// test: min || B - A.T*X ||
func TestLeastSquaresLQ(t *testing.T) {
M := 723
N := 811
K := 273
nb := 32
conf := gomas.NewConf()
conf.LB = nb
tau := cmat.NewMatrix(M, 1)
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
B0 := cmat.NewMatrix(M, K)
B0.SetFrom(src)
B := cmat.NewMatrix(N, K)
// B = A.T*B0
blasd.Mult(B, A, B0, 1.0, 0.0, gomas.TRANSA, conf)
W := lapackd.Workspace(lapackd.LQFactorWork(A, conf))
lapackd.LQFactor(A, tau, W, conf)
// B' = A.-1*B
lapackd.LQSolve(B, A, tau, W, gomas.TRANS, conf)
// expect B[0:M,0:K] == B0[0:M,0:K], B[M:N,0:K] == 0
var X cmat.FloatMatrix
X.SubMatrix(B, 0, 0, M, K)
blasd.Plus(&X, B0, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(&X, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||B0 - min( ||A.T*X - B0|| ) ||_1: %e\n", M, N, nrm)
}
func MVMult(Y, A, X *cmat.FloatMatrix, alpha, beta float64, bits int, confs ...*gomas.Config) *gomas.Error {
ok := true
yr, yc := Y.Size()
ar, ac := A.Size()
xr, xc := X.Size()
if ar*ac == 0 {
return nil
}
if yr != 1 && yc != 1 {
return gomas.NewError(gomas.ENEED_VECTOR, "MVMult")
}
if xr != 1 && xc != 1 {
return gomas.NewError(gomas.ENEED_VECTOR, "MVMult")
}
nx := X.Len()
ny := Y.Len()
if bits&gomas.TRANSA != 0 {
bits |= gomas.TRANS
}
if bits&gomas.TRANS != 0 {
ok = ny == ac && nx == ar
} else {
ok = ny == ar && nx == ac
}
if !ok {
return gomas.NewError(gomas.ESIZE, "MVMult")
}
if beta != 1.0 {
vscal(Y, beta, ny)
}
gemv(Y, A, X, alpha, beta, bits, 0, nx, 0, ny)
return nil
}
/*
* Reduce a general M-by-N matrix A to upper or lower bidiagonal form B
* by an ortogonal transformation A = Q*B*P.T, B = Q.T*A*P
*
*
* Arguments
* A On entry, the real M-by-N matrix. On exit the upper/lower
* bidiagonal matrix and ortogonal matrices Q and P.
*
* tauq Scalar factors for elementary reflector forming the
* ortogonal matrix Q.
*
* taup Scalar factors for elementary reflector forming the
* ortogonal matrix P.
*
* W Workspace needed for reduction.
*
* conf Current blocking configuration. Optional.
*
*
* Details
*
* Matrices Q and P are products of elementary reflectors H(k) and G(k)
*
* If M > N:
* Q = H(1)*H(2)*...*H(N) and P = G(1)*G(2)*...*G(N-1)
*
* where H(k) = 1 - tauq*u*u.T and G(k) = 1 - taup*v*v.T
*
* Elementary reflector H(k) are stored on columns of A below the diagonal with
* implicit unit value on diagonal entry. Vector TAUQ holds corresponding scalar
* factors. Reflector G(k) are stored on rows of A right of first superdiagonal
* with implicit unit value on superdiagonal. Corresponding scalar factors are
* stored on vector TAUP.
*
* If M < N:
* Q = H(1)*H(2)*...*H(N-1) and P = G(1)*G(2)*...*G(N)
*
* where H(k) = 1 - tauq*u*u.T and G(k) = 1 - taup*v*v.T
*
* Elementary reflector H(k) are stored on columns of A below the first sub diagonal
* with implicit unit value on sub diagonal entry. Vector TAUQ holds corresponding
* scalar factors. Reflector G(k) are sotre on rows of A right of diagonal with
* implicit unit value on superdiagonal. Corresponding scalar factors are stored
* on vector TAUP.
