func runTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {
var mintime time.Duration
M := A.Rows()
N := A.Cols()
nN := N
if M < N {
nN = M
}
ipiv := make([]int, nN, nN)
fnc := func() {
_, ERRmatops = matops.DecomposeLU(A, ipiv, 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 solveMVTest(t *testing.T, A, X0 *matrix.FloatMatrix, flags Flags, bN, bNB int) {
X1 := X0.Copy()
uplo := linalg.OptUpper
diag := linalg.OptNonUnit
if flags&LOWER != 0 {
uplo = linalg.OptLower
}
if flags&UNIT != 0 {
diag = linalg.OptUnit
}
blas.TrsvFloat(A, X0, uplo, diag)
Ar := A.FloatArray()
Xr := X1.FloatArray()
if bN == bNB {
DSolveUnblkMV(Xr, Ar, flags, 1, A.LeadingIndex(), bN)
} else {
DSolveBlkMV(Xr, Ar, flags, 1, A.LeadingIndex(), bN, bNB)
}
ok := X1.AllClose(X0)
t.Logf("X1 == X0: %v\n", ok)
if !ok && bN < 8 {
t.Logf("A=\n%v\n", A)
t.Logf("X0=\n%v\n", X0)
t.Logf("blas: X0\n%v\n", X0)
t.Logf("X1:\n%v\n", X1)
}
}
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 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 runRefTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {
var mintime time.Duration
M := A.Rows()
N := A.Cols()
nN := N
if M < N {
nN = M
}
ipiv := make([]int32, nN, nN)
fnc := func() {
ERRlapack = lapack.Getrf(A, ipiv)
}
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 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 runRefTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {
var mintime time.Duration
lopt := linalg.OptLower
if testUpper {
lopt = linalg.OptUpper
}
fnc := func() {
ERRlapack = lapack.Potrf(A, lopt)
}
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 syrk2Test(t *testing.T, C, A, B *matrix.FloatMatrix, flags Flags, vlen, nb int) bool {
//var B0 *matrix.FloatMatrix
P := A.Cols()
S := 0
E := C.Rows()
C0 := C.Copy()
trans := linalg.OptNoTrans
if flags&TRANSA != 0 {
trans = linalg.OptTrans
P = A.Rows()
}
uplo := linalg.OptUpper
if flags&LOWER != 0 {
uplo = linalg.OptLower
}
blas.Syr2kFloat(A, B, C0, 1.0, 1.0, uplo, trans)
if A.Rows() < 8 {
//t.Logf("..A\n%v\n", A)
t.Logf(" BLAS C0:\n%v\n", C0)
}
Ar := A.FloatArray()
Br := B.FloatArray()
Cr := C.FloatArray()
DSymmRank2Blk(Cr, Ar, Br, 1.0, 1.0, flags, C.LeadingIndex(), A.LeadingIndex(),
B.LeadingIndex(), P, S, E, vlen, nb)
result := C0.AllClose(C)
t.Logf(" C0 == C: %v\n", result)
if A.Rows() < 8 {
t.Logf(" DMRank2 C:\n%v\n", C)
}
return result
}
func runTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {
var flags matops.Flags
var mintime time.Duration
flags = matops.LOWER
if testUpper {
flags = matops.UPPER
}
fnc := func() {
_, ERRmatops = matops.DecomposeCHOL(A, 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 columnDiffs(A, B *matrix.FloatMatrix) *matrix.FloatMatrix {
var c matrix.FloatMatrix
nrm := matrix.FloatZeros(A.Cols(), 1)
A0 := A.Copy()
A0.Minus(B)
for k := 0; k < A.Cols(); k++ {
A0.SubMatrix(&c, 0, k, A.Rows(), 1)
nrm.SetAt(k, 0, matops.Norm2(&c))
}
return nrm
}
func rowDiffs(A, B *matrix.FloatMatrix) *matrix.FloatMatrix {
var r matrix.FloatMatrix
nrm := matrix.FloatZeros(A.Rows(), 1)
A0 := A.Copy()
A0.Minus(B)
for k := 0; k < A.Rows(); k++ {
A0.SubMatrix(&r, k, 0, 1, A.Cols())
nrm.SetAt(k, 0, matops.Norm2(&r))
}
return nrm
}
// single invocation for matops and lapack functions
func runCheck(A *matrix.FloatMatrix, LB int) (bool, time.Duration, time.Duration) {
var flags matops.Flags
N := A.Rows()
ipiv := make([]int, N, N)
ipiv0 := make([]int32, N, N)
flags = matops.LOWER
lopt := linalg.OptLower
if testUpper {
flags = matops.UPPER
