func _TestViewUpdate(t *testing.T) {
Adata2 := [][]float64{
[]float64{4.0, 2.0, 2.0},
[]float64{6.0, 4.0, 2.0},
[]float64{4.0, 6.0, 1.0},
}
A := matrix.FloatMatrixFromTable(Adata2, matrix.RowOrder)
N := A.Rows()
// simple LU decomposition without pivoting
var A11, a10, a01, a00 matrix.FloatMatrix
for k := 1; k < N; k++ {
a00.SubMatrixOf(A, k-1, k-1, 1, 1)
a01.SubMatrixOf(A, k-1, k, 1, A.Cols()-k)
a10.SubMatrixOf(A, k, k-1, A.Rows()-k, 1)
A11.SubMatrixOf(A, k, k)
//t.Logf("A11: %v a01: %v\n", A11, a01)
a10.Scale(1.0 / a00.Float())
MVRankUpdate(&A11, &a10, &a01, -1.0)
}
Ld := TriLU(A.Copy())
Ud := TriU(A)
t.Logf("Ld:\n%v\nUd:\n%v\n", Ld, Ud)
An := matrix.FloatZeros(N, N)
Mult(An, Ld, Ud, 1.0, 1.0, NOTRANS)
t.Logf("A == Ld*Ud: %v\n", An.AllClose(An))
}
func (g *matrixFs) Gf(x, y *matrix.FloatMatrix, alpha, beta float64, trans linalg.Option) error {
//
minor := 0
if !checkpnt.MinorEmpty() {
minor = checkpnt.MinorTop()
} else {
loopg += 1
minor = loopg
}
checkpnt.Check("00-Gfunc", minor)
m, n := g.A.Size()
y.Scale(beta)
// x_n = x[:n]
//x_n := matrix.FloatVector(x.FloatArray()[:n])
x_n := x.SubMatrix(0, 0, n, 1).Copy()
// x_n_2n = x[n:2*n]
//x_n_2n := matrix.FloatVector(x.FloatArray()[n : 2*n])
x_n_2n := x.SubMatrix(n, 0, n, 1).Copy()
if linalg.Equal(trans, linalg.OptNoTrans) {
// y += alpha * G * x
// y[:n] += alpha * (x[:n] - x[n:2*n])
y_n := matrix.Minus(x_n, x_n_2n).Scale(alpha)
y.SubMatrix(0, 0, n, 1).Plus(y_n)
//y.AddIndexes(matrix.Indexes(n), y_n.FloatArray())
// y[n:2*n] += alpha * (-x[:n] - x[n:2*n]) = -alpha * (x[:n]+x[n:2*n])
y_n = matrix.Plus(x_n, x_n_2n).Scale(-alpha)
y.SubMatrix(n, 0, n, 1).Plus(y_n)
//y.AddIndexes(matrix.Indexes(n, 2*n), y_n.FloatArray())
// y[2*n+1:] += -alpha * A * x[:n]
y_2n := matrix.Times(g.A, x_n).Scale(-alpha)
//y.AddIndexes(matrix.Indexes(2*n+1, y.NumElements()), y_2n.FloatArray())
y.SubMatrix(2*n+1, 0, y_2n.NumElements(), 1).Plus(y_2n)
} else {
// x_m = x[-m:]
//x_m := matrix.FloatVector(x.FloatArray()[x.NumElements()-m:])
x_m := x.SubMatrix(x.NumElements()-m, 0)
// x_tmp = (x[:n] - x[n:2*n] - A.T * x[-m:])
x_tmp := matrix.Minus(x_n, x_n_2n, matrix.Times(g.A.Transpose(), x_m))
// y[:n] += alpha * (x[:n] - x[n:2*n] - A.T * x[-m:])
//y.AddIndexes(matrix.Indexes(n), x_tmp.Scale(alpha).FloatArray())
y.SubMatrix(0, 0, n, 1).Plus(x_tmp.Scale(alpha))
x_tmp = matrix.Plus(x_n, x_n_2n).Scale(-alpha)
//y.AddIndexes(matrix.Indexes(n, y.NumElements()), x_tmp.FloatArray())
y.SubMatrix(n, 0).Plus(x_tmp)
}
checkpnt.Check("10-Gfunc", minor)
return nil
}
/*
* Compute
* C = C*diag(D) flags & RIGHT == true
* C = diag(D)*C flags & LEFT == true
*
* Arguments
* C M-by-N matrix if flags&RIGHT == true or N-by-M matrix if flags&LEFT == true
*
* D N element column or row vector or N-by-N matrix
