java.lang.Object

org.ejml.dense.row.CommonOps_ZDRM

public class CommonOps_ZDRM extends Object

Common operations on complex numbers

Method Summary

Modifier and Type

Method

Description

static void

add(ZMatrixD1 a, ZMatrixD1 b, ZMatrixD1 c)

Performs the following operation:

c = a + b
c_ij = a_ij + b_ij

static ZMatrixRMaj[]

columnsToVector(ZMatrixRMaj A, @Nullable ZMatrixRMaj[] v)

Converts the columns in a matrix into a set of vectors.

static ZMatrixD1

conjugate(ZMatrixD1 input, @Nullable ZMatrixRMaj output)

Computes the complex conjugate of the input matrix.

real_i,j = real_i,j
imaginary_i,j = -1*imaginary_i,j

static void

convert(DMatrixD1 input, ZMatrixD1 output)

Converts the real matrix into a complex matrix.

static Complex_F64

det(ZMatrixRMaj mat)

Returns the determinant of the matrix.

static ZMatrixRMaj

diag(double... data)

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

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

static ZMatrixRMaj

diag(@Nullable ZMatrixRMaj output, int N, double... data)

static ZMatrixRMaj

elementDivide(double real, double imaginary, ZMatrixD1 input, @Nullable ZMatrixRMaj output)

Performs element by element division operation with a complex number on the right

output_ij = (real + imaginary*i) / input_ij

static ZMatrixRMaj

elementDivide(ZMatrixD1 input, double real, double imaginary, @Nullable ZMatrixRMaj output)

Performs element by element division operation with a complex number on the right

output_ij = input_ij / (real + imaginary*i)

static ZMatrixRMaj

elementDivide(ZMatrixD1 inputA, ZMatrixD1 inputB, @Nullable ZMatrixRMaj output)

Performs complex division between two matrices with the same shape element by element.

output_ij = inputA_ij / inputB_ij

static double

elementMaxAbs(ZMatrixRMaj a)

Returns the largest absolute value of any element in the matrix.

Max{ |a_ij| } for all i and j

static double

elementMaxImaginary(ZMatrixD1 a)

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

Min{ a_ij } for all i and j

static double

elementMaxMagnitude2(ZMatrixD1 a)

Returns the magnitude squared of the complex element with the largest magnitude

Max{ |a_ij|^2 } for all i and j

static double

elementMaxReal(ZMatrixD1 a)

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

Min{ a_ij } for all i and j

static double

elementMinAbs(ZMatrixRMaj a)

Returns the smallest absolute value of any element in the matrix.

Min{ |a_ij| } for all i and j

static double

elementMinImaginary(ZMatrixD1 a)

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

Min{ a_ij } for all i and j

static double

elementMinReal(ZMatrixD1 a)

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

Min{ a_ij } for all i and j

static ZMatrixRMaj

elementMultiply(ZMatrixD1 input, double real, double imaginary, @Nullable ZMatrixRMaj output)

Performs element by element multiplication operation with a complex number

output_ij = input_ij * (real + imaginary*i)

static ZMatrixRMaj

elementMultiply(ZMatrixD1 inputA, ZMatrixD1 inputB, @Nullable ZMatrixRMaj output)

Performs complex multiplication between two matrices with the same shape element by element.

output_ij = inputA_ij * inputB_ij

static ZMatrixRMaj

elementPower(ZMatrixD1 input, double b, @Nullable ZMatrixRMaj output)

Element by element complex power

output_ij = inputA_ij / inputB_ij

static Complex_F64

elementSum(ZMatrixD1 input, @Nullable Complex_F64 output)

Computes the sum of all the elements in the matrix:

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

static ZMatrixRMaj

extract(ZMatrixRMaj src, int srcY0, int srcY1, int srcX0, int srcX1)

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

static void

extract(ZMatrixRMaj src, int srcY0, int srcY1, int srcX0, int srcX1, ZMatrixRMaj dst, int dstY0, int dstX0)

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

static void

extractDiag(ZMatrixRMaj src, ZMatrixRMaj dst)

Extracts the diagonal elements 'src' write it to the 'dst' vector.

static void

fill(ZMatrixD1 a, double real, double imaginary)

Sets every element in the matrix to the specified value.

a_ij = value

static ZMatrixRMaj

identity(int width)

Creates an identity matrix of the specified size.

a_ij = 0+0i if i ≠ j
a_ij = 1+0i if i = j

static ZMatrixRMaj

identity(int width, int height)

