func (gp *gpConvexProg) F1(x *matrix.FloatMatrix) (f, Df *matrix.FloatMatrix, err error) {
f = nil
Df = nil
err = nil
f = matrix.FloatZeros(gp.mnl+1, 1)
Df = matrix.FloatZeros(gp.mnl+1, gp.n)
y := gp.g.Copy()
blas.GemvFloat(gp.F, x, y, 1.0, 1.0)
for i, s := range gp.ind {
start := s[0]
stop := s[1]
// yi := exp(yi) = exp(Fi*x+gi)
ymax := maxvec(y.FloatArray()[start:stop])
// ynew = exp(y[start:stop] - ymax)
ynew := matrix.Exp(matrix.FloatVector(y.FloatArray()[start:stop]).Add(-ymax))
y.SetIndexesFromArray(ynew.FloatArray(), matrix.Indexes(start, stop)...)
// fi = log sum yi = log sum exp(Fi*x+gi)
ysum := blas.AsumFloat(y, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
f.SetIndex(i, ymax+math.Log(ysum))
blas.ScalFloat(y, 1.0/ysum, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
blas.GemvFloat(gp.F, y, Df, 1.0, 0.0, la.OptTrans, &la.IOpt{"m", stop - start},
&la.IOpt{"incy", gp.mnl + 1}, &la.IOpt{"offseta", start},
&la.IOpt{"offsetx", start}, &la.IOpt{"offsety", i})
}
return
}
func _TestMultMVTransA(t *testing.T) {
bM := 1000 * M
bN := 1000 * N
A := matrix.FloatNormal(bN, bM)
X := matrix.FloatWithValue(bN, 1, 1.0)
Y1 := matrix.FloatZeros(bM, 1)
Y0 := matrix.FloatZeros(bM, 1)
Ar := A.FloatArray()
Xr := X.FloatArray()
Y1r := Y1.FloatArray()
blas.GemvFloat(A, X, Y0, 1.0, 1.0, linalg.OptTrans)
DMultMV(Y1r, Ar, Xr, 1.0, 1.0, TRANSA, 1, A.LeadingIndex(), 1, 0, bN, 0, bM, 4, 4)
ok := Y0.AllClose(Y1)
t.Logf("Y0 == Y1: %v\n", ok)
if !ok {
var y1, y0 matrix.FloatMatrix
Y1.SubMatrix(&y1, 0, 0, 5, 1)
t.Logf("Y1[0:5]:\n%v\n", y1)
Y0.SubMatrix(&y0, 0, 0, 5, 1)
t.Logf("Y0[0:5]:\n%v\n", y0)
}
}
func _TestMultMV(t *testing.T) {
bM := 100 * M
bN := 100 * N
A := matrix.FloatNormal(bM, bN)
X := matrix.FloatNormal(bN, 1)
Y1 := matrix.FloatZeros(bM, 1)
Y0 := matrix.FloatZeros(bM, 1)
Ar := A.FloatArray()
Xr := X.FloatArray()
Y1r := Y1.FloatArray()
blas.GemvFloat(A, X, Y0, 1.0, 1.0)
DMultMV(Y1r, Ar, Xr, 1.0, 1.0, NOTRANS, 1, A.LeadingIndex(), 1, 0, bN, 0, bM, 32, 32)
t.Logf("Y0 == Y1: %v\n", Y0.AllClose(Y1))
/*
if ! Y0.AllClose(Y1) {
y0 := Y0.SubMatrix(0, 0, 2, 1)
y1 := Y1.SubMatrix(0, 0, 2, 1)
t.Logf("y0=\n%v\n", y0)
t.Logf("y1=\n%v\n", y1)
}
*/
}
/*
Matrix-vector multiplication.
A is a matrix or spmatrix of size (m, n) where
N = dims['l'] + sum(dims['q']) + sum( k**2 for k in dims['s'] )
representing a mapping from R^n to S.
