// compute:
// C*Q.T = C*(I -Y*T*Y.T).T == C - C*Y*T.T*Y.T
// or
// C*Q = (I -Y*T*Y.T)*C == C - C*Y*T*Y.T
//
//
// where C = ( C2 C1 ), Y = ( Y2 Y1 )
//
// C1 is K*nb, C2 is K*P, Y1 is nb*nb triuu, Y2 is nb*P, T is nb*nb
// W = K*nb
func updateRightRQ(C1, C2, Y1t, Y2t, T, W *cmat.FloatMatrix, transpose bool, conf *gomas.Config) {
// -- compute: W = C*Y = C1*Y1 + C2*Y2
// W = C1
blasd.Plus(W, C1, 0.0, 1.0, gomas.NONE)
// W = C1*Y1t.T
blasd.MultTrm(W, Y1t, 1.0, gomas.RIGHT|gomas.LOWER|gomas.UNIT|gomas.TRANSA, conf)
// W = W + C2*Y2t.T
blasd.Mult(W, C2, Y2t, 1.0, 1.0, gomas.TRANSB, conf)
// --- here: W == C*Y ---
tflags := gomas.RIGHT | gomas.LOWER
if transpose {
tflags |= gomas.TRANSA
}
// W = W*T or W*T.T
blasd.MultTrm(W, T, 1.0, tflags, conf)
// --- here: W == C*Y*T or C*Y*T.T ---
// C2 = C2 - W*Y2t
blasd.Mult(C2, W, Y2t, -1.0, 1.0, gomas.NONE, conf)
// C1 = C1 - W*Y1t
// W = W*Y1
blasd.MultTrm(W, Y1t, 1.0, gomas.RIGHT|gomas.LOWER|gomas.UNIT, conf)
// C1 = C1 - W
blasd.Plus(C1, W, 1.0, -1.0, gomas.NONE)
// --- here: C = (I - Y*T*Y.T).T * C ---
}
// compute:
// Q.T*C = (I -Y*T*Y.T).T*C == C - Y*(C.T*Y*T).T
// or
// Q*C = (I -Y*T*Y.T)*C == C - Y*(C.T*Y*T.T).T
//
//
// where C = ( C2 ) Y = ( Y2 Y1 )
// ( C1 )
//
// C1 is nb*K, C2 is P*K, Y1 is nb*nb triuu, Y2 is nb*P, T is nb*nb
// W = K*nb
func updateLeftRQ(C1, C2, Y1t, Y2t, T, W *cmat.FloatMatrix, transpose bool, conf *gomas.Config) {
// W = C1.T
blasd.Plus(W, C1, 0.0, 1.0, gomas.TRANSB)
// W = C1.T*Y1.T
blasd.MultTrm(W, Y1t, 1.0, gomas.RIGHT|gomas.LOWER|gomas.UNIT|gomas.TRANSA, conf)
// W = W + C2.T*Y2.T
blasd.Mult(W, C2, Y2t, 1.0, 1.0, gomas.TRANSA|gomas.TRANSB, conf)
// --- here: W == C.T*Y == C1.T*Y1.T + C2.T*Y2.T ---
tflags := gomas.RIGHT | gomas.LOWER
if !transpose {
tflags |= gomas.TRANSA
}
// W = W*T or W*T.T
blasd.MultTrm(W, T, 1.0, tflags, conf)
// --- here: W == C.T*Y*T or C.T*Y*T.T ---
// C2 = C2 - Y2*W.T
blasd.Mult(C2, Y2t, W, -1.0, 1.0, gomas.TRANSA|gomas.TRANSB, conf)
// W = Y1*W.T ==> W.T = W*Y1
blasd.MultTrm(W, Y1t, 1.0, gomas.RIGHT|gomas.LOWER|gomas.UNIT, conf)
// C1 = C1 - W.T
blasd.Plus(C1, W, 1.0, -1.0, gomas.TRANSB)
// --- here: C = (I - Y*T*Y.T).T * C ---
}
func TestDTrmmUnitUpper(t *testing.T) {
var d cmat.FloatMatrix
N := 563
K := 171
A := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(N, K)
B0 := cmat.NewMatrix(N, K)
C := cmat.NewMatrix(N, K)
zeros := cmat.NewFloatConstSource(0.0)
ones := cmat.NewFloatConstSource(1.0)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean, cmat.UPPER|cmat.UNIT)
B.SetFrom(ones)
B0.SetFrom(ones)
// B = A*B
blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.LEFT|gomas.UNIT)
d.Diag(A).SetFrom(ones)
blasd.Mult(C, A, B0, 1.0, 0.0, gomas.NONE)
ok := C.AllClose(B)
t.Logf("trmm(B, A, L|U|N|U) == gemm(C, TriUU(A), B) : %v\n", ok)
B.SetFrom(ones)
// B = A.T*B
d.Diag(A).SetFrom(zeros)
blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.LEFT|gomas.TRANSA|gomas.UNIT)
d.Diag(A).SetFrom(ones)
blasd.Mult(C, A, B0, 1.0, 0.0, gomas.TRANSA)
ok = C.AllClose(B)
t.Logf("trmm(B, A, L|U|T|U) == gemm(C, TriUU(A).T, B) : %v\n", ok)
}
func TestDTrmmLowerRight(t *testing.T) {
N := 563
K := 171
nofail := true
A := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(K, N)
B0 := cmat.NewMatrix(K, N)
C := cmat.NewMatrix(K, N)
ones := cmat.NewFloatConstSource(1.0)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean, cmat.LOWER)
B.SetFrom(ones)
B0.SetFrom(ones)
// B = B*A
blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.RIGHT)
blasd.Mult(C, B0, A, 1.0, 0.0, gomas.NONE)
