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 TestVectors(t *testing.T) {
a := matrix.FloatWithValue(1, 5, 1.0)
b := matrix.FloatWithValue(1, 5, 2.0)
c := matrix.FloatWithValue(5, 1, 2.0)
ar := a.FloatArray()
br := b.FloatArray()
cr := c.FloatArray()
v := DDot(ar, br, 1.0, a.LeadingIndex(), b.LeadingIndex(), a.NumElements())
t.Logf("a*b = %.1f\n", v)
v = DDot(cr, br, 1.0, 1, b.LeadingIndex(), c.NumElements())
t.Logf("c*b = %.1f\n", v)
v = DNorm2(br, 1, b.NumElements())
t.Logf("norm2(b) = %.1f\n", v)
b0 := matrix.FloatNew(1, 5, []float64{-1.0, 0.0, 2.0, -3.0, 5.0})
br = b0.FloatArray()
ix := DIAMax(br, 1, b0.NumElements())
t.Logf("iamax = %d: %.1f %v\n", ix, b0.GetIndex(ix), b0)
b0 = matrix.FloatNew(1, 5, []float64{-8.0, 0.0, 2.0, -3.0, 5.0})
br = b0.FloatArray()
ix = DIAMax(br, 1, b0.NumElements())
t.Logf("iamax = %d: %.1f %v\n", ix, b0.GetIndex(ix), b0)
b0 = matrix.FloatNew(1, 5, []float64{-8.0, 0.0, 2.0, -9.0, 5.0})
br = b0.FloatArray()
ix = DIAMax(br, 1, b0.NumElements())
t.Logf("iamax = %d: %.1f %v\n", ix, b0.GetIndex(ix), b0)
}
func trmmTest(t *testing.T, A *matrix.FloatMatrix, flags Flags, nb int) bool {
var B0 *matrix.FloatMatrix
N := A.Cols()
S := 0
E := A.Cols()
side := linalg.OptLeft
if flags&RIGHT != 0 {
B0 = matrix.FloatWithValue(2, A.Rows(), 2.0)
side = linalg.OptRight
E = B0.Rows()
} else {
B0 = matrix.FloatWithValue(A.Rows(), 2, 2.0)
E = B0.Cols()
}
B1 := B0.Copy()
trans := linalg.OptNoTrans
if flags&TRANSA != 0 {
trans = linalg.OptTransA
}
diag := linalg.OptNonUnit
if flags&UNIT != 0 {
diag = linalg.OptUnit
}
uplo := linalg.OptUpper
if flags&LOWER != 0 {
uplo = linalg.OptLower
}
blas.TrmmFloat(A, B0, 1.0, uplo, diag, trans, side)
if A.Rows() < 8 {
//t.Logf("..A\n%v\n", A)
t.Logf(" BLAS B0:\n%v\n", B0)
}
Ar := A.FloatArray()
Br := B1.FloatArray()
if nb != 0 {
DTrmmBlk(Br, Ar, 1.0, flags, B1.LeadingIndex(), A.LeadingIndex(),
N, S, E, nb)
} else {
DTrmmUnblk(Br, Ar, 1.0, flags, B1.LeadingIndex(), A.LeadingIndex(),
N, S, E, 0)
}
result := B0.AllClose(B1)
t.Logf(" B0 == B1: %v\n", result)
if A.Rows() < 8 {
t.Logf(" DTrmm B1:\n%v\n", B1)
}
return result
}
func trmvTest(t *testing.T, A *matrix.FloatMatrix, flags Flags, nb int) bool {
N := A.Cols()
//S := 0
//E := A.Cols()
X0 := matrix.FloatWithValue(A.Rows(), 1, 2.0)
X1 := X0.Copy()
trans := linalg.OptNoTrans
if flags&TRANS != 0 {
trans = linalg.OptTrans
}
diag := linalg.OptNonUnit
if flags&UNIT != 0 {
diag = linalg.OptUnit
}
uplo := linalg.OptUpper
if flags&LOWER != 0 {
uplo = linalg.OptLower
}
blas.TrmvFloat(A, X0, uplo, diag, trans)
Ar := A.FloatArray()
Xr := X1.FloatArray()
if nb == 0 {
DTrimvUnblkMV(Xr, Ar, flags, 1, A.LeadingIndex(), N)
