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MQL5 ReferenceMatrix and Vector MethodsOpenBLASMatrix Norm 

Matrix Norm

 

This section presents functions for computing various matrix norms for different matrix structures—general (rectangular), tridiagonal, upper Hessenberg, symmetric/Hermitian (both full and tridiagonal), and triangular/trapezoidal. Each routine is templated for four data types (double, float, std::complex<double>, std::complex<float>) and overloads the signature

bool MatrixNorm*(ENUM_BLAS_NORMX norm, T& norm_value);

where norm specifies one of:

  • 1‑norm (BLASNORMX_O)
  • Infinity‑norm (BLASNORMX_I)
  • Frobenius norm (BLASNORMX_F)
  • max‑abs element (BLASNORMX_M)

Results are returned via norm_value; the function returns true on success or false on error.

Under the hood, all routines call optimized LAPACK drivers—LANGE, LANGT, LANHS, LANSY/LANHE, LANST/LANHT, and LANTR—to guarantee both high performance and numerical reliability in large‑scale linear‑algebra computations.

Function

Action

MatrixNorm

Returns the value of the 1-norm, infinity-norm, Frobenius norm, or the largest absolute value of any element of a general rectangular matrix. LAPACK function LANGE.

MatrixNormGeTrid

Returns the value of the 1-norm, infinity-norm, Frobenius norm, or the largest absolute value of any element of a general tridiagonal matrix. LAPACK function LANGT.

MatrixNormHessenberg

Returns the value of the 1-norm, infinity-norm, Frobenius norm, or the largest absolute value of any element of an upper Hessenberg matrix. LAPACK function LANHS.

MatrixNormSy

Returns the value of the 1-norm, infinity-norm, Frobenius norm, or the largest absolute value of any element of a real symmetric or complex Hermitian matrix. LAPACK functions LANSY, LANHE.

MatrixNormComplexSy

Returns the value of the 1-norm, infinity-norm, Frobenius norm, or the largest absolute value of any element of a complexl symmetric (not Hermitian) matrix. LAPACK function LANSY.

MatrixNormSyTrid

Returns the value of the 1-norm, infinity-norm, Frobenius norm, or the largest absolute value of any element of a real symmetric or complex Hermitian tridiagonal matrix. LAPACK functions LANST, LANHT.

MatrixNormTriangular

Returns the value of the 1-norm, infinity-norm, Frobenius norm, or the largest absolute value of any element of a trapezoidal m-by-n or triangular matrix. LAPACK function LANTR.