ok := C.AllClose(B)
nofail = nofail && ok
t.Logf("trmm(B, A, R|L|N) == gemm(C, B, TriL(A)) : %v\n", ok)
B.SetFrom(ones)
// B = B*A.T
blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.RIGHT|gomas.TRANSA)
blasd.Mult(C, B0, A, 1.0, 0.0, gomas.TRANSB)
ok = C.AllClose(B)
nofail = nofail && ok
t.Logf("trmm(B, A, R|L|T) == gemm(C, B, TriL(A).T) : %v\n", ok)
}
func TestDTrmmUnitUpperRight(t *testing.T) {
var d cmat.FloatMatrix
N := 563
K := 171
A := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(K, N)
B0 := cmat.NewMatrix(K, N)
C := cmat.NewMatrix(K, N)
zeros := cmat.NewFloatConstSource(0.0)
ones := cmat.NewFloatConstSource(1.0)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean, cmat.UPPER|cmat.UNIT)
B.SetFrom(ones)
B0.SetFrom(ones)
// B = B*A
blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.RIGHT|gomas.UNIT)
d.Diag(A).SetFrom(ones)
blasd.Mult(C, B0, A, 1.0, 0.0, gomas.NONE)
ok := C.AllClose(B)
t.Logf("trmm(B, A, R|U|N|U) == gemm(C, B, TriUU(A)) : %v\n", ok)
B.SetFrom(ones)
// B = B*A.T
d.SetFrom(zeros)
blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.RIGHT|gomas.TRANSA|gomas.UNIT)
d.SetFrom(ones)
blasd.Mult(C, B0, A, 1.0, 0.0, gomas.TRANSB)
ok = C.AllClose(B)
t.Logf("trmm(B, A, R|U|T|U) == gemm(C, B, TriUU(A).T) : %v\n", ok)
}
func TestDTrmmLower(t *testing.T) {
N := 563
K := 171
nofail := true
A := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(N, K)
B0 := cmat.NewMatrix(N, K)
C := cmat.NewMatrix(N, K)
ones := cmat.NewFloatConstSource(1.0)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean, cmat.LOWER)
B.SetFrom(ones)
B0.SetFrom(ones)
// B = A*B
blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT)
blasd.Mult(C, A, B0, 1.0, 0.0, gomas.NONE)
ok := C.AllClose(B)
nofail = nofail && ok
t.Logf("trmm(B, A, L|L|N) == gemm(C, TriL(A), B) : %v\n", ok)
B.SetFrom(ones)
// B = A.T*B
blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT|gomas.TRANSA)
blasd.Mult(C, A, B0, 1.0, 0.0, gomas.TRANSA)
ok = C.AllClose(B)
nofail = nofail && ok
t.Logf("trmm(B, A, L|L|T) == gemm(C, TriL(A).T, B) : %v\n", ok)
}
func test_bdsvd(N, flags, kind int, verbose bool, t *testing.T) {
var At, sD, sE, tmp cmat.FloatMatrix
uplo := "upper"
offdiag := 1
if flags&gomas.LOWER != 0 {
offdiag = -1
uplo = "lower"
}
A0 := cmat.NewMatrix(N, N)
desc := setDiagonals(A0, offdiag, kind)
At.SubMatrix(A0, 0, 0, N, N)
sD.Diag(A0, 0)
sE.Diag(A0, offdiag)
D := cmat.NewCopy(&sD)
E := cmat.NewCopy(&sE)
// unit singular vectors
U := cmat.NewMatrix(N, N)
sD.Diag(U, 0)
sD.Add(1.0)
V := cmat.NewMatrix(N, N)
sD.Diag(V, 0)
sD.Add(1.0)
W := cmat.NewMatrix(4*N, 1)
C := cmat.NewMatrix(N, N)
lapackd.BDSvd(D, E, U, V, W, flags|gomas.WANTU|gomas.WANTV)
blasd.Mult(C, U, U, 1.0, 0.0, gomas.TRANSA)
sD.Diag(C)
sD.Add(-1.0)
nrmu := lapackd.NormP(C, lapackd.NORM_ONE)
blasd.Mult(C, V, V, 1.0, 0.0, gomas.TRANSB)
sD.Add(-1.0)
nrmv := lapackd.NormP(C, lapackd.NORM_ONE)
blasd.Mult(C, U, A0, 1.0, 0.0, gomas.TRANSA)
blasd.Mult(&At, C, V, 1.0, 0.0, gomas.TRANSB)
if verbose && N < 10 {
t.Logf("D:\n%v\n", asRow(&tmp, D))
t.Logf("U:\n%v\n", U)
t.Logf("V:\n%v\n", V)
t.Logf("U.T*A*V\n%v\n", &At)
}
sD.Diag(&At)
blasd.Axpy(&sD, D, -1.0)
nrma := lapackd.NormP(&At, lapackd.NORM_ONE)
t.Logf("N=%d [%s,%s] ||U.T*A*V - bdsvd(A)||_1: %e\n", N, uplo, desc, nrma)
t.Logf(" ||I - U.T*U||_1: %e\n", nrmu)
t.Logf(" ||I - V.T*V||_1: %e\n", nrmv)
}
// test: C = C*Q.T
func TestQLMultRightTrans(t *testing.T) {
var d, di0, di1 cmat.FloatMatrix
M := 891
N := 853
lb := 36
conf := gomas.NewConf()