Creates a matrix with diagonal elements set to 1 and the rest 0.

a_ij = 0+0i if i ≠ j
a_ij = 1+0i if i = j

static DMatrixRMaj

imaginary(ZMatrixD1 input, @Nullable DMatrixRMaj output)

Places the imaginary component of the input matrix into the output matrix.

static boolean

invert(ZMatrixRMaj A)

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

a = a^-1

static boolean

invert(ZMatrixRMaj input, ZMatrixRMaj output)

Performs a matrix inversion operation that does not modify the original and stores the results in another matrix.

static DMatrixRMaj

magnitude(ZMatrixD1 input, @Nullable DMatrixRMaj output)

Computes the magnitude of the complex number in the input matrix and stores the results in the output matrix.

static void

mult(double realAlpha, double imgAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = α * a * b

c_ij = α ∑_k=1:n { * a_ik * b_kj}

static void

mult(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = a * b

c_ij = ∑_k=1:n { * a_ik * b_kj}

static void

multAdd(double realAlpha, double imgAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = c + α * a * b
c_ij = c_ij + α * ∑_k=1:n { a_ik * b_kj}

static void

multAdd(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = c + a * b
c_ij = c_ij + ∑_k=1:n { a_ik * b_kj}

static void

multAddTransA(double realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = c + α * a^H * b
c_ij =c_ij + α * ∑_k=1:n { a_ki * b_kj}

static void

multAddTransA(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = c + a^H * b
c_ij = c_ij + ∑_k=1:n { a_ki * b_kj}

static void

multAddTransAB(double realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = c + α * a^H * b^H
c_ij = c_ij + α * ∑_k=1:n { a_ki * b_jk}

static void

multAddTransAB(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = c + a^H * b^H
c_ij = c_ij + ∑_k=1:n { a_ki * b_jk}

static void

multAddTransB(double realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = c + α * a * b^H
c_ij = c_ij + α * ∑_k=1:n { a_ik * b_jk}

static void

multAddTransB(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = c + a * b^H
c_ij = c_ij + ∑_k=1:n { a_ik * b_jk}

static void

multTransA(double realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = α * a^H * b

c_ij = α ∑_k=1:n { a_ki * b_kj}

static void

multTransA(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = a^H * b

c_ij = ∑_k=1:n { a_ki * b_kj}

static void

multTransAB(double realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = α * a^H * b^H
c_ij = α ∑_k=1:n { a_ki * b_jk}

static void

multTransAB(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = a^T * b^T
c_ij = ∑_k=1:n { a_ki * b_jk}

static void

multTransB(double realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = α * a * b^H
c_ij = α ∑_k=1:n { a_ik * b_jk}

static void

multTransB(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)

Performs the following operation:

c = a * b^H
c_ij = ∑_k=1:n { a_ik * b_jk}

static DMatrixRMaj

real(ZMatrixD1 input, @Nullable DMatrixRMaj output)

Places the real component of the input matrix into the output matrix.

static void

scale(double alphaReal, double alphaImag, ZMatrixD1 a)

Performs an in-place element by element scalar multiplication.

a_ij = α*a_ij

static void

setIdentity(ZMatrixRMaj mat)

Sets all the diagonal elements equal to one and everything else equal to zero.

static boolean

solve(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj x)

Solves for x in the following equation:

A*x = b

static void

subtract(ZMatrixD1 a, ZMatrixD1 b, ZMatrixD1 c)

Performs the following operation:

c = a - b
c_ij = a_ij - b_ij

static Complex_F64

trace(ZMatrixRMaj input, @Nullable Complex_F64 output)

Computes the matrix trace:

trace = ∑_i=1:n { a_ii }
where n = min(numRows,numCols)

static void

transpose(ZMatrixRMaj mat)

Performs an "in-place" transpose.

static ZMatrixRMaj

transpose(ZMatrixRMaj input, @Nullable ZMatrixRMaj output)

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

b_ij = a_ji
where 'b' is the transpose of 'a'.

static void

transposeConjugate(ZMatrixRMaj mat)

Performs an "in-place" conjugate transpose.

static ZMatrixRMaj

transposeConjugate(ZMatrixRMaj input, @Nullable ZMatrixRMaj output)

Conjugate transposes input matrix 'a' and stores the results in output matrix 'b':

b-real_i,j = a-real_j,i
b-imaginary_i,j = -1*a-imaginary_j,i
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

Method Details
- identity
  
  public static ZMatrixRMaj identity(int width)
  
  Creates an identity matrix of the specified size.
  
  a_ij = 0+0i if i ≠ j
  a_ij = 1+0i if i = j
  
  Parameters:
  
  width - The width and height of the identity matrix.
  
