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)
}
// Compute eigenvector corresponding precomputed deltas
func trdsecEigenVecDelta(qi, delta, z *cmat.FloatMatrix) {
var dk, zk float64
for k := 0; k < delta.Len(); k++ {
zk = z.GetAt(k)
dk = delta.GetAt(k)
qi.SetAt(k, zk/dk)
}
s := blasd.Nrm2(qi)
blasd.InvScale(qi, s)
}
// 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)
}
/*
* Compute matrix and vector norms.
*
* Arguments
* X A real valued matrix or vector
*
* norm Norm to compute
* NORM_ONE, NORM_TWO, NORM_INF
*
* Note: matrix NORM_TWO not yet implemented.
*/
func NormP(X *cmat.FloatMatrix, norm Norms) float64 {
if X.IsVector() {
switch norm {
case NORM_ONE:
return blasd.ASum(X)
case NORM_TWO:
return blasd.Nrm2(X)
case NORM_INF:
return blasd.Amax(X)
}
return 0.0
}
switch norm {
case NORM_ONE:
return mNorm1(X)
case NORM_TWO:
return 0.0
case NORM_INF:
return mNormInf(X)
}
return 0.0
}
func trdsecEigenBuildInplace(Q, z *cmat.FloatMatrix) {
var QTL, QBR, Q00, q11, q12, q21, Q22, qi cmat.FloatMatrix
var zk0, zk1, dk0, dk1 float64
util.Partition2x2(
&QTL, nil,
nil, &QBR /**/, Q, 0, 0, util.PTOPLEFT)
for m(&QBR) > 0 {
util.Repartition2x2to3x3(&QTL,
&Q00, nil, nil,
nil, &q11, &q12,
nil, &q21, &Q22 /**/, Q, 1, util.PBOTTOMRIGHT)
//---------------------------------------------------------------
k := m(&Q00)
zk0 = z.GetAt(k)
dk0 = q11.Get(0, 0)
q11.Set(0, 0, zk0/dk0)
for i := 0; i < q12.Len(); i++ {
zk1 = z.GetAt(k + i + 1)
dk0 = q12.GetAt(i)
dk1 = q21.GetAt(i)
q12.SetAt(i, zk0/dk1)
q21.SetAt(i, zk1/dk0)
}
//---------------------------------------------------------------
util.Continue3x3to2x2(
&QTL, nil,
nil, &QBR /**/, &Q00, &q11, &Q22 /**/, Q, util.PBOTTOMRIGHT)
}
// scale column eigenvectors
for k := 0; k < z.Len(); k++ {
qi.Column(Q, k)
t := blasd.Nrm2(&qi)
blasd.InvScale(&qi, t)
}
}
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)
}
/* From LAPACK/dlarfg.f
*
* Generates a real elementary reflector H of order n, such
* that
*
* H * ( alpha ) = ( beta ), H**T * H = I.
* ( x ) ( 0 )
*
* where alpha and beta are scalars, and x is an (n-1)-element real
* vector. 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 (n-1)-element
* vector.
*
* If the elements of x are all zero, then tau = 0 and H is taken to be
* the unit cmat.
*
* Otherwise 1 <= tau <= 2.
*/
func computeHouseholder(a11, x, tau *cmat.FloatMatrix) {
// norm_x2 = ||x||_2
norm_x2 := blasd.Nrm2(x)
if norm_x2 == 0.0 {
tau.Set(0, 0, 0.0)
return
}
alpha := a11.Get(0, 0)
sign := 1.0
if math.Signbit(alpha) {
sign = -1.0
}
// beta = -(alpha / |alpha|) * ||alpha x||
// = -sign(alpha) * sqrt(alpha**2, norm_x2**2)
beta := -sign * sqrtX2Y2(alpha, norm_x2)
// x = x /(a11 - beta)
blasd.InvScale(x, alpha-beta)
tau.Set(0, 0, (beta-alpha)/beta)
a11.Set(0, 0, beta)
}