/*
* Compute
* B = B*diag(D).-1 flags & RIGHT == true
* B = diag(D).-1*B flags & LEFT == true
*
* If flags is LEFT (RIGHT) then element-wise divides columns (rows) of B with vector D.
*
* Arguments:
* B M-by-N matrix if flags&RIGHT == true or N-by-M matrix if flags&LEFT == true
*
* D N element column or row vector or N-by-N matrix
*
* flags Indicator bits, LEFT or RIGHT
*/
func SolveDiag(B, D *cmat.FloatMatrix, flags int, confs ...*gomas.Config) *gomas.Error {
var c, d0 cmat.FloatMatrix
var d *cmat.FloatMatrix
conf := gomas.CurrentConf(confs...)
d = D
if !D.IsVector() {
d0.Diag(D)
d = &d0
}
dn := d0.Len()
br, bc := B.Size()
switch flags & (gomas.LEFT | gomas.RIGHT) {
case gomas.LEFT:
if br != dn {
return gomas.NewError(gomas.ESIZE, "SolveDiag")
}
// scale rows;
for k := 0; k < dn; k++ {
c.Row(B, k)
blasd.InvScale(&c, d.GetAt(k), conf)
}
case gomas.RIGHT:
if bc != dn {
return gomas.NewError(gomas.ESIZE, "SolveDiag")
}
// scale columns
for k := 0; k < dn; k++ {
c.Column(B, k)
blasd.InvScale(&c, d.GetAt(k), conf)
}
}
return nil
}
// Compute the updated rank-1 update vector with precomputed deltas
func trdsecUpdateVecDelta(z, Q, d *cmat.FloatMatrix, rho float64) {
var delta cmat.FloatMatrix
for i := 0; i < d.Len(); i++ {
delta.Column(Q, i)
zk := trdsecUpdateElemDelta(d, &delta, i, rho)
z.SetAt(i, zk)
}
}
// 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)
}
}
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
}
/*
* Generates the real orthogonal matrix Q which is defined as the product of K elementary
* reflectors of order N embedded in matrix A as returned by TRDReduce().
*
* A On entry tridiagonal reduction as returned by TRDReduce().
* On exit the orthogonal matrix Q.
*
* tau Scalar coefficients of elementary reflectors.
*
* W Workspace
*
* K Number of reflectors , 0 < K < N
*
* flags LOWER or UPPER
*
* confs Optional blocking configuration
*
* If flags has UPPER set then
* Q = H(K)...H(1)H(0) where 0 < K < N-1
*
* If flags has LOWR set then
* Q = H(0)H(1)...H(K) where 0 < K < N-1
*/
func TRDBuild(A, tau, W *cmat.FloatMatrix, K, flags int, confs ...*gomas.Config) *gomas.Error {
var err *gomas.Error = nil
var Qh, tauh cmat.FloatMatrix
var s, d cmat.FloatMatrix
if K > m(A)-1 {
K = m(A) - 1
}
switch flags & (gomas.LOWER | gomas.UPPER) {
case gomas.LOWER:
// Shift Q matrix embedded in A right and fill first column
// unit column vector
for j := m(A) - 1; j > 0; j-- {
s.SubMatrix(A, j, j-1, m(A)-j, 1)
d.SubMatrix(A, j, j, m(A)-j, 1)
blasd.Copy(&d, &s)
A.Set(0, j, 0.0)
}
// zero first column and set first entry to one
d.Column(A, 0)
blasd.Scale(&d, 0.0)
d.Set(0, 0, 1.0)
Qh.SubMatrix(A, 1, 1, m(A)-1, m(A)-1)
tauh.SubMatrix(tau, 0, 0, m(A)-1, 1)
err = QRBuild(&Qh, &tauh, W, K, confs...)
case gomas.UPPER:
// Shift Q matrix embedded in A left and fill last column
// unit column vector
for j := 1; j < m(A); j++ {
s.SubMatrix(A, 0, j, j, 1)
d.SubMatrix(A, 0, j-1, j, 1)
blasd.Copy(&d, &s)
A.Set(-1, j-1, 0.0)
}
// zero last column and set last entry to one
d.Column(A, m(A)-1)
blasd.Scale(&d, 0.0)
d.Set(-1, 0, 1.0)
Qh.SubMatrix(A, 0, 0, m(A)-1, m(A)-1)
tauh.SubMatrix(tau, 0, 0, m(A)-1, 1)
err = QLBuild(&Qh, &tauh, W, K, confs...)
}
if err != nil {
err.Update("TRDBuild")
}
return err
}
func sortEigenVec(D, U, V, C *cmat.FloatMatrix, updown int) {
var sD, m0, m1 cmat.FloatMatrix
N := D.Len()
for k := 0; k < N-1; k++ {
sD.SubVector(D, k, N-k)
pk := vecMinMax(&sD, -updown)
if pk != 0 {
t0 := D.GetAt(k)
D.SetAt(k, D.GetAt(pk+k))
D.SetAt(k+pk, t0)
if U != nil {
m0.Column(U, k)
m1.Column(U, k+pk)
blasd.Swap(&m1, &m0)
}
if V != nil {
m0.Row(V, k)
m1.Row(V, k+pk)
blasd.Swap(&m1, &m0)
}
if C != nil {
m0.Column(C, k)
m1.Column(C, k+pk)
blasd.Swap(&m1, &m0)
}
}
}
}
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)
}
}
/*
* Generate one of the orthogonal matrices Q or P.T determined by BDReduce() when
* reducing a real matrix A to bidiagonal form. Q and P.T are defined as products
* elementary reflectors H(i) or G(i) respectively.
