/**
* <p>
* Adds to A ∈ ℜ <sup>m × n</sup> the results of an outer product multiplication
* of the two vectors. This is also known as a rank 1 update.<br>
* <br>
* A = A + γ x * y<sup>T</sup>
* where x ∈ ℜ <sup>m</sup> and y ∈ ℜ <sup>n</sup> are vectors.
* </p>
* <p>
* Which is equivalent to: A<sub>ij</sub> = A<sub>ij</sub> + γ x<sub>i</sub>*y<sub>j</sub>
* </p>
*
* <p>
* These functions are often used inside of highly optimized code and therefor sanity checks are
* kept to a minimum. It is not recommended that any of these functions be used directly.
* </p>
*
* @param gamma A multiplication factor for the outer product.
* @param x A vector with m elements. Not modified.
* @param y A vector with n elements. Not modified.
* @param A A Matrix with m by n elements. Modified.
*/
public static void addOuterProd(float gamma, FMatrixD1 x, FMatrixD1 y, FMatrix1Row A)
{
int m = A.numRows;
int n = A.numCols;
int index = 0;
if (gamma == 1.0f)
{
for (int i = 0; i < m; i++)
{
float xdat = x.get(i);
for (int j = 0; j < n; j++)
{
A.plus(index++, xdat * y.get(j));
}
}
}
else
{
for (int i = 0; i < m; i++)
{
float xdat = x.get(i);
for (int j = 0; j < n; j++)
{
A.plus(index++, gamma * xdat * y.get(j));
}
}
}
}
/**
* An alternative implementation of {@link #multTransA_small} that performs well on large
* matrices. There is a relative performance hit when used on small matrices.
*
* @param A A matrix that is m by n. Not modified.
* @param B A Vector that has length m. Not modified.
* @param C A column vector that has length n. Modified.
*/
public static void multTransA_reorder(FMatrix1Row A, FMatrixD1 B, FMatrixD1 C)
{
if (C.numCols != 1)
{
throw new MatrixDimensionException("C is not a column vector");
}
else if (C.numRows != A.numCols)
{
throw new MatrixDimensionException("C is not the expected length");
}
if (B.numRows == 1)
{
if (A.numRows != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numRows != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
if (A.numRows == 0)
{
CommonOps_FDRM.fill(C, 0);
return;
}
float B_val = B.get(0);
for (int i = 0; i < A.numCols; i++)
{
C.set(i, A.get(i) * B_val);
}
int indexA = A.numCols;
for (int i = 1; i < A.numRows; i++)
{
B_val = B.get(i);
for (int j = 0; j < A.numCols; j++)
{
C.plus(j, A.get(indexA++) * B_val);
}
}
}
/**
* <p>
* Performs a matrix vector multiply.<br>
* <br>
* c = A * b <br>
* and<br>
* c = A * b<sup>T</sup> <br>
* <br>
* c<sub>i</sub> = Sum{ j=1:n, a<sub>ij</sub> * b<sub>j</sub>}<br>
* <br>
* where A is a matrix, b is a column or transposed row vector, and c is a column vector.
* </p>
*
* @param A A matrix that is m by n. Not modified.
* @param B A vector that has length n. Not modified.
* @param C A column vector that has length m. Modified.
*/
public static void mult(FMatrix1Row A, FMatrixD1 B, FMatrixD1 C)
{
if (C.numCols != 1)
{
throw new MatrixDimensionException("C is not a column vector");
}
else if (C.numRows != A.numRows)
{
throw new MatrixDimensionException("C is not the expected length");
}
if (B.numRows == 1)
{
if (A.numCols != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numCols != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
if (A.numCols == 0)
{
CommonOps_FDRM.fill(C, 0);
return;
}
int indexA = 0;
int cIndex = 0;
float b0 = B.get(0);
for (int i = 0; i < A.numRows; i++)
{
float total = A.get(indexA++) * b0;
for (int j = 1; j < A.numCols; j++)
{
total += A.get(indexA++) * B.get(j);
}
C.set(cIndex++, total);
}
}
/**
* <p>
* x<sup>T</sup>A<sup>T</sup>y
* </p>
*
* @param x A vector with n elements. Not modified.
* @param A A matrix with n by n elements. Not modified.
* @param y A vector with n elements. Not modified.
* @return The results.
*/
// TODO better name for this
public static float innerProdTranA(FMatrixD1 x, FMatrixD1 A, FMatrixD1 y)
{
int n = A.numRows;
if (n != A.numCols)
{
throw new ArgumentException("A must be square");
}
if (x.getNumElements() != n)
{
throw new ArgumentException("Unexpected number of elements in x");
}
if (y.getNumElements() != n)
{
throw new ArgumentException("Unexpected number of elements in y");
}
float result = 0;
for (int i = 0; i < n; i++)
{
float total = 0;
for (int j = 0; j < n; j++)
{
total += x.get(j) * A.unsafe_get(i, j);
}
result += total * y.get(i);
}
return(result);
}
/**
* <p>
* Multiplies a householder reflection against a vector:<br>
* <br>
* y = (I + γ u u<sup>T</sup>)x<br>
* </p>
* <p>
* The Householder reflection is used in some implementations of QR decomposition.