*
* Contents of matrix A after reductions are as follows.
*
* M = 6 and N = 5: M = 5 and N = 6:
*
* ( d e v1 v1 v1 ) ( d v1 v1 v1 v1 v1 )
* ( u1 d e v2 v2 ) ( e d v2 v2 v2 v2 )
* ( u1 u2 d e v3 ) ( u1 e d v3 v3 v3 )
* ( u1 u2 u3 d e ) ( u1 u2 e d v4 v4 )
* ( u1 u2 u3 u4 d ) ( u1 u2 u3 e d v5 )
* ( u1 u2 u3 u4 u5 )
*/
func BDReduce(A, tauq, taup, W *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
var err *gomas.Error = nil
conf := gomas.CurrentConf(confs...)
_ = conf
wmin := wsBired(A, 0)
wsz := W.Len()
if wsz < wmin {
return gomas.NewError(gomas.EWORK, "ReduceBidiag", wmin)
}
lb := conf.LB
wneed := wsBired(A, lb)
if wneed > wsz {
lb = estimateLB(A, wsz, wsBired)
}
if m(A) >= n(A) {
if lb > 0 && n(A) > lb {
blkBidiagLeft(A, tauq, taup, W, lb, conf)
} else {
unblkReduceBidiagLeft(A, tauq, taup, W)
}
} else {
if lb > 0 && m(A) > lb {
blkBidiagRight(A, tauq, taup, W, lb, conf)
} else {
unblkReduceBidiagRight(A, tauq, taup, W)
}
}
return err
}
/*
* Solve a system of linear equations A*X = B or A.T*X = B with general N-by-N
* matrix A using the LU factorization computed by LUFactor().
*
* Arguments:
* B On entry, the right hand side matrix B. On exit, the solution matrix X.
*
* A The factor L and U from the factorization A = P*L*U as computed by
* LUFactor()
*
* pivots The pivot indices from LUFactor().
*
* flags The indicator of the form of the system of equations.
* If flags&TRANSA then system is transposed. All other values
* indicate non transposed system.
*
* Compatible with lapack.DGETRS.
*/
func LUSolve(B, A *cmat.FloatMatrix, pivots Pivots, flags int, confs ...*gomas.Config) *gomas.Error {
var err *gomas.Error = nil
conf := gomas.DefaultConf()
if len(confs) > 0 {
conf = confs[0]
}
ar, ac := A.Size()
br, _ := B.Size()
if ar != ac {
return gomas.NewError(gomas.ENOTSQUARE, "SolveLU")
}
if br != ac {
return gomas.NewError(gomas.ESIZE, "SolveLU")
}
if pivots != nil {
applyPivots(B, pivots)
}
if flags&gomas.TRANSA != 0 {
// transposed X = A.-1*B == (L.T*U.T).-1*B == U.-T*(L.-T*B)
blasd.SolveTrm(B, A, 1.0, gomas.LOWER|gomas.UNIT|gomas.TRANSA, conf)
blasd.SolveTrm(B, A, 1.0, gomas.UPPER|gomas.TRANSA, conf)
} else {
// non-transposed X = A.-1*B == (L*U).-1*B == U.-1*(L.-1*B)
blasd.SolveTrm(B, A, 1.0, gomas.LOWER|gomas.UNIT, conf)
blasd.SolveTrm(B, A, 1.0, gomas.UPPER, conf)
}
return err
}
/*
* 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 cmat.
*
* 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
*
* Intermediate work space w1 required as parameter, no allocation.
