// 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 ---
}
// 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 ---
}
func TestTrdMultUpper(t *testing.T) {
var dt, et, da, ea cmat.FloatMatrix
N := 843
nb := 48
conf := gomas.NewConf()
conf.LB = nb
A := cmat.NewMatrix(N, N)
tau := cmat.NewMatrix(N, 1)
src := cmat.NewFloatNormSource()
// create symmetric matrix
A.SetFrom(src, cmat.SYMM)
A0 := cmat.NewCopy(A)
W := lapackd.Workspace(lapackd.TRDReduceWork(A, conf))
lapackd.TRDReduce(A, tau, W, gomas.UPPER, conf)
// make tridiagonal matrix T
T0 := cmat.NewMatrix(N, N)
dt.Diag(T0)
da.Diag(A)
blasd.Copy(&dt, &da)
ea.Diag(A, 1)
et.Diag(T0, 1)
blasd.Copy(&et, &ea)
et.Diag(T0, -1)
blasd.Copy(&et, &ea)
T1 := cmat.NewCopy(T0)
// compute Q*T*Q.T (unblocked)
conf.LB = 0
lapackd.TRDMult(T0, A, tau, W, gomas.LEFT|gomas.UPPER, conf)
lapackd.TRDMult(T0, A, tau, W, gomas.RIGHT|gomas.TRANS|gomas.UPPER, conf)
blasd.Plus(T0, A0, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(T0, lapackd.NORM_ONE)
t.Logf("N=%d, unblk.||A - Q*T*Q.T||_1: %e\n", N, nrm)
// compute Q*T*Q.T (blocked)
conf.LB = nb
W = lapackd.Workspace(lapackd.TRDMultWork(A, gomas.LEFT|gomas.UPPER, conf))
lapackd.TRDMult(T1, A, tau, W, gomas.LEFT|gomas.UPPER, conf)
lapackd.TRDMult(T1, A, tau, W, gomas.RIGHT|gomas.TRANS|gomas.UPPER, conf)
blasd.Plus(T1, A0, 1.0, -1.0, gomas.NONE)
nrm = lapackd.NormP(T1, lapackd.NORM_ONE)
t.Logf("N=%d, blk.||A - Q*T*Q.T||_1: %e\n", N, nrm)
}
func TestBidiagReduceUnblocked(t *testing.T) {
N := 217
M := 269
conf := gomas.NewConf()
conf.LB = 0
zeromean := cmat.NewFloatNormSource()
A := cmat.NewMatrix(M, N)
A.SetFrom(zeromean)
tauq := cmat.NewMatrix(N, 1)
taup := cmat.NewMatrix(N, 1)
At := cmat.NewMatrix(N, M)
blasd.Transpose(At, A)
tauqt := cmat.NewMatrix(N, 1)
taupt := cmat.NewMatrix(N, 1)
W := lapackd.Workspace(M + N)
lapackd.BDReduce(A, tauq, taup, W, conf)
lapackd.BDReduce(At, tauqt, taupt, W, conf)
// BiRed(A) == BiRed(A.T).T
blasd.Plus(At, A, 1.0, -1.0, gomas.TRANSB)
blasd.Axpy(tauqt, taup, -1.0)
blasd.Axpy(taupt, tauq, -1.0)
nrm := lapackd.NormP(At, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d || BiRed(A) - BiRed(A.T).T||_1 : %e\n", M, N, nrm)
nrm = lapackd.NormP(taupt, lapackd.NORM_ONE)
t.Logf(" || BiRed(A).tauq - BiRed(A.T).taup||_1 : %e\n", nrm)
nrm = lapackd.NormP(tauqt, lapackd.NORM_ONE)
t.Logf(" || BiRed(A).taup - BiRed(A.T).tauq||_1 : %e\n", nrm)
}
// test: unblk.ReduceHess(A) == blk.ReduceHess(A)
func TestReduceHess(t *testing.T) {
N := 375
nb := 16
conf := gomas.NewConf()
conf.LB = nb
A := cmat.NewMatrix(N, N)
tau := cmat.NewMatrix(N, 1)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
A0 := cmat.NewCopy(A)