  Returns:
  
  A new instance of an identity matrix.
- identity
  
  public static ZMatrixRMaj identity(int width, int height)
  
  Creates a matrix with diagonal elements set to 1 and the rest 0.
  
  a_ij = 0+0i if i ≠ j
  a_ij = 1+0i if i = j
  
  Parameters:
  
  width - The width of the identity matrix.
  
  height - The height of the identity matrix.
  
  Returns:
  
  A new instance of an identity matrix.
- diag
  
  public static ZMatrixRMaj diag(double... data)
  
  Creates a new square matrix whose diagonal elements are specified by data and all the other elements are zero.
  
  a_ij = 0 if i ≤ j
  a_ij = diag[i] if i = j
  
  Parameters:
  
  data - Contains the values of the diagonal elements of the resulting matrix.
  
  Returns:
  
  A new complex matrix.
- diag
  
  public static ZMatrixRMaj diag(@Nullable @Nullable ZMatrixRMaj output, int N, double... data)
- extractDiag
  
  public static void extractDiag(ZMatrixRMaj src, ZMatrixRMaj 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.
- convert
  
  public static void convert(DMatrixD1 input, ZMatrixD1 output)
  
  Converts the real matrix into a complex matrix.
  
  Parameters:
  
  input - Real matrix. Not modified.
  
  output - Complex matrix. Modified.
- real
  
  public static DMatrixRMaj real(ZMatrixD1 input, @Nullable @Nullable DMatrixRMaj output)
  
  Places the real component of the input matrix into the output matrix.
  
  Parameters:
  
  input - Complex matrix. Not modified.
  
  output - real matrix. Modified.
- imaginary
  
  public static DMatrixRMaj imaginary(ZMatrixD1 input, @Nullable @Nullable DMatrixRMaj output)
  
  Places the imaginary component of the input matrix into the output matrix.
  
  Parameters:
  
  input - Complex matrix. Not modified.
  
  output - real matrix. Modified.
- magnitude
  
  public static DMatrixRMaj magnitude(ZMatrixD1 input, @Nullable @Nullable DMatrixRMaj output)
  
  Computes the magnitude of the complex number in the input matrix and stores the results in the output matrix.
  magnitude = sqrt(real^2 + imaginary^2)
  
  Parameters:
  
  input - Complex matrix. Not modified.
  
  output - real matrix. Modified.
- conjugate
  
  public static ZMatrixD1 conjugate(ZMatrixD1 input, @Nullable @Nullable ZMatrixRMaj output)
  
  Computes the complex conjugate of the input matrix.
  
  real_i,j = real_i,j
  imaginary_i,j = -1*imaginary_i,j
  
  Parameters:
  
  input - Input matrix. Not modified.
  
  output - The complex conjugate of the input matrix. Modified.
- fill
  
  public static void fill(ZMatrixD1 a, double real, double imaginary)
  
  Sets every element in the matrix to the specified value.
  
  a_ij = value
  
  Parameters:
  
  a - A matrix whose elements are about to be set. Modified.
  
  real - The real component
  
  imaginary - The imaginary component
- add
  
  public static void add(ZMatrixD1 a, ZMatrixD1 b, ZMatrixD1 c)
  
  Performs the following operation:
  
  c = a + b
  c_ij = a_ij + b_ij
  
  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.
- subtract
  
  public static void subtract(ZMatrixD1 a, ZMatrixD1 b, ZMatrixD1 c)
  
  Performs the following operation:
  
  c = a - b
  c_ij = a_ij - b_ij
  
  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.
- scale
  
  public static void scale(double alphaReal, double alphaImag, ZMatrixD1 a)
  
  Performs an in-place element by element scalar multiplication.
  
  a_ij = α*a_ij
  
  Parameters:
  
  a - The matrix that is to be scaled. Modified.
  
  alphaReal - real component of scale factor
  
  alphaImag - imaginary component of scale factor
- mult
  
  public static void mult(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = a * b
  
  c_ij = ∑_k=1:n { * a_ik * b_kj}
  
  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 realAlpha, double imgAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = α * a * b
  
  c_ij = α ∑_k=1:n { * a_ik * b_kj}
  
  Parameters:
  
  realAlpha - real component of scaling factor.
  
