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)
}
*/
}
func runTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {
var W *matrix.FloatMatrix = nil
var mintime time.Duration
N := A.Cols()
tau := matrix.FloatZeros(N, 1)
if LB > 0 {
W = matrix.FloatZeros(A.Rows(), LB)
}
fnc := func() {
_, ERRmatops = matops.DecomposeQR(A, tau, W, LB)
}
A0 := A.Copy()
for n := 0; n < ntest; n++ {
if n > 0 {
// restore original A
A0.CopyTo(A)
tau.Scale(0.0)
}
mperf.FlushCache()
time0 := mperf.Timeit(fnc)
if n == 0 || time0 < mintime {
mintime = time0
}
if verbose {
fmt.Printf("%.4f ms\n", time0.Seconds()*1000.0)
}
}
return mintime
}
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 _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 _TestMultSymmLowerSmall(t *testing.T) {
//bM := 5
bN := 7
bP := 7
Adata := [][]float64{
[]float64{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
[]float64{1.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0},
[]float64{1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 0.0},
[]float64{1.0, 2.0, 3.0, 4.0, 0.0, 0.0, 0.0},
[]float64{1.0, 2.0, 3.0, 4.0, 5.0, 0.0, 0.0},
[]float64{1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 0.0},
[]float64{1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0}}
A := matrix.FloatMatrixFromTable(Adata, matrix.RowOrder)
B := matrix.FloatNormal(bN, bP)
C0 := matrix.FloatZeros(bN, bP)
C1 := matrix.FloatZeros(bN, bP)
Ar := A.FloatArray()
Br := B.FloatArray()
C1r := C1.FloatArray()
blas.SymmFloat(A, B, C0, 1.0, 1.0, linalg.OptLower, linalg.OptRight)
DMultSymm(C1r, Ar, Br, 1.0, 1.0, LOWER|RIGHT, bN, A.LeadingIndex(), bN,
bN, 0, bP, 0, bN, 2, 2, 2)
ok := C0.AllClose(C1)
t.Logf("C0 == C1: %v\n", ok)
if !ok {
t.Logf("A=\n%v\n", A)
t.Logf("blas: C=A*B\n%v\n", C0)
t.Logf("C1: C1 = A*X\n%v\n", C1)
}
}
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 TestUpdateTrmMV(t *testing.T) {
//bM := 5
bN := 8
//bP := 4
nb := 4
X := matrix.FloatNormal(bN, 1)
//B := matrix.FloatNormal(bP, bN)
Y := X.Copy()
C0 := matrix.FloatZeros(bN, bN)
C2 := matrix.FloatZeros(bN, bN)
C1 := matrix.FloatZeros(bN, bN)
Xr := X.FloatArray()
Yr := Y.FloatArray()
C1r := C1.FloatArray()
C0r := C0.FloatArray()
C2r := C2.FloatArray()
// no transpose
DRankMV(C1r, Xr, Yr, 1.0, C1.LeadingIndex(), 1, 1,
0, bN, 0, bN, nb, nb)
DTrmUpdMV(C0r, Xr, Yr, 1.0, LOWER, C0.LeadingIndex(), 1, 1,
0, bN, nb)
DTrmUpdMV(C2r, Xr, Yr, 1.0, UPPER, C2.LeadingIndex(), 1, 1,
0, bN, nb)
t.Logf("C1:\n%v\nC0:\n%v\nC2:\n%v\n", C1, C0, C2)
// C0 == C2.T
t.Logf("C0 == C2.T: %v\n", C0.AllClose(C2.Transpose()))
// C1 == C1 - C2 + C0.T
Cn := matrix.Minus(C1, C2)
Cn.Plus(C0.Transpose())
t.Logf("C1 == C1 - C2 + C0.T: %v\n", Cn.AllClose(C1))
}
func TestQRSmal(t *testing.T) {
data := [][]float64{
[]float64{12.0, -51.0, 4.0},
[]float64{6.0, 167.0, -68.0},
[]float64{-4.0, 24.0, -41.0}}
A := matrix.FloatMatrixFromTable(data, matrix.RowOrder)
T := matrix.FloatZeros(A.Cols(), A.Cols())
T0 := T.Copy()
M := A.Rows()
//N := A.Cols()
Tau := matrix.FloatZeros(M, 1)
X, _ := DecomposeQR(A.Copy(), Tau, nil, 0)
t.Logf("A\n%v\n", A)