*/
func applyHouseholder2x1(tau, v, a1, A2, w1 *cmat.FloatMatrix, flags int) *gomas.Error {
var err *gomas.Error = nil
tval := tau.Get(0, 0)
if tval == 0.0 {
return err
}
// shape oblivious vector copy.
blasd.Axpby(w1, a1, 1.0, 0.0)
if flags&gomas.LEFT != 0 {
// w1 = a1 + A2.T*v
err = blasd.MVMult(w1, A2, v, 1.0, 1.0, gomas.TRANSA)
} else {
// w1 = a1 + A2*v
err = blasd.MVMult(w1, A2, v, 1.0, 1.0, gomas.NONE)
}
// w1 = tau*w1
blasd.Scale(w1, tval)
// a1 = a1 - w1
blasd.Axpy(a1, w1, -1.0)
// A2 = A2 - v*w1
if flags&gomas.LEFT != 0 {
err = blasd.MVUpdate(A2, v, w1, -1.0)
} else {
err = blasd.MVUpdate(A2, w1, v, -1.0)
}
return err
}
// Simple and slow LQ decomposition with Givens rotations
func TestGivensLQ(t *testing.T) {
var d cmat.FloatMatrix
M := 149
N := 167
A := cmat.NewMatrix(M, N)
A1 := cmat.NewCopy(A)
ones := cmat.NewFloatConstSource(1.0)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
A0 := cmat.NewCopy(A)
Qt := cmat.NewMatrix(N, N)
d.Diag(Qt)
d.SetFrom(ones)
// R = G(n)...G(2)G(1)*A; Q = G(1).T*G(2).T...G(n).T ; Q.T = G(n)...G(2)G(1)
for i := 0; i < M; i++ {
// zero elements right of diagonal
for j := N - 2; j >= i; j-- {
c, s, r := lapackd.ComputeGivens(A.Get(i, j), A.Get(i, j+1))
A.Set(i, j, r)
A.Set(i, j+1, 0.0)
// apply rotation to this column starting from row i+1
lapackd.ApplyGivensRight(A, j, j+1, i+1, M-i-1, c, s)
// update Qt = G(k)*Qt
lapackd.ApplyGivensRight(Qt, j, j+1, 0, N, c, s)
}
}
// A = L*Q
blasd.Mult(A1, A, Qt, 1.0, 0.0, gomas.TRANSB)
blasd.Plus(A0, A1, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||A - L*G(1)..G(n)||_1: %e\n", M, N, nrm)
}
func TestSubMatrixGob(t *testing.T) {
var B, As cmat.FloatMatrix
var network bytes.Buffer
N := 32
A := cmat.NewMatrix(N, N)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
As.SubMatrix(A, 3, 3, N-6, N-6)
enc := gob.NewEncoder(&network)
dec := gob.NewDecoder(&network)
// encode to network
err := enc.Encode(&As)
if err != nil {
t.Logf("encode error: %v\n", err)
t.FailNow()
}
// decode from network
err = dec.Decode(&B)
if err != nil {
t.Logf("decode error: %v\n", err)
t.FailNow()
}
ar, ac := As.Size()
br, bc := B.Size()
t.Logf("As[%d,%d] == B[%d,%d]: %v\n", ar, ac, br, bc, B.AllClose(&As))
}
/*
* Symmetric matrix-vector multiplication. Y = beta*Y + alpha*A*X
*/
func MVMultSym(Y, A, X *cmat.FloatMatrix, alpha, beta float64, bits int, confs ...*gomas.Config) *gomas.Error {
ok := true
yr, yc := Y.Size()
ar, ac := A.Size()
xr, xc := X.Size()
if ar*ac == 0 {
return nil
}
if yr != 1 && yc != 1 {
return gomas.NewError(gomas.ENEED_VECTOR, "MVMultSym")
}
if xr != 1 && xc != 1 {
return gomas.NewError(gomas.ENEED_VECTOR, "MVMultSym")
}
nx := X.Len()
ny := Y.Len()
ok = ny == ar && nx == ac && ac == ar
if !ok {
return gomas.NewError(gomas.ESIZE, "MVMultSym")
}
if beta != 1.0 {
vscal(Y, beta, ny)
}
symv(Y, A, X, alpha, bits, nx)
return nil
}
func TestJSON(t *testing.T) {
var B cmat.FloatMatrix
var network bytes.Buffer
N := 26
A := cmat.NewMatrix(N, N)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
enc := json.NewEncoder(&network)
dec := json.NewDecoder(&network)
// encode to network
err := enc.Encode(A)
//t.Logf("bytes: %v\n", string(network.Bytes()))