If trans is 'N':
y := alpha*A*x + beta * y (trans = 'N').
x is a vector of length n. y is a vector of length N.
If trans is 'T':
y := alpha*A'*x + beta * y (trans = 'T').
x is a vector of length N. y is a vector of length n.
The 's' components in S are stored in unpacked 'L' storage.
*/
func sgemv(A, x, y *matrix.FloatMatrix, alpha, beta float64, dims *sets.DimensionSet, opts ...la_.Option) error {
m := dims.Sum("l", "q") + dims.SumSquared("s")
n := la_.GetIntOpt("n", -1, opts...)
if n == -1 {
n = A.Cols()
}
trans := la_.GetIntOpt("trans", int(la_.PNoTrans), opts...)
offsetX := la_.GetIntOpt("offsetx", 0, opts...)
offsetY := la_.GetIntOpt("offsety", 0, opts...)
offsetA := la_.GetIntOpt("offseta", 0, opts...)
if trans == int(la_.PTrans) && alpha != 0.0 {
trisc(x, dims, offsetX)
//fmt.Printf("trisc x=\n%v\n", x.ConvertToString())
}
//fmt.Printf("alpha=%.4f beta=%.4f m=%d n=%d\n", alpha, beta, m, n)
//fmt.Printf("A=\n%v\nx=\n%v\ny=\n%v\n", A, x.ConvertToString(), y.ConvertToString())
err := blas.GemvFloat(A, x, y, alpha, beta, &la_.IOpt{"trans", trans},
&la_.IOpt{"n", n}, &la_.IOpt{"m", m}, &la_.IOpt{"offseta", offsetA},
&la_.IOpt{"offsetx", offsetX}, &la_.IOpt{"offsety", offsetY})
//fmt.Printf("gemv y=\n%v\n", y.ConvertToString())
if trans == int(la_.PTrans) && alpha != 0.0 {
triusc(x, dims, offsetX)
}
return err
}
func CTestGemv(m, n, p int) (fnc func(), A, X, Y *matrix.FloatMatrix) {
A = matrix.FloatNormal(m, n)
X = matrix.FloatNormal(n, 1)
Y = matrix.FloatZeros(m, 1)
fnc = func() {
blas.GemvFloat(A, X, Y, 1.0, 1.0)
}
return
}
func (gp *gpConvexProg) F2(x, z *matrix.FloatMatrix) (f, Df, H *matrix.FloatMatrix, err error) {
err = nil
f = matrix.FloatZeros(gp.mnl+1, 1)
Df = matrix.FloatZeros(gp.mnl+1, gp.n)
H = matrix.FloatZeros(gp.n, gp.n)
y := gp.g.Copy()
Fsc := matrix.FloatZeros(gp.maxK, gp.n)
blas.GemvFloat(gp.F, x, y, 1.0, 1.0)
//fmt.Printf("y=\n%v\n", y.ToString("%.3f"))
for i, s := range gp.ind {
start := s[0]
stop := s[1]
// yi := exp(yi) = exp(Fi*x+gi)
ymax := maxvec(y.FloatArray()[start:stop])
ynew := matrix.Exp(matrix.FloatVector(y.FloatArray()[start:stop]).Add(-ymax))
y.SetIndexesFromArray(ynew.FloatArray(), matrix.Indexes(start, stop)...)
