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)
}
}
/*
* Blocked QR decomposition with compact WY transform. As implemented
* in lapack.xGEQRF subroutine.
*/
func blockedQR(A, Tvec, Twork, W *matrix.FloatMatrix, nb int) {
var ATL, ATR, ABL, ABR, AL, AR matrix.FloatMatrix
var A00, A01, A02, A10, A11, A12, A20, A21, A22 matrix.FloatMatrix
var TT, TB matrix.FloatMatrix
var t0, tau, t2, Tdiag, WT, WB, W0, W1, W2 matrix.FloatMatrix
//var Twork, W *matrix.FloatMatrix
Tdiag.DiagOf(Twork)
partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, 0, 0, pTOPLEFT)
partition2x1(
&TT,
&TB, Tvec, 0, pTOP)
partition2x1(
&WT,
&WB, W, 0, pTOP)
for ABR.Rows() > 0 && ABR.Cols() > 0 {
repartition2x2to3x3(&ATL,
&A00, &A01, &A02,
&A10, &A11, &A12,
&A20, &A21, &A22, A, nb, pBOTTOMRIGHT)
repartition2x1to3x1(&TT,
&t0,
&tau,
&t2, Tvec, nb, pBOTTOM)
repartition2x1to3x1(&WT,
&W0,
&W1,
&W2, W, nb, pBOTTOM)
partition1x2(
&AL, &AR, &ABR, nb, pLEFT)
// current block size
cb, rb := A11.Size()
if rb < cb {
cb = rb
}
// --------------------------------------------------------
// decompose left side AL == /A11\
// \A21/
unblockedQRT(&AL, Twork)
// copy scaling from T diagonal to tau-vector
Tdiag.CopyTo(&tau)
// update A'tail i.e. A12 and A22 with (I - Y*T*Y.T).T * A'tail
// compute: C - Y*(C.T*Y*T).T
updateWithQT(&A12, &A22, &A11, &A21, Twork, &W2, cb, true)
// --------------------------------------------------------
continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &A11, &A22, A, pBOTTOMRIGHT)
continue3x1to2x1(
&TT,
&TB, &t0, &tau, Tvec, pBOTTOM)
continue3x1to2x1(
&WT,
&WB, &W0, &W1, W, pBOTTOM)
}
}