lopt = linalg.OptUpper
}
W := matrix.FloatZeros(A.Rows(), LB+2)
fnc := func() {
_, ERRmatops = matops.DecomposeBK(A, W, ipiv, flags, LB)
}
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "A start:\n%v\n", A)
}
A0 := A.Copy()
mperf.FlushCache()
time0 := mperf.Timeit(fnc)
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "ipiv:%v\n", ipiv)
fmt.Fprintf(os.Stderr, "A end:\n%v\n", A)
}
fn2 := func() {
ERRlapack = lapack.Sytrf(A0, ipiv0, lopt)
}
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "A0 start:\n%v\n", A0)
}
mperf.FlushCache()
time2 := mperf.Timeit(fn2)
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "ipiv0:%v\n", ipiv0)
fmt.Fprintf(os.Stderr, "A0 end:\n%v\n", A0)
}
// now A == A0 && ipiv == ipiv0
ok := A.AllClose(A0)
okip := checkIPIV(ipiv, ipiv0)
if !ok || !okip {
// save result to globals
Rlapack = A0
Rmatops = A
IPIVlapack = ipiv0
IPIVmatops = ipiv
}
return ok && okip, time0, time2
}
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
}
// single invocation for matops and lapack functions
func runCheck(A *matrix.FloatMatrix, LB int) (bool, time.Duration, time.Duration) {
M := A.Rows()
N := A.Cols()
nN := N
if M < N {
nN = M
}
ipiv := make([]int, nN, nN)
ipiv0 := make([]int32, nN, nN)
fnc := func() {
_, ERRmatops = matops.DecomposeLU(A, ipiv, LB)
}
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "A start:\n%v\n", A)
}
A0 := A.Copy()
mperf.FlushCache()
time0 := mperf.Timeit(fnc)
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "A end:\n%v\n", A)
fmt.Fprintf(os.Stderr, "ipiv:%v\n", ipiv)
}
fn2 := func() {
ERRlapack = lapack.Getrf(A0, ipiv0)
}
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "A0 start:\n%v\n", A0)
}
mperf.FlushCache()
time2 := mperf.Timeit(fn2)
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "A0 end:\n%v\n", A0)
fmt.Fprintf(os.Stderr, "ipiv0:%v\n", ipiv0)
}
// now A == A0 && ipiv == ipiv0
ok := A.AllClose(A0)
okip := checkIPIV(ipiv, ipiv0)
_ = okip
if !ok || !okip {
// save result to globals
Rlapack = A0
Rmatops = A
IPIVlapack = ipiv0
IPIVmatops = ipiv
}
return ok && okip, time0, time2
}
// 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
}
// Here problem is already translated to epigraph format except original convex problem.
// We wrap it and create special CP epigraph kktsolver.
func cp_problem(F ConvexProg, c MatrixVariable, G MatrixVarG, h *matrix.FloatMatrix, A MatrixVarA,
b MatrixVariable, dims *sets.DimensionSet, kktsolver KKTCpSolver,
solopts *SolverOptions, x0 *matrix.FloatMatrix, mnl int) (sol *Solution, err error) {
err = nil
F_e := &cpProg{F}
//mx0 := newEpigraph(x0, 0.0)
cdim := dims.Sum("l", "q") + dims.SumSquared("s")
ux := x0.Copy()
uz := matrix.FloatZeros(mnl+cdim, 1)
kktsolver_e := func(W *sets.FloatMatrixSet, xa MatrixVariable, znl *matrix.FloatMatrix) (KKTFuncVar, error) {
x, x_ok := xa.(*epigraph)
_ = x_ok
We := W.Copy()
// dnl is matrix
dnl := W.At("dnl")[0]
dnli := W.At("dnli")[0]
We.Set("dnl", matrix.FloatVector(dnl.FloatArray()[1:]))
We.Set("dnli", matrix.FloatVector(dnli.FloatArray()[1:]))
g, err := kktsolver(We, x.m(), znl)
_, Df, _ := F.F1(x.m())
gradf0 := Df.GetRow(0, nil).Transpose()
solve := func(xa, ya MatrixVariable, z *matrix.FloatMatrix) (err error) {
x, x_ok := xa.(*epigraph)
_ = x_ok // TODO: remove or use x_ok
y := ya.Matrix()
err = nil
a := z.GetIndex(0)
blas.Copy(x.m(), ux)
blas.AxpyFloat(gradf0, ux, x.t())
blas.Copy(z, uz, &la.IOpt{"offsetx", 1})
err = g(ux, y, uz)
z.SetIndex(0, -x.t()*dnl.GetIndex(0))
blas.Copy(uz, z, &la.IOpt{"offsety", 1})
