Matrix.h File Reference

General routine to interpolate (or even extrapolate small amounts) audio when a few of the samples are bad. Works great for a few dozen bad samples, but not so well with hundreds. Uses the least-squares autoregression (LSAR) algorithm, as described in: More...

#include "SampleFormat.h"

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Classes
class	Vector
	Holds a matrix of doubles and supports arithmetic operations, including Vector-Matrix operations. Used by InterpolateAudio. More...
class	Matrix
	Holds a matrix of doubles and supports arithmetic, subsetting, and matrix inversion. Used by InterpolateAudio. More...

Functions
bool	InvertMatrix (const Matrix &input, Matrix &Minv)
Matrix	TransposeMatrix (const Matrix &M)
Matrix	IdentityMatrix (unsigned N)
Vector	operator+ (const Vector &left, const Vector &right)
Vector	operator- (const Vector &left, const Vector &right)
Vector	operator* (const Vector &left, const Vector &right)
Vector	operator* (const Vector &left, double right)
Vector	VectorSubset (const Vector &other, unsigned start, unsigned len)
Vector	VectorConcatenate (const Vector &left, const Vector &right)
Vector	operator* (const Vector &left, const Matrix &right)
Vector	operator* (const Matrix &left, const Vector &right)
Matrix	operator+ (const Matrix &left, const Matrix &right)
Matrix	operator* (const Matrix &left, const double right)
Matrix	ScalarMultiply (const Matrix &left, const Matrix &right)
Matrix	MatrixMultiply (const Matrix &left, const Matrix &right)
Matrix	MatrixSubset (const Matrix &M, unsigned startRow, unsigned numRows, unsigned startCol, unsigned numCols)
Matrix	MatrixConcatenateCols (const Matrix &left, const Matrix &right)

Detailed Description

General routine to interpolate (or even extrapolate small amounts) audio when a few of the samples are bad. Works great for a few dozen bad samples, but not so well with hundreds. Uses the least-squares autoregression (LSAR) algorithm, as described in:

Holds both the Matrix and Vector classes, supporting linear algebra operations, including matrix inversion. Used by InterpolateAudio.

Simon Godsill, Peter Rayner, and Olivier Cappe. Digital Audio Restoration. Berlin: Springer, 1998.

This is the same work used by Gnome Wave Cleaner (GWC), however this implementation is original.

Definition in file Matrix.h.

Function Documentation

IdentityMatrix()

Matrix IdentityMatrix

(

unsigned

N

)

Definition at line 127 of file Matrix.cpp.

{
   Matrix M(N, N);
   for(unsigned i = 0; i < N; i++)
      M[i][i] = 1.0;
   return M;
}

Referenced by InvertMatrix().

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InvertMatrix()

bool InvertMatrix	(	const Matrix &	input,
		Matrix &	Minv
	)

Definition at line 289 of file Matrix.cpp.

{
   // Very straightforward implementation of
   // Gauss-Jordan elimination to invert a matrix.
   // Returns true if successful
 
   wxASSERT(input.Rows() == input.Cols());
   auto N = input.Rows();
 
   Matrix M = input;
   Minv = IdentityMatrix(N);
 
   // Do the elimination one column at a time
   for(unsigned i = 0; i < N; i++) {
      // Pivot the row with the largest absolute value in
      // column i, into row i
      double absmax = 0.0;
      unsigned int argmax = 0;
 
      for(unsigned j = i; j < N; j++)
         if (fabs(M[j][i]) > absmax) {
            absmax = fabs(M[j][i]);
            argmax = j;
         }
 
      // If no row has a nonzero value in that column,
      // the matrix is singular and we have to give up.
      if (absmax == 0)
         return false;
 
      if (i != argmax) {
         M.SwapRows(i, argmax);
         Minv.SwapRows(i, argmax);
      }
 
      // Divide this row by the value of M[i][i]
      double factor = 1.0 / M[i][i];
      M[i] = M[i] * factor;
      Minv[i] = Minv[i] * factor;
 
      // Eliminate the rest of the column
      for(unsigned j = 0; j < N; j++) {
         if (j == i)
            continue;
         if (fabs(M[j][i]) > 0) {
            // Subtract a multiple of row i from row j
            factor = M[j][i];
            for(unsigned k = 0; k < N; k++) {
               M[j][k] -= (M[i][k] * factor);
               Minv[j][k] -= (Minv[i][k] * factor);
            }
         }
      }
   }
 
   return true;
}

References Matrix::Cols(), IdentityMatrix(), Matrix::Rows(), and Matrix::SwapRows().