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
C0 := cmat.NewMatrix(N, M)
d.Diag(C0, M-N)
ones := cmat.NewFloatConstSource(1.0)
d.SetFrom(ones)
C1 := cmat.NewCopy(C0)
I0 := cmat.NewMatrix(N, N)
I1 := cmat.NewCopy(I0)
di0.Diag(I0)
di1.Diag(I1)
tau := cmat.NewMatrix(N, 1)
W := cmat.NewMatrix(lb*(M+N), 1)
conf.LB = lb
lapackd.QLFactor(A, tau, W, conf)
conf.LB = 0
lapackd.QLMult(C0, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
// I = Q*Q.T - I
blasd.Mult(I0, C0, C0, 1.0, 0.0, gomas.TRANSB, conf)
blasd.Add(&di0, -1.0)
n0 := lapackd.NormP(I0, lapackd.NORM_ONE)
conf.LB = lb
lapackd.QLMult(C1, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
// I = Q*Q.T - I
blasd.Mult(I1, C1, C1, 1.0, 0.0, gomas.TRANSB, conf)
blasd.Add(&di1, -1.0)
n1 := lapackd.NormP(I1, lapackd.NORM_ONE)
if N < 10 {
t.Logf("unblk C0*Q:\n%v\n", C0)
t.Logf("blk. C2*Q:\n%v\n", C1)
}
blasd.Plus(C0, C1, 1.0, -1.0, gomas.NONE)
n2 := lapackd.NormP(C0, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||unblk.QLMult(C) - blk.QLMult(C)||_1: %e\n", M, N, n2)
t.Logf("unblk M=%d, N=%d ||I - Q*Q.T||_1: %e\n", M, N, n0)
t.Logf("blk M=%d, N=%d ||I - Q*Q.T||_1: %e\n", M, N, n1)
}
func TestUpperCHOL(t *testing.T) {
N := 311
K := 43
nb := 0
conf := gomas.NewConf()
conf.LB = nb
Z := cmat.NewMatrix(N, N)
A := cmat.NewMatrix(N, N)
A0 := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(N, K)
X := cmat.NewMatrix(N, K)
unitrand := cmat.NewFloatUniformSource()
Z.SetFrom(unitrand)
blasd.Mult(A, Z, Z, 1.0, 0.0, gomas.TRANSB)
A0.Copy(A)
B.SetFrom(unitrand)
X.Copy(B)
// A = chol(A) = U.T*U
t.Logf("Unblocked version: nb=%d\n", conf.LB)
lapackd.CHOLFactor(A, gomas.UPPER, conf)
// X = A.-1*B = U.-1*(U.-T*B)
lapackd.CHOLSolve(X, A, gomas.UPPER)
// B = B - A*X
blasd.Mult(B, A0, X, -1.0, 1.0, gomas.NONE)
// ||B - A*X||_1
nrm := lapackd.NormP(B, lapackd.NORM_ONE)
t.Logf("N=%d: ||B - A*X||_1: %e\n", N, nrm)
// A = chol(A) = U.T*U
A.Copy(A0)
B.SetFrom(unitrand)
X.Copy(B)
conf.LB = 16
t.Logf("Blocked version: nb=%d\n", conf.LB)
lapackd.CHOLFactor(A, gomas.UPPER, conf)
// X = A.-1*B = U.-1*(U.-T*B)
lapackd.CHOLSolve(X, A, gomas.UPPER)
// B = B - A*X
blasd.Mult(B, A0, X, -1.0, 1.0, gomas.NONE)
// ||B - A*X||_1
nrm = lapackd.NormP(B, lapackd.NORM_ONE)
t.Logf("N=%d: ||B - A*X||_1: %e\n", N, nrm)
}
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 test_trdevd(N, flags, kind int, verbose bool, t *testing.T) {
var At, sD, sE, tmp cmat.FloatMatrix
A0 := cmat.NewMatrix(N, N)
desc := setTrdDiagonals(A0, kind)
At.SubMatrix(A0, 0, 0, N, N)
sD.Diag(A0, 0)
sE.Diag(A0, 1)
D := cmat.NewCopy(&sD)
E := cmat.NewCopy(&sE)
V := cmat.NewMatrix(N, N)
sD.Diag(V, 0)
sD.Add(1.0)
W := cmat.NewMatrix(4*N, 1)
C := cmat.NewMatrix(N, N)
if verbose && N < 10 {
t.Logf("A0:\n%v\n", A0.ToString("%6.3f"))
t.Logf("V.pre:\n%v\n", V.ToString("%6.3f"))
}
lapackd.TRDEigen(D, E, V, W, flags|gomas.WANTV)
for k := 0; k < N-1; k++ {
if E.GetAt(k) != 0.0 {
t.Logf("E[%d] != 0.0 (%e)\n", k, E.GetAt(k))
}
}
blasd.Mult(C, V, V, 1.0, 0.0, gomas.TRANSB)
sD.Diag(C)
sD.Add(-1.0)
nrmv := lapackd.NormP(C, lapackd.NORM_ONE)
blasd.Mult(C, V, A0, 1.0, 0.0, gomas.TRANSA)
blasd.Mult(&At, C, V, 1.0, 0.0, gomas.NONE)
if verbose && N < 10 {
t.Logf("D:\n%v\n", asRow(&tmp, D).ToString("%6.3f"))
t.Logf("V:\n%v\n", V.ToString("%6.3f"))
t.Logf("V.T*A*V\n%v\n", At.ToString("%6.3f"))
}
sD.Diag(&At)
blasd.Axpy(&sD, D, -1.0)
nrma := lapackd.NormP(&At, lapackd.NORM_ONE)
t.Logf("N=%d [%s] ||V.T*A*V - eigen(A)||_1: %e\n", N, desc, nrma)
t.Logf(" ||I - V.T*V||_1: %e\n", nrmv)
}