}
result := X0.AllClose(X1)
t.Logf(" X0 == X1: %v\n", result)
if !result && A.Rows() < 8 {
t.Logf(" BLAS TRMV X0:\n%v\n", X0)
t.Logf(" DTrmv X1:\n%v\n", X1)
}
return result
}
func _TestSolveBlockedSmall(t *testing.T) {
L := matrix.FloatMatrixFromTable(lower5, matrix.RowOrder)
N := L.Rows()
nb := 4
U := L.Transpose()
X0 := matrix.FloatWithValue(L.Rows(), 1, 1.0)
X1 := X0.Copy()
xsum := 0.0
for i := 0; i < N; i++ {
xsum += float64(i)
X0.Add(xsum, i)
X1.Add(xsum, -(i + 1))
}
t.Logf("-- SOLVE LOWER, NON-UNIT ---\n")
solveMVTest(t, L, X0.Copy(), LOWER, N, nb)
t.Logf("-- SOLVE UPPER, NON-UNIT ---\n")
solveMVTest(t, U, X1.Copy(), UPPER, N, nb)
t.Logf("-- SOLVE LOWER, UNIT ---\n")
solveMVTest(t, L, X0.Copy(), LOWER|UNIT, N, nb)
t.Logf("-- SOLVE UPPER, UNIT ---\n")
solveMVTest(t, U, X1.Copy(), UPPER|UNIT, N, nb)
}
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 _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 _TestMultSymmSmall(t *testing.T) {
//bM := 5
bN := 7
bP := 7
Adata := [][]float64{
[]float64{1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0},
[]float64{0.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0},
[]float64{0.0, 0.0, 3.0, 3.0, 3.0, 3.0, 3.0},
[]float64{0.0, 0.0, 0.0, 4.0, 4.0, 4.0, 4.0},
[]float64{0.0, 0.0, 0.0, 0.0, 5.0, 5.0, 5.0},
[]float64{0.0, 0.0, 0.0, 0.0, 0.0, 6.0, 6.0},
[]float64{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 7.0}}
A := matrix.FloatMatrixFromTable(Adata, matrix.RowOrder)
B := matrix.FloatWithValue(bN, bP, 2.0)
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.OptUpper, linalg.OptRight)
DMultSymm(C1r, Ar, Br, 1.0, 1.0, UPPER|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 _TestRankSmall(t *testing.T) {
bM := 5
bN := 5
//bP := 5
Adata := [][]float64{
[]float64{1.0, 1.0, 1.0, 1.0, 1.0},
[]float64{2.0, 2.0, 2.0, 2.0, 2.0},
[]float64{3.0, 3.0, 3.0, 3.0, 3.0},
[]float64{4.0, 4.0, 4.0, 4.0, 4.0},
[]float64{5.0, 5.0, 5.0, 5.0, 5.0}}
A := matrix.FloatMatrixFromTable(Adata, matrix.RowOrder)
A0 := matrix.FloatMatrixFromTable(Adata, matrix.RowOrder)
X := matrix.FloatVector([]float64{1.0, 2.0, 3.0, 4.0, 5.0})
Y := matrix.FloatWithValue(bN, 1, 2.0)
Ar := A.FloatArray()
Xr := X.FloatArray()
Yr := Y.FloatArray()
blas.GerFloat(X, Y, A0, 1.0)
DRankMV(Ar, Xr, Yr, 1.0, A.LeadingIndex(), 1, 1, 0, bN, 0, bM, 4, 4)
ok := A0.AllClose(A)
t.Logf("A0 == A1: %v\n", ok)
if !ok {
t.Logf("blas ger:\n%v\n", A0)
t.Logf("A1: \n%v\n", A)
}
}
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 _TestRank(t *testing.T) {
bM := M * 100
bN := N * 100
//bP := 5
A := matrix.FloatWithValue(bM, bN, 1.0)
A0 := matrix.FloatWithValue(bM, bN, 1.0)
X := matrix.FloatNormal(bM, 1)
