6.2 Creating Least Squares Objects

NMath Matrix provides least squares classes for four datatypes: single- and double-precision floating point numbers, and single- and double-precision complex numbers. The classnames are shown in Table 6.

Instances of the least squares classes are constructed from general matrices of the appropriate datatype. For example, this code creates a FloatCholeskyLeastSq from a FloatMatrix:

FloatMatrix A = new FloatMatrix( "4x2[ 1 0  0 1  0 0  0 0 ]" );
FloatCholeskyLeastSq lsq = new FloatCholeskyLeastSq( A );

QR and SVD least squares classes also provide constructor overloads that accept a tolerance value. The specified tolerance is used in computing the numerical rank of the matrix. For example, if is the QR factorization of a matrix A, then elements on the main diagonal of R are considered to be zero if their absolute value is less than or equal to the tolerance. Similarly, in singular value decomposition, all singular values of the matrix A less than the tolerance are set to zero. Thus, this code sets all singular values less than 10-13 to zero:

DoubleMatrix A = new DoubleMatrix( "4x2[ 1 0  0 1  0 0  0 0 ]" );
DoubleSVDLeastSq lsq = new DoubleSVDLeastSq( A, 1e-13 );

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