// Simple and slow LQ decomposition with Givens rotations
func TestGivensLQ(t *testing.T) {
var d cmat.FloatMatrix
M := 149
N := 167
A := cmat.NewMatrix(M, N)
A1 := cmat.NewCopy(A)
ones := cmat.NewFloatConstSource(1.0)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
A0 := cmat.NewCopy(A)
Qt := cmat.NewMatrix(N, N)
d.Diag(Qt)
d.SetFrom(ones)
// R = G(n)...G(2)G(1)*A; Q = G(1).T*G(2).T...G(n).T ; Q.T = G(n)...G(2)G(1)
for i := 0; i < M; i++ {
// zero elements right of diagonal
for j := N - 2; j >= i; j-- {
c, s, r := lapackd.ComputeGivens(A.Get(i, j), A.Get(i, j+1))
A.Set(i, j, r)
A.Set(i, j+1, 0.0)
// apply rotation to this column starting from row i+1
lapackd.ApplyGivensRight(A, j, j+1, i+1, M-i-1, c, s)
// update Qt = G(k)*Qt
lapackd.ApplyGivensRight(Qt, j, j+1, 0, N, c, s)
}
}
// A = L*Q
blasd.Mult(A1, A, Qt, 1.0, 0.0, gomas.TRANSB)
blasd.Plus(A0, A1, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||A - L*G(1)..G(n)||_1: %e\n", M, N, nrm)
}
// Simple and slow QR decomposition with Givens rotations
func TestGivensQR(t *testing.T) {
var d cmat.FloatMatrix
M := 181
N := 159
A := cmat.NewMatrix(M, N)
A1 := cmat.NewCopy(A)
ones := cmat.NewFloatConstSource(1.0)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
A0 := cmat.NewCopy(A)
Qt := cmat.NewMatrix(M, M)
d.Diag(Qt)
d.SetFrom(ones)
// R = G(n)...G(2)G(1)*A; Q = G(1).T*G(2).T...G(n).T ; Q.T = G(n)...G(2)G(1)
// for all columns ...
for j := 0; j < N; j++ {
// ... zero elements below diagonal, starting from bottom
for i := M - 2; i >= j; i-- {
c, s, r := lapackd.ComputeGivens(A.Get(i, j), A.Get(i+1, j))
A.Set(i, j, r)
A.Set(i+1, j, 0.0)
// apply rotations on this row starting from column j, N-j column
lapackd.ApplyGivensLeft(A, i, i+1, j+1, N-j-1, c, s)
// update Qt = G(k)*Qt
lapackd.ApplyGivensLeft(Qt, i, i+1, 0, M, c, s)
}
}
// check: A = Q*R
blasd.Mult(A1, Qt, A, 1.0, 0.0, gomas.TRANSA)
blasd.Plus(A0, A1, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||A - G(n)..G(1)*R||_1: %e\n", M, N, nrm)
}