* </p>
* @param u A vector. Not modified.
* @param x a vector. Not modified.
* @param y Vector where the result are written to.
*/
public static void householder(float gamma,
FMatrixD1 u,
FMatrixD1 x, FMatrixD1 y)
{
int n = u.getNumElements();
float sum = 0;
for (int i = 0; i < n; i++)
{
sum += u.get(i) * x.get(i);
}
for (int i = 0; i < n; i++)
{
y.set(i, x.get(i) + gamma * u.get(i) * sum);
}
}
/**
* Checks to see all the elements in the matrix are zeros
*
* @param m A matrix. Not modified.
* @return True if all elements are zeros or false if not
*/
public static bool isZeros(FMatrixD1 m, float tol)
{
int length = m.getNumElements();
for (int i = 0; i < length; i++)
{
if (Math.Abs(m.get(i)) > tol)
{
return(false);
}
}
return(true);
}
/**
* Checks to see if any element in the matrix is NaN.
*
* @param m A matrix. Not modified.
* @return True if any element in the matrix is NaN.
*/
public static bool hasNaN(FMatrixD1 m)
{
int length = m.getNumElements();
for (int i = 0; i < length; i++)
{
if (float.IsNaN(m.get(i)))
{
return(true);
}
}
return(false);
}
/**
* <p>
* Computes the inner product of the two vectors. In geometry this is known as the dot product.<br>
* <br>
* ∑<sub>k=1:n</sub> x<sub>k</sub> * y<sub>k</sub><br>
* where x and y are vectors with n elements.
* </p>
*
* <p>
* These functions are often used inside of highly optimized code and therefor sanity checks are
* kept to a minimum. It is not recommended that any of these functions be used directly.
* </p>
*
* @param x A vector with n elements. Not modified.
* @param y A vector with n elements. Not modified.
* @return The inner product of the two vectors.
*/
public static float innerProd(FMatrixD1 x, FMatrixD1 y)
{
int m = x.getNumElements();
float total = 0;
for (int i = 0; i < m; i++)
{
total += x.get(i) * y.get(i);
}
return(total);
}
/**
* <p>
* This implementation of the Frobenius norm is a straight forward implementation and can
* be susceptible for overflow/underflow issues. A more resilient implementation is
* {@link #normF}.
* </p>
*
* @param a The matrix whose norm is computed. Not modified.
*/
public static float fastNormF(FMatrixD1 a)
{
float total = 0;
int size = a.getNumElements();
for (int i = 0; i < size; i++)
{
float val = a.get(i);
total += val * val;
}
return((float)Math.Sqrt(total));
}
/**
* Checks to see if any element in the matrix is NaN of Infinite.
*
* @param m A matrix. Not modified.
* @return True if any element in the matrix is NaN of Infinite.
*/
public static bool hasUncountable(FMatrixD1 m)
{
int length = m.getNumElements();
for (int i = 0; i < length; i++)
{
float a = m.get(i);
if (float.IsNaN(a) || float.IsInfinity(a))
{
return(true);
}
}
return(false);
}
/**
* <p>
* Sets A ∈ ℜ <sup>m × n</sup> equal to an outer product multiplication of the two
* vectors. This is also known as a rank-1 operation.<br>
* <br>
* A = x * y'
* where x ∈ ℜ <sup>m</sup> and y ∈ ℜ <sup>n</sup> are vectors.
* </p>
* <p>
* Which is equivalent to: A<sub>ij</sub> = x<sub>i</sub>*y<sub>j</sub>
* </p>
*
* <p>
* These functions are often used inside of highly optimized code and therefor sanity checks are
* kept to a minimum. It is not recommended that any of these functions be used directly.
* </p>
*
* @param x A vector with m elements. Not modified.
* @param y A vector with n elements. Not modified.
* @param A A Matrix with m by n elements. Modified.
*/
public static void outerProd(FMatrixD1 x, FMatrixD1 y, FMatrix1Row A)
{
int m = A.numRows;
int n = A.numCols;
int index = 0;
for (int i = 0; i < m; i++)
{
float xdat = x.get(i);
for (int j = 0; j < n; j++)
{
A.set(index++, xdat * y.get(j));
}
}
}
/**
* <p>
* Returns the absolute value of the digonal element in the matrix that has the largest absolute value.<br>
* <br>
* Max{ |a<sub>ij</sub>| } for all i and j<br>
* </p>
*
* @param a A matrix. Not modified.
