/*
* 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
}
/*
* Blocked QR decomposition with compact WY transform.
*
* Compatible with lapack.DGEQRF.
*/
func blockedQL(A, Tvec, Twork, W *cmat.FloatMatrix, lb int, conf *gomas.Config) {
var ATL, ATR, ABL, ABR, AL cmat.FloatMatrix
var A00, A01, A10, A11, A22 cmat.FloatMatrix
var TT, TB cmat.FloatMatrix
var t0, tau, t2 cmat.FloatMatrix
var Wrk, w1 cmat.FloatMatrix
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, 0, 0, util.PBOTTOMRIGHT)
util.Partition2x1(
&TT,
&TB, Tvec, 0, util.PBOTTOM)
nb := lb
for m(&ATL)-nb > 0 && n(&ATL)-nb > 0 {
util.Repartition2x2to3x3(&ATL,
&A00, &A01, nil,
&A10, &A11, nil,
nil, nil, &A22, A, nb, util.PTOPLEFT)
util.Repartition2x1to3x1(&TT,
&t0,
&tau,
&t2, Tvec, nb, util.PTOP)
// current block size
cb, rb := A11.Size()
if rb < cb {
cb = rb
}
// --------------------------------------------------------
// decompose righ side AL == /A01\
// \A11/
w1.SubMatrix(W, 0, 0, cb, 1)
util.Merge2x1(&AL, &A01, &A11)
unblockedQL(&AL, &tau, &w1)
// build block reflector
unblkQLBlockReflector(Twork, &AL, &tau)
// update A'tail i.e. A10 and A00 with (I - Y*T*Y.T).T * A'tail
// compute: C - Y*(C.T*Y*T).T
ar, ac := A10.Size()
Wrk.SubMatrix(W, 0, 0, ac, ar)
updateQLLeft(&A10, &A00, &A11, &A01, Twork, &Wrk, true, conf)
// --------------------------------------------------------
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &A11, &A22, A, util.PTOPLEFT)
util.Continue3x1to2x1(
&TT,
&TB, &t0, &tau, Tvec, util.PTOP)
}
// last block with unblocked
if m(&ATL) > 0 && n(&ATL) > 0 {
w1.SubMatrix(W, 0, 0, n(&ATL), 1)
unblockedQL(&ATL, &t0, &w1)
}
}
/*
* Solve a system of linear equations A*X = B or A.T*X = B with general N-by-N
* matrix A using the LU factorization computed by LUFactor().
*
* Arguments:
* B On entry, the right hand side matrix B. On exit, the solution matrix X.
*
* A The factor L and U from the factorization A = P*L*U as computed by
* LUFactor()
*
* pivots The pivot indices from LUFactor().
*
* flags The indicator of the form of the system of equations.
* If flags&TRANSA then system is transposed. All other values
* indicate non transposed system.
*
* Compatible with lapack.DGETRS.