Y := matrix.FloatNormal(bN, 1)
Ar := A.FloatArray()
Xr := X.FloatArray()
Yr := Y.FloatArray()
blas.GerFloat(X, Y, A0, 1.0)
DRankMV(Ar, Xr, Yr, 1.0, A.LeadingIndex(), 1, 1, 0, bN, 0, bM, 4, 4)
t.Logf("GER A0 == A1: %v\n", A0.AllClose(A))
}
func _TestBKpivot1U(t *testing.T) {
Ldata := [][]float64{
[]float64{7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0},
[]float64{1.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0},
[]float64{1.0, 2.0, 5.0, 4.0, 3.0, 5.0, 1.0},
[]float64{1.0, 2.0, 3.0, 4.0, 3.0, 2.0, 1.0},
[]float64{1.0, 5.0, 3.0, 4.0, 3.0, 2.0, 1.0},
[]float64{1.0, 2.0, 3.0, 4.0, 5.0, 2.0, 1.0},
[]float64{1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 1.0}}
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}}
A := matrix.FloatMatrixFromTable(Ldata, matrix.RowOrder)
X := matrix.FloatMatrixFromTable(Bdata, matrix.RowOrder)
N := A.Rows()
B := matrix.FloatZeros(N, 2)
MultSym(B, A, X, 1.0, 0.0, UPPER|LEFT)
//t.Logf("initial B:\n%v\n", B)
//N := 8
//A := matrix.FloatUniformSymmetric(N)
W := matrix.FloatWithValue(A.Rows(), 5, 0.0)
nb := 0
ipiv := make([]int, N, N)
L, _ := DecomposeBK(A.Copy(), W, ipiv, UPPER, nb)
t.Logf("ipiv: %v\n", ipiv)
t.Logf("L:\n%v\n", L)
nb = 4
//ipiv0 := make([]int, N, N)
//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.SytrfFloat(A, ipiv2, linalg.OptUpper)
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 _TestMultSyr2Small(t *testing.T) {
bN := 7
//A := matrix.FloatNormal(bN, bN)
//B := matrix.FloatNormal(bN, bP)
//A := matrix.FloatWithValue(bM, bP, 1.0)
X := matrix.FloatWithValue(bN, 1, 1.0)
Y := matrix.FloatWithValue(bN, 1, 1.0)
C0 := matrix.FloatZeros(bN, bN)
C1 := matrix.FloatZeros(bN, bN)
for i := 0; i < bN; i++ {
X.Add(1.0+float64(i), i)
Y.Add(2.0+float64(i), i)
}
t.Logf("X=\n%v\nY=\n%v\n", X, Y)
Xr := X.FloatArray()
Yr := Y.FloatArray()
C1r := C1.FloatArray()
blas.Syr2Float(X, Y, C0, 1.0, linalg.OptUpper)
DSymmRank2MV(C1r, Xr, Yr, 1.0, UPPER, C1.LeadingIndex(), 1, 1, 0, bN, 4)
ok := C0.AllClose(C1)
t.Logf("UPPER C0 == C1: %v\n", ok)
if !ok {
t.Logf("C1: C1 = A*X\n%v\n", C1)
t.Logf("blas: C0\n%v\n", C0)
}
blas.Syr2Float(X, Y, C0, 1.0, linalg.OptLower)
DSymmRank2MV(C1r, Xr, Yr, 1.0, LOWER, C1.LeadingIndex(), 1, 1, 0, bN, 4)
ok = C0.AllClose(C1)
t.Logf("LOWER C0 == C1: %v\n", ok)
if !ok {
t.Logf("blas: C0\n%v\n", C0)
t.Logf("C1: C1 = A*X\n%v\n", C1)
}
}
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))
}
func _TestSolveRandom(t *testing.T) {
bN := 22
nb := 4
L := matrix.FloatNormalSymmetric(bN, matrix.Lower)
U := L.Transpose()
X0 := matrix.FloatWithValue(L.Rows(), 1, 1.0)
t.Logf("-- BLOCKED SOLVE LOWER NON-UNIT ---\n")