t.Logf("X\n%v\n", X)
t.Logf("Tau\n%v\n", Tau)
Tau0 := matrix.FloatZeros(M, 1)
lapack.Geqrf(A, Tau0)
t.Logf("lapack X\n%v\n", A)
t.Logf("lapack Tau\n%v\n", Tau0)
unblkQRBlockReflector(X, Tau, T)
t.Logf("T:\n%v\n", T)
V := TriLU(X.Copy())
lapack.LarftFloat(V, Tau, T0)
t.Logf("T0:\n%v\n", T0)
}
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 main() {
flag.Parse()
if len(spPath) > 0 {
checkpnt.Reset(spPath)
checkpnt.Activate()
checkpnt.Verbose(spVerbose)
checkpnt.Format("%.17f")
}
adata := [][]float64{
[]float64{0.3, -0.4, -0.2, -0.4, 1.3},
[]float64{0.6, 1.2, -1.7, 0.3, -0.3},
[]float64{-0.3, 0.0, 0.6, -1.2, -2.0}}
A := matrix.FloatMatrixFromTable(adata, matrix.ColumnOrder)
b := matrix.FloatVector([]float64{1.5, 0.0, -1.2, -0.7, 0.0})
_, n := A.Size()
N := n + 1 + n
h := matrix.FloatZeros(N, 1)
h.SetIndex(n, 1.0)
I0 := matrix.FloatDiagonal(n, -1.0)
I1 := matrix.FloatIdentity(n)
G, _ := matrix.FloatMatrixStacked(matrix.StackDown, I0, matrix.FloatZeros(1, n), I1)
At := A.Transpose()
P := At.Times(A)
q := At.Times(b).Scale(-1.0)
dims := sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{n})
dims.Set("q", []int{n + 1})
var solopts cvx.SolverOptions
solopts.MaxIter = 20
solopts.ShowProgress = true
if maxIter > 0 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
sol, err := cvx.ConeQp(P, q, G, h, nil, nil, dims, &solopts, nil)
if err == nil {
x := sol.Result.At("x")[0]
s := sol.Result.At("s")[0]
z := sol.Result.At("z")[0]
fmt.Printf("Optimal\n")
fmt.Printf("x=\n%v\n", x.ToString("%.9f"))
fmt.Printf("s=\n%v\n", s.ToString("%.9f"))
fmt.Printf("z=\n%v\n", z.ToString("%.9f"))
check(x, s, z)
}
}
//
// Solves a geometric program
//
// minimize log sum exp (F0*x+g0)
// subject to log sum exp (Fi*x+gi) <= 0, i=1,...,m
// G*x <= h
// A*x = b
//
func Gp(K []int, F, g, G, h, A, b *matrix.FloatMatrix, solopts *SolverOptions) (sol *Solution, err error) {
if err = checkArgK(K); err != nil {
return
}
l := sumdim(K)
if F == nil || F.Rows() != l {
err = errors.New(fmt.Sprintf("'F' must matrix with %d rows", l))
return
}
if g == nil || !g.SizeMatch(l, 1) {
err = errors.New(fmt.Sprintf("'g' must matrix with size (%d,1)", l))
return
}
n := F.Cols()
if G == nil {
G = matrix.FloatZeros(0, n)
}
if h == nil {
h = matrix.FloatZeros(0, 1)
}
if G.Cols() != n {
err = errors.New(fmt.Sprintf("'G' must matrix with size %d columns", n))
return
}
ml := G.Rows()
if h == nil || !h.SizeMatch(ml, 1) {
err = errors.New(fmt.Sprintf("'h' must matrix with size (%d,1)", ml))
return
}
if A == nil {
A = matrix.FloatZeros(0, n)
}
if b == nil {
b = matrix.FloatZeros(0, 1)
}
if A.Cols() != n {
err = errors.New(fmt.Sprintf("'A' must matrix with size %d columns", n))
return
}
p := A.Rows()
if b == nil || !b.SizeMatch(p, 1) {
err = errors.New(fmt.Sprintf("'b' must matrix with size (%d,1)", p))
return
}
dims := sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{ml})
gpProg := createGpProg(K, F, g)
return Cp(gpProg, G, h, A, b, dims, solopts)
}
// Returns min {t | x + t*e >= 0}, where e is defined as follows
//
// - For the nonlinear and 'l' blocks: e is the vector of ones.