tau0 := cmat.NewCopy(tau)
// blocked reduction
W := lapackd.Workspace(lapackd.HessReduceWork(A, conf))
lapackd.HessReduce(A, tau, W, conf)
// unblocked reduction
conf.LB = 0
lapackd.HessReduce(A0, tau0, W, conf)
ok := A.AllClose(A0)
t.Logf("blk.ReduceHess(A) == unblk.ReduceHess(A): %v\n", ok)
ok = tau0.AllClose(tau)
t.Logf("blk HessQ.tau == unblk HessQ.tau: %v\n", ok)
// ||A - A0||_1
blasd.Plus(A, A0, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(A, lapackd.NORM_ONE)
t.Logf("||H - H0||_1: %e\n", nrm)
}
// 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 TestLQFactor(t *testing.T) {
M := 611
N := 715
nb := 32
conf := gomas.NewConf()
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
tau := cmat.NewMatrix(M, 1)
A1 := cmat.NewCopy(A)
tau1 := cmat.NewCopy(tau)
conf.LB = 0
W := cmat.NewMatrix(M+N, 1)
lapackd.LQFactor(A, tau, W, conf)
conf.LB = nb
W1 := lapackd.Workspace(lapackd.LQFactorWork(A1, conf))
lapackd.LQFactor(A1, tau1, W1, conf)
blasd.Plus(A1, A, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(A1, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||blk.LQ(A) - unblk.LQ(A)||_1: %e\n", M, N, nrm)
}
// QR decompose A, then compute ||A - Q*R||_1, should be small
func TestUnblkQRMultLeft(t *testing.T) {
M := 711
N := 593
A := cmat.NewMatrix(M, N)
tau := cmat.NewMatrix(N, 1)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
A0 := cmat.NewCopy(A)
conf := gomas.NewConf()
conf.LB = 0
// QR = A = Q*R
W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
lapackd.QRFactor(A, tau, W, conf)
// C = TriU(QR) = R
C := cmat.TriU(cmat.NewCopy(A), cmat.NONE)
// C = Q*C
W = lapackd.Workspace(lapackd.QRMultWork(C, gomas.LEFT, conf))
err := lapackd.QRMult(C, A, tau, W, gomas.LEFT, conf)
if err != nil {
t.Logf("err: %v\n", err)
}
// A = A - QR
blasd.Plus(A0, C, 1.0, -1.0, gomas.NONE)
// ||A - Q*R||_1
nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
t.Logf("M=%d,N=%d ||A - Q*R||_1: %e\n", M, N, nrm)
}
// m > n: A[m,n], I[m,m] --> A == I*A == Q*Q.T*A
func TestQRTMultLeftIdent(t *testing.T) {
M := 411
N := 399
nb := 16
A := cmat.NewMatrix(M, N)
T := cmat.NewMatrix(nb, N)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
A0 := cmat.NewCopy(A)
C := cmat.NewCopy(A)
conf := gomas.NewConf()
conf.LB = nb
//t.Logf("A0:\n%v\n", A0)
// QR = A = Q*R
W := lapackd.Workspace(lapackd.QRTFactorWork(A, conf))
lapackd.QRTFactor(A, T, W, conf)
//t.Logf("T:\n%v\n", T)
// C = Q.T*A
W = lapackd.Workspace(lapackd.QRTMultWork(C, T, gomas.LEFT, conf))
lapackd.QRTMult(C, A, T, W, gomas.LEFT|gomas.TRANS, conf)
// C = Q*C == Q*Q.T*A
lapackd.QRTMult(C, A, T, W, gomas.LEFT, conf)
//t.Logf("A*Q*Q.T:\n%v\n", C)
// A = A - Q*Q.T*A