solveMVTest(t, L, X0.Copy(), LOWER, bN, nb)
t.Logf("-- BLOCKED SOLVE LOWER UNIT ---\n")
solveMVTest(t, L, X0.Copy(), LOWER|UNIT, bN, nb)
t.Logf("-- BLOCKED SOLVE UPPER NON-UNIT ---\n")
solveMVTest(t, U, X0.Copy(), UPPER, bN, nb)
t.Logf("-- BLOCKED SOLVE UPPER UNIT ---\n")
solveMVTest(t, U, X0.Copy(), UPPER|UNIT, bN, nb)
}
func main() {
flag.Parse()
x := floorplan(matrix.FloatWithValue(5, 1, 100.0))
if x != nil {
W := x.GetIndex(0)
H := x.GetIndex(1)
xs := matrix.FloatVector(x.FloatArray()[2:7])
ys := matrix.FloatVector(x.FloatArray()[7:12])
ws := matrix.FloatVector(x.FloatArray()[12:17])
hs := matrix.FloatVector(x.FloatArray()[17:])
fmt.Printf("W = %.5f, H = %.5f\n", W, H)
fmt.Printf("x = \n%v\n", xs.ToString("%.5f"))
fmt.Printf("y = \n%v\n", ys.ToString("%.5f"))
fmt.Printf("w = \n%v\n", ws.ToString("%.5f"))
fmt.Printf("h = \n%v\n", hs.ToString("%.5f"))
check(x)
}
}
func _TestBKSolve(t *testing.T) {
Ldata := [][]float64{
[]float64{1.0, 2.0, 3.0, 4.0},
[]float64{2.0, 2.0, 3.0, 4.0},
[]float64{3.0, 3.0, 3.0, 4.0},
[]float64{4.0, 4.0, 4.0, 4.0}}
Xdata := [][]float64{
[]float64{1.0, 2.0},
[]float64{1.0, 2.0},
[]float64{1.0, 2.0},
[]float64{1.0, 2.0}}
A := matrix.FloatMatrixFromTable(Ldata, matrix.RowOrder)
X := matrix.FloatMatrixFromTable(Xdata, matrix.RowOrder)
N := A.Rows()
B := matrix.FloatZeros(N, 2)
Mult(B, A, X, 1.0, 0.0, NOTRANS)
S := matrix.FloatZeros(N, 2)
MultSym(S, A, X, 1.0, 0.0, LOWER|LEFT)
t.Logf("B:\n%v\n", B)
t.Logf("S:\n%v\n", S)
//N := 8
//A := matrix.FloatUniformSymmetric(N)
nb := 0
W := matrix.FloatWithValue(A.Rows(), 5, 0.0)
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)
B0 := B.Copy()
SolveBK(B0, L, ipiv, 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)
}
func _TestMultTransASmall(t *testing.T) {
bM := 7
bN := 7
bP := 7
D := matrix.FloatNormal(bM, bP)
E := matrix.FloatNormal(bP, bN)
C0 := matrix.FloatWithValue(bM, bN, 0.0)
C1 := C0.Copy()
Dt := D.Transpose()
Dr := Dt.FloatArray()
Er := E.FloatArray()
C1r := C1.FloatArray()
blas.GemmFloat(Dt, E, C0, 1.0, 1.0, linalg.OptTransA)
t.Logf("blas: C=D*E\n%v\n", C0)
DMult(C1r, Dr, Er, 1.0, 1.0, TRANSA, bM, bM, bP, bP, 0, bN, 0, bM, 4, 4, 4)
t.Logf("C0 == C1: %v\n", C0.AllClose(C1))
t.Logf("C1: C1=D*E\n%v\n", C1)
}
func _TestMultSmall(t *testing.T) {
bM := 6
bN := 6
bP := 6
D := matrix.FloatNormal(bM, bP)
E := matrix.FloatNormal(bP, bN)
C0 := matrix.FloatWithValue(bM, bN, 1.0)
C1 := C0.Copy()
Dr := D.FloatArray()
Er := E.FloatArray()
C1r := C1.FloatArray()
blas.GemmFloat(D, E, C0, 1.0, 1.0)
t.Logf("blas: C=D*E\n%v\n", C0)
DMult(C1r, Dr, Er, 1.0, 1.0, NOTRANS, bM, bM, bP, bP, 0, bN, 0, bM, 4, 4, 4)
t.Logf("C0 == C1: %v\n", C0.AllClose(C1))
