vectorNorm

swordfish.function.vectorNorm()

Compute a matrix or vector norm. Note that it’s not recommended to use vectorNorm in SQL statements.

Parameters:

• x (Constant) – A vector or matrix of any numeric type except DECIMAL. It cannot be empty.

• ord (Constant, optional) –

  An INT, STRING or floating-point scalar indicating the order of norm, by default DFLT.

  Note

  When ord is a string, it must be: ‘inf’, ‘-inf’, ‘nuc’, or ‘fro’.

  When ord is less than 1, the result is technically not a mathematical “norm”, but it may still be useful for various numerical purposes.

  The following describes the method for computing the norm based on different x and ord:

  ord	norm for vectors	norm for matrices
  None	2-norm	Frobenius norm
  0	sum(x != 0)	&#45
  -1	sum(abs(x)^ord)^(1/ord)	min(sum(abs(x), axis=0))
  1	sum(abs(x)^ord)^(1/ord)	max(sum(abs(x), axis=0))
  -2	sum(abs(x)^ord)^(1/ord)	2-norm (largest sing. value)
  2	sum(abs(x)^ord)^(1/ord)	smallest singular value
  inf	max(abs(x))	max(sum(abs(x), axis=1))
  -inf	min(abs(x))	min(sum(abs(x), axis=1))
  nuc	&#45	nuclear norm
  fro	&#45	Frobenius norm
  other	sum(abs(x)^ord)^(1/ord)	&#45

• axis (Constant, optional) –

  An integer vector or scalar indicating the direction along which to compute the norm, by default DFLT. It cannot contain empty elements.

  • When x is a vector, axis can only be 0.

  • When x is a matrix, axis:

  • Has a length of no more than 2.

  • Cannot contain duplicate elements.

  • Has elements with values of 0 or 1.

• keepDims (Constant, optional) – A boolean scalar indicating whether the returned result should maintain the same form as x, by default DFLT.

Returns:

An INT, LONG, or DOUBLE scalar, vector, or matrix.

Return type:

Constant