if err != nil {
t.Logf("encode error: %v\n", err)
t.FailNow()
}
// decode from network
err = dec.Decode(&B)
if err != nil {
t.Logf("decode error: %v\n", err)
t.FailNow()
}
t.Logf("A == B: %v\n", B.AllClose(A))
}
func TestPartition2D(t *testing.T) {
var ATL, ATR, ABL, ABR, As cmat.FloatMatrix
var A00, a01, A02, a10, a11, a12, A20, a21, A22 cmat.FloatMatrix
csource := cmat.NewFloatConstSource(1.0)
A := cmat.NewMatrix(6, 6)
As.SubMatrix(A, 1, 1, 4, 4)
As.SetFrom(csource)
Partition2x2(&ATL, &ATR, &ABL, &ABR, &As, 0, 0, PTOPLEFT)
t.Logf("ATL:\n%v\n", &ATL)
t.Logf("n(ATL)=%d, n(As)=%d\n", n(&ATL), n(&As))
k := 0
for n(&ATL) < n(&As) && k < n(&As) {
Repartition2x2to3x3(&ATL,
&A00, &a01, &A02,
&a10, &a11, &a12,
&A20, &a21, &A22, &As, 1, PBOTTOMRIGHT)
t.Logf("n(A00)=%d, n(a01)=%d, n(A02)=%d\n", n(&A00), n(&a01), n(&A02))
t.Logf("n(a10)=%d, n(a11)=%d, n(a12)=%d\n", n(&a10), n(&a11), n(&a12))
t.Logf("n(A20)=%d, n(a21)=%d, n(A22)=%d\n", n(&A20), n(&a21), n(&A22))
//t.Logf("n(a12)=%d [%d], n(a11)=%d\n", n(&a12), a12.Len(), a11.Len())
a11.Set(0, 0, a11.Get(0, 0)+1.0)
addConst(&a21, -2.0)
Continue3x3to2x2(&ATL, &ATR, &ABL, &ABR, &A00, &a11, &A22, &As, PBOTTOMRIGHT)
t.Logf("n(ATL)=%d, n(As)=%d\n", n(&ATL), n(&As))
k += 1
}
t.Logf("A:\n%v\n", A)
}
// test: min ||X|| s.t A.T*X = B
func TestSolveQR(t *testing.T) {
M := 799
N := 711
K := 241
nb := 32
conf := gomas.NewConf()
conf.LB = nb
tau := cmat.NewMatrix(N, 1)
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
A0 := cmat.NewCopy(A)
B0 := cmat.NewMatrix(M, K)
B0.SetFrom(src)
B := cmat.NewCopy(B0)
W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
lapackd.QRFactor(A, tau, W, conf)
lapackd.QRSolve(B, A, tau, W, gomas.TRANS, conf)
var Bmin cmat.FloatMatrix
Bmin.SubMatrix(B0, 0, 0, N, K)
blasd.Mult(&Bmin, A0, B, 1.0, -1.0, gomas.TRANSA, conf)
nrm := lapackd.NormP(&Bmin, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||B - A.T*X||_1: %e\n", M, N, nrm)
}
// unblocked LU decomposition w/o pivots, FLAME LU nopivots variant 5
func unblockedLUnoPiv(A *cmat.FloatMatrix, conf *gomas.Config) *gomas.Error {
var ATL, ATR, ABL, ABR cmat.FloatMatrix
var A00, a01, A02, a10, a11, a12, A20, a21, A22 cmat.FloatMatrix
var err *gomas.Error = nil
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, 0, 0, util.PTOPLEFT)
for m(&ATL) < m(A) {
util.Repartition2x2to3x3(&ATL,
&A00, &a01, &A02,
&a10, &a11, &a12,
&A20, &a21, &A22, A, 1, util.PBOTTOMRIGHT)
// a21 = a21/a11
blasd.InvScale(&a21, a11.Get(0, 0))
// A22 = A22 - a21*a12
blasd.MVUpdate(&A22, &a21, &a12, -1.0)
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &a11, &A22, A, util.PBOTTOMRIGHT)
}
return err
}
func minvscale(A *cmat.FloatMatrix, alpha float64, M, N int) {
var a C.mdata_t
a.md = (*C.double)(unsafe.Pointer(&A.Data()[0]))
a.step = C.int(A.Stride())
C.__d_blk_invscale(
(*C.mdata_t)(unsafe.Pointer(&a)), C.double(alpha), C.int(M), C.int(N))
return
}
func Transpose(A, B *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
ar, ac := A.Size()
br, bc := B.Size()
if ar != bc || ac != br {
return gomas.NewError(gomas.ESIZE, "Transpose")
}
mtranspose(A, B, br, bc)
return nil
}
/*
* Build block reflector for QL factorized matrix.