blas.Copy(ux, x.m())
val := blas.DotFloat(gradf0, x.m()) + dnl.GetIndex(0)*dnl.GetIndex(0)*x.t() - a
x.set(val)
return
}
return solve, err
}
return cpl_solver(F_e, c, G, h, A, b, dims, kktsolver_e, solopts, nil, mnl)
}
// single invocation for matops and lapack functions
func runCheck(A *matrix.FloatMatrix, LB int) (bool, time.Duration, time.Duration) {
var flags matops.Flags
N := A.Rows()
flags = matops.LOWER
lopt := linalg.OptLower
if testUpper {
flags = matops.UPPER
lopt = linalg.OptUpper
}
fnc := func() {
_, ERRmatops = matops.DecomposeCHOL(A, flags, LB)
}
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "A start:\n%v\n", A)
}
A0 := A.Copy()
mperf.FlushCache()
time0 := mperf.Timeit(fnc)
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "A end:\n%v\n", A)
}
fn2 := func() {
ERRlapack = lapack.Potrf(A0, lopt)
}
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "A0 start:\n%v\n", A0)
}
mperf.FlushCache()
time2 := mperf.Timeit(fn2)
if verbose && N < 10 {
fmt.Fprintf(os.Stderr, "A0 end:\n%v\n", A0)
}
// now A == A0 && ipiv == ipiv0
ok := A.AllClose(A0)
if !ok {
// save result to globals
Rlapack = A0
Rmatops = A
}
return ok, time0, time2
}
func cpl_problem(F ConvexProg, c MatrixVariable, G MatrixVarG, h *matrix.FloatMatrix, A MatrixVarA,
b MatrixVariable, dims *sets.DimensionSet, kktsolver KKTCpSolver,
solopts *SolverOptions, x0 *matrix.FloatMatrix, mnl int) (sol *Solution, err error) {
err = nil
F_e := &convexVarProg{F}
mx0 := &matrixVar{x0.Copy()}
kktsolver_u := func(W *sets.FloatMatrixSet, x MatrixVariable, z *matrix.FloatMatrix) (KKTFuncVar, error) {
g, err := kktsolver(W, x.Matrix(), z)
solver := func(x, y MatrixVariable, z *matrix.FloatMatrix) error {
return g(x.Matrix(), y.Matrix(), z)
}
return solver, err
}
return cpl_solver(F_e, c, G, h, A, b, dims, kktsolver_u, solopts, mx0, mnl)
}
func ldlbkDecomposeLowerTest(A *matrix.FloatMatrix, t *testing.T) {
TriL(A)
N := A.Cols()
nb := 0
W := matrix.FloatZeros(A.Rows(), 5)
ipiv := make([]int, N, N)
L, _ := DecomposeBK(A.Copy(), W, ipiv, LOWER, nb)
t.Logf("L:\n%v\n", L)
t.Logf("unblked ipiv: %v\n", ipiv)
ipiv0 := make([]int, N, N)
nb = 4
L0, _ := DecomposeBK(A.Copy(), W, ipiv0, LOWER, nb)
t.Logf("L:\n%v\n", L0)
t.Logf("blked ipiv: %v\n", ipiv0)
ipiv2 := make([]int32, N, N)
lapack.SytrfFloat(A, ipiv2, linalg.OptLower)
t.Logf("lapack A:\n%v\n", A)
t.Logf("lapack ipiv: %v\n", ipiv2)
}
/* From LAPACK/dlarf.f
*
* Applies a real elementary reflector H to a real m by n matrix A,
* from either the left or the right. H is represented in the form
*
* H = I - tau * ( 1 ) * ( 1 v.T )
* ( v )
*
* where tau is a real scalar and v is a real vector.
*
* If tau = 0, then H is taken to be the unit matrix.
*
* A is /a1\ a1 := a1 - w1
* \A2/ A2 := A2 - v*w1
* w1 := tau*(a1 + A2.T*v) if side == LEFT
* := tau*(a1 + A2*v) if side == RIGHT
*
* Allocates/frees intermediate work space matrix w1.
*/
func applyHouseholder(tau, v, a1, A2 *matrix.FloatMatrix, flags Flags) {
tval := tau.GetAt(0, 0)
if tval == 0.0 {
return
}
w1 := a1.Copy()
if flags&LEFT != 0 {
// w1 = a1 + A2.T*v
MVMult(w1, A2, v, 1.0, 1.0, TRANSA)
} else {
// w1 = a1 + A2*v
MVMult(w1, A2, v, 1.0, 1.0, NOTRANS)
}
// w1 = tau*w1
Scale(w1, tval)
// a1 = a1 - w1
a1.Minus(w1)
// A2 = A2 - v*w1
MVRankUpdate(A2, v, w1, -1.0)
}
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
}
func newEpigraph(m *matrix.FloatMatrix, t float64) *epigraph {
return &epigraph{m.Copy(), t}
}
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)
}
