func testEigen(N int, bits int, t *testing.T) {
var A, A0, W, D, V *cmat.FloatMatrix
var sD cmat.FloatMatrix
var s string = "lower"
if bits&gomas.UPPER != 0 {
s = "upper"
}
wsize := N * N
if wsize < 100 {
wsize = 100
}
D = cmat.NewMatrix(N, 1)
A = cmat.NewMatrix(N, N)
V = cmat.NewMatrix(N, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src, cmat.SYMM)
A0 = cmat.NewCopy(A)
W = cmat.NewMatrix(wsize, 1)
if err := lapackd.EigenSym(D, A, W, bits|gomas.WANTV); err != nil {
t.Errorf("EigenSym error: %v\n", err)
return
}
// ||I - V.T*V||
sD.Diag(V)
blasd.Mult(V, A, A, 1.0, 0.0, gomas.TRANSA)
blasd.Add(&sD, -1.0)
nrm1 := lapackd.NormP(V, lapackd.NORM_ONE)
// left vectors are M-by-N
V.Copy(A)
lapackd.MultDiag(V, D, gomas.RIGHT)
blasd.Mult(A0, V, A, -1.0, 1.0, gomas.TRANSB)
nrm2 := lapackd.NormP(A0, lapackd.NORM_ONE)
t.Logf("N=%d, [%s] ||A - V*D*V.T||_1 :%e\n", N, s, nrm2)
t.Logf(" ||I - V.T*V||_1 : %e\n", nrm1)
}
// test: M < N, U=[m,m] and V=[m,n] or V=[n,n] (square)
func testWide(M, N int, square bool, t *testing.T) {
var A, A0, W, S, U, Uu, V, Vv *cmat.FloatMatrix
var sD cmat.FloatMatrix
var s string
wsize := M * N
if wsize < 100 {
wsize = 100
}
S = cmat.NewMatrix(M, 1)
A = cmat.NewMatrix(M, N)
U = cmat.NewMatrix(M, M)
Uu = cmat.NewMatrix(M, M)
if square {
V = cmat.NewMatrix(N, N)
Vv = cmat.NewMatrix(N, N)
} else {
V = cmat.NewMatrix(M, N)
Vv = cmat.NewMatrix(M, M)
}
src := cmat.NewFloatNormSource()
A.SetFrom(src)
A0 = cmat.NewCopy(A)
W = cmat.NewMatrix(wsize, 1)
if err := lapackd.SVD(S, U, V, A, W, gomas.WANTU|gomas.WANTV); err != nil {
t.Errorf("SVD error: %v\n", err)
return
}
// ||I - U.T*U||
sD.Diag(Uu)
blasd.Mult(Uu, U, U, 1.0, 0.0, gomas.TRANSA)
blasd.Add(&sD, -1.0)
nrm0 := lapackd.NormP(Uu, lapackd.NORM_ONE)
// ||I - V*V.T||
sD.Diag(Vv)
blasd.Mult(Vv, V, V, 1.0, 0.0, gomas.TRANSB)
blasd.Add(&sD, -1.0)
nrm1 := lapackd.NormP(Vv, lapackd.NORM_ONE)
if square {
// right vectors are N-by-N
Sg := cmat.NewMatrix(M, N)
A1 := cmat.NewMatrix(M, N)
sD.Diag(Sg)
blasd.Copy(&sD, S)
blasd.Mult(A1, Sg, V, 1.0, 0.0, gomas.NONE)
blasd.Mult(A0, U, A1, -1.0, 1.0, gomas.NONE)
s = "U=[m,m], V=[n,n]"
} else {
// right vectors are M-by-N
lapackd.MultDiag(V, S, gomas.LEFT)
blasd.Mult(A0, U, V, -1.0, 1.0, gomas.NONE)
s = "U=[m,m], V=[m,n]"
}
nrm2 := lapackd.NormP(A0, lapackd.NORM_ONE)
if N < 10 {
t.Logf("A - U*S*V.T:\n%v\n", A0)
}
t.Logf("M=%d, N=%d, %s ||A - U*S*V.T||_1 :%e\n", M, N, s, nrm2)
t.Logf(" ||I - U.T*U||_1 : %e\n", nrm0)
t.Logf(" ||I - V*V.T||_1 : %e\n", nrm1)
}