*/
func QLReflector(T, A, tau *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
var tauh cmat.FloatMatrix
if n(T) < n(A) || m(T) < n(A) {
return gomas.NewError(gomas.ESIZE, "QLReflector")
}
tauh.SubMatrix(tau, 0, 0, imin(m(A), n(A)), 1)
unblkQLBlockReflector(T, A, &tauh)
return nil
}
// Compute rational approximation backward
func rationalBackward(z, delta *cmat.FloatMatrix, start, end int) (float64, float64) {
var val, dval float64
val, dval = 0.0, 0.0
for i := end - 1; i >= start; i-- {
dj := delta.GetAtUnsafe(i)
zj := z.GetAtUnsafe(i)
tval := zj / dj
val = val + zj*tval
dval = dval + tval*tval
}
return val, dval
}
func mNormInf(A *cmat.FloatMatrix) float64 {
var amax float64 = 0.0
var row cmat.FloatMatrix
arows, _ := A.Size()
for k := 0; k < arows; k++ {
row.Row(A, k)
rmax := blasd.ASum(&row)
if rmax > amax {
amax = rmax
}
}
return amax
}
func mNorm1(A *cmat.FloatMatrix) float64 {
var amax float64 = 0.0
var col cmat.FloatMatrix
_, acols := A.Size()
for k := 0; k < acols; k++ {
col.Column(A, k)
cmax := blasd.ASum(&col)
if cmax > amax {
amax = cmax
}
}
return amax
}
// Computes eigenvectors corresponding the updated eigenvalues and rank-one update vector.
// The matrix Qd holds precomputed deltas as returned by TRDSecularSolveAll(). If Qd is nil or
// Qd same as the matrix Q then computation is in-place and Q is assumed to hold precomputed
// deltas. On exit, Q holds the column eigenvectors.
func TRDSecularEigen(Q, v, Qd *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
if m(Q) != n(Q) || (Qd != nil && (m(Qd) != n(Qd) || m(Qd) != m(Q))) {
return gomas.NewError(gomas.ESIZE, "TRDSecularEigen")
}
if m(Q) != v.Len() {
return gomas.NewError(gomas.ESIZE, "TRDSecularEigen")
}
if Qd == nil || Qd == Q {
trdsecEigenBuildInplace(Q, v)
} else {
trdsecEigenBuild(Q, v, Qd)
}
return nil
}
func TestPartition1H(t *testing.T) {
var AL, AR, A0, a1, A2 cmat.FloatMatrix
A := cmat.NewMatrix(1, 6)
Partition1x2(&AL, &AR, A, 0, PLEFT)
t.Logf("n(AL)=%d, n(AR)=%d\n", n(&AL), n(&AR))
for n(&AL) < n(A) {
addConst(&AR, 1.0)
t.Logf("n(AR)=%d; %v\n", n(&AR), &AR)
Repartition1x2to1x3(&AL, &A0, &a1, &A2, A, 1, PRIGHT)
t.Logf("n(A0)=%d, n(A2)=%d, a1=%.1f\n", n(&A0), n(&A2), a1.Get(0, 0))
Continue1x3to1x2(&AL, &AR, &A0, &a1, A, PRIGHT)
}
t.Logf("A:%v\n", A)
}
/*
* Partition p to 2 by 1 blocks.
