/*
* Multiply and replace C with product of C and Q or P where Q and P are real orthogonal matrices
* defined as the product of k elementary reflectors.
*
* Q = H(1) H(2) . . . H(k) and P = G(1) G(2). . . G(k)
*
* as returned by ReduceBidiag().
*
* Arguments:
* C On entry, the M-by-N matrix C or if flag bit RIGHT is set then N-by-M matrix
* On exit C is overwritten by Q*C or Q.T*C. If bit RIGHT is set then C is
* overwritten by C*Q or C*Q.T
*
* A Bidiagonal reduction as returned by ReduceBidiag() where the lower trapezoidal
* part, on and below first subdiagonal, holds the product Q. The upper
* trapezoidal part holds the product P.
*
* tau The scalar factors of the elementary reflectors. If flag MULTQ is set then holds
* scalar factors for Q. If flag MULTP is set then holds scalar factors for P.
* Expected to be column vector is size min(M(A), N(A)).
*
* bits Indicators, valid bits LEFT, RIGHT, TRANS, MULTQ, MULTP
*
* flags result
* ------------------------------------------
* MULTQ,LEFT C = Q*C n(A) == m(C)
* MULTQ,RIGHT C = C*Q n(C) == m(A)
* MULTQ,TRANS,LEFT C = Q.T*C n(A) == m(C)
* MULTQ,TRANS,RIGHT C = C*Q.T n(C) == m(A)
* MULTP,LEFT C = P*C n(A) == m(C)
* MULTP,RIGHT C = C*P n(C) == m(A)
* MULTP,TRANS,LEFT C = P.T*C n(A) == m(C)
* MULTP,TRANS,RIGHT C = C*P.T n(C) == m(A)
*
*/
func BDMult(C, A, tau, W *cmat.FloatMatrix, flags int, confs ...*gomas.Config) *gomas.Error {
var Qh, Ch, Ph, tauh cmat.FloatMatrix
var err *gomas.Error = nil
// default to multiply from left if side not defined
if flags&(gomas.LEFT|gomas.RIGHT) == 0 {
flags = flags | gomas.LEFT
}
// if MULTP then flip TRANSPOSE-bit
if flags&gomas.MULTP != 0 {
// LQ.P = G(k)G(k-1)...G(1) and
// Bidiag.P = G(1)G(2)...G(k)
// therefore flip the TRANSPOSE bit.
if flags&gomas.TRANS != 0 {
flags &= ^gomas.TRANS
} else {
flags |= gomas.TRANS
}
}
if m(A) > n(A) || (m(A) == n(A) && flags&gomas.LOWER == 0) {
switch flags & (gomas.MULTQ | gomas.MULTP) {
case gomas.MULTQ:
tauh.SubMatrix(tau, 0, 0, n(A), 1)
err = QRMult(C, A, &tauh, W, flags, confs...)
case gomas.MULTP:
Ph.SubMatrix(A, 0, 1, n(A)-1, n(A)-1)
tauh.SubMatrix(tau, 0, 0, n(A)-1, 1)
if flags&gomas.RIGHT != 0 {
Ch.SubMatrix(C, 0, 1, m(C), n(C)-1)
} else {
Ch.SubMatrix(C, 1, 0, m(C)-1, n(C))
}
err = LQMult(&Ch, &Ph, &tauh, W, flags, confs...)
}
} else {
switch flags & (gomas.MULTQ | gomas.MULTP) {
case gomas.MULTQ:
Qh.SubMatrix(A, 1, 0, m(A)-1, m(A)-1)
tauh.SubMatrix(tau, 0, 0, m(A)-1, 1)
if flags&gomas.RIGHT != 0 {
Ch.SubMatrix(C, 0, 1, m(C), n(C)-1)
} else {
Ch.SubMatrix(C, 1, 0, m(C)-1, n(C))
}
err = QRMult(&Ch, &Qh, &tauh, W, flags, confs...)
case gomas.MULTP:
tauh.SubMatrix(tau, 0, 0, m(A), 1)
err = LQMult(C, A, &tauh, W, flags, confs...)
}
}
if err != nil {
err.Update("BDMult")
}
return err
}
/*
* 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
}
/*
* 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
}