blasd.Plus(A0, C, 1.0, -1.0, gomas.NONE)
// ||A - Q*Q.T*A||_1
nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
t.Logf("M=%d,N=%d ||A - Q*Q.T*A||_1: %e\n", M, N, nrm)
}
// QR decompose A, then compute ||A - (R.T*Q.T).T||_1, should be small
func TestUnblkQRMultRight(t *testing.T) {
M := 711
N := 593
A := cmat.NewMatrix(M, N)
C := cmat.NewMatrix(N, M)
tau := cmat.NewMatrix(N, 1)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
A0 := cmat.NewCopy(A)
conf := gomas.NewConf()
conf.LB = 0
// QR = A = Q*R
W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
lapackd.QRFactor(A, tau, W, conf)
// C = transpose(TriU(QR)) = R.T
C.Transpose(cmat.TriU(cmat.NewCopy(A), cmat.NONE))
// C = C*Q.T = R.T*Q.T
W = lapackd.Workspace(lapackd.QRMultWork(C, gomas.RIGHT, conf))
err := lapackd.QRMult(C, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
if err != nil {
t.Logf("err: %v\n", err)
}
// A = A - QR
blasd.Plus(A0, C, 1.0, -1.0, gomas.TRANSB)
// ||A - Q*R||_1
nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
t.Logf("M=%d,N=%d ||A - (R.T*Q.T).T||_1: %e\n", M, N, nrm)
}
// m > n: A[m,n], I[m,m] --> A.T == A.T*I == A.T*Q*Q.T
func TestBlockedQRMultRightIdent(t *testing.T) {
M := 511
N := 489
A := cmat.NewMatrix(M, N)
C := cmat.NewMatrix(N, M)
tau := cmat.NewMatrix(N, 1)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
A0 := cmat.NewCopy(A)
C.Transpose(A)
conf := gomas.NewConf()
conf.LB = 32
// QR = A = Q*R
W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
lapackd.QRFactor(A, tau, W, conf)
// C = A.T*Q
W = lapackd.Workspace(lapackd.QRMultWork(C, gomas.RIGHT, conf))
lapackd.QRMult(C, A, tau, W, gomas.RIGHT, conf)
// C = C*Q.T == A.T*Q*Q.T
lapackd.QRMult(C, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
//t.Logf("A*Q*Q.T:\n%v\n", C)
// A = A - (A.T*Q*Q.T).T
blasd.Plus(A0, C, 1.0, -1.0, gomas.TRANSB)
// ||A - (A.T*Q*Q.T).T||_1
nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
t.Logf("M=%d,N=%d ||A - (A.T*Q*Q.T).T||_1: %e\n", M, N, nrm)
}
// 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 TestTriRedUpper(t *testing.T) {
N := 843
nb := 48
conf := gomas.NewConf()
conf.LB = 0
A := cmat.NewMatrix(N, N)
tau := cmat.NewMatrix(N, 1)
src := cmat.NewFloatNormSource()
A.SetFrom(src, cmat.UPPER)
A1 := cmat.NewCopy(A)
tau1 := cmat.NewCopy(tau)
_ = A1
W := lapackd.Workspace(N)
W1 := lapackd.Workspace(N * nb)
lapackd.TRDReduce(A, tau, W, gomas.UPPER, conf)
conf.LB = nb
lapackd.TRDReduce(A1, tau1, W1, gomas.UPPER, conf)
blasd.Plus(A, A1, -1.0, 1.0, gomas.NONE)
nrm := lapackd.NormP(A, lapackd.NORM_ONE)
t.Logf("N=%d, ||unblk.Trired(A) - blk.Trired(A)||_1: %e\n", N, nrm)
blasd.Axpy(tau, tau1, -1.0)