*
* AT
* A --> --
* AB
*
* Parameter nb is initial block size for AT (pTOP) or AB (pBOTTOM).
*/
func Partition2x1(AT, AB, A *cmat.FloatMatrix, nb int, side Direction) {
ar, ac := A.Size()
if nb > ar {
nb = ar
}
switch side {
case PTOP:
AT.SubMatrix(A, 0, 0, nb, ac)
AB.SubMatrix(A, nb, 0, ar-nb, ac)
case PBOTTOM:
AT.SubMatrix(A, 0, 0, ar-nb, ac)
AB.SubMatrix(A, ar-nb, 0, nb, ac)
}
}
/*
* Partition A to 1 by 2 blocks.
*
* A --> AL | AR
*
* Parameter nb is initial block size for AL (pLEFT) or AR (pRIGHT).
*/
func Partition1x2(AL, AR, A *cmat.FloatMatrix, nb int, side Direction) {
ar, ac := A.Size()
if nb > ac {
nb = ac
}
switch side {
case PLEFT:
AL.SubMatrix(A, 0, 0, ar, nb)
AR.SubMatrix(A, 0, nb, ar, ac-nb)
case PRIGHT:
AL.SubMatrix(A, 0, 0, ar, ac-nb)
AR.SubMatrix(A, 0, ac-nb, ar, nb)
}
}
// d = |d| - |s|
func absMinus(d, s *cmat.FloatMatrix) *cmat.FloatMatrix {
for k := 0; k < d.Len(); k++ {
tmp := math.Abs(d.GetAt(k))
d.SetAt(k, math.Abs(s.GetAt(k))-tmp)
}
return d
}
/*
* Build full block reflect T for nc columns from sequence of reflector stored in S.
* Reflectors in S are the diagonal of T, off-diagonal values of reflector are computed
* from elementary reflector store in lower triangular part of A.
*/
func buildQRTReflector(T, A, S *cmat.FloatMatrix, nc int, conf *gomas.Config) *gomas.Error {
var ATL, ATR, ABL, ABR cmat.FloatMatrix
var A00, A10, A11, A20, A21, A22 cmat.FloatMatrix
var TTL, TTR, TBL, TBR cmat.FloatMatrix
var T00, T01, T02, T11, T12, T22 cmat.FloatMatrix
var SL, SR cmat.FloatMatrix
var S00, S01, S02 cmat.FloatMatrix
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, 0, 0, util.PTOPLEFT)
util.Partition2x2(
&TTL, &TTR,
&TBL, &TBR, T, 0, 0, util.PTOPLEFT)
util.Partition1x2(
&SL, &SR, S, 0, util.PLEFT)
nb := conf.LB
for m(&ABR)-nb > 0 && n(&ABR)-nb > 0 {
util.Repartition2x2to3x3(&ATL,
&A00, nil, nil,
&A10, &A11, nil,
&A20, &A21, &A22, A, nb, util.PBOTTOMRIGHT)
util.Repartition2x2to3x3(&TTL,
&T00, &T01, &T02,
nil, &T11, &T12,
nil, nil, &T22, T, nb, util.PBOTTOMRIGHT)
util.Repartition1x2to1x3(&SL,
&S00, &S01, &S02, S, nb, util.PRIGHT)
// --------------------------------------------------------
// update T01: T01 = -T00*Y1.T*Y2*T11
// Y1 = /A10\ Y2 = /A11\
// \A20/ \A21/
//
T11.Copy(&S01)
updateQRTReflector(&T01, &A10, &A20, &A11, &A21, &T00, &S01, conf)
// --------------------------------------------------------
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &A11, &A22, A, util.PBOTTOMRIGHT)
util.Continue3x3to2x2(
&TTL, &TTR,
&TBL, &TBR, &T00, &T11, &T22, T, util.PBOTTOMRIGHT)
util.Continue1x3to1x2(
&SL, &SR, &S00, &S01, S, util.PRIGHT)
}
if m(&ABR) > 0 && n(&ABR) > 0 {
}
return nil
}
func TestQLBuildwithK(t *testing.T) {
var dc cmat.FloatMatrix