  imgAlpha - imaginary component of 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.
- multAdd
  
  public static void multAdd(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = c + a * b
  c_ij = c_ij + ∑_k=1:n { a_ik * b_kj}
  
  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 realAlpha, double imgAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = c + α * a * b
  c_ij = c_ij + α * ∑_k=1:n { a_ik * b_kj}
  
  Parameters:
  
  realAlpha - real component of scaling factor.
  
  imgAlpha - imaginary component of 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(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = a^H * b
  
  c_ij = ∑_k=1:n { a_ki * b_kj}
  
  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 realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = α * a^H * b
  
  c_ij = α ∑_k=1:n { a_ki * b_kj}
  
  Parameters:
  
  realAlpha - Real component of scaling factor.
  
  imagAlpha - Imaginary component of 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(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = a * b^H
  c_ij = ∑_k=1:n { a_ik * b_jk}
  
  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 realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = α * a * b^H
  c_ij = α ∑_k=1:n { a_ik * b_jk}
  
  Parameters:
  
  realAlpha - Real component of scaling factor.
  
  imagAlpha - Imaginary component of 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(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = a^T * b^T
  c_ij = ∑_k=1:n { a_ki * b_jk}
  
  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 realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = α * a^H * b^H
  c_ij = α ∑_k=1:n { a_ki * b_jk}
  
  Parameters:
  
  realAlpha - Real component of scaling factor.
  
  imagAlpha - Imaginary component of 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(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = c + a^H * b
  c_ij = c_ij + ∑_k=1:n { a_ki * b_kj}
  
  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 realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = c + α * a^H * b
  c_ij =c_ij + α * ∑_k=1:n { a_ki * b_kj}
  
  Parameters:
  
  realAlpha - Real component of scaling factor.
  
  imagAlpha - Imaginary component of 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(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = c + a * b^H
  c_ij = c_ij + ∑_k=1:n { a_ik * b_jk}
  
  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 realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = c + α * a * b^H
  c_ij = c_ij + α * ∑_k=1:n { a_ik * b_jk}
  
  Parameters:
  
  realAlpha - Real component of scaling factor.
  
  imagAlpha - Imaginary component of 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(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = c + a^H * b^H
  c_ij = c_ij + ∑_k=1:n { a_ki * b_jk}
  
  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 realAlpha, double imagAlpha, ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj c)
  
  Performs the following operation:
  
  c = c + α * a^H * b^H
  c_ij = c_ij + α * ∑_k=1:n { a_ki * b_jk}
  
  Parameters:
  
  realAlpha - Real component of scaling factor.
  
  imagAlpha - Imaginary component of 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.
- transpose
  
  public static void transpose(ZMatrixRMaj 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(ZMatrixRMaj, ZMatrixRMaj) is invoked.
  
  Parameters:
  
  mat - The matrix that is to be transposed. Modified.
- transposeConjugate
  
  public static void transposeConjugate(ZMatrixRMaj mat)
  
  Performs an "in-place" conjugate transpose.
  Parameters:
  
  mat - The matrix that is to be transposed. Modified.
  
  See Also:
  
  transpose(ZMatrixRMaj)
- transpose
  
  public static ZMatrixRMaj transpose(ZMatrixRMaj input, @Nullable @Nullable ZMatrixRMaj output)
  
  Transposes input matrix 'a' and stores the results in output matrix 'b':
  
  b_ij = a_ji
  where 'b' is the transpose of 'a'.
  
  Parameters:
  
  input - The original matrix. Not modified.
  
  output - Where the transpose is stored. If null a new matrix is created. Modified.
  
  Returns:
  
  The transposed matrix.
- transposeConjugate
  
  public static ZMatrixRMaj transposeConjugate(ZMatrixRMaj input, @Nullable @Nullable ZMatrixRMaj output)
  
  Conjugate transposes input matrix 'a' and stores the results in output matrix 'b':
  
  b-real_i,j = a-real_j,i
  b-imaginary_i,j = -1*a-imaginary_j,i
  where 'b' is the transpose of 'a'.
  
  Parameters:
  
  input - The original matrix. Not modified.
  
  output - Where the transpose is stored. If null a new matrix is created. Modified.
  
  Returns:
  
  The transposed matrix.
- trace
  
  public static Complex_F64 trace(ZMatrixRMaj input, @Nullable @Nullable Complex_F64 output)
  
  Computes the matrix trace:
  
  trace = ∑_i=1:n { a_ii }
  where n = min(numRows,numCols)
  
  Parameters:
  
  input - (Input) A matrix
  
  output - (Output) Storage for the trace. Can be null.
  