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)
}
// 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)
}
// 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)
}
// blocked LU decomposition w/o pivots, FLAME LU nopivots variant 5
func blockedLUnoPiv(A *cmat.FloatMatrix, nb int, conf *gomas.Config) *gomas.Error {
var err *gomas.Error = nil
var ATL, ATR, ABL, ABR cmat.FloatMatrix
var A00, A01, A02, A10, A11, A12, A20, A21, A22 cmat.FloatMatrix
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, 0, 0, util.PTOPLEFT)
for m(&ATL) < m(A)-nb {
util.Repartition2x2to3x3(&ATL,
&A00, &A01, &A02,
&A10, &A11, &A12,
&A20, &A21, &A22, A, nb, util.PBOTTOMRIGHT)
// A00 = LU(A00)
unblockedLUnoPiv(&A11, conf)
// A12 = trilu(A00)*A12.-1 (TRSM)
blasd.SolveTrm(&A12, &A11, 1.0, gomas.LEFT|gomas.LOWER|gomas.UNIT)
// A21 = A21.-1*triu(A00) (TRSM)
blasd.SolveTrm(&A21, &A11, 1.0, gomas.RIGHT|gomas.UPPER)
// A22 = A22 - A21*A12
blasd.Mult(&A22, &A21, &A12, -1.0, 1.0, gomas.NONE)
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &A11, &A22, A, util.PBOTTOMRIGHT)
}
// last block
if m(&ATL) < m(A) {
unblockedLUnoPiv(&ABR, conf)
}
return err
}
// 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 TestBlockedDecomposeCHOL(t *testing.T) {
N := 119
nb := 16
conf := gomas.NewConf()
conf.LB = nb
Z := cmat.NewMatrix(N, N)
AL := cmat.NewMatrix(N, N)
AU := cmat.NewMatrix(N, N)
unitrand := cmat.NewFloatUniformSource()
Z.SetFrom(unitrand)
blasd.Mult(AL, Z, Z, 1.0, 0.0, gomas.TRANSB)
AU.Copy(AL)
eu := lapackd.CHOLFactor(AU, gomas.UPPER, conf)
el := lapackd.CHOLFactor(AL, gomas.LOWER, conf)
_, _ = eu, el
Z.Transpose(AU)
if N < 10 {
t.Logf("AU.T:\n%v\n", Z)
t.Logf("AL:\n%v\n", AL)
}
ok := AL.AllClose(Z)
t.Logf("Decompose(AL) == Decompose(AU).T: %v\n", ok)
}
func TestLU(t *testing.T) {
N := 119
K := 41
nb := 0
A := cmat.NewMatrix(N, N)
A0 := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(N, K)
X := cmat.NewMatrix(N, K)
unitrand := cmat.NewFloatUniformSource()
A.SetFrom(unitrand)
A0.Copy(A)
B.SetFrom(unitrand)
X.Copy(B)
piv := lapackd.NewPivots(N)
conf := gomas.DefaultConf()
conf.LB = nb
// R = lu(A) = P*L*U
lapackd.LUFactor(A, piv, conf)
// X = A.-1*B = U.-1*(L.-1*B)
lapackd.LUSolve(X, A, piv, gomas.NONE)
// B = B - A*X
blasd.Mult(B, A0, X, -1.0, 1.0, gomas.NONE)
nrm := lapackd.NormP(B, lapackd.NORM_ONE)
t.Logf("Unblocked decomposition: nb=%d\n", conf.LB)
t.Logf("N=%d ||B - A*X||_1: %e\n", N, nrm)
// blocked
conf.LB = 16
A.Copy(A0)
B.SetFrom(unitrand)
X.Copy(B)
// lu(A) = P*L*U
lapackd.LUFactor(A, piv, conf)
// X = A.-1*B = U.-1*(L.-1*B)
lapackd.LUSolve(X, A, piv, gomas.NONE)
// B = B - A*X
blasd.Mult(B, A0, X, -1.0, 1.0, gomas.NONE)
nrm = lapackd.NormP(B, lapackd.NORM_ONE)
t.Logf("Blocked decomposition: nb=%d\n", conf.LB)
t.Logf("N=%d ||B - A*X||_1: %e\n", N, nrm)
}
func TestQRBuild(t *testing.T) {
var d cmat.FloatMatrix
M := 911
N := 899
K := 873
lb := 36
conf := gomas.NewConf()
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
tau := cmat.NewMatrix(N, 1)
W := cmat.NewMatrix(N+M, 1)
C := cmat.NewMatrix(N, N)
d.Diag(C)
conf.LB = lb
lapackd.QRFactor(A, tau, W, conf)
A1 := cmat.NewCopy(A)
conf.LB = 0
lapackd.QRBuild(A, tau, W, K, conf)
blasd.Mult(C, A, A, 1.0, 0.0, gomas.TRANSA, conf)
blasd.Add(&d, -1.0)
n0 := lapackd.NormP(C, lapackd.NORM_ONE)
conf.LB = lb
W2 := lapackd.Workspace(lapackd.QRBuildWork(A, conf))
lapackd.QRBuild(A1, tau, W2, K, conf)
blasd.Mult(C, A1, A1, 1.0, 0.0, gomas.TRANSA, conf)
blasd.Add(&d, -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.QRBuild(A) - blk.QRBuild(A)||_1 :%e\n", M, N, K, n2)