// - For the 'q' blocks: e is the first unit vector.
// - For the 's' blocks: e is the identity matrix.
//
// When called with the argument sigma, also returns the eigenvalues
// (in sigma) and the eigenvectors (in x) of the 's' components of x.
func maxStep(x *matrix.FloatMatrix, dims *sets.DimensionSet, mnl int, sigma *matrix.FloatMatrix) (rval float64, err error) {
/*DEBUGGED*/
rval = 0.0
err = nil
t := make([]float64, 0, 10)
ind := mnl + dims.Sum("l")
if ind > 0 {
t = append(t, -minvec(x.FloatArray()[:ind]))
}
for _, m := range dims.At("q") {
if m > 0 {
v := blas.Nrm2Float(x, &la_.IOpt{"offset", ind + 1}, &la_.IOpt{"n", m - 1})
v -= x.GetIndex(ind)
t = append(t, v)
}
ind += m
}
//var Q *matrix.FloatMatrix
//var w *matrix.FloatMatrix
ind2 := 0
//if sigma == nil && len(dims.At("s")) > 0 {
// mx := dims.Max("s")
// Q = matrix.FloatZeros(mx, mx)
// w = matrix.FloatZeros(mx, 1)
//}
for _, m := range dims.At("s") {
if sigma == nil {
Q := matrix.FloatZeros(m, m)
w := matrix.FloatZeros(m, 1)
blas.Copy(x, Q, &la_.IOpt{"offsetx", ind}, &la_.IOpt{"n", m * m})
err = lapack.SyevrFloat(Q, w, nil, 0.0, nil, []int{1, 1}, la_.OptRangeInt,
&la_.IOpt{"n", m}, &la_.IOpt{"lda", m})
if m > 0 && err == nil {
t = append(t, -w.GetIndex(0))
}
} else {
err = lapack.SyevdFloat(x, sigma, la_.OptJobZValue, &la_.IOpt{"n", m},
&la_.IOpt{"lda", m}, &la_.IOpt{"offseta", ind}, &la_.IOpt{"offsetw", ind2})
if m > 0 {
t = append(t, -sigma.GetIndex(ind2))
}
}
ind += m * m
ind2 += m
}
if len(t) > 0 {
rval = maxvec(t)
}
return
}
// single invocation for matops and lapack functions
func runCheck(A *matrix.FloatMatrix, LB int) (bool, time.Duration, time.Duration) {
var W *matrix.FloatMatrix = nil
N := A.Cols()
tau := matrix.FloatZeros(N, 1)
if LB > 0 {
W = matrix.FloatZeros(A.Rows(), LB)
}
fnc := func() {
_, ERRmatops = matops.DecomposeQR(A, tau, W, LB)
}
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "A start:\n%v\n", A)
}
A0 := A.Copy()
tau0 := tau.Copy()
mperf.FlushCache()
time0 := mperf.Timeit(fnc)
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "A end:\n%v\n", A)
tau.SetSize(1, N, 1)
fmt.Fprintf(os.Stderr, "tau: %v\n", tau)
}
fn2 := func() {
ERRlapack = lapack.Geqrf(A0, tau0)
}
mperf.FlushCache()
time2 := mperf.Timeit(fn2)
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "A0 end:\n%v\n", A0)
tau0.SetSize(1, N, 1) // row vector
fmt.Fprintf(os.Stderr, "tau0: %v\n", tau0)
}
// now A == A0 && tau == tau0
ok := A.AllClose(A0)
oktau := tau.AllClose(tau0)
if !ok || !oktau {
// save result to globals
Rlapack = A0
Rmatops = A
TAUlapack = tau0
TAUmatops = tau
}
