SymSchurDecomp::SymSchurDecomp(const GeneralMatrix& mata)
: lambda(mata.numRows()), q(mata.numRows())
{
// check mata is square
if (mata.numRows() != mata.numCols())
throw SYLV_MES_EXCEPTION("Matrix is not square in SymSchurDecomp constructor");
// prepare for dsyevr
const char* jobz = "V";
const char* range = "A";
const char* uplo = "U";
lapack_int n = mata.numRows();
GeneralMatrix tmpa(mata);
double* a = tmpa.base();
lapack_int lda = tmpa.getLD();
double dum;
double* vl = &dum;
double* vu = &dum;
lapack_int idum;
lapack_int* il = &idum;
lapack_int* iu = &idum;
double abstol = 0.0;
lapack_int m = n;
double* w = lambda.base();
double* z = q.base();
lapack_int ldz = q.getLD();
lapack_int* isuppz = new lapack_int[2*std::max(1,(int) m)];
double tmpwork;
lapack_int lwork = -1;
lapack_int tmpiwork;
lapack_int liwork = -1;
lapack_int info;
// query for lwork and liwork
dsyevr(jobz, range, uplo, &n, a, &lda, vl, vu, il, iu, &abstol,
&m, w, z, &ldz, isuppz, &tmpwork, &lwork, &tmpiwork, &liwork, &info);
lwork = (int)tmpwork;
liwork = tmpiwork;
// allocate work arrays
double* work = new double[lwork];
lapack_int* iwork = new lapack_int[liwork];
// do the calculation
dsyevr(jobz, range, uplo, &n, a, &lda, vl, vu, il, iu, &abstol,
&m, w, z, &ldz, isuppz, work, &lwork, iwork, &liwork, &info);
if (info < 0)
throw SYLV_MES_EXCEPTION("Internal error in SymSchurDecomp constructor");
if (info > 0)
throw SYLV_MES_EXCEPTION("Internal LAPACK error in DSYEVR");
delete [] work;
delete [] iwork;
delete [] isuppz;
}
void SymSchurDecomp::getFactor(GeneralMatrix& f) const
{
if (f.numRows() != q.numRows())
throw SYLV_MES_EXCEPTION("Wrong dimension of factor matrix in SymSchurDecomp::getFactor");
if (f.numRows() != f.numCols())
throw SYLV_MES_EXCEPTION("Factor matrix is not square in SymSchurDecomp::getFactor");
if (! isPositiveSemidefinite())
throw SYLV_MES_EXCEPTION("Symmetric decomposition not positive semidefinite in SymSchurDecomp::getFactor");
f = q;
for (int i = 0; i < f.numCols(); i++) {
Vector fi(f, i);
fi.mult(std::sqrt(lambda[i]));
}
}
void SylvMatrix::multLeft(int zero_cols, const GeneralMatrix& a, const GeneralMatrix& b)
{
int off = a.numRows() - a.numCols();
if (off < 0 || a.numRows() != rows || off != zero_cols ||
rows != b.numRows() || cols != b.numCols()) {
throw SYLV_MES_EXCEPTION("Wrong matrix dimensions for multLeft.");
}
// here we cannot call SylvMatrix::gemm since it would require
// another copy of (usually big) b (we are not able to do inplace
// submatrix of const GeneralMatrix)
if (a.getLD() > 0 && ld > 0) {
blas_int mm = a.numRows();
blas_int nn = cols;
blas_int kk = a.numCols();
double alpha = 1.0;
blas_int lda = a.getLD();
blas_int ldb = ld;
double beta = 0.0;
blas_int ldc = ld;
dgemm("N", "N", &mm, &nn, &kk, &alpha, a.getData().base(), &lda,
b.getData().base()+off, &ldb, &beta, data.base(), &ldc);
}
}
void SqSylvMatrix::multInvLeft2(GeneralMatrix& a, GeneralMatrix& b,
double& rcond1, double& rcondinf) const
{
if (rows != a.numRows() || rows != b.numRows()) {
throw SYLV_MES_EXCEPTION("Wrong dimensions for multInvLeft2.");
}
// PLU factorization
Vector inv(data);
lapack_int * const ipiv = new lapack_int[rows];
lapack_int info;
lapack_int rows2 = rows;
dgetrf(&rows2, &rows2, inv.base(), &rows2, ipiv, &info);
// solve a
lapack_int acols = a.numCols();
double* abase = a.base();
dgetrs("N", &rows2, &acols, inv.base(), &rows2, ipiv,
abase, &rows2, &info);
// solve b
lapack_int bcols = b.numCols();
double* bbase = b.base();
dgetrs("N", &rows2, &bcols, inv.base(), &rows2, ipiv,
bbase, &rows2, &info);
delete [] ipiv;
// condition numbers
double* const work = new double[4*rows];
lapack_int* const iwork = new lapack_int[rows];
double norm1 = getNorm1();
dgecon("1", &rows2, inv.base(), &rows2, &norm1, &rcond1,
work, iwork, &info);
double norminf = getNormInf();
dgecon("I", &rows2, inv.base(), &rows2, &norminf, &rcondinf,
work, iwork, &info);
delete [] iwork;
delete [] work;
}
Vector::Vector(GeneralMatrix& m, int col)
: len(m.numRows()), s(1), data(&(m.get(0, col))), destroy(false)
{
}
SchurDecompZero::SchurDecompZero(const GeneralMatrix& m)
: SchurDecomp(SqSylvMatrix(m, m.numRows()-m.numCols(), 0, m.numCols())),
ru(m, 0, 0, m.numRows()-m.numCols(), m.numCols())
{
ru.multRight(getQ());
}