t.Logf("unblk M=%d, N=%d, K=%d ||I - Q.T*Q||_1: %e\n", M, N, K, n0)
t.Logf(" blk M=%d, N=%d, K=%d ||I - Q.T*Q||_1: %e\n", M, N, K, n1)
}
func testEigen(N int, bits int, t *testing.T) {
var A, A0, W, D, V *cmat.FloatMatrix
var sD cmat.FloatMatrix
var s string = "lower"
if bits&gomas.UPPER != 0 {
s = "upper"
}
wsize := N * N
if wsize < 100 {
wsize = 100
}
D = cmat.NewMatrix(N, 1)
A = cmat.NewMatrix(N, N)
V = cmat.NewMatrix(N, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src, cmat.SYMM)
A0 = cmat.NewCopy(A)
W = cmat.NewMatrix(wsize, 1)
if err := lapackd.EigenSym(D, A, W, bits|gomas.WANTV); err != nil {
t.Errorf("EigenSym error: %v\n", err)
return
}
// ||I - V.T*V||
sD.Diag(V)
blasd.Mult(V, A, A, 1.0, 0.0, gomas.TRANSA)
blasd.Add(&sD, -1.0)
nrm1 := lapackd.NormP(V, lapackd.NORM_ONE)
// left vectors are M-by-N
V.Copy(A)
lapackd.MultDiag(V, D, gomas.RIGHT)
blasd.Mult(A0, V, A, -1.0, 1.0, gomas.TRANSB)
nrm2 := lapackd.NormP(A0, lapackd.NORM_ONE)
t.Logf("N=%d, [%s] ||A - V*D*V.T||_1 :%e\n", N, s, nrm2)
t.Logf(" ||I - V.T*V||_1 : %e\n", nrm1)
}
func TestDSyrkUpper(t *testing.T) {
var ok bool
conf := gomas.NewConf()
A := cmat.NewMatrix(N, N)
A0 := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(N, K)
Bt := cmat.NewMatrix(K, N)
ones := cmat.NewFloatConstSource(1.0)
zeromean := cmat.NewFloatUniformSource()
_, _ = ones, zeromean
A.SetFrom(ones, cmat.UPPER)
A0.Copy(A)
B.SetFrom(ones)
Bt.Transpose(B)
// B = A*B
blasd.UpdateSym(A, B, 1.0, 1.0, gomas.UPPER, conf)
blasd.Mult(A0, B, B, 1.0, 1.0, gomas.TRANSB)
cmat.TriU(A0, cmat.NONE)
ok = A0.AllClose(A)
t.Logf("UpdateSym(A, B, U|N) == TriU(Mult(A, B, B.T)) : %v\n", ok)
if N < 10 {
t.Logf("UpdateSym(A, B)\n%v\n", A)
t.Logf("Mult(A, B.T, B)\n%v\n", A0)
}
A.SetFrom(ones, cmat.UPPER)
A0.Copy(A)
blasd.UpdateSym(A, Bt, 1.0, 1.0, gomas.UPPER|gomas.TRANSA, conf)
blasd.Mult(A0, Bt, Bt, 1.0, 1.0, gomas.TRANSA)
cmat.TriU(A0, cmat.NONE)
ok = A0.AllClose(A)
t.Logf("UpdateSym(A, B, U|T) == TriU(Mult(A, B.T, B)) : %v\n", ok)
if N < 10 {
t.Logf("UpdateSym(A, B)\n%v\n", A)
t.Logf("Mult(A, B.T, B)\n%v\n", A0)
}
}
/*
* test2: C0 = A*B.T; C1 = B*A.T; C0 == C1.T
* A[M,K], B[K,N], C[M,N] and M != N == K
*/
func TestDGemm2(t *testing.T) {
M := 411
N := 377
K := N
A := cmat.NewMatrix(M, K)
B := cmat.NewMatrix(K, N)
C := cmat.NewMatrix(M, N)
Ct := cmat.NewMatrix(N, M)
T := cmat.NewMatrix(M, N)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
B.SetFrom(zeromean)
blasd.Mult(C, A, B, 1.0, 0.0, gomas.TRANSB)
blasd.Mult(Ct, B, A, 1.0, 0.0, gomas.TRANSB)
T.Transpose(Ct)
ok := C.AllClose(T)
t.Logf("gemm(A, B.T) == transpose(gemm(B, A.T)) : %v\n", ok)
}
// update T: T = -T1*Y1.T*Y2*T2
// Y1 = /Y10\ Y2 = /Y11\
// \Y20/ \Y21/
//
// T = -T1 * [Y10.T*Y11 + Y20.T*Y21]*T2
//
// T1 is K*K triangular upper matrix
// T2 is nb*nb triangular upper matrix
// T is K*nb block matrix
// Y10 is nb*K block matrix
// Y20 is M-K-nb*K block matrix
// Y11 is nb*nb triangular lower unit diagonal matrix
// Y21 is M-K-nb*nb block matrix
//
func updateQRTReflector(T, Y10, Y20, Y11, Y21, T1, T2 *cmat.FloatMatrix, conf *gomas.Config) {
// T = Y10.T
if n(Y10) == 0 {
return
}
// T = Y10.T
blasd.Plus(T, Y10, 0.0, 1.0, gomas.TRANSB)
// T = Y10.T*Y11
blasd.MultTrm(T, Y11, 1.0, gomas.LOWER|gomas.UNIT|gomas.RIGHT, conf)
// T = T + Y20.T*Y21
blasd.Mult(T, Y20, Y21, 1.0, 1.0, gomas.TRANSA, conf)
// -- here: T == Y1.T*Y2
// T = -T1*T
blasd.MultTrm(T, T1, -1.0, gomas.UPPER, conf)
// T = T*T2
blasd.MultTrm(T, T2, 1.0, gomas.UPPER|gomas.RIGHT, conf)
