func test_trdevd(N, flags, kind int, verbose bool, t *testing.T) {
var At, sD, sE, tmp cmat.FloatMatrix
A0 := cmat.NewMatrix(N, N)
desc := setTrdDiagonals(A0, kind)
At.SubMatrix(A0, 0, 0, N, N)
sD.Diag(A0, 0)
sE.Diag(A0, 1)
D := cmat.NewCopy(&sD)
E := cmat.NewCopy(&sE)
V := cmat.NewMatrix(N, N)
sD.Diag(V, 0)
sD.Add(1.0)
W := cmat.NewMatrix(4*N, 1)
C := cmat.NewMatrix(N, N)
if verbose && N < 10 {
t.Logf("A0:\n%v\n", A0.ToString("%6.3f"))
t.Logf("V.pre:\n%v\n", V.ToString("%6.3f"))
}
lapackd.TRDEigen(D, E, V, W, flags|gomas.WANTV)
for k := 0; k < N-1; k++ {
if E.GetAt(k) != 0.0 {
t.Logf("E[%d] != 0.0 (%e)\n", k, E.GetAt(k))
}
}
blasd.Mult(C, V, V, 1.0, 0.0, gomas.TRANSB)
sD.Diag(C)
sD.Add(-1.0)
nrmv := lapackd.NormP(C, lapackd.NORM_ONE)
blasd.Mult(C, V, A0, 1.0, 0.0, gomas.TRANSA)
blasd.Mult(&At, C, V, 1.0, 0.0, gomas.NONE)
if verbose && N < 10 {
t.Logf("D:\n%v\n", asRow(&tmp, D).ToString("%6.3f"))
t.Logf("V:\n%v\n", V.ToString("%6.3f"))
t.Logf("V.T*A*V\n%v\n", At.ToString("%6.3f"))
}
sD.Diag(&At)
blasd.Axpy(&sD, D, -1.0)
nrma := lapackd.NormP(&At, lapackd.NORM_ONE)
t.Logf("N=%d [%s] ||V.T*A*V - eigen(A)||_1: %e\n", N, desc, nrma)
t.Logf(" ||I - V.T*V||_1: %e\n", nrmv)
}
func test_bdsvd(N, flags, kind int, verbose bool, t *testing.T) {
var At, sD, sE, tmp cmat.FloatMatrix
uplo := "upper"
offdiag := 1
if flags&gomas.LOWER != 0 {
offdiag = -1
uplo = "lower"
}
A0 := cmat.NewMatrix(N, N)
desc := setDiagonals(A0, offdiag, kind)
At.SubMatrix(A0, 0, 0, N, N)
sD.Diag(A0, 0)
sE.Diag(A0, offdiag)
D := cmat.NewCopy(&sD)
E := cmat.NewCopy(&sE)
// unit singular vectors
U := cmat.NewMatrix(N, N)
sD.Diag(U, 0)
sD.Add(1.0)
V := cmat.NewMatrix(N, N)
sD.Diag(V, 0)
sD.Add(1.0)
W := cmat.NewMatrix(4*N, 1)
C := cmat.NewMatrix(N, N)
lapackd.BDSvd(D, E, U, V, W, flags|gomas.WANTU|gomas.WANTV)
blasd.Mult(C, U, U, 1.0, 0.0, gomas.TRANSA)
sD.Diag(C)
sD.Add(-1.0)
nrmu := lapackd.NormP(C, lapackd.NORM_ONE)
blasd.Mult(C, V, V, 1.0, 0.0, gomas.TRANSB)
sD.Add(-1.0)
nrmv := lapackd.NormP(C, lapackd.NORM_ONE)
blasd.Mult(C, U, A0, 1.0, 0.0, gomas.TRANSA)
blasd.Mult(&At, C, V, 1.0, 0.0, gomas.TRANSB)
if verbose && N < 10 {
t.Logf("D:\n%v\n", asRow(&tmp, D))
t.Logf("U:\n%v\n", U)
t.Logf("V:\n%v\n", V)
t.Logf("U.T*A*V\n%v\n", &At)
}
sD.Diag(&At)
blasd.Axpy(&sD, D, -1.0)
nrma := lapackd.NormP(&At, lapackd.NORM_ONE)
t.Logf("N=%d [%s,%s] ||U.T*A*V - bdsvd(A)||_1: %e\n", N, uplo, desc, nrma)
t.Logf(" ||I - U.T*U||_1: %e\n", nrmu)
t.Logf(" ||I - V.T*V||_1: %e\n", nrmv)
}
func test1(N int, beta float64, t *testing.T) {
var sI cmat.FloatMatrix
if N&0x1 != 0 {
N = N + 1
}
D := cmat.NewMatrix(N, 1)
Z := cmat.NewMatrix(N, 1)
Y := cmat.NewMatrix(N, 1)
V := cmat.NewMatrix(N, 1)
Q := cmat.NewMatrix(N, N)
I := cmat.NewMatrix(N, N)
D.SetAt(0, 1.0)
Z.SetAt(0, 2.0)
for i := 1; i < N-1; i++ {
if i < N/2 {
D.SetAt(i, 2.0-float64(N/2-i)*beta)
} else {
D.SetAt(i, 2.0+float64(i+1-N/2)*beta)
}
Z.SetAt(i, beta)
}
D.SetAt(N-1, 10.0/3.0)
Z.SetAt(N-1, 2.0)
w := blasd.Nrm2(Z)
blasd.InvScale(Z, w)
rho := 1.0 / (w * w)
lapackd.TRDSecularSolveAll(Y, V, Q, D, Z, rho)
lapackd.TRDSecularEigen(Q, V, nil)
blasd.Mult(I, Q, Q, 1.0, 0.0, gomas.TRANSA)
sI.Diag(I)
sI.Add(-1.0)
nrm := lapackd.NormP(I, lapackd.NORM_ONE)
t.Logf("N=%d, beta=%e ||I - Q.T*Q||_1: %e\n", N, beta, nrm)
}