nrm = blasd.Nrm2(tau)
t.Logf(" ||unblk.Trired(tau) - blk.Trired(tau)||_1: %e\n", nrm)
}
func TestSolveBKLowerBig(t *testing.T) {
N := 427
normsrc := cmat.NewFloatNormSource(5.0, 10.0)
A := cmat.NewMatrix(N, N)
A.SetFrom(normsrc, cmat.LOWER)
X := cmat.NewMatrix(N, 2)
X.SetFrom(normsrc)
B := cmat.NewCopy(X)
blasd.MultSym(B, A, X, 1.0, 0.0, gomas.LOWER|gomas.LEFT)
ipiv := lapackd.NewPivots(N)
conf := gomas.NewConf()
conf.LB = 16
W := lapackd.Workspace(lapackd.BKFactorWork(A, conf))
lapackd.BKFactor(A, W, ipiv, gomas.LOWER, conf)
lapackd.BKSolve(B, A, ipiv, gomas.LOWER, conf)
ok := B.AllClose(X)
t.Logf("N=%d unblk.BK(X) == A.-1*B : %v\n", N, ok)
blasd.Plus(B, X, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(B, lapackd.NORM_ONE)
t.Logf(" ||X - A.-1*B||_1: %.4e\n", nrm)
}
func TestBiredWide(t *testing.T) {
N := 811
M := 693
nb := 32
conf := gomas.NewConf()
conf.LB = 0
ediag := -1
zeromean := cmat.NewFloatNormSource()
A := cmat.NewMatrix(M, N)
A.SetFrom(zeromean)
A0 := cmat.NewCopy(A)
tauq := cmat.NewMatrix(N, 1)
taup := cmat.NewMatrix(N, 1)
W := lapackd.Workspace(M + N)
lapackd.BDReduce(A, tauq, taup, W, conf)
var D, E, Bd, Be cmat.FloatMatrix
D.Diag(A)
E.Diag(A, ediag)
B := cmat.NewMatrix(M, N)
Bd.Diag(B)
Be.Diag(B, ediag)
blasd.Copy(&Bd, &D)
blasd.Copy(&Be, &E)
Bt := cmat.NewMatrix(N, M)
blasd.Transpose(Bt, B)
conf.LB = nb
W0 := lapackd.Workspace(lapackd.BDMultWork(B, conf))
lapackd.BDMult(B, A, tauq, W0, gomas.MULTQ|gomas.LEFT, conf)
lapackd.BDMult(Bt, A, tauq, W0, gomas.MULTQ|gomas.RIGHT|gomas.TRANS, conf)
lapackd.BDMult(B, A, taup, W0, gomas.MULTP|gomas.RIGHT|gomas.TRANS, conf)
lapackd.BDMult(Bt, A, taup, W0, gomas.MULTP|gomas.LEFT, conf)
blasd.Plus(B, A0, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(B, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||A - Q*B*P.T||_1 : %e\n", M, N, nrm)
blasd.Plus(Bt, A0, 1.0, -1.0, gomas.TRANSB)
nrm = lapackd.NormP(Bt, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||A.T - P*B.T*Q.T||_1 : %e\n", M, N, nrm)
}
// test: A - Q*Hess(A)*Q.T == 0
func TestMultHess(t *testing.T) {
N := 377
nb := 16
conf := gomas.NewConf()
conf.LB = nb
A := cmat.NewMatrix(N, N)
tau := cmat.NewMatrix(N, 1)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
A0 := cmat.NewCopy(A)
// reduction
W := lapackd.Workspace(lapackd.HessReduceWork(A, conf))
lapackd.HessReduce(A, tau, W, conf)
var Hlow cmat.FloatMatrix
H := cmat.NewCopy(A)
// set triangular part below first subdiagonal to zeros
zeros := cmat.NewFloatConstSource(0.0)
Hlow.SubMatrix(H, 1, 0, N-1, N-1)
Hlow.SetFrom(zeros, cmat.LOWER|cmat.UNIT)
H1 := cmat.NewCopy(H)
// H := Q*H*Q.T
conf.LB = nb
lapackd.HessMult(H, A, tau, W, gomas.LEFT, conf)