}
func main() {
flag.Parse()
C := cmat.NewMatrix(N, N)
A := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(N, N)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
B.SetFrom(zeromean)
cumtime := 0.0
mintime := 0.0
maxtime := 0.0
for i := 0; i < count; i++ {
flushCache()
t1 := time.Now()
// ----------------------------------------------
blasd.Mult(C, A, B, 1.0, 0.0, gomas.NONE)
// ----------------------------------------------
t2 := time.Now()
tm := t2.Sub(t1)
if mintime == 0.0 || tm.Seconds() < mintime {
mintime = tm.Seconds()
}
if maxtime == 0.0 || tm.Seconds() > maxtime {
maxtime = tm.Seconds()
}
cumtime += tm.Seconds()
if verbose {
fmt.Printf("%3d %12.4f msec, %9.4f gflops\n",
i, 1e+3*tm.Seconds(), gflops(N, tm.Seconds()))
}
}
cumtime /= float64(count)
minflops := gflops(N, maxtime)
avgflops := gflops(N, cumtime)
maxflops := gflops(N, mintime)
fmt.Printf("%5d %9.4f %9.4f %9.4f Gflops\n", N, minflops, avgflops, maxflops)
}
// test: min || B - A*X ||
func TestLeastSquaresQR(t *testing.T) {
M := 811
N := 723
K := 311
nb := 32
conf := gomas.NewConf()
conf.LB = nb
tau := cmat.NewMatrix(N, 1)
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
B0 := cmat.NewMatrix(N, K)
B0.SetFrom(src)
B := cmat.NewMatrix(M, K)
// B = A*B0
blasd.Mult(B, A, B0, 1.0, 0.0, gomas.NONE, conf)
W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
err := lapackd.QRFactor(A, tau, W, conf)
if err != nil {
t.Logf("DecomposeQR: %v\n", err)
}
// B' = A.-1*B
err = lapackd.QRSolve(B, A, tau, W, gomas.NONE, conf)
if err != nil {
t.Logf("SolveQR: %v\n", err)
}
// expect B[0:N,0:K] == B0[0:N,0:K], B[N:M,0:K] == 0
var X cmat.FloatMatrix
X.SubMatrix(B, 0, 0, N, 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*X - B0|| ) ||_1: %e\n", M, N, nrm)
}
// Simple and slow QR decomposition with Givens rotations
func TestGivensQR(t *testing.T) {
var d cmat.FloatMatrix
M := 181
N := 159
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(M, M)
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 all columns ...
for j := 0; j < N; j++ {
// ... zero elements below diagonal, starting from bottom
for i := M - 2; i >= j; i-- {
c, s, r := lapackd.ComputeGivens(A.Get(i, j), A.Get(i+1, j))
A.Set(i, j, r)
A.Set(i+1, j, 0.0)
// apply rotations on this row starting from column j, N-j column
lapackd.ApplyGivensLeft(A, i, i+1, j+1, N-j-1, c, s)
// update Qt = G(k)*Qt
lapackd.ApplyGivensLeft(Qt, i, i+1, 0, M, c, s)
}
}
// check: A = Q*R
blasd.Mult(A1, Qt, A, 1.0, 0.0, gomas.TRANSA)
blasd.Plus(A0, A1, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||A - G(n)..G(1)*R||_1: %e\n", M, N, nrm)
}
func test1(N int, beta float64, t *testing.T) {
var sI cmat.FloatMatrix
if N&0x1 != 0 {
N = N + 1
}
D := cmat.NewMatrix(N, 1)
Z := cmat.NewMatrix(N, 1)
Y := cmat.NewMatrix(N, 1)
V := cmat.NewMatrix(N, 1)
Q := cmat.NewMatrix(N, N)
I := cmat.NewMatrix(N, N)
D.SetAt(0, 1.0)
Z.SetAt(0, 2.0)
for i := 1; i < N-1; i++ {
if i < N/2 {
D.SetAt(i, 2.0-float64(N/2-i)*beta)
} else {
D.SetAt(i, 2.0+float64(i+1-N/2)*beta)
}
Z.SetAt(i, beta)
}
D.SetAt(N-1, 10.0/3.0)
Z.SetAt(N-1, 2.0)
w := blasd.Nrm2(Z)
blasd.InvScale(Z, w)
rho := 1.0 / (w * w)
lapackd.TRDSecularSolveAll(Y, V, Q, D, Z, rho)
lapackd.TRDSecularEigen(Q, V, nil)
blasd.Mult(I, Q, Q, 1.0, 0.0, gomas.TRANSA)
sI.Diag(I)
sI.Add(-1.0)
nrm := lapackd.NormP(I, lapackd.NORM_ONE)
t.Logf("N=%d, beta=%e ||I - Q.T*Q||_1: %e\n", N, beta, nrm)
}
/*
* Blocked version of Hessenberg reduction algorithm as presented in (1). This
* version uses compact-WY transformation.