t.Logf("C1: C1=D*E\n%v\n", C1)
}
func main() {
Sdata := [][]float64{
[]float64{4e-2, 6e-3, -4e-3, 0.0},
[]float64{6e-3, 1e-2, 0.0, 0.0},
[]float64{-4e-3, 0.0, 2.5e-3, 0.0},
[]float64{0.0, 0.0, 0.0, 0.0}}
pbar := matrix.FloatVector([]float64{.12, .10, .07, .03})
S := matrix.FloatMatrixFromTable(Sdata)
n := pbar.Rows()
G := matrix.FloatDiagonal(n, -1.0)
h := matrix.FloatZeros(n, 1)
A := matrix.FloatWithValue(1, n, 1.0)
b := matrix.FloatNew(1, 1, []float64{1.0})
var solopts cvx.SolverOptions
solopts.MaxIter = 30
solopts.ShowProgress = true
mu := 1.0
Smu := matrix.Scale(S, mu)
pbarNeg := matrix.Scale(pbar, -1.0)
fmt.Printf("Smu=\n%v\n", Smu.String())
fmt.Printf("-pbar=\n%v\n", pbarNeg.String())
sol, err := cvx.Qp(Smu, pbarNeg, G, h, A, b, &solopts, nil)
fmt.Printf("status: %v\n", err)
if sol != nil && sol.Status == cvx.Optimal {
x := sol.Result.At("x")[0]
ret := blas.DotFloat(x, pbar)
risk := math.Sqrt(blas.DotFloat(x, S.Times(x)))
fmt.Printf("ret=%.3f, risk=%.3f\n", ret, risk)
fmt.Printf("x=\n%v\n", x)
}
}
// not run
func _TestPanic(t *testing.T) {
PanicOnError(true)
X := matrix.FloatWithValue(10, 1, 1.0)
ScalFloat(X, 2.0, &linalg.IOpt{"offset", -1})
}
func mcsdp(w *matrix.FloatMatrix) (*Solution, error) {
//
// Returns solution x, z to
//
// (primal) minimize sum(x)
// subject to w + diag(x) >= 0
//
// (dual) maximize -tr(w*z)
// subject to diag(z) = 1
// z >= 0.
//
n := w.Rows()
G := &matrixFs{n}
cngrnc := func(r, x *matrix.FloatMatrix, alpha float64) (err error) {
// Congruence transformation
//
// x := alpha * r'*x*r.
//
// r and x are square matrices.
//
err = nil
// tx = matrix(x, (n,n)) is copying and reshaping
// scale diagonal of x by 1/2, (x is (n,n))
tx := x.Copy()
matrix.Reshape(tx, n, n)
tx.Diag().Scale(0.5)
// a := tril(x)*r
// (python: a = +r is really making a copy of r)
a := r.Copy()
err = blas.TrmmFloat(tx, a, 1.0, linalg.OptLeft)
// x := alpha*(a*r' + r*a')
err = blas.Syr2kFloat(r, a, tx, alpha, 0.0, linalg.OptTrans)
// x[:] = tx[:]
tx.CopyTo(x)
return
}
Fkkt := func(W *sets.FloatMatrixSet) (KKTFunc, error) {
// Solve
// -diag(z) = bx
// -diag(x) - inv(rti*rti') * z * inv(rti*rti') = bs
//
// On entry, x and z contain bx and bs.
// On exit, they contain the solution, with z scaled
// (inv(rti)'*z*inv(rti) is returned instead of z).
//
// We first solve
//
// ((rti*rti') .* (rti*rti')) * x = bx - diag(t*bs*t)
//
// and take z = -rti' * (diag(x) + bs) * rti.
var err error = nil
rti := W.At("rti")[0]
// t = rti*rti' as a nonsymmetric matrix.
t := matrix.FloatZeros(n, n)
err = blas.GemmFloat(rti, rti, t, 1.0, 0.0, linalg.OptTransB)
if err != nil {
return nil, err
}
// Cholesky factorization of tsq = t.*t.