lapackd.HessMult(H, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
// H := Q*H*Q.T
conf.LB = 0
lapackd.HessMult(H1, A, tau, W, gomas.LEFT, conf)
lapackd.HessMult(H1, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
// compute ||Q*Hess(A)*Q.T - A||_1
blasd.Plus(H, A0, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(H, lapackd.NORM_ONE)
t.Logf(" blk.|| Q*Hess(A)*Q.T - A ||_1 : %e\n", nrm)
blasd.Plus(H1, A0, 1.0, -1.0, gomas.NONE)
nrm = lapackd.NormP(H1, lapackd.NORM_ONE)
t.Logf("unblk.|| Q*Hess(A)*Q.T - A ||_1 : %e\n", nrm)
}
// 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)
}
// test: ||A - A*Q*Q.T||_1 ~= 0
func TestLQMultRight(t *testing.T) {
M := 511
N := 627
nb := 24
conf := gomas.NewConf()
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
tau := cmat.NewMatrix(M, 1)
W := cmat.NewMatrix(M+N, 1)
A0 := cmat.NewCopy(A)
A1 := cmat.NewCopy(A)
A2 := cmat.NewCopy(A)
conf.LB = 0
lapackd.LQFactor(A, tau, W, conf)
// unblocked A1 := A1*Q*Q.T
conf.LB = 0
lapackd.LQMult(A1, A, tau, W, gomas.RIGHT, conf)
lapackd.LQMult(A1, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
// blocked A2 := A2*Q*Q.T
conf.LB = nb
W = lapackd.Workspace(lapackd.LQMultWork(A2, gomas.RIGHT, conf))
lapackd.LQMult(A2, A, tau, W, gomas.RIGHT, conf)
lapackd.LQMult(A2, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
// A1 - A0 == 0
blasd.Plus(A1, A0, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(A1, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d, unblk.||A - A*Q*Q.T||_1: %e\n", M, N, nrm)
// A2 - A0 == 0
blasd.Plus(A2, A0, 1.0, -1.0, gomas.NONE)
nrm = lapackd.NormP(A2, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d, nb=%d blk.||A - A*Q*Q.T||_1: %e\n", M, N, nb, nrm)
}
// test: ||C - Q*Q.T*C||_1 ~= 0;
// multipling from left requires: m(C) == n(A) [n(Q)]
func TestLQMultLeft(t *testing.T) {
M := 771
N := 813
nb := 16
conf := gomas.NewConf()
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
// C0 := A
C0 := cmat.NewCopy(A)
C1t := cmat.NewMatrix(N, M)
blasd.Transpose(C1t, C0)
C2t := cmat.NewCopy(C1t)
tau := cmat.NewMatrix(M, 1)
W := cmat.NewMatrix(M+N, 1)
conf.LB = 0
lapackd.LQFactor(A, tau, W, conf)
// A0 := Q.T*A0
conf.LB = 0
lapackd.LQMult(C2t, A, tau, W, gomas.LEFT, conf)
lapackd.LQMult(C2t, A, tau, W, gomas.LEFT|gomas.TRANS, conf)
// A0 := Q.T*A0
conf.LB = nb
W1 := lapackd.Workspace(lapackd.LQMultWork(C1t, gomas.LEFT, conf))
lapackd.LQMult(C1t, A, tau, W1, gomas.LEFT, conf)
lapackd.LQMult(C1t, A, tau, W1, gomas.LEFT|gomas.TRANS, conf)
blasd.Plus(C0, C1t, 1.0, -1.0, gomas.TRANSB)
nrm := lapackd.NormP(C0, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d, ||C - Q*Q*T*C||_1: %e\n", M, N, nrm)
