are stored. Can be null. Modified.
      Returns:
      The results.
    • add

      public static void add​(DMatrixD1 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 <T extends DMatrixD1> T add​(T a, double val, T output)

      Performs scalar addition:

      c = a + val
      cij = aij + val

      Parameters:
      a - A matrix. Not modified.
      val - The value that's added to each element.
      output - (output) Storage for results. Can be null. Modified.
      Returns:
      The resulting matrix
    • subtract

      public static <T extends DMatrixD1> T subtract​(T a, double val, @Nullable T output)

      Performs matrix scalar subtraction:

      c = a - val
      cij = aij - val

      Parameters:
      a - (input) A matrix. Not modified.
      val - (input) The value that's subtracted to each element.
      output - (output) Storage for results. Can be null. Modified.
      Returns:
      The resulting matrix
    • subtract

      public static <T extends DMatrixD1> T subtract​(double val, T a, @Nullable T output)

      Performs matrix scalar subtraction:

      c = val - a
      cij = val - aij

      Parameters:
      val - (input) The value that's subtracted to each element.
      a - (input) A matrix. Not modified.
      output - (output) Storage for results. Can be null. Modified.
      Returns:
      The resulting matrix
    • subtractEquals

      public static void subtractEquals​(DMatrixD1 a, DMatrixD1 b)

      Performs the following subtraction operation:

      a = a - b
      aij = aij - bij

      Parameters:
      a - (input) A Matrix. Modified.
      b - (input) A Matrix. Not modified.
    • subtract

      public static <T extends DMatrixD1> T subtract​(T a, T b, @Nullable T output)

      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 - (input) A Matrix. Not modified.
      b - (input) A Matrix. Not modified.
      output - (output) A Matrix. Can be null. Modified.
      Returns:
      The resulting matrix
    • scale

      public static void scale​(double alpha, DMatrixD1 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, DMatrixD1 a, DMatrixD1 b)

      Performs an element by element scalar multiplication.

      bij = α*aij

      Parameters:
      alpha - the amount each element is multiplied by.
      a - The matrix that is to be scaled. Not modified.
      b - Where the scaled matrix is stored. Modified.
    • scaleRow

      public static void scaleRow​(double alpha, DMatrixRMaj A, int row)
      In-place scaling of a row in A
      Parameters:
      alpha - scale factor
      A - matrix
      row - which row in A
    • scaleCol

      public static void scaleCol​(double alpha, DMatrixRMaj A, int col)
      In-place scaling of a column in A
      Parameters:
      alpha - scale factor
      A - matrix
      col - which row in A
    • divide

      public static void divide​(double alpha, DMatrixD1 a)

      Performs an in-place element by element scalar division with the scalar on top.

      aij = α/aij

      Parameters:
      a - (input/output) The matrix whose elements are divide the scalar. Modified.
      alpha - top value in division
    • divide

      public static void divide​(DMatrixD1 a, double alpha)

      Performs an in-place element by element scalar division with the scalar on bottom.

      aij = aij

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

      public static <T extends DMatrixD1> T divide​(double alpha, T input, T output)

      Performs an element by element scalar division with the scalar on top.

      bij = α/aij

      Parameters:
      alpha - The numerator.
      input - The matrix whose elements are the divisor. Not modified.
      output - Where the results are stored. Modified. Can be null.
      Returns:
      The resulting matrix
    • divide

      public static <T extends DMatrixD1> T divide​(T input, double alpha, @Nullable T output)

      Performs an element by element scalar division with the scalar on botton.

      bij = aij

      Parameters:
      input - The matrix whose elements are to be divided. Not modified.
      alpha - the amount each element is divided by.
      output - Where the results are stored. Modified. Can be null.
      Returns:
      The resulting matrix
    • changeSign

      public static void changeSign​(DMatrixD1 a)

      Changes the sign of every element in the matrix.

      aij = -aij

      Parameters:
      a - A matrix. Modified.
    • changeSign

      public static <T extends DMatrixD1> T changeSign​(T input, @Nullable T output)

      Changes the sign of every element in the matrix.

      outputij = -inputij

      Parameters:
      input - A matrix. Modified.
    • fill

      public static void fill​(DMatrixD1 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 DMatrixRMaj rref​(DMatrixRMaj A, int numUnknowns, @Nullable @Nullable DMatrixRMaj reduced)

      Puts the augmented system matrix into reduced row echelon form (RREF) using Gauss-Jordan elimination with row (partial) pivots. 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 A.numCols, which works for most applications.
      reduced - Storage for reduced echelon matrix. If null then a new matrix is returned. Modified.
      Returns:
      Reduced echelon form of A
      See Also:
      RrefGaussJordanRowPivot_DDRM
    • elementLessThan

      public static BMatrixRMaj elementLessThan​(DMatrixRMaj A, double value, BMatrixRMaj output)
      Applies the > operator to each element in A. Results are stored in a boolean matrix.
      Parameters:
      A - Input matrx
      value - value each element is compared against
      output - (Optional) Storage for results. Can be null. Is reshaped.
      Returns:
      Boolean matrix with results
    • elementLessThanOrEqual

      public static BMatrixRMaj elementLessThanOrEqual​(DMatrixRMaj A, double value, BMatrixRMaj output)
      Applies the ≥ operator to each element in A. Results are stored in a boolean matrix.
      Parameters:
      A - Input matrix
      value - value each element is compared against
      output - (Optional) Storage for results. Can be null. Is reshaped.
      Returns:
      Boolean matrix with results
    • elementMoreThan

