func TestSolveLeastSquaresQRT(t *testing.T) {
M := 60
N := 40
K := 30
nb := 12
A := matrix.FloatUniform(M, N)
B := matrix.FloatZeros(M, K)
X0 := matrix.FloatUniform(N, K)
// B = A*X0
Mult(B, A, X0, 1.0, 0.0, NOTRANS)
W := matrix.FloatZeros(N, nb)
T := matrix.FloatZeros(N, N)
QR, err := DecomposeQRT(A, T, W, nb)
if err != nil {
t.Logf("decompose error: %v\n", err)
}
// B' = A.-1*B
err = SolveQRT(B, QR, T, W, NOTRANS, nb)
// expect B[0:N, 0:K] == X0, B[N:M, 0:K] == 0.0
var Xref matrix.FloatMatrix
Bref := matrix.FloatZeros(M, K)
Bref.SubMatrix(&Xref, 0, 0, N, K)
Xref.Plus(X0)
Bref.Minus(B)
t.Logf("\nmin ||B - A*X0||\n\twhere B = A*X0\n")
t.Logf("||B - A*X0||_1 ~~ 0.0: %e\n", NormP(Bref, NORM_ONE))
}
func TestMultQT(t *testing.T) {
M := 60
N := 40
K := 30
nb := 12
A := matrix.FloatUniform(M, N)
B := matrix.FloatUniform(M, K)
W := matrix.FloatZeros(N, nb)
T := matrix.FloatZeros(N, N)
// QR = Q*R
QR, err := DecomposeQRT(A.Copy(), T, W, nb)
if err != nil {
t.Logf("decompose-err: %v\n", err)
}
// compute: B - Q*Q.T*B = 0
// X = Q*Q.T*B
X := B.Copy()
MultQT(X, QR, T, W, LEFT|TRANS, nb)
MultQT(X, QR, T, W, LEFT, nb)
B.Minus(X)
// ||B - Q*Q.T*B||_1
nrm := NormP(B, NORM_ONE)
t.Logf("||B - Q*Q.T*B||_1: %e\n", nrm)
}
func _TestLDLnoPiv(t *testing.T) {
N := 42
nb := 8
A0 := matrix.FloatUniform(N, N)
A := matrix.FloatZeros(N, N)
Mult(A, A0, A0, 1.0, 1.0, TRANSB)
B := matrix.FloatNormal(A.Rows(), 2)
w := matrix.FloatWithValue(A.Rows(), 2, 1.0)
// B0 = A*B
B0 := B.Copy()
nb = 2
L, _ := DecomposeLDLnoPiv(A.Copy(), w, LOWER, nb)
Mult(B0, A, B, 1.0, 0.0, NOTRANS)
SolveLDLnoPiv(B0, L, LOWER)
t.Logf("L*D*L.T: ||B - A*X||_1: %e\n", NormP(B0.Minus(B), NORM_ONE))
U, _ := DecomposeLDLnoPiv(A.Copy(), w, UPPER, nb)
Mult(B0, A, B, 1.0, 0.0, NOTRANS)
SolveLDLnoPiv(B0, U, UPPER)
t.Logf("U*D*U.T: ||B - A*X||_1: %e\n", NormP(B0.Minus(B), NORM_ONE))
}
func TestLDLlower(t *testing.T) {
/*
Ldata := [][]float64{
[]float64{7.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
[]float64{7.0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0},
[]float64{7.0, 6.0, 5.0, 0.0, 0.0, 0.0, 0.0},
[]float64{7.0, 6.0, 5.0, 4.0, 0.0, 0.0, 0.0},
[]float64{7.0, 6.0, 5.0, 4.0, 6.0, 0.0, 0.0},
[]float64{7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 0.0},
[]float64{7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0}}
A := matrix.FloatMatrixFromTable(Ldata, matrix.RowOrder)
N := A.Rows()
*/
N := 7
nb := 0
A0 := matrix.FloatUniform(N, N)