M := 711
N := 707
K := 691
lb := 36
conf := gomas.NewConf()
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
tau := cmat.NewMatrix(N, 1)
W := cmat.NewMatrix(M+N, 1)
C := cmat.NewMatrix(N, N)
conf.LB = lb
lapackd.QLFactor(A, tau, W, conf)
A1 := cmat.NewCopy(A)
conf.LB = 0
lapackd.QLBuild(A, tau, W, K, conf)
blasd.Mult(C, A, A, 1.0, 0.0, gomas.TRANSA, conf)
dc.Diag(C)
blasd.Add(&dc, -1.0)
if N < 10 {
t.Logf("unblk.QLBuild Q:\n%v\n", A)
t.Logf("unblk.QLBuild Q.T*Q:\n%v\n", C)
}
n0 := lapackd.NormP(C, lapackd.NORM_ONE)
conf.LB = lb
W1 := lapackd.Workspace(lapackd.QLBuildWork(A1, conf))
lapackd.QLBuild(A1, tau, W1, K, conf)
if N < 10 {
t.Logf("blk.QLBuild Q:\n%v\n", A1)
}
// compute: I - Q.T*Q
blasd.Mult(C, A1, A1, 1.0, 0.0, gomas.TRANSA, conf)
blasd.Add(&dc, -1.0)
n1 := lapackd.NormP(C, lapackd.NORM_ONE)
blasd.Plus(A, A1, 1.0, -1.0, gomas.NONE)
n2 := lapackd.NormP(A, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d, K=%d ||unblk.QLBuild(A) - blk.QLBuild(A)||_1 :%e\n", M, N, K, n2)
t.Logf("unblk M=%d, N=%d, K=%d ||Q.T*Q - I||_1 : %e\n", M, N, K, n0)
t.Logf("blk M=%d, N=%d, K=%d ||Q.T*Q - I||_1 : %e\n", M, N, K, n1)
}
func Swap(X, Y *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
xr, xc := X.Size()
yr, yc := Y.Size()
if xr != 1 && xc != 1 {
return gomas.NewError(gomas.ENEED_VECTOR, "Swap")
}
if yr != 1 && yc != 1 {
return gomas.NewError(gomas.ENEED_VECTOR, "Swap")
}
if X.Len() != Y.Len() {
return gomas.NewError(gomas.ESIZE, "Swap")
}
vswap(X, Y, X.Len())
return nil
}
func TestLQBuild(t *testing.T) {
var dc cmat.FloatMatrix
M := 877
N := 913
K := 831
lb := 48
conf := gomas.NewConf()
_ = lb
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
tau := cmat.NewMatrix(M, 1)
W := cmat.NewMatrix(M, 1)
C := cmat.NewMatrix(M, M)
dc.Diag(C)
conf.LB = lb
lapackd.LQFactor(A, tau, W, conf)
A1 := cmat.NewCopy(A)
conf.LB = 0
lapackd.LQBuild(A, tau, W, K, conf)
if N < 10 {
t.Logf("unblk.LQBuild Q:\n%v\n", A)
}
blasd.Mult(C, A, A, 1.0, 0.0, gomas.TRANSB, conf)
blasd.Add(&dc, -1.0)
n0 := lapackd.NormP(C, lapackd.NORM_ONE)
conf.LB = lb
W2 := lapackd.Workspace(lapackd.LQBuildWork(A, conf))
lapackd.LQBuild(A1, tau, W2, K, conf)
if N < 10 {
t.Logf("blk.LQBuild Q:\n%v\n", A1)
}
blasd.Mult(C, A1, A1, 1.0, 0.0, gomas.TRANSB, conf)
blasd.Add(&dc, -1.0)
n1 := lapackd.NormP(C, lapackd.NORM_ONE)
blasd.Plus(A, A1, 1.0, -1.0, gomas.NONE)
n2 := lapackd.NormP(A, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d, K=%d ||unblk.LQBuild(A) - blk.LQBuild(A)||_1 :%e\n", M, N, K, n2)
t.Logf("unblk M=%d, N=%d, K=%d ||I - Q*Q.T||_1 : %e\n", M, N, K, n0)
t.Logf(" blk M=%d, N=%d, K=%d ||I - Q*Q.T||_1 : %e\n", M, N, K, n1)
}
/*
* Unblocked QR decomposition with block reflector T.