  Returns:
  
  The trace's value
- invert
  
  public static boolean invert(ZMatrixRMaj A)
  
  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:
  
  A - 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(ZMatrixRMaj input, ZMatrixRMaj output)
  
  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_ZDRM instead.
  
  Parameters:
  
  input - The matrix that is to be inverted. Not modified.
  
  output - Where the inverse matrix is stored. Modified.
  
  Returns:
  
  true if it could invert the matrix false if it could not.
- solve
  
  public static boolean solve(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj 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_ZDRM 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.
- det
  
  public static Complex_F64 det(ZMatrixRMaj mat)
  
  Returns the determinant of the matrix. If the inverse of the matrix is also needed, then using LUDecompositionAlt_ZDRM directly (or any similar algorithm) can be more efficient.
  
  Parameters:
  
  mat - The matrix whose determinant is to be computed. Not modified.
  
  Returns:
  
  The determinant.
- elementMultiply
  
  public static ZMatrixRMaj elementMultiply(ZMatrixD1 input, double real, double imaginary, @Nullable @Nullable ZMatrixRMaj output)
  
  Performs element by element multiplication operation with a complex number
  
  output_ij = input_ij * (real + imaginary*i)
  
  Parameters:
  
  input - The left matrix in the multiplication operation. Not modified.
  
  real - Real component of the number it is multiplied by
  
  imaginary - Imaginary component of the number it is multiplied by
  
  output - Where the results of the operation are stored. Modified.
- elementMultiply
  
  public static ZMatrixRMaj elementMultiply(ZMatrixD1 inputA, ZMatrixD1 inputB, @Nullable @Nullable ZMatrixRMaj output)
  
  Performs complex multiplication between two matrices with the same shape element by element.
  
  output_ij = inputA_ij * inputB_ij
  
  Parameters:
  
  inputA - First input matrix. Not modified.
  
  inputB - Second input matrix. Not modified.
  
  output - Where the results of the operation are stored. Modified.
- elementDivide
  
  public static ZMatrixRMaj elementDivide(ZMatrixD1 input, double real, double imaginary, @Nullable @Nullable ZMatrixRMaj output)
  
  Performs element by element division operation with a complex number on the right
  
  output_ij = input_ij / (real + imaginary*i)
  
  Parameters:
  
  input - The left matrix in the multiplication operation. Not modified.
  
  real - Real component of the number it is multiplied by
  
  imaginary - Imaginary component of the number it is multiplied by
  
  output - Where the results of the operation are stored. Modified.
- elementDivide
  
  public static ZMatrixRMaj elementDivide(double real, double imaginary, ZMatrixD1 input, @Nullable @Nullable ZMatrixRMaj output)
  
  Performs element by element division operation with a complex number on the right
  
  output_ij = (real + imaginary*i) / input_ij
  
  Parameters:
  
  real - Real component of the number it is multiplied by
  
  imaginary - Imaginary component of the number it is multiplied by
  
  input - The right matrix in the multiplication operation. Not modified.
  
  output - Where the results of the operation are stored. Modified.
- elementDivide
  
  public static ZMatrixRMaj elementDivide(ZMatrixD1 inputA, ZMatrixD1 inputB, @Nullable @Nullable ZMatrixRMaj output)
  
  Performs complex division between two matrices with the same shape element by element.
  
  output_ij = inputA_ij / inputB_ij
  
  Parameters:
  
  inputA - First input matrix. Not modified.
  
  inputB - Second input matrix. Not modified.
  
  output - Where the results of the operation are stored. Modified.
- elementPower
  
  public static ZMatrixRMaj elementPower(ZMatrixD1 input, double b, @Nullable @Nullable ZMatrixRMaj output)
  
  Element by element complex power
  
  output_ij = inputA_ij / inputB_ij
  
  Parameters:
  
  input - Input matrix. Not modified.
  
  b - Power
  
  output - Where the results of the operation are stored. Modified.
- elementSum
  
  public static Complex_F64 elementSum(ZMatrixD1 input, @Nullable @Nullable Complex_F64 output)
  
  Computes the sum of all the elements in the matrix:
  
  sum(i=1:m , j=1:n ; a_ij)
  
  Parameters:
  
  input - An m by n matrix. Not modified.
  
  output - (Output) Storage for the sum. Can be null.
  