A := matrix.FloatZeros(N, N)
Mult(A, A0, A0, 1.0, 1.0, TRANSB)
B := matrix.FloatNormal(A.Rows(), 2)
B0 := B.Copy()
B1 := B.Copy()
Mult(B0, A, B, 1.0, 0.0, NOTRANS)
_, _, _ = B0, B1, A0
ipiv := make([]int, N, N)
L, _ := DecomposeLDL(A.Copy(), nil, ipiv, LOWER, 0)
//t.Logf("unblk: ipiv = %v\n", ipiv)
//t.Logf("unblk: L\n%v\n", L)
ApplyRowPivots(B, ipiv, FORWARD)
MultTrm(B, L, 1.0, LOWER|UNIT|TRANSA)
MultDiag(B, L, LEFT)
MultTrm(B, L, 1.0, LOWER|UNIT)
ApplyRowPivots(B0, ipiv, FORWARD)
t.Logf(" unblk: L*D*L.T %d pivots: ||A*B - L*D*L.T*B||_1: %e\n",
NumPivots(ipiv), NormP(B.Minus(B0), NORM_ONE))
t.Logf("pivots: %v\n", ipiv)
nb = 4
w := matrix.FloatWithValue(A.Rows(), nb, 1.0)
L, _ = DecomposeLDL(A.Copy(), w, ipiv, LOWER, nb)
//t.Logf("blk: ipiv = %v\n", ipiv)
//t.Logf("blk: L\n%v\n", L)
// B2 = A*B1 == A*B
B2 := B1.Copy()
Mult(B2, A, B1, 1.0, 0.0, NOTRANS)
ApplyRowPivots(B1, ipiv, FORWARD)
MultTrm(B1, L, 1.0, LOWER|UNIT|TRANSA)
MultDiag(B1, L, LEFT)
MultTrm(B1, L, 1.0, LOWER|UNIT)
ApplyRowPivots(B2, ipiv, FORWARD)
t.Logf(" blk: L*D*L.T %d pivots: ||A*B - L*D*L.T*B||_1: %e\n",
NumPivots(ipiv), NormP(B2.Minus(B1), NORM_ONE))
t.Logf("pivots: %v\n", ipiv)
}
func _TestSwap(t *testing.T) {
A := matrix.FloatUniform(5, 5)
t.Logf("A:\n%v\n", A)
swapRows(A, 0, 4)
t.Logf("A: 0,4 swapped\n%v\n", A)
swapRows(A, 4, 0)
t.Logf("A: 4,0 swapped again\n%v\n", A)
}
func TestLU(t *testing.T) {
N := 60
K := 30
nb := 12
A := matrix.FloatUniform(N, N)
B := matrix.FloatUniform(N, K)
X := B.Copy()
piv := make([]int, N, N)
// R = lu(A) = P*L*U
R, _ := DecomposeLU(A.Copy(), piv, nb)
// X = A.-1*B = U.-1*(L.-1*B)
SolveLU(X, R, piv, NONE)
// B = B - A*X
Mult(B, A, X, -1.0, 1.0, NONE)
nrm := NormP(B, NORM_ONE)
t.Logf("||B - A*X||_1: %e\n", nrm)
}
func TestLowerCHOL(t *testing.T) {
N := 60
K := 30
nb := 16
Z := matrix.FloatUniform(N, N)
A := matrix.Times(Z, Z.Transpose())
B := matrix.FloatUniform(N, K)
X := B.Copy()
// R = chol(A) = L*L.T
R, _ := DecomposeCHOL(A.Copy(), LOWER, nb)
// X = A.-1*B = L.-T*(L.-1*B)
SolveCHOL(X, R, LOWER)
// B = B - A*X
Mult(B, A, X, -1.0, 1.0, NONE)
nrm := NormP(B, NORM_ONE)
t.Logf("||B - A*X||_1: %e\n", nrm)
}
func TestUpperCHOL(t *testing.T) {
N := 60
K := 30
nb := 16
Z := matrix.FloatUniform(N, N)
A := matrix.Times(Z, Z.Transpose())
B := matrix.FloatUniform(N, K)
X := B.Copy()
// R = chol(A) = U.T*U
R, _ := DecomposeCHOL(TriU(A.Copy()), UPPER, nb)
// X = A.-1*B = U.-1*(U.-T*B)