*/
func LUSolve(B, A *cmat.FloatMatrix, pivots Pivots, flags int, confs ...*gomas.Config) *gomas.Error {
var err *gomas.Error = nil
conf := gomas.DefaultConf()
if len(confs) > 0 {
conf = confs[0]
}
ar, ac := A.Size()
br, _ := B.Size()
if ar != ac {
return gomas.NewError(gomas.ENOTSQUARE, "SolveLU")
}
if br != ac {
return gomas.NewError(gomas.ESIZE, "SolveLU")
}
if pivots != nil {
applyPivots(B, pivots)
}
if flags&gomas.TRANSA != 0 {
// transposed X = A.-1*B == (L.T*U.T).-1*B == U.-T*(L.-T*B)
blasd.SolveTrm(B, A, 1.0, gomas.LOWER|gomas.UNIT|gomas.TRANSA, conf)
blasd.SolveTrm(B, A, 1.0, gomas.UPPER|gomas.TRANSA, conf)
} else {
// non-transposed X = A.-1*B == (L*U).-1*B == U.-1*(L.-1*B)
blasd.SolveTrm(B, A, 1.0, gomas.LOWER|gomas.UNIT, conf)
blasd.SolveTrm(B, A, 1.0, gomas.UPPER, conf)
}
return err
}
func updtrmv(A, X, Y *cmat.FloatMatrix, alpha float64, bits, N, M int) error {
var Am C.mdata_t
var Xm, Ym C.mvec_t
xr, _ := X.Size()
yr, _ := Y.Size()
Am.md = (*C.double)(unsafe.Pointer(&A.Data()[0]))
Am.step = C.int(A.Stride())
Xm.md = (*C.double)(unsafe.Pointer(&X.Data()[0]))
Ym.md = (*C.double)(unsafe.Pointer(&Y.Data()[0]))
Ym.inc = C.int(1)
Xm.inc = C.int(1)
// if row vectors, change increment
if xr == 1 {
Xm.inc = C.int(X.Stride())
}
if yr == 1 {
Ym.inc = C.int(Y.Stride())
}
C.__d_update_trmv_unb(
(*C.mdata_t)(unsafe.Pointer(&Am)),
(*C.mvec_t)(unsafe.Pointer(&Xm)),
(*C.mvec_t)(unsafe.Pointer(&Ym)),
C.double(alpha), C.int(bits), C.int(N), C.int(M))
return nil
}
/*
* Blocked LQ decomposition with compact WY transform. As implemented
* in lapack.DGELQF subroutine.
*/
func blockedLQ(A, Tvec, Twork, W *cmat.FloatMatrix, lb int, conf *gomas.Config) {
var ATL, ATR, ABL, ABR, AR cmat.FloatMatrix
var A00, A11, A12, A21, A22 cmat.FloatMatrix
var TT, TB cmat.FloatMatrix
var t0, tau, t2 cmat.FloatMatrix
var Wrk, w1 cmat.FloatMatrix
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, 0, 0, util.PTOPLEFT)
util.Partition2x1(
&TT,
&TB, Tvec, 0, util.PTOP)
//nb := conf.LB
for m(&ABR)-lb > 0 && n(&ABR)-lb > 0 {
util.Repartition2x2to3x3(&ATL,
&A00, nil, nil,
nil, &A11, &A12,
nil, &A21, &A22, A, lb, util.PBOTTOMRIGHT)
util.Repartition2x1to3x1(&TT,
&t0,
&tau,
&t2, Tvec, lb, util.PBOTTOM)
// current block size
cb, rb := A11.Size()
if rb < cb {
cb = rb
}
// --------------------------------------------------------
// decompose left side AL == /A11\
// \A21/
w1.SubMatrix(W, 0, 0, cb, 1)
util.Merge1x2(&AR, &A11, &A12)
unblockedLQ(&AR, &tau, &w1)
// build block reflector
unblkBlockReflectorLQ(Twork, &AR, &tau)
// update A'tail i.e. A21 and A22 with A'*(I - Y*T*Y.T).T
// compute: C - Y*(C.T*Y*T).T
ar, ac := A21.Size()
Wrk.SubMatrix(W, 0, 0, ar, ac)
updateRightLQ(&A21, &A22, &A11, &A12, Twork, &Wrk, true, conf)
// --------------------------------------------------------
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &A11, &A22, A, util.PBOTTOMRIGHT)