blasd.Plus(C1t, C2t, 1.0, -1.0, gomas.NONE)
nrm = lapackd.NormP(C1t, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d, ||unblk(Q*Q.T*C) - blk(Q*Q*T*C)||_1: %e\n", M, 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 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)
}
// 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 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)
}
// test: unblk.QLFactor == blk.QLFactor
func TestQLFactor(t *testing.T) {
var t0 cmat.FloatMatrix
M := 911
N := 835
nb := 32
conf := gomas.NewConf()
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
tau := cmat.NewMatrix(M, 1)
W := cmat.NewMatrix(M+N, 1)
A1 := cmat.NewCopy(A)
tau1 := cmat.NewCopy(tau)
conf.LB = 0
lapackd.QLFactor(A, tau, W, conf)
conf.LB = nb
W1 := lapackd.Workspace(lapackd.QLFactorWork(A1, conf))
lapackd.QLFactor(A1, tau1, W1, conf)
if N < 10 {
t.Logf("unblkQL(A):\n%v\n", A)
t0.SetBuf(1, tau.Len(), 1, tau.Data())
t.Logf("unblkQL.tau:\n%v\n", &t0)
t.Logf("blkQL(A):\n%v\n", A1)
t0.SetBuf(1, tau1.Len(), 1, tau1.Data())
t.Logf("blkQL.tau:\n%v\n", &t0)
}
blasd.Plus(A1, A, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(A1, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||blkQL(A) - unblkQL(A)||_1: %e\n", M, N, nrm)
blasd.Axpy(tau1, tau, -1.0)
nrm = blasd.Nrm2(tau1)
t.Logf(" ||blkQL.tau - unblkQL.tau||_1: %e\n", nrm)
}
// 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)
}
// m > n: A[m,n], I[m,m] --> A.T == A.T*I == A.T*Q*Q.T
func TestQRTMultRightIdent(t *testing.T) {
M := 511
N := 399
nb := 16
A := cmat.NewMatrix(M, N)
C := cmat.NewMatrix(N, M)
T := cmat.NewMatrix(nb, N)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
A0 := cmat.NewCopy(A)
C.Transpose(A)
conf := gomas.NewConf()
conf.LB = nb
// QR = A = Q*R
W := lapackd.Workspace(lapackd.QRTFactorWork(A, conf))
lapackd.QRTFactor(A, T, W, conf)
// C = A*Q
W = lapackd.Workspace(lapackd.QRTMultWork(C, T, gomas.RIGHT, conf))
err := lapackd.QRTMult(C, A, T, W, gomas.RIGHT, conf)
if err != nil {
t.Logf("err: %v\n", err)
}
// C = C*Q.T == A*Q*Q.T
err = lapackd.QRTMult(C, A, T, W, gomas.RIGHT|gomas.TRANS, conf)
if err != nil {
t.Logf("err: %v\n", err)
}
// A = A - (A.T*Q*Q.T).T
blasd.Plus(A0, C, 1.0, -1.0, gomas.TRANSB)
// ||A - Q*R||_1
nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
t.Logf("M=%d,N=%d ||A - (A.T*Q*Q.T).T||_1: %e\n", M, N, nrm)
}
func TestBidiagReduceBlockedTall(t *testing.T) {
N := 711
M := 883
nb := 64
conf := gomas.NewConf()
conf.LB = 0
zeromean := cmat.NewFloatNormSource()
A := cmat.NewMatrix(M, N)
A.SetFrom(zeromean)
tauq := cmat.NewMatrix(N, 1)
taup := cmat.NewMatrix(N, 1)
A1 := cmat.NewCopy(A)