return ok && oktau, time0, time2
}
func _TestBK2U(t *testing.T) {
Bdata := [][]float64{
[]float64{10.0, 20.0},
[]float64{10.0, 20.0},
[]float64{10.0, 20.0},
[]float64{10.0, 20.0},
[]float64{10.0, 20.0},
[]float64{10.0, 20.0},
[]float64{10.0, 20.0}}
N := 7
A0 := matrix.FloatNormal(N, N)
A := matrix.FloatZeros(N, N)
// A is symmetric, posivite definite
Mult(A, A0, A0, 1.0, 1.0, TRANSB)
X := matrix.FloatMatrixFromTable(Bdata, matrix.RowOrder)
B := matrix.FloatZeros(N, 2)
MultSym(B, A, X, 1.0, 0.0, LOWER|LEFT)
t.Logf("initial B:\n%v\n", B)
nb := 0
W := matrix.FloatWithValue(A.Rows(), 5, 1.0)
A.SetAt(4, 1, A.GetAt(4, 1)+1.0)
A.SetAt(1, 4, A.GetAt(4, 1))
ipiv := make([]int, N, N)
L, _ := DecomposeBK(A.Copy(), W, ipiv, LOWER, nb)
t.Logf("ipiv: %v\n", ipiv)
t.Logf("L:\n%v\n", L)
ipiv0 := make([]int, N, N)
nb = 4
L0, _ := DecomposeBK(A.Copy(), W, ipiv0, LOWER, nb)
t.Logf("ipiv: %v\n", ipiv0)
t.Logf("L:\n%v\n", L0)
B0 := B.Copy()
SolveBK(B0, L0, ipiv0, LOWER)
t.Logf("B0:\n%v\n", B0)
ipiv2 := make([]int32, N, N)
lapack.Sytrf(A, ipiv2, linalg.OptLower)
t.Logf("ipiv2: %v\n", ipiv2)
t.Logf("lapack A:\n%v\n", A)
lapack.Sytrs(A, B, ipiv2, linalg.OptLower)
t.Logf("lapack B:\n%v\n", B)
t.Logf("B == B0: %v\n", B.AllClose(B0))
}
// In-place version of pack(), which also accepts matrix arguments x.
// The columns of x are elements of S, with the 's' components stored
// in unpacked storage. On return, the 's' components are stored in
// packed storage and the off-diagonal entries are scaled by sqrt(2).
//
func pack2(x *matrix.FloatMatrix, dims *sets.DimensionSet, mnl int) (err error) {
if len(dims.At("s")) == 0 {
return nil
}
const sqrt2 = 1.41421356237309504880
iu := mnl + dims.Sum("l", "q")
ip := iu
row := matrix.FloatZeros(1, x.Cols())
//fmt.Printf("x.size = %d %d\n", x.Rows(), x.Cols())
for _, n := range dims.At("s") {
for k := 0; k < n; k++ {
cnt := n - k
row = x.GetRow(iu+(n+1)*k, row)
//fmt.Printf("%02d: %v\n", iu+(n+1)*k, x.FloatArray())
x.SetRow(ip, row)
for i := 1; i < n-k; i++ {
row = x.GetRow(iu+(n+1)*k+i, row)
//fmt.Printf("%02d: %v\n", iu+(n+1)*k+i, x.FloatArray())
x.SetRow(ip+i, row.Scale(sqrt2))
}
ip += cnt
}
iu += n * n
}
return nil
}
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 MakeData(M, N, P int, randomData, diagonal bool) (A, B, C *matrix.FloatMatrix) {
if diagonal && M != N {
diagonal = false
fmt.Printf("cannot make diagonal if B.rows != B.cols\n")
}
if randomData {
A = matrix.FloatNormal(M, P)
if diagonal {
d := matrix.FloatNormal(P, 1)
B := matrix.FloatDiagonal(P, 0.0)
B.SetIndexesFromArray(d.FloatArray(), matrix.DiagonalIndexes(B)...)