util.Continue3x1to2x1(
&TT,
&TB, &t0, &tau, Tvec, util.PBOTTOM)
}
// last block with unblocked
if m(&ABR) > 0 && n(&ABR) > 0 {
w1.SubMatrix(W, 0, 0, m(&ABR), 1)
unblockedLQ(&ABR, &t2, &w1)
}
}
func gemv(Y, A, X *cmat.FloatMatrix, alpha, beta float64, bits, S, L, R, E int) {
var Am C.mdata_t
var Xm, Ym C.mvec_t
xr, _ := X.Size()
yr, _ := Y.Size()
Am.md = (*C.double)(unsafe.Pointer(&A.Data()[0]))
Am.step = C.int(A.Stride())
Xm.md = (*C.double)(unsafe.Pointer(&X.Data()[0]))
Ym.md = (*C.double)(unsafe.Pointer(&Y.Data()[0]))
Ym.inc = C.int(1)
Xm.inc = C.int(1)
// if row vectors, change increment
if xr == 1 {
Xm.inc = C.int(X.Stride())
}
if yr == 1 {
Ym.inc = C.int(Y.Stride())
}
C.__d_gemv_unb(
(*C.mvec_t)(unsafe.Pointer(&Ym)),
(*C.mdata_t)(unsafe.Pointer(&Am)),
(*C.mvec_t)(unsafe.Pointer(&Xm)),
C.double(alpha),
/*C.double(beta),*/
C.int(bits),
C.int(S), C.int(L), C.int(R), C.int(E))
}
func axpby(Y, X *cmat.FloatMatrix, alpha, beta float64, N int) {
var x, y C.mvec_t
xr, _ := X.Size()
x.md = (*C.double)(unsafe.Pointer(&X.Data()[0]))
x.inc = C.int(1)
if xr == 1 {
x.inc = C.int(X.Stride())
}
yr, _ := Y.Size()
y.md = (*C.double)(unsafe.Pointer(&Y.Data()[0]))
y.inc = C.int(1)
if yr == 1 {
y.inc = C.int(Y.Stride())
}
if beta == 1.0 {
C.__d_vec_axpy(
(*C.mvec_t)(unsafe.Pointer(&y)),
(*C.mvec_t)(unsafe.Pointer(&x)),
C.double(alpha), C.int(N))
} else {
C.__d_vec_axpby(
(*C.mvec_t)(unsafe.Pointer(&y)),
(*C.mvec_t)(unsafe.Pointer(&x)),
C.double(alpha), C.double(beta), C.int(N))
}
return
}
/*
* Compute QR factorization of a M-by-N matrix A using compact WY transformation: A = Q * R,
* where Q = I - Y*T*Y.T, T is block reflector and Y holds elementary reflectors as lower
* trapezoidal matrix saved below diagonal elements of the matrix A.
*
* Arguments:
* A On entry, the M-by-N matrix A. On exit, the elements on and above
* the diagonal contain the min(M,N)-by-N upper trapezoidal matrix R.
* The elements below the diagonal with the matrix 'T', represent
* the ortogonal matrix Q as product of elementary reflectors.
*
* T On exit, the K block reflectors which, together with trilu(A) represent
* the ortogonal matrix Q as Q = I - Y*T*Y.T where Y = trilu(A).
* K is ceiling(N/LB) where LB is blocking size from used blocking configuration.
* The matrix T is LB*N augmented matrix of K block reflectors,
* T = [T(0) T(1) .. T(K-1)]. Block reflector T(n) is LB*LB matrix, expect
* reflector T(K-1) that is IB*IB matrix where IB = min(LB, K % LB)
*
* W Workspace, required size returned by QRTFactorWork().
*
* conf Optional blocking configuration. If not provided then default configuration
* is used.
*
* Returns:
* Error indicator.
*
* QRTFactor is compatible with lapack.DGEQRT
*/
func QRTFactor(A, T, W *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
var err *gomas.Error = nil
conf := gomas.CurrentConf(confs...)