*
* flags Indicator bits, LEFT or RIGHT
*/
func MultDiag(C, D *matrix.FloatMatrix, flags Flags) {
var c, d0 matrix.FloatMatrix
if D.Cols() == 1 {
// diagonal is column vector
switch flags & (LEFT | RIGHT) {
case LEFT:
// scale rows; for each column element-wise multiply with D-vector
for k := 0; k < C.Cols(); k++ {
C.SubMatrix(&c, 0, k, C.Rows(), 1)
c.Mul(D)
}
case RIGHT:
// scale columns
for k := 0; k < C.Cols(); k++ {
C.SubMatrix(&c, 0, k, C.Rows(), 1)
// scale the column
c.Scale(D.GetAt(k, 0))
}
}
} else {
// diagonal is row vector
var d *matrix.FloatMatrix
if D.Rows() == 1 {
d = D
} else {
D.SubMatrix(&d0, 0, 0, 1, D.Cols(), D.LeadingIndex()+1)
d = &d0
}
switch flags & (LEFT | RIGHT) {
case LEFT:
for k := 0; k < C.Rows(); k++ {
C.SubMatrix(&c, k, 0, 1, C.Cols())
// scale the row
c.Scale(d.GetAt(0, k))
}
case RIGHT:
// scale columns
for k := 0; k < C.Cols(); k++ {
C.SubMatrix(&c, 0, k, C.Rows(), 1)
// scale the column
c.Scale(d.GetAt(0, k))
}
}
}
}
func blkDecompBKLower(A, W *matrix.FloatMatrix, p *pPivots, nb int) (err error) {
var ATL, ATR, ABL, ABR matrix.FloatMatrix
var A00, A10, A11, A20, A21, A22 matrix.FloatMatrix
var wrk matrix.FloatMatrix
var pT, pB, p0, p1, p2 pPivots
var nblk int = 0
err = nil
partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, 0, 0, pTOPLEFT)
partitionPivot2x1(
&pT,
&pB, p, 0, pTOP)
for ABR.Cols() >= nb {
err, nblk = unblkBoundedBKLower(&ABR, W, &pB, nb)
// repartition nblk size
repartition2x2to3x3(&ATL,
&A00, nil, nil,
&A10, &A11, nil,
&A20, &A21, &A22, A, nblk, pBOTTOMRIGHT)
repartPivot2x1to3x1(&pT,
&p0, &p1, &p2 /**/, p, nblk, pBOTTOM)
// --------------------------------------------------------
// here [A11;A21] has been decomposed by unblkBoundedBKLower()
// Now we need update A22
// wrk is original A21
W.SubMatrix(&wrk, nblk, 0, A21.Rows(), nblk)
// A22 = A22 - L21*D1*L21.T = A22 - L21*W.T
UpdateTrm(&A22, &A21, &wrk, -1.0, 1.0, LOWER|TRANSB)
// partially undo row pivots left of diagonal
for k := nblk; k > 0; k-- {
var s, d matrix.FloatMatrix
r := p1.pivots[k-1]
rlen := k - 1
if r < 0 {
r = -r
rlen--
}
if r == k {
// no pivot
continue
}
ABR.SubMatrix(&s, k-1, 0, 1, rlen)
ABR.SubMatrix(&d, r-1, 0, 1, rlen)
Swap(&d, &s)
if p1.pivots[k-1] < 0 {
k-- // skip other entry in 2x2 pivots
}
}
// shift pivot values
for k, n := range p1.pivots {
if n > 0 {
p1.pivots[k] += ATL.Rows()
} else {
p1.pivots[k] -= ATL.Rows()
}
}
// zero work for debuging
W.Scale(0.0)
// ---------------------------------------------------------
continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &A11, &A22, A, pBOTTOMRIGHT)
contPivot3x1to2x1(
&pT,
&pB, &p0, &p1, p, pBOTTOM)
}
// do the last part with unblocked code
if ABR.Cols() > 0 {
unblkDecompBKLower(&ABR, W, &pB)
// shift pivot values