SolveCHOL(X, R, UPPER)
// B = B - A*X
Mult(B, A, X, -1.0, 1.0, NONE)
// ||B - A*X||_1
nrm := NormP(B, NORM_ONE)
t.Logf("||B - A*X||_1: %e\n", nrm)
}
func TestSolveMinQRT(t *testing.T) {
var QR *matrix.FloatMatrix
var err error
N := 40
K := 30
nb := 12
A := matrix.FloatUniform(N, N)
B0 := matrix.FloatUniform(N, K)
W := matrix.FloatZeros(N, nb)
T := matrix.FloatZeros(N, N)
QR, err = DecomposeQRT(A.Copy(), T, W, nb)
if err != nil {
t.Logf("decompose error: %v\n", err)
}
// B' = A.-1*B
B := B0.Copy()
err = SolveQRT(B, QR, T, W, TRANS, nb)
Mult(B0, A, B, -1.0, 1.0, TRANSA)
t.Logf("\nmin ||X||\n\ts.t. A.T*X = B\n\twhere A is N-by-N, B is N-by-K\n")
t.Logf("||B - A.T*X||_1 ~~ 0.0: %e\n", NormP(B0, NORM_ONE))
}
func TestLDLSolve(t *testing.T) {
N := 7
nb := 4
K := 6
A0 := matrix.FloatUniform(N, N)
A := matrix.FloatZeros(N, N)
Mult(A, A0, A0, 1.0, 1.0, TRANSB)
X0 := matrix.FloatNormal(A.Rows(), K)
B0 := matrix.FloatZeros(X0.Size())
Mult(B0, A, X0, 1.0, 0.0, NOTRANS)
B := B0.Copy()
_ = B
w := matrix.FloatZeros(A.Rows(), nb)
ipiv := make([]int, N, N)
L, _ := DecomposeLDL(A.Copy(), w, ipiv, LOWER, nb)
ipiv0 := make([]int, N, N)
L0, _ := DecomposeLDL(A.Copy(), w, ipiv0, LOWER, 0)
t.Logf("L:\n%v\n", L)
t.Logf("ipiv: %v\n", ipiv)
t.Logf("L0:\n%v\n", L0)
t.Logf("ipiv0: %v\n", ipiv0)
t.Logf("L == L0: %v", L.AllClose(L0))
// B = A*X0; solve and B should be X0
/*
SolveLDL(B, L, ipiv, LOWER)
B.Minus(X0)
t.Logf("L*D*L.T: ||A*X - B||_1: %e\n", NormP(B, NORM_ONE))
t.Logf("ipiv: %v\n", ipiv)
*/
/*
B = B0.Copy()
U, _ := DecomposeLDL(A.Copy(), w, ipiv, UPPER, nb)
// B = A*X0; solve and B should be X0
SolveLDL(B, U, ipiv, UPPER)
B.Minus(X0)
t.Logf("U*D*U.T: ||A*X - B||_1: %e\n", NormP(B, NORM_ONE))
*/
}
func TestDecomposeQRT(t *testing.T) {
M := 60
N := 40
nb := 12
A := matrix.FloatUniform(M, N)
W := matrix.FloatZeros(N, N)
T := matrix.FloatZeros(N, N)
// QR = Q*R
QR, _ := DecomposeQRT(A.Copy(), T, W, nb)
// A2 = Q*R
A2 := TriU(QR.Copy())
MultQT(A2, QR, T, W, LEFT, 0)
A.Minus(A2)
// ||A - Q*R||_1
nrm := NormP(A, NORM_ONE)
t.Logf("||A - Q*R||_1: %e\n", nrm)
}
func _TestLDLupper(t *testing.T) {
N := 8
nb := 0
A0 := matrix.FloatUniform(N, N)
A := matrix.FloatZeros(N, N)
Mult(A, A0, A0, 1.0, 1.0, TRANSB)
B := matrix.FloatNormal(A.Rows(), 2)
B0 := B.Copy()
B1 := B.Copy()
Mult(B0, A, B, 1.0, 0.0, NOTRANS)
ipiv := make([]int, N, N)
U, _ := DecomposeLDL(A.Copy(), nil, ipiv, UPPER, 0)
ApplyRowPivots(B, ipiv, BACKWARD)
