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 (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 _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 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 _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 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 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 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 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
}
//
// 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 _TestBK2(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))
}
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 _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 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
}
// 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 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 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 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)
}
// 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 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
}
/*
* Compute QR factorization of a M-by-N matrix A: A = Q * R.
*
* Arguments:
* A On entry, the M-by-N matrix A. On exit, the elements on and above
* the diagonal contain the min(M,N)-by-N upper trapezoidal matrix R.
* The elements below the diagonal with the column vector 'tau', represent
* the ortogonal matrix Q as product of elementary reflectors.
*
* tau On exit, the scalar factors of the elemenentary reflectors.
*
* W Workspace, N-by-nb matrix used for work space in blocked invocations.
*
* nb The block size used in blocked invocations. If nb is zero on N <= nb
* unblocked algorithm is used.
*
* Returns:
* Decomposed matrix A and error indicator.
*
* DecomposeQR is compatible with lapack.DGEQRF
*/
func DecomposeQR(A, tau, W *matrix.FloatMatrix, nb int) (*matrix.FloatMatrix, error) {
var err error = nil
if nb == 0 || A.Cols() <= nb {
unblockedQR(A, tau)
} else {
Twork := matrix.FloatZeros(nb, nb)
if W == nil {
W = matrix.FloatZeros(A.Cols(), nb)
} else if W.Cols() < nb || W.Rows() < A.Cols() {
return nil, errors.New("work space too small")
}
var Wrk matrix.FloatMatrix
Wrk.SubMatrixOf(W, 0, 0, A.Cols(), nb)
blockedQR(A, tau, Twork, &Wrk, nb)
}
return A, err
}
func CTestBlasUp(m, n, p int) (fnc func(), A, B, C *matrix.FloatMatrix) {
A = matrix.FloatNormalSymmetric(m, matrix.Lower)
B = matrix.FloatNormal(m, n)
C = matrix.FloatZeros(m, n)
fnc = func() {
blas.SymmFloat(A, B, C, 1.0, 1.0, linalg.OptUpper)
}
return fnc, A, B, C
}
func CTestSymmLower(m, n, p int) (fnc func(), A, B, C *matrix.FloatMatrix) {
A = matrix.FloatNormalSymmetric(m, matrix.Upper)
B = matrix.FloatNormal(m, n)
C = matrix.FloatZeros(m, n)
fnc = func() {
matops.MultSym(C, A, B, 1.0, 1.0, matops.LEFT|matops.LOWER)
}
return fnc, A, B, C
}
func TestTemplate(m, n, p int) (fnc func(), A, B, C *matrix.FloatMatrix) {
A = matrix.FloatNormalSymmetric(m, matrix.Upper)
B = matrix.FloatNormal(m, n)
C = matrix.FloatZeros(m, n)
fnc = func() {
// test core here
}
return
}