// test: unblk.ReduceHess(A) == blk.ReduceHess(A)
func TestReduceHess(t *testing.T) {
N := 375
nb := 16
conf := gomas.NewConf()
conf.LB = nb
A := cmat.NewMatrix(N, N)
tau := cmat.NewMatrix(N, 1)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
A0 := cmat.NewCopy(A)
tau0 := cmat.NewCopy(tau)
// blocked reduction
W := lapackd.Workspace(lapackd.HessReduceWork(A, conf))
lapackd.HessReduce(A, tau, W, conf)
// unblocked reduction
conf.LB = 0
lapackd.HessReduce(A0, tau0, W, conf)
ok := A.AllClose(A0)
t.Logf("blk.ReduceHess(A) == unblk.ReduceHess(A): %v\n", ok)
ok = tau0.AllClose(tau)
t.Logf("blk HessQ.tau == unblk HessQ.tau: %v\n", ok)
// ||A - A0||_1
blasd.Plus(A, A0, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(A, lapackd.NORM_ONE)
t.Logf("||H - H0||_1: %e\n", nrm)
}
// test: A - Q*Hess(A)*Q.T == 0
func TestMultHess(t *testing.T) {
N := 377
nb := 16
conf := gomas.NewConf()
conf.LB = nb
A := cmat.NewMatrix(N, N)
tau := cmat.NewMatrix(N, 1)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
A0 := cmat.NewCopy(A)
// reduction
W := lapackd.Workspace(lapackd.HessReduceWork(A, conf))
lapackd.HessReduce(A, tau, W, conf)
var Hlow cmat.FloatMatrix
H := cmat.NewCopy(A)
// set triangular part below first subdiagonal to zeros
zeros := cmat.NewFloatConstSource(0.0)
Hlow.SubMatrix(H, 1, 0, N-1, N-1)
Hlow.SetFrom(zeros, cmat.LOWER|cmat.UNIT)
H1 := cmat.NewCopy(H)
// H := Q*H*Q.T
conf.LB = nb
lapackd.HessMult(H, A, tau, W, gomas.LEFT, conf)
lapackd.HessMult(H, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
// H := Q*H*Q.T
conf.LB = 0
lapackd.HessMult(H1, A, tau, W, gomas.LEFT, conf)
lapackd.HessMult(H1, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
// compute ||Q*Hess(A)*Q.T - A||_1
blasd.Plus(H, A0, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(H, lapackd.NORM_ONE)
t.Logf(" blk.|| Q*Hess(A)*Q.T - A ||_1 : %e\n", nrm)
blasd.Plus(H1, A0, 1.0, -1.0, gomas.NONE)
nrm = lapackd.NormP(H1, lapackd.NORM_ONE)
t.Logf("unblk.|| Q*Hess(A)*Q.T - A ||_1 : %e\n", nrm)
}