tsq := matrix.Mul(t, t)
err = lapack.Potrf(tsq)
if err != nil {
return nil, err
}
f := func(x, y, z *matrix.FloatMatrix) (err error) {
// tbst := t * zs * t = t * bs * t
tbst := z.Copy()
matrix.Reshape(tbst, n, n)
cngrnc(t, tbst, 1.0)
// x := x - diag(tbst) = bx - diag(rti*rti' * bs * rti*rti')
diag := tbst.Diag().Transpose()
x.Minus(diag)
// x := (t.*t)^{-1} * x = (t.*t)^{-1} * (bx - diag(t*bs*t))
err = lapack.Potrs(tsq, x)
// z := z + diag(x) = bs + diag(x)
// z, x are really column vectors here
z.AddIndexes(matrix.MakeIndexSet(0, n*n, n+1), x.FloatArray())
// z := -rti' * z * rti = -rti' * (diag(x) + bs) * rti
cngrnc(rti, z, -1.0)
return nil
}
return f, nil
}
c := matrix.FloatWithValue(n, 1, 1.0)
// initial feasible x: x = 1.0 - min(lmbda(w))
lmbda := matrix.FloatZeros(n, 1)
wp := w.Copy()
lapack.Syevx(wp, lmbda, nil, 0.0, nil, []int{1, 1}, linalg.OptRangeInt)
x0 := matrix.FloatZeros(n, 1).Add(-lmbda.GetAt(0, 0) + 1.0)
s0 := w.Copy()
s0.Diag().Plus(x0.Transpose())
matrix.Reshape(s0, n*n, 1)
// initial feasible z is identity
z0 := matrix.FloatIdentity(n)
matrix.Reshape(z0, n*n, 1)
dims := sets.DSetNew("l", "q", "s")
dims.Set("s", []int{n})
primalstart := sets.FloatSetNew("x", "s")
dualstart := sets.FloatSetNew("z")
primalstart.Set("x", x0)
primalstart.Set("s", s0)
dualstart.Set("z", z0)
var solopts SolverOptions
solopts.MaxIter = 30
solopts.ShowProgress = false
h := w.Copy()
matrix.Reshape(h, h.NumElements(), 1)
return ConeLpCustomMatrix(c, G, h, nil, nil, dims, Fkkt, &solopts, primalstart, dualstart)
}
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())
}
func trsmSolve(t *testing.T, A *matrix.FloatMatrix, flags Flags, rand bool, nrhs, nb int) bool {
var B0 *matrix.FloatMatrix
side := linalg.OptLeft
trans := linalg.OptNoTrans
N := A.Cols()
S := 0
E := A.Rows()
_ = S
_ = E
if flags&RIGHT != 0 {
if rand {
B0 = matrix.FloatNormal(nrhs, A.Rows())
} else {
B0 = matrix.FloatWithValue(nrhs, A.Rows(), 2.0)
}
side = linalg.OptRight
E = B0.Rows()
} else {
if rand {
B0 = matrix.FloatNormal(A.Rows(), nrhs)
} else {
B0 = matrix.FloatWithValue(A.Rows(), nrhs, 2.0)
}
E = B0.Cols()
}
B1 := B0.Copy()
diag := linalg.OptNonUnit
if flags&UNIT != 0 {
diag = linalg.OptUnit
}
uplo := linalg.OptUpper
if flags&LOWER != 0 {
uplo = linalg.OptLower
}
if flags&TRANSA != 0 {
trans = linalg.OptTransA
}
blas.TrsmFloat(A, B0, 1.0, uplo, diag, side, trans)
Ar := A.FloatArray()
Br := B1.FloatArray()
if nb == 0 || nb == N {
DSolveUnblk(Br, Ar, 1.0, flags, B1.LeadingIndex(), A.LeadingIndex(), N, S, E)
} else {
DSolveBlk(Br, Ar, 1.0, flags, B1.LeadingIndex(), A.LeadingIndex(), N, S, E, nb)
}
result := B1.AllClose(B0)
t.Logf("B1 == B0: %v\n", result)
if !result {
if nrhs < 10 {
t.Logf("blas: B0\n%v\n", B0)
t.Logf("B1:\n%v\n", B1)
} else {
b0 := B0.FloatArray()
b1 := B1.FloatArray()
for k := 0; k < len(b0); k++ {
if !isClose(b0[k], b1[k]) {
t.Logf("first divergences at %d ... col %d, row %d\n", k, k/B0.Rows(), k%B0.Rows())
break
}
}
}
}
return result
}