* @return The max abs element value of the matrix.
*/
public static float elementDiagonalMaxAbs(FMatrixD1 a)
{
int size = Math.Min(a.numRows, a.numCols);
float max = 0;
for (int i = 0; i < size; i++)
{
float val = Math.Abs(a.get(i, i));
if (val > max)
{
max = val;
}
}
return(max);
}
/**
* <p>
* Computes the p=1 p-norm of the difference between the two Matrices:<br>
* <br>
* ∑<sub>i=1:m</sub> ∑<sub>j=1:n</sub> | a<sub>ij</sub> - b<sub>ij</sub>| <br>
* <br>
* where |x| is the absolute value of x.
* </p>
* <p>
* This is often used as a cost function.
* </p>
*
* @param a m by n matrix. Not modified.
* @param b m by n matrix. Not modified.
*
* @return The p=1 p-norm of the difference matrix.
*/
public static float diffNormP1(FMatrixD1 a, FMatrixD1 b)
{
if (a.numRows != b.numRows || a.numCols != b.numCols)
{
throw new ArgumentException("Both matrices must have the same shape.");
}
int size = a.getNumElements();
float total = 0;
for (int i = 0; i < size; i++)
{
total += Math.Abs(b.get(i) - a.get(i));
}
return(total);
}
/**
* <p>
* Computes the F norm of the difference between the two Matrices:<br>
* <br>
* Sqrt{∑<sub>i=1:m</sub> ∑<sub>j=1:n</sub> ( a<sub>ij</sub> - b<sub>ij</sub>)<sup>2</sup>}
* </p>
* <p>
* This is often used as a cost function.
* </p>
*
* @see NormOps_FDRM#fastNormF
*
* @param a m by n matrix. Not modified.
* @param b m by n matrix. Not modified.
*
* @return The F normal of the difference matrix.
*/
public static float diffNormF(FMatrixD1 a, FMatrixD1 b)
{
if (a.numRows != b.numRows || a.numCols != b.numCols)
{
throw new ArgumentException("Both matrices must have the same shape.");
}
int size = a.getNumElements();
FMatrixRMaj diff = new FMatrixRMaj(size, 1);
for (int i = 0; i < size; i++)
{
diff.set(i, b.get(i) - a.get(i));
}
return(NormOps_FDRM.normF(diff));
}
/**
* <p>
* Performs a matrix vector multiply.<br>
* <br>
* C = C + A<sup>T</sup> * B <br>
* or<br>
* C = C<sup>T</sup> + A<sup>T</sup> * B<sup>T</sup> <br>
* <br>
* c<sub>i</sub> = Sum{ j=1:n, c<sub>i</sub> + a<sub>ji</sub> * b<sub>j</sub>}<br>
* <br>
* where A is a matrix, B is a column or transposed row vector, and C is a column vector.
* </p>
* <p>
* This implementation is optimal for small matrices. There is a huge performance hit when
* used on large matrices due to CPU cache issues.
* </p>
*
* @param A A matrix that is m by n. Not modified.
* @param B A vector that has length m. Not modified.
* @param C A column vector that has length n. Modified.
*/
public static void multAddTransA_small(FMatrix1Row A, FMatrixD1 B, FMatrixD1 C)
{
if (C.numCols != 1)
{
throw new MatrixDimensionException("C is not a column vector");
}
else if (C.numRows != A.numCols)
{
throw new MatrixDimensionException("C is not the expected length");
}
if (B.numRows == 1)
{
if (A.numRows != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numRows != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
int cIndex = 0;
for (int i = 0; i < A.numCols; i++)
{
float total = 0.0f;
int indexA = i;
for (int j = 0; j < A.numRows; j++)
{
total += A.get(indexA) * B.get(j);
indexA += A.numCols;
}
C.plus(cIndex++, total);
}
}
public static float diffNormF_fast(FMatrixD1 a, FMatrixD1 b)
{
if (a.numRows != b.numRows || a.numCols != b.numCols)
{
throw new ArgumentException("Both matrices must have the same shape.");
}
int size = a.getNumElements();
float total = 0;
for (int i = 0; i < size; i++)
{
float diff = b.get(i) - a.get(i);
total += diff * diff;
}
return((float)Math.Sqrt(total));
}
/**
* <p>
* Checks to see if each element in the two matrices are equal:
* a<sub>ij</sub> == b<sub>ij</sub>
* <p>
*
* <p>
* NOTE: If any of the elements are NaN then false is returned. If two corresponding
* elements are both positive or negative infinity then they are equal.
* </p>
*
* @param a A matrix. Not modified.
* @param b A matrix. Not modified.
* @return true if identical and false otherwise.