tauq1 := cmat.NewMatrix(N, 1)
taup1 := cmat.NewMatrix(N, 1)
W := lapackd.Workspace(M + N)
W1 := lapackd.Workspace(nb * (M + N + 1))
lapackd.BDReduce(A, tauq, taup, W, conf)
conf.LB = nb
lapackd.BDReduce(A1, tauq1, taup1, W1, conf)
// unblk.BiRed(A) == blk.BiRed(A)
blasd.Plus(A1, A, 1.0, -1.0, gomas.NONE)
blasd.Axpy(tauq1, tauq, -1.0)
blasd.Axpy(taup1, taup, -1.0)
nrm := lapackd.NormP(A1, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d || unblk.BiRed(A) - blk.BiRed(A)||_1 : %e\n", M, N, nrm)
nrm = lapackd.NormP(taup1, lapackd.NORM_ONE)
t.Logf(" || unblk.BiRed(A).tauq - blk.BiRed(A).taup||_1 : %e\n", nrm)
nrm = lapackd.NormP(tauq1, lapackd.NORM_ONE)
t.Logf(" || unblk.BiRed(A).taup - blk.BiRed(A).tauq||_1 : %e\n", nrm)
}
func TestReduceBidiagBlkWide(t *testing.T) {
N := 911
M := 823
nb := 48
conf := gomas.NewConf()
conf.LB = 0
zeromean := cmat.NewFloatNormSource()
A := cmat.NewMatrix(M, N)
A.SetFrom(zeromean)
tauq := cmat.NewMatrix(N, 1)
taup := cmat.NewMatrix(N, 1)
A1 := cmat.NewCopy(A)
tauq1 := cmat.NewMatrix(N, 1)
taup1 := cmat.NewMatrix(N, 1)
W := lapackd.Workspace(M + N)
lapackd.BDReduce(A, tauq, taup, W, conf)
conf.LB = nb
W1 := lapackd.Workspace(lapackd.BDReduceWork(A1, conf))
lapackd.BDReduce(A1, tauq1, taup1, W1, conf)
// BiRed(A) == BiRed(A.T).T
blasd.Plus(A1, A, 1.0, -1.0, gomas.NONE)
blasd.Axpy(tauq1, tauq, -1.0)
blasd.Axpy(taup1, taup, -1.0)
nrm := lapackd.NormP(A1, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d || BiRed(A) - blk.BiRed(A)||_1 : %e\n", M, N, nrm)
nrm = lapackd.NormP(taup1, lapackd.NORM_ONE)
t.Logf(" || BiRed(A).tauq - blk.BiRed(A).taup||_1 : %e\n", nrm)
nrm = lapackd.NormP(tauq1, lapackd.NORM_ONE)
t.Logf(" || BiRed(A).taup - blk.BiRed(A).tauq||_1 : %e\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)
}
// QR decompose A, then compute ||A - Q*R||_1, should be small
func TestMultQTLeft(t *testing.T) {
M := 513
N := 477
nb := 16
A := cmat.NewMatrix(M, N)
T := cmat.NewMatrix(nb, N)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
A0 := cmat.NewCopy(A)
conf := gomas.NewConf()
conf.LB = nb
//t.Logf("A0:\n%v\n", A0)
// QR = A = Q*R
W := lapackd.Workspace(lapackd.QRTFactorWork(A, conf))
lapackd.QRTFactor(A, T, W, conf)
//t.Logf("T:\n%v\n", T)
// C = TriU(QR) = R
C := cmat.TriU(cmat.NewCopy(A), cmat.NONE)
//t.Logf("R:\n%v\n", C)
// C = Q*C
W = lapackd.Workspace(lapackd.QRTMultWork(C, T, gomas.LEFT, conf))
err := lapackd.QRTMult(C, A, T, W, gomas.LEFT, conf)
if err != nil {
t.Logf("err: %v\n", err)
}
// A = A - QR
blasd.Plus(A0, C, 1.0, -1.0, gomas.NONE)
// ||A - Q*R||_1
nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
t.Logf("M=%d,N=%d ||A - Q*R||_1: %e\n", M, N, nrm)
}