} else {
B = matrix.FloatNormal(P, N)
}
} else {
A = matrix.FloatWithValue(M, P, 1.0)
if diagonal {
B = matrix.FloatDiagonal(P, 1.0)
} else {
B = matrix.FloatWithValue(P, N, 1.0)
}
}
C = matrix.FloatZeros(M, N)
return
}
func runTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {
var flags matops.Flags
var mintime time.Duration
N := A.Rows()
ipiv := make([]int, N, N)
flags = matops.LOWER
if testUpper {
flags = matops.UPPER
}
W := matrix.FloatZeros(A.Rows(), LB+2)
fnc := func() {
_, ERRmatops = matops.DecomposeBK(A, W, ipiv, flags, LB)
}
A0 := A.Copy()
for n := 0; n < ntest; n++ {
if n > 0 {
// restore original A
A0.CopyTo(A)
}
mperf.FlushCache()
time0 := mperf.Timeit(fnc)
if n == 0 || time0 < mintime {
mintime = time0
}
if verbose {
fmt.Printf("%.4f ms\n", time0.Seconds()*1000.0)
}
}
return mintime
}
func runRefTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {
var mintime time.Duration
N := A.Cols()
tau := matrix.FloatZeros(N, 1)
fnc := func() {
ERRlapack = lapack.Geqrf(A, tau)
}
A0 := A.Copy()
for n := 0; n < ntest; n++ {
if n > 0 {
// restore original A
A0.CopyTo(A)
tau.Scale(0.0)
}
mperf.FlushCache()
time0 := mperf.Timeit(fnc)
if n == 0 || time0 < mintime {
mintime = time0
}
}
return mintime
}
func runRefTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {
var flags matops.Flags
var mintime time.Duration
N := A.Rows()
ipiv := make([]int, N, N)
flags = matops.LOWER
if testUpper {
flags = matops.UPPER
}
W := matrix.FloatZeros(A.Rows(), LB+2)
fnc := func() {
_, ERRref = matops.DecomposeLDL(A, W, ipiv, flags, 0)
}
A0 := A.Copy()
for n := 0; n < ntest; n++ {
if n > 0 {
// restore original A
A0.CopyTo(A)
}
mperf.FlushCache()
time0 := mperf.Timeit(fnc)
if n == 0 || time0 < mintime {
mintime = time0
}
}
return mintime
}
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 blockedBuildQ(A, tau, W *matrix.FloatMatrix, nb int) error {
var err error = nil
var ATL, ATR, ABL, ABR, AL matrix.FloatMatrix
var A00, A01, A02, A10, A11, A12, A20, A21, A22 matrix.FloatMatrix
var tT, tB matrix.FloatMatrix
var t0, tau1, t2, Tw, Wrk matrix.FloatMatrix
var mb int
mb = A.Rows() - A.Cols()
Twork := matrix.FloatZeros(nb, nb)
partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, mb, 0, pBOTTOMRIGHT)
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,
&A10, &A11, &A12,
&A20, &A21, &A22, A, nb, pTOPLEFT)
repartition2x1to3x1(&tT,
&t0,
&tau1,
&t2, tau, nb, pTOP)
// --------------------------------------------------------
// build block reflector from current block
merge2x1(&AL, &A11, &A21)
Twork.SubMatrix(&Tw, 0, 0, A11.Cols(), A11.Cols())
unblkQRBlockReflector(&Tw, &AL, &tau1)
// update with current block reflector (I - Y*T*Y.T)*Atrailing