ok := false
rsize := 0
if m(A) < n(A) {
return gomas.NewError(gomas.ESIZE, "QRTFactor")
}
wsz := QRTFactorWork(A, conf)
if W == nil || W.Len() < wsz {
return gomas.NewError(gomas.EWORK, "QRTFactor", wsz)
}
tr, tc := T.Size()
if conf.LB == 0 || conf.LB > n(A) {
ok = tr == tc && tr == n(A)
rsize = n(A) * n(A)
} else {
ok = tr == conf.LB && tc == n(A)
rsize = conf.LB * n(A)
}
if !ok {
return gomas.NewError(gomas.ESMALL, "QRTFactor", rsize)
}
if conf.LB == 0 || n(A) <= conf.LB {
err = unblockedQRT(A, T, W)
} else {
Wrk := cmat.MakeMatrix(n(A), conf.LB, W.Data())
err = blockedQRT(A, T, Wrk, conf)
}
return err
}
func TestSubMatrixGob(t *testing.T) {
var B, As cmat.FloatMatrix
var network bytes.Buffer
N := 32
A := cmat.NewMatrix(N, N)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
As.SubMatrix(A, 3, 3, N-6, N-6)
enc := gob.NewEncoder(&network)
dec := gob.NewDecoder(&network)
// encode to network
err := enc.Encode(&As)
if err != nil {
t.Logf("encode error: %v\n", err)
t.FailNow()
}
// decode from network
err = dec.Decode(&B)
if err != nil {
t.Logf("decode error: %v\n", err)
t.FailNow()
}
ar, ac := As.Size()
br, bc := B.Size()
t.Logf("As[%d,%d] == B[%d,%d]: %v\n", ar, ac, br, bc, B.AllClose(&As))
}
/*
* Apply diagonal pivot (row and column swapped) to symmetric matrix blocks.
* AR[0,0] is on diagonal and AL is block to the left of diagonal and AR the
* triangular diagonal block. Need to swap row and column.
*
* LOWER triangular; moving from top-left to bottom-right
*
* d
* x d |
* --------------------------
* x x | d
* S1 S1| S1 P1 x x x P2 -- current row/col 'srcix'
* x x | x S2 d x x x
* x x | x S2 x d x x
* x x | x S2 x x d x
* D1 D1| D1 P2 D2 D2 D2 P3 -- swap with row/col 'dstix'
* x x | x S3 x x x D3 d
* x x | x S3 x x x D3 x d
* (ABL) (ABR)
*
* UPPER triangular; moving from bottom-right to top-left
*
* (ATL) (ATR)
* d x x D3 x x x S3 x | x
* d x D3 x x x S3 x | x
* d D3 x x x S3 x | x
* P3 D2 D2 D2 P2 D1| D1 -- dstinx
* d x x S2 x | x
* d x S2 x | x
* d S2 x | x
* P1 S1| S1 -- srcinx
* d | x
* -----------------------------
* | d
* (ABR)
*/
func applyPivotSym2(AL, AR *cmat.FloatMatrix, srcix, dstix int, flags int) {
var s, d cmat.FloatMatrix
_, lc := AL.Size()
rr, rc := AR.Size()
if flags&gomas.LOWER != 0 {
// AL is [ABL]; AR is [ABR]; P1 is AR[0,0], P2 is AR[index, 0]
// S1 -- D1
AL.SubMatrix(&s, srcix, 0, 1, lc)
AL.SubMatrix(&d, dstix, 0, 1, lc)
blasd.Swap(&s, &d)
if srcix > 0 {
AR.SubMatrix(&s, srcix, 0, 1, srcix)
AR.SubMatrix(&d, dstix, 0, 1, srcix)
blasd.Swap(&s, &d)
}
// S2 -- D2
AR.SubMatrix(&s, srcix+1, srcix, dstix-srcix-1, 1)