*/
public static bool isEquals(FMatrixD1 a, FMatrixD1 b)
{
if (a.numRows != b.numRows || a.numCols != b.numCols)
{
return(false);
}
int length = a.getNumElements();
for (int i = 0; i < length; i++)
{
if (!(a.get(i) == b.get(i)))
{
return(false);
}
}
return(true);
}
/**
* <p>
* Checks to see if the two matrices are the negative of each other:<br>
* <br>
* a<sub>ij</sub> = -b<sub>ij</sub>
* </p>
*
* @param a First matrix. Not modified.
* @param b Second matrix. Not modified.
* @param tol Numerical tolerance.
* @return True if they are the negative of each other within tolerance.
*/
public static bool isNegative(FMatrixD1 a, FMatrixD1 b, float tol)
{
if (a.numRows != b.numRows || a.numCols != b.numCols)
{
throw new ArgumentException("Matrix dimensions must match");
}
int length = a.getNumElements();
for (int i = 0; i < length; i++)
{
if (!(Math.Abs(a.get(i) + b.get(i)) <= tol))
{
return(false);
}
}
return(true);
}
/**
* <p>
* Computes the Frobenius matrix norm:<br>
* <br>
* normF = Sqrt{ ∑<sub>i=1:m</sub> ∑<sub>j=1:n</sub> { a<sub>ij</sub><sup>2</sup>} }
* </p>
* <p>
* This is equivalent to the element wise p=2 norm. See {@link #fastNormF} for another implementation
* that is faster, but more prone to underflow/overflow errors.
* </p>
*
* @param a The matrix whose norm is computed. Not modified.
* @return The norm's value.
*/
public static float normF(FMatrixD1 a)
{
float total = 0;
float scale = CommonOps_FDRM.elementMaxAbs(a);
if (scale == 0.0f)
{
return(0.0f);
}
int size = a.getNumElements();
for (int i = 0; i < size; i++)
{
float val = a.get(i) / scale;
total += val * val;
}
return(scale * (float)Math.Sqrt(total));
}
/**
* Same as {@link #elementP} but runs faster by not mitigating overflow/underflow related problems.
*
* @param A Matrix. Not modified.
* @param p p value.
* @return The norm's value.
*/
public static float fastElementP(FMatrixD1 A, float p)
{
if (p == 2)
{
return(fastNormF(A));
}
else
{
float total = 0;
int size = A.getNumElements();
for (int i = 0; i < size; i++)
{
float a = A.get(i);
total += (float)Math.Pow(Math.Abs(a), p);
}
return((float)Math.Pow(total, 1.0f / p));
}
}
/**
* <p>
* Checks to see if each corresponding element in the two matrices are
* within tolerance of each other or have the some symbolic meaning. This
* can handle NaN and Infinite numbers.
* <p>
*
* <p>
* If both elements are countable then the following equality test is used:<br>
* |a<sub>ij</sub> - b<sub>ij</sub>| ≤ tol.<br>
* Otherwise both numbers must both be Float.NaN, Float.POSITIVE_INFINITY, or
* Float.NEGATIVE_INFINITY to be identical.
* </p>
*
* @param a A matrix. Not modified.
* @param b A matrix. Not modified.
* @param tol Tolerance for equality.
* @return true if identical and false otherwise.
*/
public static bool isIdentical(FMatrixD1 a, FMatrixD1 b, float tol)
{
if (a.numRows != b.numRows || a.numCols != b.numCols)
{
return(false);
}
if (tol < 0)
{
throw new ArgumentException("Tolerance must be greater than or equal to zero.");
}
int length = a.getNumElements();
for (int i = 0; i < length; i++)
{
if (!isIdentical(a.get(i), b.get(i), tol))
{
return(false);
}
}
return(true);
}
/**
* <p>
* Checks to see if each element in the two matrices are within tolerance of
* each other: tol ≥ |a<sub>ij</sub> - b<sub>ij</sub>|.
* <p>
*
* <p>
* NOTE: If any of the elements are not countable then false is returned.<br>
* NOTE: If a tolerance of zero is passed in this is equivalent to calling
* {@link #isEquals(FMatrixD1, FMatrixD1)}
* </p>
*
* @param a A matrix. Not modified.
* @param b A matrix. Not modified.
* @param tol How close to being identical each element needs to be.
* @return true if equals and false otherwise.
*/
public static bool isEquals(FMatrixD1 a, FMatrixD1 b, float tol)
{
if (a.numRows != b.numRows || a.numCols != b.numCols)
{
return(false);
}
if (tol == 0.0f)
{
return(isEquals(a, b));
}
int length = a.getNumElements();
for (int i = 0; i < length; i++)
{
if (!(tol >= Math.Abs(a.get(i) - b.get(i))))
{
return(false);
}
}
return(true);
}