W.SubMatrix(&Wrk, 0, 0, A12.Cols(), A11.Cols())
updateWithQT(&A12, &A22, &A11, &A21, &Tw, &Wrk, nb, false)
// use unblocked version to compute current block
W.SubMatrix(&Wrk, 0, 0, 1, A11.Cols())
unblockedBuildQ(&AL, &tau1, &Wrk, 0)
// zero upper part
A01.SetIndexes(0.0)
// --------------------------------------------------------
continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &A11, &A22, A, pTOPLEFT)
continue3x1to2x1(
&tT,
&tB, &t0, &tau1, tau, pTOP)
}
return err
}
func (p *floorPlan) F0() (mnl int, x0 *matrix.FloatMatrix, err error) {
err = nil
mnl = 5
x0 = matrix.FloatZeros(22, 1)
// set last 5 elements to 1.0
x0.SetIndexes(1.0, -1, -2, -3, -4, -5)
return
}
// Solves a quadratic program
//
// minimize (1/2)*x'*P*x + q'*x
// subject to G*x <= h
// A*x = b.
//
//
func Qp(P, q, G, h, A, b *matrix.FloatMatrix, solopts *SolverOptions,
initvals *sets.FloatMatrixSet) (sol *Solution, err error) {
sol = nil
if P == nil || P.Rows() != P.Cols() {
err = errors.New("'P' must a non-nil square matrix")
return
}
if q == nil {
err = errors.New("'q' must a non-nil matrix")
return
}
if q.Rows() != P.Rows() || q.Cols() > 1 {
err = errors.New(fmt.Sprintf("'q' must be matrix of size (%d,1)", P.Rows()))
return
}
if G == nil {
G = matrix.FloatZeros(0, P.Rows())
}
if G.Cols() != P.Rows() {
err = errors.New(fmt.Sprintf("'G' must be matrix of %d columns", P.Rows()))
return
}
if h == nil {
h = matrix.FloatZeros(G.Rows(), 1)
}
if h.Rows() != G.Rows() || h.Cols() > 1 {
err = errors.New(fmt.Sprintf("'h' must be matrix of size (%d,1)", G.Rows()))
return
}
if A == nil {
A = matrix.FloatZeros(0, P.Rows())
}
if A.Cols() != P.Rows() {
err = errors.New(fmt.Sprintf("'A' must be matrix of %d columns", P.Rows()))
return
}
if b == nil {
b = matrix.FloatZeros(A.Rows(), 1)
}
if b.Rows() != A.Rows() {
err = errors.New(fmt.Sprintf("'b' must be matrix of size (%d,1)", A.Rows()))
return
}
return ConeQp(P, q, G, h, A, b, nil, solopts, initvals)
}
func TestTemplate(m, n, p int) (fnc func(), A, B, C *matrix.FloatMatrix) {
A = matrix.FloatNormal(m, p)
B = matrix.FloatNormal(p, n)
C = matrix.FloatZeros(m, n)
fnc = func() {
// test core here
}
return
}
func CTestMVMultTransA(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)
fnc = func() {
matops.MVMultTransA(Y, A, X, 1.0, 1.0)
}
return
}
func TestTemplate(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() {
// test core here
}
return
}
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 MMTestMultTransAB(m, n, p int) (fnc func(), A, B, C *matrix.FloatMatrix) {
A = matrix.FloatNormal(p, m)
B = matrix.FloatNormal(n, p)
C = matrix.FloatZeros(m, n)
fnc = func() {
matops.Mult(C, A, B, 1.0, 1.0, matops.TRANSA|matops.TRANSB)
}
return
}