doc/html/test_smgs.html

 // ========================================================================= //
 // This file is part of MyraMath, copyright (c) 2014-2019 by Ryan A Chilton  //
 // and distributed by MyraCore, LLC. See LICENSE.txt for license terms.      //
 // ========================================================================= //

 // Containers.
 #include <myramath/utility/Number.h>
 #include <myramath/dense/Matrix.h>
 #include <myramath/dense/Vector.h>
 #include <myramath/dense/MatrixRange.h>
 #include <myramath/dense/VectorRange.h>

 // Algorithms.
 #include <myramath/dense/gemm.h>
 #include <myramath/dense/gramschmidt.h>
 #include <myramath/dense/frobenius.h>

 // Reporting.
 #include <tests/myratest.h>

 using namespace myra;

 namespace {

 template<class Number> void test(int I, int J1, int J2, typename ReflectPrecision<Number>::type tolerance)
   {
   typedef typename ReflectPrecision<Number>::type Precision;
   myra::out() << typestring<Number>() << std::endl;

   // Use mgs() to factor a random A into Q*R
   auto A = Matrix<Number>::random(I,J1);
   auto QR = mgs(A);
   const Matrix<Number>& Q = QR.first;
   const Matrix<Number>& R = QR.second;

   // Verify Q'Q = I, A = QR
   Precision Q_error = frobenius( gemm(Q,'H',Q)-Matrix<Number>::identity(J1) );
   Precision A_error = frobenius( gemm(Q,R)-A );
   myra::out() << "  |Q'Q-I| = " << Q_error << std::endl;
   REQUIRE(Q_error < tolerance);
   myra::out() << "  |Q*R-A| = " << A_error << std::endl;
   REQUIRE(A_error < tolerance);

   // Make random v, deflate it by Q using cgs_inplace()
   auto v = Matrix<Number>::random(I,J2);
   cgs_inplace(Q,v);
   Precision v_error = frobenius( gemm(Q,'H',v) );
   myra::out() << "  |Q'v| = " << v_error << std::endl;
   REQUIRE(v_error < tolerance);
   }

 } // namespace

 ADD_TEST("smgs","[dense]")
   { test<NumberS>(10,4,5,1.0e-4f); }

 ADD_TEST("dmgs","[dense]")
   { test<NumberD>(10,4,5,1.0e-10); }

 ADD_TEST("cmgs","[dense]")
   { test<NumberC>(10,4,5,1.0e-4f); }

 ADD_TEST("zmgs","[dense]")
   { test<NumberZ>(10,4,5,1.0e-10); }

MatrixRange.h
Interface class for representing subranges of dense Matrix&#39;s.

gramschmidt.h
Routines for orthogonalizing column vectors via classical and modified gram-schmidt.

VectorRange.h
Interface class for representing subranges of dense Vector&#39;s.

myra::Matrix
Tabulates an IxJ matrix. Allows random access, has column major layout to be compatible with BLAS/LAP...
Definition: bdsqr.h:20

frobenius.h
Routines for computing Frobenius norms of various algebraic containers.

myra::Matrix::random
static Matrix< Number > random(int I, int J)
Generates a random Matrix of specified size.
Definition: Matrix.cpp:353

myra
Definition: syntax.dox:1

Number.h
Various utility functions/classes related to scalar Number types.

Matrix.h
General purpose dense matrix container, O(i*j) storage.

Vector.h
Container for either a column vector or row vector (depends upon the usage context) ...

myra::ReflectPrecision
Reflects Precision trait for a Number, scalar Number types should specialize it.
Definition: Number.h:33

gemm.h
Variety of routines all for dense Matrix*Matrix multiplies. Delegates to the BLAS.