AR.SubMatrix(&d, dstix, srcix+1, 1, dstix-srcix-1)
blasd.Swap(&s, &d)
// S3 -- D3
AR.SubMatrix(&s, dstix+1, srcix, rr-dstix-1, 1)
AR.SubMatrix(&d, dstix+1, dstix, rr-dstix-1, 1)
blasd.Swap(&s, &d)
// swap P1 and P3
p1 := AR.Get(srcix, srcix)
p3 := AR.Get(dstix, dstix)
AR.Set(srcix, srcix, p3)
AR.Set(dstix, dstix, p1)
return
}
if flags&gomas.UPPER != 0 {
// AL is ATL, AR is ATR; P1 is AL[srcix, srcix];
// S1 -- D1;
AR.SubMatrix(&s, srcix, 0, 1, rc)
AR.SubMatrix(&d, dstix, 0, 1, rc)
blasd.Swap(&s, &d)
if srcix < lc-1 {
// not the corner element
AL.SubMatrix(&s, srcix, srcix+1, 1, srcix)
AL.SubMatrix(&d, dstix, srcix+1, 1, srcix)
blasd.Swap(&s, &d)
}
// S2 -- D2
AL.SubMatrix(&s, dstix+1, srcix, srcix-dstix-1, 1)
AL.SubMatrix(&d, dstix, dstix+1, 1, srcix-dstix-1)
blasd.Swap(&s, &d)
// S3 -- D3
AL.SubMatrix(&s, 0, srcix, dstix, 1)
AL.SubMatrix(&d, 0, dstix, dstix, 1)
blasd.Swap(&s, &d)
//fmt.Printf("3, AR=%v\n", AR)
// swap P1 and P3
p1 := AR.Get(0, 0)
p3 := AL.Get(dstix, dstix)
AR.Set(srcix, srcix, p3)
AL.Set(dstix, dstix, p1)
return
}
}
/*
* Blocked RQ decomposition with compact WY transform. As implemented
* in lapack.DGERQF subroutine.
*/
func blockedRQ(A, Tvec, Twork, W *cmat.FloatMatrix, lb int, conf *gomas.Config) {
var ATL, ABR, AL cmat.FloatMatrix
var A00, A01, A10, A11, A22 cmat.FloatMatrix
var TT, TB cmat.FloatMatrix
var t0, tau, t2 cmat.FloatMatrix
var Wrk, w1 cmat.FloatMatrix
util.Partition2x2(
&ATL, nil,
nil, &ABR /**/, A, 0, 0, util.PBOTTOMRIGHT)
util.Partition2x1(
&TT,
&TB /**/, Tvec, 0, util.PBOTTOM)
for m(&ATL)-lb > 0 && n(&ATL)-lb > 0 {
util.Repartition2x2to3x3(&ATL,
&A00, &A01, nil,
&A10, &A11, nil,
nil, nil, &A22 /**/, A, lb, util.PTOPLEFT)
util.Repartition2x1to3x1(&TT,
&t0,
&tau,
&t2 /**/, Tvec, n(&A11), util.PTOP)
// current block size
cb, rb := A11.Size()
if rb < cb {
cb = rb
}
// --------------------------------------------------------
// decompose left side AL == ( A10 A11 )
w1.SubMatrix(W, 0, 0, cb, 1)
util.Merge1x2(&AL, &A10, &A11)
unblockedRQ(&AL, &tau, &w1)
// build block reflector
unblkBlockReflectorRQ(Twork, &AL, &tau)
// compute: (A00 A01)(I - Y*T*Y.T)
ar, ac := A01.Size()
Wrk.SubMatrix(W, 0, 0, ar, ac)
updateRightRQ(&A01, &A00, &A11, &A10, Twork, &Wrk, false, conf)
// --------------------------------------------------------
util.Continue3x3to2x2(
&ATL, nil,
nil, &ABR, &A00, &A11, &A22, A, util.PTOPLEFT)
util.Continue3x1to2x1(
&TT,
&TB, &t0, &tau, Tvec, util.PTOP)
}
// last block with unblocked
if m(&ATL) > 0 && n(&ATL) > 0 {
w1.SubMatrix(W, 0, 0, m(&ATL), 1)
unblockedRQ(&ATL, &TT, &w1)
}
}
/*
* Merge 1 by 1 block from 1 by 2 block.