for k, n := range pB.pivots {
if n > 0 {
pB.pivots[k] += ATL.Rows()
} else {
pB.pivots[k] -= ATL.Rows()
}
}
}
return
}
func main() {
m := 6
Vdata := [][]float64{
[]float64{1.0, -1.0, -2.0, -2.0, 0.0, 1.5, 1.0},
[]float64{1.0, 2.0, 1.0, -1.0, -2.0, -1.0, 1.0}}
V := matrix.FloatMatrixFromTable(Vdata, matrix.RowOrder)
// V[1, :m] - V[1,1:]
a0 := matrix.Minus(V.GetSubMatrix(1, 0, 1, m), V.GetSubMatrix(1, 1, 1))
// V[0, :m] - V[0,1:]
a1 := matrix.Minus(V.GetSubMatrix(0, 0, 1, m), V.GetSubMatrix(0, 1, 1))
A0, _ := matrix.FloatMatrixStacked(matrix.StackDown, a0.Scale(-1.0), a1)
A0 = A0.Transpose()
b0 := matrix.Mul(A0, V.GetSubMatrix(0, 0, 2, m).Transpose())
b0 = matrix.Times(b0, matrix.FloatWithValue(2, 1, 1.0))
A := make([]*matrix.FloatMatrix, 0)
b := make([]*matrix.FloatMatrix, 0)
A = append(A, A0)
b = append(b, b0)
// List of symbols
C := make([]*matrix.FloatMatrix, 0)
C = append(C, matrix.FloatZeros(2, 1))
var row *matrix.FloatMatrix = nil
for k := 0; k < m; k++ {
row = A0.GetRow(k, row)
nrm := blas.Nrm2Float(row)
row.Scale(2.0 * b0.GetIndex(k) / (nrm * nrm))
C = append(C, row.Transpose())
}
// Voronoi set around C[1]
A1 := matrix.FloatZeros(3, 2)
A1.SetSubMatrix(0, 0, A0.GetSubMatrix(0, 0, 1).Scale(-1.0))
A1.SetSubMatrix(1, 0, matrix.Minus(C[m], C[1]).Transpose())
A1.SetSubMatrix(2, 0, matrix.Minus(C[2], C[1]).Transpose())
b1 := matrix.FloatZeros(3, 1)
b1.SetIndex(0, -b0.GetIndex(0))
v := matrix.Times(A1.GetRow(1, nil), matrix.Plus(C[m], C[1])).Float() * 0.5
b1.SetIndex(1, v)
v = matrix.Times(A1.GetRow(2, nil), matrix.Plus(C[2], C[1])).Float() * 0.5
b1.SetIndex(2, v)
A = append(A, A1)
b = append(b, b1)
// Voronoi set around C[2] ... C[5]
for k := 2; k < 6; k++ {
A1 = matrix.FloatZeros(3, 2)
A1.SetSubMatrix(0, 0, A0.GetSubMatrix(k-1, 0, 1).Scale(-1.0))
A1.SetSubMatrix(1, 0, matrix.Minus(C[k-1], C[k]).Transpose())
A1.SetSubMatrix(2, 0, matrix.Minus(C[k+1], C[k]).Transpose())
b1 = matrix.FloatZeros(3, 1)
b1.SetIndex(0, -b0.GetIndex(k-1))
v := matrix.Times(A1.GetRow(1, nil), matrix.Plus(C[k-1], C[k])).Float() * 0.5
b1.SetIndex(1, v)
v = matrix.Times(A1.GetRow(2, nil), matrix.Plus(C[k+1], C[k])).Float() * 0.5
b1.SetIndex(2, v)
A = append(A, A1)
b = append(b, b1)
}
// Voronoi set around C[6]
A1 = matrix.FloatZeros(3, 2)
A1.SetSubMatrix(0, 0, A0.GetSubMatrix(5, 0, 1).Scale(-1.0))
A1.SetSubMatrix(1, 0, matrix.Minus(C[1], C[6]).Transpose())
A1.SetSubMatrix(2, 0, matrix.Minus(C[5], C[6]).Transpose())
b1 = matrix.FloatZeros(3, 1)
b1.SetIndex(0, -b0.GetIndex(5))
v = matrix.Times(A1.GetRow(1, nil), matrix.Plus(C[1], C[6])).Float() * 0.5
b1.SetIndex(1, v)
v = matrix.Times(A1.GetRow(2, nil), matrix.Plus(C[5], C[6])).Float() * 0.5
b1.SetIndex(2, v)
A = append(A, A1)
b = append(b, b1)
P := matrix.FloatIdentity(2)