// fi = log sum yi = log sum exp(Fi*x+gi)
ysum := blas.AsumFloat(y, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
f.SetIndex(i, ymax+math.Log(ysum))
blas.ScalFloat(y, 1.0/ysum, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
blas.GemvFloat(gp.F, y, Df, 1.0, 0.0, la.OptTrans, &la.IOpt{"m", stop - start},
&la.IOpt{"incy", gp.mnl + 1}, &la.IOpt{"offseta", start},
&la.IOpt{"offsetx", start}, &la.IOpt{"offsety", i})
Fsc.SetSubMatrix(0, 0, gp.F.GetSubMatrix(start, 0, stop-start))
for k := start; k < stop; k++ {
blas.AxpyFloat(Df, Fsc, -1.0, &la.IOpt{"n", gp.n},
&la.IOpt{"incx", gp.mnl + 1}, &la.IOpt{"incy", Fsc.Rows()},
&la.IOpt{"offsetx", i}, &la.IOpt{"offsety", k - start})
blas.ScalFloat(Fsc, math.Sqrt(y.GetIndex(k)),
&la.IOpt{"inc", Fsc.Rows()}, &la.IOpt{"offset", k - start})
}
// H += z[i]*Hi = z[i] *Fisc' * Fisc
blas.SyrkFloat(Fsc, H, z.GetIndex(i), 1.0, la.OptTrans,
&la.IOpt{"k", stop - start})
}
return
}
func CTestGemvTransA(m, n, p int) (fnc func(), A, X, Y *matrix.FloatMatrix) {
A = matrix.FloatNormal(n, m)
X = matrix.FloatNormal(n, 1)
Y = matrix.FloatZeros(m, 1)
A = A.Transpose()
fnc = func() {
blas.GemvFloat(A, X, Y, 1.0, 1.0, linalg.OptTrans)
}
return
}
func _TestMultMVSmall(t *testing.T) {
bM := 5
bN := 4
A := matrix.FloatNormal(bM, bN)
X := matrix.FloatVector([]float64{1.0, 2.0, 3.0, 4.0})
Y1 := matrix.FloatZeros(bM, 1)
Y0 := matrix.FloatZeros(bM, 1)
Ar := A.FloatArray()
Xr := X.FloatArray()
Y1r := Y1.FloatArray()
blas.GemvFloat(A, X, Y0, 1.0, 1.0)
DMultMV(Y1r, Ar, Xr, 1.0, 1.0, NOTRANS, 1, A.LeadingIndex(), 1, 0, bN, 0, bM, 4, 4)
ok := Y0.AllClose(Y1)
t.Logf("Y0 == Y1: %v\n", ok)
if !ok {
t.Logf("blas: Y=A*X\n%v\n", Y0)
t.Logf("Y1: Y1 = A*X\n%v\n", Y1)
}
}
func TestMultMVTransASmall(t *testing.T) {
data6 := [][]float64{
[]float64{-1.59e+00, 6.56e-02, 2.14e-01, 6.79e-01, 2.93e-01, 5.24e-01},
[]float64{4.28e-01, 1.57e-01, 3.81e-01, 2.19e-01, 2.97e-01, 2.83e-02},
[]float64{3.02e-01, 9.70e-02, 3.18e-01, 2.03e-01, 7.53e-01, 1.58e-01},
[]float64{1.99e-01, 3.01e-01, 4.69e-01, 3.61e-01, 2.07e-01, 6.07e-01},
[]float64{1.93e-01, 5.15e-01, 2.83e-01, 5.71e-01, 8.65e-01, 9.75e-01},
[]float64{3.13e-01, 8.14e-01, 2.93e-01, 8.62e-01, 6.97e-01, 7.95e-02}}
data5 := [][]float64{
[]float64{1.57e-01, 3.81e-01, 2.19e-01, 2.97e-01, 2.83e-02},
[]float64{9.70e-02, 3.18e-01, 2.03e-01, 7.53e-01, 1.58e-01},
[]float64{3.01e-01, 4.69e-01, 3.61e-01, 2.07e-01, 6.07e-01},
[]float64{5.15e-01, 2.83e-01, 5.71e-01, 8.65e-01, 9.75e-01},
[]float64{8.14e-01, 2.93e-01, 8.62e-01, 6.97e-01, 7.95e-02}}