MultTrm(B, U, 1.0, UPPER|UNIT|TRANSA)
MultDiag(B, U, LEFT)
MultTrm(B, U, 1.0, UPPER|UNIT)
ApplyRowPivots(B0, ipiv, BACKWARD)
t.Logf(" unblk: U*D*U.T %d pivots: ||A*B - U*D*U.T*B||_1: %e\n",
NumPivots(ipiv), NormP(B.Minus(B0), NORM_ONE))
t.Logf("pivots: %v\n", ipiv)
nb = 4
w := matrix.FloatZeros(A.Rows(), nb)
U, _ = DecomposeLDL(A.Copy(), w, ipiv, UPPER, nb)
// B2 = A*B1 == A*B
B2 := B1.Copy()
Mult(B2, A, B1, 1.0, 0.0, NOTRANS)
ApplyRowPivots(B1, ipiv, BACKWARD)
MultTrm(B1, U, 1.0, UPPER|UNIT|TRANSA)
MultDiag(B1, U, LEFT)
MultTrm(B1, U, 1.0, UPPER|UNIT)
ApplyRowPivots(B2, ipiv, BACKWARD)
t.Logf(" blk: U*D*U.T %d pivots: ||A*B - U*D*U.T*B||_1: %e\n",
NumPivots(ipiv), NormP(B2.Minus(B1), NORM_ONE))
t.Logf("pivots: %v\n", ipiv)
}
func TestQRBlk(t *testing.T) {
M := 8
N := 6
nb := 2
A := matrix.FloatUniform(M, N)
Tau := matrix.FloatZeros(M, 1)
Tz := matrix.FloatZeros(N, N)
Tx := matrix.FloatZeros(N, N)
DecomposeBlockSize(0)
Z, _ := DecomposeQRT(A.Copy(), Tz, nil, 0)
_ = Z
DecomposeBlockSize(nb)
//X, _ := DecomposeQR(A.Copy(), Tau, nil)
X, _ := DecomposeQRT(A.Copy(), Tx, nil, nb)
Tau0 := matrix.FloatZeros(M, 1)
A0 := A.Copy()
lapack.Geqrf(A0, Tau0)
ok := X.AllClose(A0)
var dx matrix.FloatMatrix
dx.DiagOf(Tx)
//okt := Tau.AllClose(Tau0)
okt := true
_ = Tau
t.Logf("lapack QR == DecomposeQR: %v\n", ok && okt)
if !ok || !okt || true {
t.Logf("A0: %d, %d, %d\n", A0.Rows(), A0.Cols(), A0.LeadingIndex())
t.Logf("A\n%v\n", A)
t.Logf("X\n%v\n", X)
t.Logf("Tz\n%v\n", Tz)
t.Logf("Tx\n%v\n", Tx)
t.Logf("Tau\n%v\n", &dx)
t.Logf("lapack X\n%v\n", A0)
t.Logf("lapack Tau\n%v\n", Tau0)
}
}
func TestQRT(t *testing.T) {
M := 6
N := 5
var Tau matrix.FloatMatrix
A := matrix.FloatUniform(M, N)
T := matrix.FloatZeros(A.Cols(), A.Cols())
T0 := T.Copy()
X, _ := DecomposeQRT(A.Copy(), T, nil, 0)
Tau.DiagOf(T)
Tau0 := matrix.FloatZeros(M, 1)
A0 := A.Copy()
lapack.Geqrf(A0, Tau0)
ok := X.AllClose(A0)
okt := Tau.AllClose(Tau0)
t.Logf("lapack QR == DecomposeQR: %v\n", ok && okt)
if !ok || !okt {
t.Logf("A0: %d, %d, %d\n", A0.Rows(), A0.Cols(), A0.LeadingIndex())
t.Logf("A\n%v\n", A)
t.Logf("X\n%v\n", X)
t.Logf("Tau\n%v\n", &Tau)
t.Logf("lapack X\n%v\n", A0)
t.Logf("lapack Tau\n%v\n", Tau0)
}
// build block reflectors
//unblkQRBlockReflector(X, Tau, T)
V := TriLU(A0.Copy())
lapack.LarftFloat(V, Tau0, T0)
ok = T0.AllClose(T)
t.Logf("lapack.dlarft == QRBlockReflector: %v\n", ok)
if !ok {
t.Logf("T:\n%v\n", T)
t.Logf("lapack T0:\n%v\n", T0)
}
}