Referenced by InterpolateAudio().

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MatrixConcatenateCols()

Matrix MatrixConcatenateCols	(	const Matrix &	left,
		const Matrix &	right
	)

Definition at line 267 of file Matrix.cpp.

{
   wxASSERT(left.Rows() == right.Rows());
   Matrix M(left.Rows(), left.Cols() + right.Cols());
   for(unsigned i = 0; i < left.Rows(); i++) {
      for(unsigned j = 0; j < left.Cols(); j++)
         M[i][j] = left[i][j];
      for(unsigned j = 0; j < right.Cols(); j++)
         M[i][j+left.Cols()] = right[i][j];
   }
   return M;
}

References Matrix::Cols(), and Matrix::Rows().

Referenced by InterpolateAudio().

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MatrixMultiply()

Matrix MatrixMultiply	(	const Matrix &	left,
		const Matrix &	right
	)

Definition at line 243 of file Matrix.cpp.

{
   wxASSERT(left.Cols() == right.Rows());
   Matrix M(left.Rows(), right.Cols());
   for(unsigned i = 0; i < left.Rows(); i++)
      for(unsigned j = 0; j < right.Cols(); j++) {
         M[i][j] = 0.0;
         for(unsigned k = 0; k < left.Cols(); k++)
            M[i][j] += left[i][k] * right[k][j];
      }
   return M;
}

References Matrix::Cols(), and Matrix::Rows().

Referenced by InterpolateAudio().

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MatrixSubset()

Matrix MatrixSubset	(	const Matrix &	M,
		unsigned	startRow,
		unsigned	numRows,
		unsigned	startCol,
		unsigned	numCols
	)

Definition at line 256 of file Matrix.cpp.

{
   Matrix M(numRows, numCols);
   for(unsigned i = 0; i < numRows; i++)
      for(unsigned j = 0; j < numCols; j++)
         M[i][j] = input[startRow+i][startCol+j];
   return M;
}

Referenced by InterpolateAudio().

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operator*() [1/5]

Matrix operator*	(	const Matrix &	left,
		const double	right
	)

Definition at line 223 of file Matrix.cpp.

{
   Matrix M(left.Rows(), left.Cols());
   for(unsigned i = 0; i < left.Rows(); i++)
      for(unsigned j = 0; j < left.Cols(); j++)
         M[i][j] = left[i][j] * right;
   return M;
}

References Matrix::Cols(), and Matrix::Rows().

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operator*() [2/5]

Vector operator*	(	const Matrix &	left,
		const Vector &	right
	)

Definition at line 200 of file Matrix.cpp.

{
   wxASSERT(left.Cols() == right.Len());
   Vector v(left.Rows());
   for(unsigned i = 0; i < left.Rows(); i++) {
      v[i] = 0.0;
      for(unsigned j = 0; j < left.Cols(); j++)
         v[i] += left[i][j] * right[j];
   }
   return v;
}

References Matrix::Cols(), Vector::Len(), and Matrix::Rows().

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operator*() [3/5]

Vector operator*	(	const Vector &	left,
		const Matrix &	right
	)

Definition at line 188 of file Matrix.cpp.

{
   wxASSERT(left.Len() == right.Rows());
   Vector v(right.Cols());
   for(unsigned i = 0; i < right.Cols(); i++) {
      v[i] = 0.0;
      for(unsigned j = 0; j < right.Rows(); j++)
         v[i] += left[j] * right[j][i];
   }
   return v;
}

References Matrix::Cols(), Vector::Len(), and Matrix::Rows().