*
* ABLK <-- AL | AR
*
*/
func Merge1x2(ABLK, AL, AR *cmat.FloatMatrix) {
lr, lc := AL.Size()
_, rc := AR.Size()
if lc > 0 {
ABLK.SubMatrix(AL, 0, 0, lr, lc+rc)
} else {
ABLK.SubMatrix(AR, 0, 0, lr, rc)
}
}
func Transpose(A, B *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
ar, ac := A.Size()
br, bc := B.Size()
if ar != bc || ac != br {
return gomas.NewError(gomas.ESIZE, "Transpose")
}
mtranspose(A, B, br, bc)
return nil
}
/*
* Merge 1 by 1 block from 2 by 1 block.
*
* AT
* Abkl <-- --
* AB
*
*/
func Merge2x1(ABLK, AT, AB *cmat.FloatMatrix) {
tr, tc := AT.Size()
br, _ := AB.Size()
if tr > 0 {
ABLK.SubMatrix(AT, 0, 0, tr+br, tc)
} else {
ABLK.SubMatrix(AB, 0, 0, br, tc)
}
}
func Sum(X *cmat.FloatMatrix, confs ...*gomas.Config) float64 {
if X.Len() == 0 {
return 0.0
}
xr, xc := X.Size()
if xr != 1 && xc != 1 {
return 0.0
}
return sum(X, X.Len())
}
func swapCols(A *cmat.FloatMatrix, src, dst int) {
var c0, c1 cmat.FloatMatrix
ar, _ := A.Size()
if src == dst || ar == 0 {
return
}
c0.SubMatrix(A, 0, src, ar, 1)
c1.SubMatrix(A, 0, dst, ar, 1)
blasd.Swap(&c0, &c1)
}
func IAmax(X *cmat.FloatMatrix, confs ...*gomas.Config) int {
if X.Len() == 0 {
return -1
}
xr, xc := X.Size()
if xr != 1 && xc != 1 {
return -1
}
return iamax(X, X.Len())
}
func swapRows(A *cmat.FloatMatrix, src, dst int) {
var r0, r1 cmat.FloatMatrix
ar, ac := A.Size()
if src == dst || ar == 0 {
return
}
r0.SubMatrix(A, src, 0, 1, ac)
r1.SubMatrix(A, dst, 0, 1, ac)
blasd.Swap(&r0, &r1)
}
func Nrm2(X *cmat.FloatMatrix, confs ...*gomas.Config) float64 {
if X.Len() == 0 {
return 0.0
}
xr, xc := X.Size()
if xr != 1 && xc != 1 {
return 0.0
}
nx := X.Len()
return vnrm2(X, nx)
}
/*
* Triangular matrix multiplication.
*/
func MultTrm(B, A *cmat.FloatMatrix, alpha float64, bits int, confs ...*gomas.Config) *gomas.Error {
conf := gomas.DefaultConf()
if len(confs) > 0 {
conf = confs[0]
}
if B.Len() == 0 || A.Len() == 0 {
return nil
}
ok := true
ar, ac := A.Size()
br, bc := B.Size()
P := ac
E := bc
switch {
case bits&gomas.RIGHT != 0:
ok = bc == ar && ar == ac
E = br
case bits&gomas.LEFT != 0:
fallthrough
default:
ok = ac == br && ar == ac
}
if !ok {
return gomas.NewError(gomas.ESIZE, "MultTrm")
}
// single threaded
if conf.NProc == 1 || conf.WB <= 0 || E < conf.WB/2 {
trmm(B, A, alpha, bits, P, 0, E, conf)
return nil
}
// parallelized
wait := make(chan int, 4)
_, nN := blocking(0, E, conf.WB/2)
nT := 0
for j := 0; j < nN; j++ {
jS := blockIndex(j, nN, conf.WB/2, E)
jL := blockIndex(j+1, nN, conf.WB/2, E)
task := func(q chan int) {
trmm(B, A, alpha, bits, P, jS, jL, conf)
q <- 1
}
conf.Sched.Schedule(gomas.NewTask(task, wait))
nT += 1
}