data2 := []float64{4.28e-01, 3.02e-01, 1.99e-01, 1.93e-01, 3.13e-01}
bM := 5
bN := 4
nb := 2
//A := matrix.FloatNormal(bN, bM)
//X := matrix.FloatWithValue(bN, 1, 1.0)
A := matrix.FloatMatrixFromTable(data5, matrix.RowOrder)
X := matrix.FloatNew(5, 1, data2)
bM = A.Rows()
bN = A.Cols()
Ym := matrix.FloatZeros(3, bM)
Y1 := matrix.FloatZeros(bM, 1)
Y0 := matrix.FloatZeros(bM, 1)
Ar := A.FloatArray()
Xr := X.FloatArray()
Y1r := Y1.FloatArray()
blas.GemvFloat(A, X, Y0, 1.0, 1.0, linalg.OptTrans)
DMultMV(Y1r, Ar, Xr, 1.0, 1.0, TRANSA, 1, A.LeadingIndex(), 1, 0, bN, 0, bM, nb, nb)
ok := Y0.AllClose(Y1)
t.Logf("Y0 == Y1: %v\n", ok)
if ok || !ok {
t.Logf("blas: Y=A.T*X\n%v\n", Y0)
t.Logf("Y1: Y1 = A*X\n%v\n", Y1)
}
// zero Y0, Y1
Y0.Scale(0.0)
Y1.Scale(0.0)
// test with matrix view; A is view
var A0 matrix.FloatMatrix
A6 := matrix.FloatMatrixFromTable(data6, matrix.RowOrder)
A0.SubMatrixOf(A6, 1, 1)
blas.GemvFloat(&A0, X, Y0, 1.0, 1.0, linalg.OptTrans)
Ar = A0.FloatArray()
DMultMV(Y1r, Ar, Xr, 1.0, 1.0, TRANSA, 1, A0.LeadingIndex(), 1, 0, bN, 0, bM, nb, nb)
ok = Y0.AllClose(Y1)
t.Logf("lda>rows: Y0 == Y1: %v\n", ok)
if ok || !ok {
t.Logf("blas: Y=A.T*X\n%v\n", Y0)
t.Logf("Y1: Y1 = A*X\n%v\n", Y1)
}
// Y is view too.
Y1.SubMatrixOf(Ym, 0, 0, 1, bM)
Y1r = Y1.FloatArray()
DMultMV(Y1r, Ar, Xr, 1.0, 1.0, TRANSA, Y1.LeadingIndex(), A0.LeadingIndex(), 1, 0, bN, 0, bM, nb, nb)
ok = Y0.AllClose(Y1.Transpose())
t.Logf("Y0 == Y1 row: %v\n", ok)
t.Logf("row Y1: %v\n", Y1)
}
func CheckTransA(A, X, Y *matrix.FloatMatrix) {
blas.GemvFloat(A, X, Y, 1.0, 1.0, linalg.OptTrans)
}
func CheckNoTrans(A, X, Y *matrix.FloatMatrix) {
blas.GemvFloat(A, X, Y, 1.0, 1.0)
}
/*
Applies Nesterov-Todd scaling or its inverse.
Computes
x := W*x (trans is false 'N', inverse = false 'N')
x := W^T*x (trans is true 'T', inverse = false 'N')
x := W^{-1}*x (trans is false 'N', inverse = true 'T')
x := W^{-T}*x (trans is true 'T', inverse = true 'T').
x is a dense float matrix.
W is a MatrixSet with entries:
- W['dnl']: positive vector
- W['dnli']: componentwise inverse of W['dnl']
- W['d']: positive vector
- W['di']: componentwise inverse of W['d']
- W['v']: lists of 2nd order cone vectors with unit hyperbolic norms
- W['beta']: list of positive numbers
- W['r']: list of square matrices
- W['rti']: list of square matrices. rti[k] is the inverse transpose
of r[k].
The 'dnl' and 'dnli' entries are optional, and only present when the
function is called from the nonlinear solver.