q := matrix.FloatZeros(2, 1)
solopts := &cvx.SolverOptions{ShowProgress: false, MaxIter: 30}
ovals := make([]float64, 0)
for k := 1; k < 7; k++ {
sol, err := cvx.Qp(P, q, A[k], b[k], nil, nil, solopts, nil)
_ = err
x := sol.Result.At("x")[0]
ovals = append(ovals, math.Pow(blas.Nrm2Float(x), 2.0))
}
optvals := matrix.FloatVector(ovals)
//fmt.Printf("optvals=\n%v\n", optvals)
rangeFunc := func(n int) []float64 {
r := make([]float64, 0)
for i := 0; i < n; i++ {
r = append(r, float64(i))
}
return r
}
nopts := 200
sigmas := matrix.FloatVector(rangeFunc(nopts))
sigmas.Scale((0.5 - 0.2) / float64(nopts)).Add(0.2)
bndsVal := func(sigma float64) float64 {
// 1.0 - sum(exp( -optvals/(2*sigma**2)))
return 1.0 - matrix.Exp(matrix.Scale(optvals, -1.0/(2*sigma*sigma))).Sum()
}
bnds := matrix.FloatZeros(sigmas.NumElements(), 1)
for j, v := range sigmas.FloatArray() {
bnds.SetIndex(j, bndsVal(v))
}
plotData("plot.png", sigmas.FloatArray(), bnds.FloatArray())
}
// Build Q in place by applying elementary reflectors in reverse order to
// an implied identity matrix. This forms Q = H(1)H(2) ... H(k)
//
// this is compatibe with lapack.DORG2R
func unblockedBuildQ(A, tau, w *matrix.FloatMatrix, kb int) error {
var err error = nil
var ATL, ATR, ABL, ABR matrix.FloatMatrix
var A00, a01, A02, a10t, a11, a12t, A20, a21, A22 matrix.FloatMatrix
var tT, tB matrix.FloatMatrix
var t0, tau1, t2, w1 matrix.FloatMatrix
var mb int
var rowvec bool
mb = A.Rows() - A.Cols()
rowvec = tau.Rows() == 1
partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, mb, 0, pBOTTOMRIGHT)
if rowvec {
partition1x2(
&tT, &tB, tau, 0, pRIGHT)
} else {
partition2x1(
&tT,
&tB, tau, 0, pBOTTOM)
}
// clearing of the columns of the right and setting ABR to unit diagonal
// (only if not applying all reflectors, kb > 0)
for ATL.Rows() > 0 && ATL.Cols() > 0 {
repartition2x2to3x3(&ATL,
&A00, &a01, &A02,
&a10t, &a11, &a12t,
&A20, &a21, &A22, A, 1, pTOPLEFT)
if rowvec {
repartition1x2to1x3(&tT,
&t0, &tau1, &t2, tau, 1, pLEFT)
} else {
repartition2x1to3x1(&tT,
&t0,
&tau1,
&t2, tau, 1, pTOP)
}
// --------------------------------------------------------
// adjust workspace to correct size
w.SubMatrix(&w1, 0, 0, 1, a12t.Cols())
// apply Householder reflection from left
applyHHTo2x1(&tau1, &a21, &a12t, &A22, &w1, LEFT)
// apply (in-place) current elementary reflector to unit vector
a21.Scale(-tau1.Float())
a11.SetAt(0, 0, 1.0-tau1.Float())
// zero the upper part
a01.SetIndexes(0.0)
// --------------------------------------------------------
continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &a11, &A22, A, pTOPLEFT)
if rowvec {
continue1x3to1x2(
&tT, &tB, &t0, &tau1, tau, pLEFT)
} else {
continue3x1to2x1(
&tT,
&tB, &t0, &tau1, tau, pTOP)
}
}
return err
}