*
* Orthogonal matrix Q is generated if flag WANTQ is set. And matrix P respectively
* if flag WANTP is set.
*/
func BDBuild(A, tau, W *cmat.FloatMatrix, K, flags int, confs ...*gomas.Config) *gomas.Error {
var Qh, Ph, tauh, d, s cmat.FloatMatrix
var err *gomas.Error = nil
if m(A) == 0 || n(A) == 0 {
return nil
}
if m(A) > n(A) || (m(A) == n(A) && flags&gomas.LOWER == 0) {
switch flags & (gomas.WANTQ | gomas.WANTP) {
case gomas.WANTQ:
tauh.SubMatrix(tau, 0, 0, n(A), 1)
err = QRBuild(A, &tauh, W, K, confs...)
case gomas.WANTP:
// Shift P matrix embedded in A down and fill first column and row
// to unit vector
for j := n(A) - 1; j > 0; j-- {
s.SubMatrix(A, j-1, j, 1, n(A)-j)
d.SubMatrix(A, j, j, 1, n(A)-j)
blasd.Copy(&d, &s)
A.Set(j, 0, 0.0)
}
// zero first row and set first entry to one
d.Row(A, 0)
blasd.Scale(&d, 0.0)
d.Set(0, 0, 1.0)
Ph.SubMatrix(A, 1, 1, n(A)-1, n(A)-1)
tauh.SubMatrix(tau, 0, 0, n(A)-1, 1)
if K > n(A)-1 {
K = n(A) - 1
}
err = LQBuild(&Ph, &tauh, W, K, confs...)
}
} else {
switch flags & (gomas.WANTQ | gomas.WANTP) {
case gomas.WANTQ:
// Shift Q matrix embedded in A right and fill first column and row
// to unit vector
for j := m(A) - 1; j > 0; j-- {
s.SubMatrix(A, j, j-1, m(A)-j, 1)
d.SubMatrix(A, j, j, m(A)-j, 1)
blasd.Copy(&d, &s)
A.Set(0, j, 0.0)
}
// zero first column and set first entry to one
d.Column(A, 0)
blasd.Scale(&d, 0.0)
d.Set(0, 0, 1.0)
Qh.SubMatrix(A, 1, 1, m(A)-1, m(A)-1)
tauh.SubMatrix(tau, 0, 0, m(A)-1, 1)
if K > m(A)-1 {
K = m(A) - 1
}
err = QRBuild(&Qh, &tauh, W, K, confs...)
case gomas.WANTP:
tauh.SubMatrix(tau, 0, 0, m(A), 1)
err = LQBuild(A, &tauh, W, K, confs...)
}
}
if err != nil {
err.Update("BDBuild")
}
return err
}
// unblocked LU decomposition with pivots: FLAME LU variant 3; Left-looking
func unblockedLUpiv(A *cmat.FloatMatrix, p *Pivots, offset 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
var AL, AR, A0, a1, A2, aB1, AB0 cmat.FloatMatrix
var pT, pB, p0, p1, p2 Pivots
err = nil
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, 0, 0, util.PTOPLEFT)
util.Partition1x2(
&AL, &AR, A, 0, util.PLEFT)
partitionPivot2x1(
&pT,
&pB, *p, 0, util.PTOP)
for m(&ATL) < m(A) && n(&ATL) < n(A) {
util.Repartition2x2to3x3(&ATL,
&A00, &a01, &A02,
&a10, &a11, &a12,
&A20, &a21, &A22 /**/, A, 1, util.PBOTTOMRIGHT)
util.Repartition1x2to1x3(&AL,
&A0, &a1, &A2 /**/, A, 1, util.PRIGHT)
repartPivot2x1to3x1(&pT,
&p0, &p1, &p2 /**/, *p, 1, util.PBOTTOM)
// apply previously computed pivots on current column
applyPivots(&a1, p0)
// a01 = trilu(A00) \ a01 (TRSV)
blasd.MVSolveTrm(&a01, &A00, 1.0, gomas.LOWER|gomas.UNIT)
// a11 = a11 - a10 *a01
aval := a11.Get(0, 0) - blasd.Dot(&a10, &a01)
a11.Set(0, 0, aval)
// a21 = a21 -A20*a01
blasd.MVMult(&a21, &A20, &a01, -1.0, 1.0, gomas.NONE)
// pivot index on current column [a11, a21].T
aB1.Column(&ABR, 0)
p1[0] = pivotIndex(&aB1)
// pivots to current column
applyPivots(&aB1, p1)
// a21 = a21 / a11
if aval == 0.0 {
if err == nil {
ij := m(&ATL) + p1[0] - 1
err = gomas.NewError(gomas.ESINGULAR, "DecomposeLU", ij)
}
} else {
blasd.InvScale(&a21, a11.Get(0, 0))
}
// apply pivots to previous columns
AB0.SubMatrix(&ABL, 0, 0)
applyPivots(&AB0, p1)
// scale last pivots to origin matrix row numbers
p1[0] += m(&ATL)
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &a11, &A22, A, util.PBOTTOMRIGHT)
util.Continue1x3to1x2(
&AL, &AR, &A0, &a1, A, util.PRIGHT)
contPivot3x1to2x1(
&pT,
&pB, p0, p1, *p, util.PBOTTOM)
}
if n(&ATL) < n(A) {
applyPivots(&ATR, *p)
blasd.SolveTrm(&ATR, &ATL, 1.0, gomas.LEFT|gomas.UNIT|gomas.LOWER, conf)
}
return err
}