*/
func scale(x *matrix.FloatMatrix, W *sets.FloatMatrixSet, trans, inverse bool) (err error) {
/*DEBUGGED*/
var wl []*matrix.FloatMatrix
var w *matrix.FloatMatrix
ind := 0
err = nil
// var minor int = 0
//if ! checkpnt.MinorEmpty() {
// minor = checkpnt.MinorTop()
//}
//fmt.Printf("\n%d.%04d scaling x=\n%v\n", checkpnt.Major(), minor, x.ToString("%.17f"))
// Scaling for nonlinear component xk is xk := dnl .* xk; inverse
// scaling is xk ./ dnl = dnli .* xk, where dnl = W['dnl'],
// dnli = W['dnli'].
if wl = W.At("dnl"); wl != nil {
if inverse {
w = W.At("dnli")[0]
} else {
w = W.At("dnl")[0]
}
for k := 0; k < x.Cols(); k++ {
err = blas.TbmvFloat(w, x, &la_.IOpt{"n", w.Rows()}, &la_.IOpt{"k", 0},
&la_.IOpt{"lda", 1}, &la_.IOpt{"offsetx", k * x.Rows()})
if err != nil {
//fmt.Printf("1. TbmvFloat: %v\n", err)
return
}
}
ind += w.Rows()
}
//if ! checkpnt.MinorEmpty() {
// checkpnt.Check("000scale", minor)
//}
// Scaling for linear 'l' component xk is xk := d .* xk; inverse
// scaling is xk ./ d = di .* xk, where d = W['d'], di = W['di'].
if inverse {
w = W.At("di")[0]
} else {
w = W.At("d")[0]
}
for k := 0; k < x.Cols(); k++ {
err = blas.TbmvFloat(w, x, &la_.IOpt{"n", w.Rows()}, &la_.IOpt{"k", 0},
&la_.IOpt{"lda", 1}, &la_.IOpt{"offsetx", k*x.Rows() + ind})
if err != nil {
//fmt.Printf("2. TbmvFloat: %v\n", err)
return
}
}
ind += w.Rows()
//if ! checkpnt.MinorEmpty() {
// checkpnt.Check("010scale", minor)
//}
// Scaling for 'q' component is
//
// xk := beta * (2*v*v' - J) * xk
// = beta * (2*v*(xk'*v)' - J*xk)
//
// where beta = W['beta'][k], v = W['v'][k], J = [1, 0; 0, -I].
//
//Inverse scaling is
//
// xk := 1/beta * (2*J*v*v'*J - J) * xk
// = 1/beta * (-J) * (2*v*((-J*xk)'*v)' + xk).
//wf := matrix.FloatZeros(x.Cols(), 1)
w = matrix.FloatZeros(x.Cols(), 1)
for k, v := range W.At("v") {
m := v.Rows()
if inverse {
blas.ScalFloat(x, -1.0, &la_.IOpt{"offset", ind}, &la_.IOpt{"inc", x.Rows()})
}
err = blas.GemvFloat(x, v, w, 1.0, 0.0, la_.OptTrans, &la_.IOpt{"m", m},
&la_.IOpt{"n", x.Cols()}, &la_.IOpt{"offsetA", ind},
&la_.IOpt{"lda", x.Rows()})
if err != nil {
//fmt.Printf("3. GemvFloat: %v\n", err)
return
}
err = blas.ScalFloat(x, -1.0, &la_.IOpt{"offset", ind}, &la_.IOpt{"inc", x.Rows()})
if err != nil {
return
}
err = blas.GerFloat(v, w, x, 2.0, &la_.IOpt{"m", m},
&la_.IOpt{"n", x.Cols()}, &la_.IOpt{"lda", x.Rows()},
&la_.IOpt{"offsetA", ind})
if err != nil {
//fmt.Printf("4. GerFloat: %v\n", err)
return
}
var a float64
if inverse {
blas.ScalFloat(x, -1.0,
&la_.IOpt{"offset", ind}, &la_.IOpt{"inc", x.Rows()})
// a[i,j] := 1.0/W[i,j]
a = 1.0 / W.At("beta")[0].GetIndex(k)
} else {
a = W.At("beta")[0].GetIndex(k)
}
for i := 0; i < x.Cols(); i++ {
blas.ScalFloat(x, a, &la_.IOpt{"n", m}, &la_.IOpt{"offset", ind + i*x.Rows()})
}
ind += m
}
//if ! checkpnt.MinorEmpty() {
// checkpnt.Check("020scale", minor)
//}
// Scaling for 's' component xk is
//
// xk := vec( r' * mat(xk) * r ) if trans = 'N'
// xk := vec( r * mat(xk) * r' ) if trans = 'T'.