*/
func unblockedQRT(A, T, W *cmat.FloatMatrix) *gomas.Error {
var err *gomas.Error = nil
var ATL, ATR, ABL, ABR cmat.FloatMatrix
var A00, a10, a11, a12, A20, a21, A22 cmat.FloatMatrix
var TTL, TTR, TBL, TBR cmat.FloatMatrix
var T00, t01, T02, t11, t12, T22, w12 cmat.FloatMatrix
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, 0, 0, util.PTOPLEFT)
util.Partition2x2(
&TTL, &TTR,
&TBL, &TBR, T, 0, 0, util.PTOPLEFT)
for m(&ABR) > 0 && n(&ABR) > 0 {
util.Repartition2x2to3x3(&ATL,
&A00, nil, nil,
&a10, &a11, &a12,
&A20, &a21, &A22, A, 1, util.PBOTTOMRIGHT)
util.Repartition2x2to3x3(&TTL,
&T00, &t01, &T02,
nil, &t11, &t12,
nil, nil, &T22, T, 1, util.PBOTTOMRIGHT)
// ------------------------------------------------------
computeHouseholder(&a11, &a21, &t11)
// H*[a12 A22].T
w12.SubMatrix(W, 0, 0, a12.Len(), 1)
applyHouseholder2x1(&t11, &a21, &a12, &A22, &w12, gomas.LEFT)
// update T
tauval := t11.Get(0, 0)
if tauval != 0.0 {
// t01 := -tauval*(a10.T + &A20.T*a21)
//a10.CopyTo(&t01)
blasd.Axpby(&t01, &a10, 1.0, 0.0)
blasd.MVMult(&t01, &A20, &a21, -tauval, -tauval, gomas.TRANSA)
// t01 := T00*t01
blasd.MVMultTrm(&t01, &T00, 1.0, gomas.UPPER)
}
// ------------------------------------------------------
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &a11, &A22, A, util.PBOTTOMRIGHT)
util.Continue3x3to2x2(
&TTL, &TTR,
&TBL, &TBR, &T00, &t11, &T22, T, util.PBOTTOMRIGHT)
}
return err
}
// Compute eigenmatrix Q for updated eigenvalues in 'dl'.
func trdsecEigenBuild(Q, z, Q2 *cmat.FloatMatrix) {
var qi, delta cmat.FloatMatrix
for k := 0; k < z.Len(); k++ {
qi.Column(Q, k)
delta.Row(Q2, k)
trdsecEigenVecDelta(&qi, &delta, z)
}
}
/*
* Merge 1 by 1 block from 1 by 2 block.
*
* ABLK <-- AL | AR
*
*/
func Merge1x2(ABLK, AL, AR *cmat.FloatMatrix) {
lr, lc := AL.Size()
_, rc := AR.Size()
if lc > 0 {
ABLK.SubMatrix(AL, 0, 0, lr, lc+rc)
} else {
ABLK.SubMatrix(AR, 0, 0, lr, rc)
}
}