*
* Some notes:
*
* Elementary reflectors stored in [A11; A21].T are not on diagonal of A11. Update of
* a block aligned with A11; A21 is as follow
*
* 1. Update from left Q(k)*C:
* c0 0 c0
* (I - Y*T*Y.T).T*C = C - Y*(C.T*Y)*T.T = C1 - Y1 * (C1.T.Y1+C2.T*Y2)*T.T = C1-Y1*W
* C2 Y2 C2-Y2*W
*
* where W = (C1.T*Y1+C2.T*Y2)*T.T and first row of C is not affected by update
*
* 2. Update from right C*Q(k):
* 0
* C - C*Y*T*Y.T = c0;C1;C2 - c0;C1;C2 * Y1 *T*(0;Y1;Y2) = c0; C1-W*Y1; C2-W*Y2
* Y2
* where W = (C1*Y1 + C2*Y2)*T and first column of C is not affected
*
*/
func blkHessGQvdG(A, Tvec, W *cmat.FloatMatrix, nb int, conf *gomas.Config) *gomas.Error {
var ATL, ATR, ABL, ABR cmat.FloatMatrix
var A00, A11, A12, A21, A22, A2 cmat.FloatMatrix
var tT, tB, td cmat.FloatMatrix
var t0, t1, t2, T cmat.FloatMatrix
var V, VT, VB /*V0, V1, V2,*/, Y1, Y2, W0 cmat.FloatMatrix
//fmt.Printf("blkHessGQvdG...\n")
T.SubMatrix(W, 0, 0, conf.LB, conf.LB)
V.SubMatrix(W, conf.LB, 0, m(A), conf.LB)
td.Diag(&T)
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, 0, 0, util.PTOPLEFT)
util.Partition2x1(
&tT,
&tB, Tvec, 0, util.PTOP)
for m(&ABR) > nb+1 && n(&ABR) > nb {
util.Repartition2x2to3x3(&ATL,
&A00, nil, nil,
nil, &A11, &A12,
nil, &A21, &A22, A, nb, util.PBOTTOMRIGHT)
util.Repartition2x1to3x1(&tT,
&t0,
&t1,
&t2, Tvec, nb, util.PBOTTOM)
util.Partition2x1(
&VT,
&VB, &V, m(&ATL), util.PTOP)
// ------------------------------------------------------
unblkBuildHessGQvdG(&ABR, &T, &VB, nil)
blasd.Copy(&t1, &td)
// m(Y) == m(ABR)-1, n(Y) == n(A11)
Y1.SubMatrix(&ABR, 1, 0, n(&A11), n(&A11))
Y2.SubMatrix(&ABR, 1+n(&A11), 0, m(&A21)-1, n(&A11))
// [A01; A02] == ATR := ATR*(I - Y*T*Y.T)
updateHessRightWY(&ATR, &Y1, &Y2, &T, &VT, conf)
// A2 = [A12; A22].T
util.Merge2x1(&A2, &A12, &A22)
// A2 := A2 - VB*T*A21.T
be := A21.Get(0, -1)
A21.Set(0, -1, 1.0)
blasd.MultTrm(&VB, &T, 1.0, gomas.UPPER|gomas.RIGHT)
blasd.Mult(&A2, &VB, &A21, -1.0, 1.0, gomas.TRANSB, conf)
A21.Set(0, -1, be)
// A2 := (I - Y*T*Y.T).T * A2
W0.SubMatrix(&V, 0, 0, n(&A2), n(&Y2))
updateHessLeftWY(&A2, &Y1, &Y2, &T, &W0, conf)
// ------------------------------------------------------
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &A11, &A22, A, util.PBOTTOMRIGHT)
util.Continue3x1to2x1(
&tT,
&tB, &t0, &t1, Tvec, util.PBOTTOM)
}
if m(&ABR) > 1 {
// do the rest with unblocked
util.Merge2x1(&A2, &ATR, &ABR)
W0.SetBuf(m(A), 1, m(A), W.Data())
unblkHessGQvdG(&A2, &tB, &W0, m(&ATR))
}
return nil
}
/*
* Unblocked solve A*X = B for Bunch-Kauffman factorized symmetric real matrix.
*/
func unblkSolveBKUpper(B, A *cmat.FloatMatrix, p Pivots, phase int, conf *gomas.Config) *gomas.Error {
var err *gomas.Error = nil
var ATL, ATR, ABL, ABR cmat.FloatMatrix
var A00, a01, A02, a11, a12t, A22 cmat.FloatMatrix
var Aref *cmat.FloatMatrix
var BT, BB, B0, b1, B2, Bx cmat.FloatMatrix
var pT, pB, p0, p1, p2 Pivots
var aStart, aDir, bStart, bDir util.Direction
var nc int
np := 0
if phase == 2 {
aStart = util.PTOPLEFT
aDir = util.PBOTTOMRIGHT
bStart = util.PTOP
bDir = util.PBOTTOM
nc = 1
Aref = &ABR
} else {
aStart = util.PBOTTOMRIGHT
aDir = util.PTOPLEFT
bStart = util.PBOTTOM
bDir = util.PTOP
nc = m(A)
Aref = &ATL
}
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, 0, 0, aStart)
util.Partition2x1(
&BT,
&BB, B, 0, bStart)
partitionPivot2x1(
&pT,
&pB, p, 0, bStart)
// phase 1:
// - solve U*D*X = B, overwriting B with X
// - looping from BOTTOM to TOP
// phase 1:
// - solve U*X = B, overwriting B with X
// - looping from TOP to BOTTOM
for n(Aref) > 0 {
// see if next diagonal block is 1x1 or 2x2
np = 1
if p[nc-1] < 0 {
np = 2
}
// repartition according the pivot size
util.Repartition2x2to3x3(&ATL,
&A00, &a01, &A02,
nil, &a11, &a12t,
nil, nil, &A22 /**/, A, np, aDir)
util.Repartition2x1to3x1(&BT,
&B0,
&b1,
&B2 /**/, B, np, bDir)
repartPivot2x1to3x1(&pT,
&p0,
&p1,
&p2 /**/, p, np, bDir)
// ------------------------------------------------------------
switch phase {
case 1:
// computes D.-1*(U.-1*B);
// b1 is current row, last row of BT
if np == 1 {
if p1[0] != nc {
// swap rows on top part of B
swapRows(&BT, m(&BT)-1, p1[0]-1)
}
// B0 = B0 - a01*b1
blasd.MVUpdate(&B0, &a01, &b1, -1.0)