//
// r is kth element of W['r'].
//
// Inverse scaling is
//
// xk := vec( rti * mat(xk) * rti' ) if trans = 'N'
// xk := vec( rti' * mat(xk) * rti ) if trans = 'T'.
//
// rti is kth element of W['rti'].
maxn := 0
for _, r := range W.At("r") {
if r.Rows() > maxn {
maxn = r.Rows()
}
}
a := matrix.FloatZeros(maxn, maxn)
for k, v := range W.At("r") {
t := trans
var r *matrix.FloatMatrix
if !inverse {
r = v
t = !trans
} else {
r = W.At("rti")[k]
}
n := r.Rows()
for i := 0; i < x.Cols(); i++ {
// scale diagonal of xk by 0.5
blas.ScalFloat(x, 0.5, &la_.IOpt{"offset", ind + i*x.Rows()},
&la_.IOpt{"inc", n + 1}, &la_.IOpt{"n", n})
// a = r*tril(x) (t is 'N') or a = tril(x)*r (t is 'T')
blas.Copy(r, a)
if !t {
err = blas.TrmmFloat(x, a, 1.0, la_.OptRight, &la_.IOpt{"m", n},
&la_.IOpt{"n", n}, &la_.IOpt{"lda", n}, &la_.IOpt{"ldb", n},
&la_.IOpt{"offsetA", ind + i*x.Rows()})
if err != nil {
//fmt.Printf("5. TrmmFloat: %v\n", err)
return
}
// x := (r*a' + a*r') if t is 'N'
err = blas.Syr2kFloat(r, a, x, 1.0, 0.0, la_.OptNoTrans, &la_.IOpt{"n", n},
&la_.IOpt{"k", n}, &la_.IOpt{"ldb", n}, &la_.IOpt{"ldc", n},
&la_.IOpt{"offsetC", ind + i*x.Rows()})
if err != nil {
//fmt.Printf("6. Syr2kFloat: %v\n", err)
return
}
} else {
err = blas.TrmmFloat(x, a, 1.0, la_.OptLeft, &la_.IOpt{"m", n},
&la_.IOpt{"n", n}, &la_.IOpt{"lda", n}, &la_.IOpt{"ldb", n},
&la_.IOpt{"offsetA", ind + i*x.Rows()})
if err != nil {
//fmt.Printf("7. TrmmFloat: %v\n", err)
return
}
// x := (r'*a + a'*r) if t is 'T'
err = blas.Syr2kFloat(r, a, x, 1.0, 0.0, la_.OptTrans, &la_.IOpt{"n", n},
&la_.IOpt{"k", n}, &la_.IOpt{"ldb", n}, &la_.IOpt{"ldc", n},
&la_.IOpt{"offsetC", ind + i*x.Rows()})
if err != nil {
//fmt.Printf("8. Syr2kFloat: %v\n", err)
return
}
}
}
ind += n * n
}
//if ! checkpnt.MinorEmpty() {
// checkpnt.Check("030scale", minor)
//}
return
}
func (a *matrixA) Af(x, y *matrix.FloatMatrix, alpha, beta float64, trans la.Option) error {
return blas.GemvFloat(a.mA, x, y, alpha, beta, trans)
}