      public static BMatrixRMaj elementMoreThan​(DMatrixRMaj A, double value, BMatrixRMaj output)
      Applies the > operator to each element in A. Results are stored in a boolean matrix.
      Parameters:
      A - Input matrix
      value - value each element is compared against
      output - (Optional) Storage for results. Can be null. Is reshaped.
      Returns:
      Boolean matrix with results
    • elementMoreThanOrEqual

      public static BMatrixRMaj elementMoreThanOrEqual​(DMatrixRMaj A, double value, BMatrixRMaj output)
      Applies the ≥ operator to each element in A. Results are stored in a boolean matrix.
      Parameters:
      A - Input matrix
      value - value each element is compared against
      output - (Optional) Storage for results. Can be null. Is reshaped.
      Returns:
      Boolean matrix with results
    • elementLessThan

      public static BMatrixRMaj elementLessThan​(DMatrixRMaj A, DMatrixRMaj B, BMatrixRMaj output)
      Applies the < operator to each element in A. Results are stored in a boolean matrix.
      Parameters:
      A - Input matrix
      B - Input matrix
      output - (Optional) Storage for results. Can be null. Is reshaped.
      Returns:
      Boolean matrix with results
    • elementLessThanOrEqual

      public static BMatrixRMaj elementLessThanOrEqual​(DMatrixRMaj A, DMatrixRMaj B, BMatrixRMaj output)
      Applies the A ≤ B operator to each element. Results are stored in a boolean matrix.
      Parameters:
      A - Input matrix
      B - Input matrix
      output - (Optional) Storage for results. Can be null. Is reshaped.
      Returns:
      Boolean matrix with results
    • elements

      public static DMatrixRMaj elements​(DMatrixRMaj A, BMatrixRMaj marked, @Nullable @Nullable DMatrixRMaj output)
      Returns a row matrix which contains all the elements in A which are flagged as true in 'marked'
      Parameters:
      A - Input matrix
      marked - Input matrix marking elements in A
      output - Storage for output row vector. Can be null. Will be reshaped.
      Returns:
      Row vector with marked elements
    • countTrue

      public static int countTrue​(BMatrixRMaj A)
      Counts the number of elements in A which are true
      Parameters:
      A - input matrix
      Returns:
      number of true elements
    • concatColumns

      public static DMatrixRMaj concatColumns​(DMatrixRMaj a, DMatrixRMaj b, @Nullable @Nullable DMatrixRMaj output)
      output = [a , b]
    • concatColumnsMulti

      public static DMatrixRMaj concatColumnsMulti​(DMatrixRMaj... m)

      Concatinates all the matrices together along their columns. If the rows do not match the upper elements are set to zero.

      A = [ m[0] , ... , m[n-1] ]
      Parameters:
      m - Set of matrices
      Returns:
      Resulting matrix
    • concatRows

      public static void concatRows​(DMatrixRMaj a, DMatrixRMaj b, DMatrixRMaj output)
      output = [a ; b]
    • concatRowsMulti

      public static DMatrixRMaj concatRowsMulti​(DMatrixRMaj... m)

      Concatinates all the matrices together along their columns. If the rows do not match the upper elements are set to zero.

      A = [ m[0] ; ... ; m[n-1] ]
      Parameters:
      m - Set of matrices
      Returns:
      Resulting matrix
    • permuteRowInv

      public static DMatrixRMaj permuteRowInv​(int[] pinv, DMatrixRMaj input, DMatrixRMaj output)
      Applies the row permutation specified by the vector to the input matrix and save the results in the output matrix. output[perm[j],:] = input[j,:]
      Parameters:
      pinv - (Input) Inverse permutation vector. Specifies new order of the rows.
      input - (Input) Matrix which is to be permuted
      output - (Output) Matrix which has the permutation stored in it. Is reshaped.
    • abs

      public static void abs​(DMatrixD1 a, DMatrixD1 c)

      Performs absolute value of a matrix:

      c = abs(a)
      cij = abs(aij)

      Parameters:
      a - A matrix. Not modified.
      c - A matrix. Modified.
    • abs

      public static void abs​(DMatrixD1 a)

      Performs absolute value of a matrix:

      a = abs(a)
      aij = abs(aij)

      Parameters:
      a - A matrix. Modified.
    • symmLowerToFull

      public static void symmLowerToFull​(DMatrixRMaj A)
      Given a symmetric matrix which is represented by a lower triangular matrix convert it back into a full symmetric matrix.
      Parameters:
      A - (Input) Lower triangular matrix (Output) symmetric matrix
    • symmUpperToFull

      public static void symmUpperToFull​(DMatrixRMaj A)
      Given a symmetric matrix which is represented by a lower triangular matrix convert it back into a full symmetric matrix.
      Parameters:
      A - (Input) Lower triangular matrix (Output) symmetric matrix
    • apply

      public static DMatrixRMaj apply​(DMatrixRMaj input, DOperatorUnary func, @Nullable @Nullable DMatrixRMaj output)
      This applies a given unary function on every value stored in the matrix
       output[i,j] = func(input[i,j])
       
      A and B can be the same instance.
      Parameters:
      input - (Input) input matrix. Not modified
      func - Unary function accepting a double
      output - (Output) Matrix. Can be same instance as A. Modified.
      Returns:
      The output matrix
    • apply

      public static DMatrixRMaj apply​(DMatrixRMaj input, DOperatorUnary func)