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operator*() [4/5]

Vector operator*	(	const Vector &	left,
		const Vector &	right
	)

Definition at line 153 of file Matrix.cpp.

{
   wxASSERT(left.Len() == right.Len());
   Vector v(left.Len());
   for(unsigned i = 0; i < left.Len(); i++)
      v[i] = left[i] * right[i];
   return v;
}

References Vector::Len().

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operator*() [5/5]

Vector operator*	(	const Vector &	left,
		double	right
	)

Definition at line 162 of file Matrix.cpp.

{
   Vector v(left.Len());
   for(unsigned i = 0; i < left.Len(); i++)
      v[i] = left[i] * right;
   return v;
}

References Vector::Len().

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operator+() [1/2]

Matrix operator+	(	const Matrix &	left,
		const Matrix &	right
	)

Definition at line 212 of file Matrix.cpp.

{
   wxASSERT(left.Rows() == right.Rows());
   wxASSERT(left.Cols() == right.Cols());
   Matrix M(left.Rows(), left.Cols());
   for(unsigned i = 0; i < left.Rows(); i++)
      for(unsigned j = 0; j < left.Cols(); j++)
         M[i][j] = left[i][j] + right[i][j];
   return M;
}

References Matrix::Cols(), and Matrix::Rows().

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operator+() [2/2]

Vector operator+	(	const Vector &	left,
		const Vector &	right
	)

Definition at line 135 of file Matrix.cpp.

{
   wxASSERT(left.Len() == right.Len());
   Vector v(left.Len());
   for(unsigned i = 0; i < left.Len(); i++)
      v[i] = left[i] + right[i];
   return v;
}

References Vector::Len().

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operator-()

Vector operator-	(	const Vector &	left,
		const Vector &	right
	)

Definition at line 144 of file Matrix.cpp.

{
   wxASSERT(left.Len() == right.Len());
   Vector v(left.Len());
   for(unsigned i = 0; i < left.Len(); i++)
      v[i] = left[i] - right[i];
   return v;
}

References Vector::Len().

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ScalarMultiply()

Matrix ScalarMultiply	(	const Matrix &	left,
		const Matrix &	right
	)

Definition at line 232 of file Matrix.cpp.

{
   wxASSERT(left.Rows() == right.Rows());
   wxASSERT(left.Cols() == right.Cols());
   Matrix M(left.Rows(), left.Cols());
   for(unsigned i = 0; i < left.Rows(); i++)
      for(unsigned j = 0; j < left.Cols(); j++)
         M[i][j] = left[i][j] * right[i][j];
   return M;
}

References Matrix::Cols(), and Matrix::Rows().

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TransposeMatrix()

Matrix TransposeMatrix

(

const Matrix &

M

)

Definition at line 280 of file Matrix.cpp.

{
   Matrix M(other.Cols(), other.Rows());
   for(unsigned i = 0; i < other.Rows(); i++)
      for(unsigned j = 0; j < other.Cols(); j++)
         M[j][i] = other[i][j];
   return M;
}

References Matrix::Cols(), and Matrix::Rows().

Referenced by InterpolateAudio().

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VectorConcatenate()

Vector VectorConcatenate	(	const Vector &	left,
		const Vector &	right
	)

Definition at line 178 of file Matrix.cpp.

{
   Vector v(left.Len() + right.Len());
   for(unsigned i = 0; i < left.Len(); i++)
      v[i] = left[i];
   for(unsigned i = 0; i < right.Len(); i++)
      v[i + left.Len()] = right[i];
   return v;
}

References Vector::Len().

Referenced by InterpolateAudio().

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VectorSubset()

Vector VectorSubset	(	const Vector &	other,
		unsigned	start,
		unsigned	len
	)

Definition at line 170 of file Matrix.cpp.

{
   Vector v(len);
   for(unsigned i = 0; i < len; i++)
      v[i] = other[start+i];
   return v;
}

Referenced by InterpolateAudio().

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