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Matrix.cpp
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Thu, Jul 11, 17:19

Matrix.cpp
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#include "DenseMatrix.h"
#include "Solver.h"
//-----------------------------------------------------------------------------
//* performs a matrix-matrix multiply with optional transposes BLAS version
// C = b*C + a*A*B
//-----------------------------------------------------------------------------
void MultAB(const MATRIX &A, const MATRIX &B, DENS_MAT &C,
const bool At, const bool Bt, double a, double b)
{
static char t[2] = {'N','T'};
char *ta=t+At, *tb=t+Bt;
int sA[2] = {A.nRows(), A.nCols()}; // sizes of A
int sB[2] = {B.nRows(), B.nCols()}; // sizes of B
GCK(A, B, sA[!At]!=sB[Bt], "MultAB<double>: matrix-matrix multiply");
if (!C.is_size(sA[At],sB[!Bt]))
{
C.resize(sA[At],sB[!Bt]);
if (b != 0.0) C.zero();
}
// get pointers to the matrix sizes needed by BLAS
int *M = sA+At; // # of rows in op[A] (op[A] = A' if At='T' else A)
int *N = sB+!Bt; // # of cols in op[B]
int *K = sA+!At; // # of cols in op[A] or # of rows in op[B]
double *pa=A.get_ptr(), *pb=B.get_ptr(), *pc=C.get_ptr();
#ifdef COL_STORAGE
dgemm_(ta, tb, M, N, K, &a, pa, sA, pb, sB, &b, pc, M);
#else
dgemm_(tb, ta, N, M, K, &a, pb, sB+1, pa, sA+1, &b, pc, N);
#endif
}
//-----------------------------------------------------------------------------
//* returns the inverse of a double precision matrix
//-----------------------------------------------------------------------------
DenseMatrix<double> inv(const MATRIX& A)
{
SQCK(A, "DenseMatrix::inv(), matrix not square"); // check matrix is square
DENS_MAT invA(A); // Make copy of A to invert
// setup for call to BLAS
int m, info, lwork=-1;
m = invA.nRows();
int *ipiv = new int[m<<1]; // need 2m storage
int *iwork=ipiv+m;
dgetrf_(&m,&m,invA.get_ptr(),&m,ipiv,&info); // compute LU factorization
GCK(A,A,info<0,"DenseMatrix::inv() dgetrf error: Argument had bad value.");
GCK(A,A,info>0,"DenseMatrix::inv() dgetrf error: Matrix not invertable.");
// LU factorization succeeded
// Compute 1-norm of original matrix for use with dgecon
char norm = '1'; // Use 1-norm
double rcond, anorm, *workc = new double[4*m];
anorm = dlange_(&norm,&m,&m,A.get_ptr(),&m,workc);
// Condition number estimation (warn if bad)
dgecon_(&norm,&m,invA.get_ptr(),&m,&anorm,&rcond,workc,iwork,&info);
GCK(A,A,info<0, "DenseMatrix::inv(): dgecon error: Argument had bad value.");
GCK(A,A,rcond<1e-14,"DenseMatrix::inv(): Matrix nearly singular, RCOND<e-14");
// Now determine optimal work size for computation of matrix inverse
double work_dummy[2] = {0.0,0.0};
dgetri_(&m, invA.get_ptr(), &m, ipiv, work_dummy, &lwork, &info);
GCK(A,A,info<0,"DenseMatrix::inv() dgetri error: Argument had bad value.");
GCK(A,A,info>0,"DenseMatrix::inv() dgetri error: Matrix not invertable.");
// Work size query succeded
lwork = (int)work_dummy[0];
double *work = new double[lwork]; // Allocate vector of appropriate size
// Compute and store matrix inverse
dgetri_(&m,invA.get_ptr(),&m,ipiv,work,&lwork,&info);
GCK(A,A,info<0,"DenseMatrix::inv() dgetri error: Argument had bad value.");
GCK(A,A,info>0,"DenseMatrix::inv() dgetri error: Matrix not invertable.");
// Clean-up
delete [] ipiv;
delete [] workc;
delete [] work;
return invA;
}
//-----------------------------------------------------------------------------
//* computes the determinant of a square matrix by LU decomposition (if n>3)
//-----------------------------------------------------------------------------
double det(const MATRIX& A)
{
static const double sign[2] = {1.0, -1.0};
SQCK(A, "Matrix::det(), matrix not square"); // check matrix is square
int m = A.nRows();
switch (m) // explicit determinant for small matrix sizes
{
case 1: return A(0,0);
case 2: return A(0,0)*A(1,1)-A(0,1)*A(1,0);
case 3:
return A(0,0)*(A(1,1)*A(2,2)-A(1,2)*A(2,1))
+ A(0,1)*(A(1,2)*A(2,0)-A(1,0)*A(2,2))
+ A(0,2)*(A(1,0)*A(2,1)-A(1,1)*A(2,0));
default: break;
}
// First compute LU factorization
int info, *ipiv = new int[m];
double det = 1.0;
DENS_MAT PLUA(A);
dgetrf_(&m,&m,PLUA.get_ptr(),&m,ipiv,&info);
GCK(A,A,info>0,"Matrix::det() dgetrf error: Bad argument value.");
if (!info) // matrix is non-singular
{
// Compute det(A) = det(P)*det(L)*det(U) = +/-1 * det(U)
int i, OddNumPivots;
det = PLUA(0,0);
OddNumPivots = ipiv[0]!=(1);
for(i=1; i<m; i++)
{
det *= PLUA(i,i);
OddNumPivots += (ipiv[i]!=(i+1)); // # pivots even/odd
}
det *= sign[OddNumPivots&1];
}
delete [] ipiv; // Clean-up
return det;
}
//-----------------------------------------------------------------------------
//* Returns the maximum eigenvalue of a matrix.
//-----------------------------------------------------------------------------
double max_eigenvalue(const Matrix<double>& A)
{
GCK(A,A,!is_size(3,3), "max_eigenvalue only implimented for 3x3");
const double c0 = det(A);
const double c1 = A(1,0)*A(0,1) + A(2,0)*A(0,2) + A(1,2)*A(2,1)
- A(0,0)*A(1,1) - A(0,0)*A(2,2) - A(1,1)*A(2,2);
const double c2 = trace(A);
double c[4] = {c0, c1, c2, -1.0}, x[3];
int num_roots = ATC::solve_cubic(c, x);
double max_root = 0.0;
for (int i=0; i<num_roots; i++) max_root = std::max(x[i], max_root);
return max_root;
}

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