  Returns:
  
  The sum of the elements.
- elementMinReal
  
  public static double elementMinReal(ZMatrixD1 a)
  
  Returns the value of the real element in the matrix that has the minimum value.
  
  Min{ a_ij } for all i and j
  
  Parameters:
  
  a - A matrix. Not modified.
  
  Returns:
  
  The minimum value out of all the real values.
- elementMinImaginary
  
  public static double elementMinImaginary(ZMatrixD1 a)
  
  Returns the value of the imaginary element in the matrix that has the minimum value.
  
  Min{ a_ij } for all i and j
  
  Parameters:
  
  a - A matrix. Not modified.
  
  Returns:
  
  The minimum value out of all the real values.
- elementMaxReal
  
  public static double elementMaxReal(ZMatrixD1 a)
  
  Returns the value of the real element in the matrix that has the minimum value.
  
  Min{ a_ij } for all i and j
  
  Parameters:
  
  a - A matrix. Not modified.
  
  Returns:
  
  The minimum value out of all the real values.
- elementMaxImaginary
  
  public static double elementMaxImaginary(ZMatrixD1 a)
  
  Returns the value of the imaginary element in the matrix that has the minimum value.
  
  Min{ a_ij } for all i and j
  
  Parameters:
  
  a - A matrix. Not modified.
  
  Returns:
  
  The minimum value out of all the real values.
- elementMaxMagnitude2
  
  public static double elementMaxMagnitude2(ZMatrixD1 a)
  
  Returns the magnitude squared of the complex element with the largest magnitude
  
  Max{ |a_ij|^2 } for all i and j
  
  Parameters:
  
  a - A matrix. Not modified.
  
  Returns:
  
  The max magnitude squared
- setIdentity
  
  public static void setIdentity(ZMatrixRMaj 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.
- extract
  
  public static ZMatrixRMaj extract(ZMatrixRMaj src, int srcY0, int srcY1, int srcX0, int srcX1)
  
  Creates a new matrix which is the specified submatrix of 'src'
  
  s_{i-y0 , j-x0} = o_ij for all y0 ≤ i < y1 and x0 ≤ j < x1
  
  where 's_ij' is an element in the submatrix and 'o_ij' 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 void extract(ZMatrixRMaj src, int srcY0, int srcY1, int srcX0, int srcX1, ZMatrixRMaj dst, int dstY0, int dstX0)
  
  Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.
  
  s_{i-y0 , j-x0} = o_ij for all y0 ≤ i < y1 and x0 ≤ j < x1
  
  where 's_ij' is an element in the submatrix and 'o_ij' 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.
- columnsToVector
  
  public static ZMatrixRMaj[] columnsToVector(ZMatrixRMaj A, @Nullable @Nullable ZMatrixRMaj[] v)
  
  Converts the columns in a matrix into a set of vectors.
  
  Parameters:
  
  A - Matrix. Not modified.
  
  v - Optional storage for columns.
  
  Returns:
  
  An array of vectors.
- elementMaxAbs
  
  public static double elementMaxAbs(ZMatrixRMaj a)
  
  Returns the largest absolute value of any element in the matrix.
  
  Max{ |a_ij| } for all i and j
  
  Parameters:
  
  a - A matrix. Not modified.
  
  Returns:
  
  The max abs element value in the matrix.
- elementMinAbs
  
  public static double elementMinAbs(ZMatrixRMaj a)
  
  Returns the smallest absolute value of any element in the matrix.
  
  Min{ |a_ij| } for all i and j
  
  Parameters:
  
  a - A matrix. Not modified.
  
  Returns:
  
  The min abs element value in the matrix.

Class CommonOps_ZDRM

Method Summary

Methods inherited from class java.lang.Object

Method Details

identity

identity

diag

diag

extractDiag

convert

real

imaginary

magnitude

conjugate

fill

add

subtract

scale

mult

mult

multAdd

multAdd

multTransA

multTransA

multTransB

multTransB

multTransAB

multTransAB

multAddTransA

multAddTransA

multAddTransB

multAddTransB

multAddTransAB

multAddTransAB

transpose

transposeConjugate

transpose

transposeConjugate

trace

invert

invert

solve

det

elementMultiply

elementMultiply

elementDivide

elementDivide

elementDivide

elementPower

elementSum

elementMinReal

elementMinImaginary

elementMaxReal

elementMaxImaginary

elementMaxMagnitude2

setIdentity

extract

extract

columnsToVector

elementMaxAbs

elementMinAbs