// b1 = b1/d1
blasd.InvScale(&b1, a11.Get(0, 0))
nc -= 1
} else if np == 2 {
if p1[0] != -nc {
// swap rows on top part of B
swapRows(&BT, m(&BT)-2, -p1[0]-1)
}
b := a11.Get(0, 1)
apb := a11.Get(0, 0) / b
dpb := a11.Get(1, 1) / b
// (a/b)*(d/b)-1.0 == (a*d - b^2)/b^2
scale := apb*dpb - 1.0
scale *= b
// B0 = B0 - a01*b1
blasd.Mult(&B0, &a01, &b1, -1.0, 1.0, gomas.NONE, conf)
// b1 = a11.-1*b1.T
//(2x2 block, no subroutine for doing this in-place)
for k := 0; k < n(&b1); k++ {
s0 := b1.Get(0, k)
s1 := b1.Get(1, k)
b1.Set(0, k, (dpb*s0-s1)/scale)
b1.Set(1, k, (apb*s1-s0)/scale)
}
nc -= 2
}
case 2:
// compute X = U.-T*B
if np == 1 {
blasd.MVMult(&b1, &B0, &a01, -1.0, 1.0, gomas.TRANS)
if p1[0] != nc {
// swap rows on bottom part of B
util.Merge2x1(&Bx, &B0, &b1)
swapRows(&Bx, m(&Bx)-1, p1[0]-1)
}
nc += 1
} else if np == 2 {
blasd.Mult(&b1, &a01, &B0, -1.0, 1.0, gomas.TRANSA, conf)
if p1[0] != -nc {
// swap rows on bottom part of B
util.Merge2x1(&Bx, &B0, &b1)
swapRows(&Bx, m(&Bx)-2, -p1[0]-1)
}
nc += 2
}
}
// ------------------------------------------------------------
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &a11, &A22, A, aDir)
util.Continue3x1to2x1(
&BT,
&BB, &B0, &b1, B, bDir)
contPivot3x1to2x1(
&pT,
&pB, p0, p1, p, bDir)
}
return err
}
func unblkBoundedBKUpper(A, wrk *cmat.FloatMatrix, p *Pivots, ncol int, conf *gomas.Config) (*gomas.Error, int) {
var err *gomas.Error = nil
var ATL, ATR, ABL, ABR cmat.FloatMatrix
var A00, a01, A02, a11, a12, A22, a11inv cmat.FloatMatrix
var w00, w01, w11 cmat.FloatMatrix
var cwrk cmat.FloatMatrix
var pT, pB, p0, p1, p2 Pivots
err = nil
nc := 0
if ncol > n(A) {
ncol = n(A)
}
// permanent working space for symmetric inverse of a11
a11inv.SubMatrix(wrk, m(wrk)-2, 0, 2, 2)
a11inv.Set(0, 1, -1.0)
a11inv.Set(1, 0, -1.0)
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, 0, 0, util.PBOTTOMRIGHT)
partitionPivot2x1(
&pT,
&pB, *p, 0, util.PBOTTOM)
for n(&ATL) > 0 && nc < ncol {
util.Partition2x2(
&w00, &w01,
nil, &w11, wrk, nc, nc, util.PBOTTOMRIGHT)
r, np := findAndBuildBKPivotUpper(&ATL, &ATR, &w00, &w01, nc)
if np > ncol-nc {
// next pivot does not fit into ncol columns,
// return with number of factorized columns
return err, nc
}
cwrk.SubMatrix(&w00, 0, n(&w00)-np, m(&ATL), np)
if r != -1 {
// pivoting needed; do swaping here
k := m(&ATL) - np
applyBKPivotSymUpper(&ATL, k, r)
// swap right hand rows to get correct updates
swapRows(&ATR, k, r)
swapRows(&w01, k, r)
if np == 2 && r != k {
/* for 2x2 blocks we need diagonal pivots.
* [r, r] | [ r,-1]
* a11 == ---------------- 2-by-2 pivot, swapping [1,0] and [r,0]
* [-1,r] | [-1,-1]
*/
t0 := w00.Get(k, -1)
tr := w00.Get(r, -1)
w00.Set(k, -1, tr)
w00.Set(r, -1, t0)
t0 = w00.Get(k, -2)
tr = w00.Get(r, -2)
w00.Set(k, -2, tr)
w00.Set(r, -2, t0)
}
}
// repartition according the pivot size
util.Repartition2x2to3x3(&ATL,
&A00, &a01, &A02,
nil, &a11, &a12,
nil, nil, &A22 /**/, A, np, util.PTOPLEFT)
repartPivot2x1to3x1(&pT,
&p0,
&p1,
&p2 /**/, *p, np, util.PTOP)
// ------------------------------------------------------------
wlc := n(&w00) - np
cwrk.SubMatrix(&w00, 0, wlc, m(&a01), n(&a01))
if np == 1 {
//
a11.Set(0, 0, w00.Get(m(&a01), wlc))
// a21 = a21/a11
blasd.Copy(&a01, &cwrk)
blasd.InvScale(&a01, a11.Get(0, 0))
// store pivot point relative to original matrix
if r == -1 {
p1[0] = m(&ATL)
} else {
p1[0] = r + 1
}
} else if np == 2 {
/* a | b d/b | -1
* w00 == ------ == a11 --> a11.-1 == -------- * scale
* . | d -1 | a/b
*/
a := w00.Get(m(&ATL)-2, -2)
b := w00.Get(m(&ATL)-2, -1)
d := w00.Get(m(&ATL)-1, -1)
a11inv.Set(0, 0, d/b)
a11inv.Set(1, 1, a/b)
// denominator: (a/b)*(d/b)-1.0 == (a*d - b^2)/b^2
scale := 1.0 / ((a/b)*(d/b) - 1.0)
scale /= b
// a01 = a01*a11.-1
blasd.Mult(&a01, &cwrk, &a11inv, scale, 0.0, gomas.NONE, conf)
a11.Set(0, 0, a)
a11.Set(0, 1, b)
a11.Set(1, 1, d)
// store pivot point relative to original matrix
p1[0] = -(r + 1)
p1[1] = p1[0]
}
// ------------------------------------------------------------
nc += np
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &a11, &A22, A, util.PTOPLEFT)
contPivot3x1to2x1(
&pT,
&pB, p0, p1, *p, util.PTOP)
}
return err, nc
}