for nT > 0 {
<-wait
nT -= 1
}
return nil
}
func computeHouseholderVec(x, tau *cmat.FloatMatrix) {
var alpha, x2 cmat.FloatMatrix
r, _ := x.Size()
alpha.SubMatrix(x, 0, 0, 1, 1)
if r == 1 {
x2.SubMatrix(x, 0, 1, 1, x.Len()-1) // row vector
} else {
x2.SubMatrix(x, 1, 0, x.Len()-1, 1)
}
computeHouseholder(&alpha, &x2, tau)
}
func Scale(A *cmat.FloatMatrix, alpha float64, confs ...*gomas.Config) *gomas.Error {
if A.Len() == 0 {
return nil
}
ar, ac := A.Size()
if ar != 1 && ac != 1 {
mscale(A, alpha, ar, ac)
return nil
}
vscal(A, alpha, A.Len())
return nil
}
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
}
func vinvscal(X *cmat.FloatMatrix, alpha float64, N int) {
var x C.mvec_t
xr, _ := X.Size()
x.md = (*C.double)(unsafe.Pointer(&X.Data()[0]))
x.inc = C.int(1)
if xr == 1 {
x.inc = C.int(X.Stride())
}
C.__d_vec_invscal(
(*C.mvec_t)(unsafe.Pointer(&x)), C.double(alpha), C.int(N))
return
}
func mNormInf(A *cmat.FloatMatrix) float64 {
var amax float64 = 0.0
var row cmat.FloatMatrix
arows, _ := A.Size()
for k := 0; k < arows; k++ {
row.Row(A, k)
rmax := blasd.ASum(&row)
if rmax > amax {
amax = rmax
}
}
return amax
}
/*
* Partition p to 2 by 1 blocks.
*
* AT
* A --> --
* AB
*
* Parameter nb is initial block size for AT (pTOP) or AB (pBOTTOM).
*/
func Partition2x1(AT, AB, A *cmat.FloatMatrix, nb int, side Direction) {
ar, ac := A.Size()
if nb > ar {
nb = ar
}
switch side {
case PTOP:
AT.SubMatrix(A, 0, 0, nb, ac)
AB.SubMatrix(A, nb, 0, ar-nb, ac)
case PBOTTOM:
AT.SubMatrix(A, 0, 0, ar-nb, ac)
AB.SubMatrix(A, ar-nb, 0, nb, ac)
}
}
/*
* Apply diagonal pivot (row and column swapped) to symmetric matrix blocks.
* AR[0,0] is on diagonal and AL is block to the left of diagonal and AR the
* triangular diagonal block. Need to swap row and column.
*
* LOWER triangular; moving from top-left to bottom-right
*
* d
* x d
* x x d |
* --------------------------
* S1 S1 S1 | P1 x x x P2 -- current row
* x x x | S2 d x x x
* x x x | S2 x d x x
* x x x | S2 x x d x
* D1 D1 D1 | P2 D2 D2 D2 P3 -- swap with row 'index'
* x x x | S3 x x x D3 d
* x x x | S3 x x x D3 x d
* (ABL) (ABR)
*
* UPPER triangular; moving from bottom-right to top-left
*
* (ATL) (ATR)
* d x x D3 x x x | S3 x x
* d x D3 x x x | S3 x x
* d D3 x x x | S3 x x
* P3 D2 D2 D2| P2 D1 D1
* d x x | S2 x x
* d x | S2 x x
* d | S2 x x
* -----------------------------
* | P1 S1 S1
* | d x
* | d
* (ABR)
*/
func applyPivotSym(AL, AR *cmat.FloatMatrix, index int, flags int) {
var s, d cmat.FloatMatrix
lr, lc := AL.Size()
rr, rc := AR.Size()
if flags&gomas.LOWER != 0 {
// AL is [ABL]; AR is [ABR]; P1 is AR[0,0], P2 is AR[index, 0]
// S1 -- D1
s.SubMatrix(AL, 0, 0, 1, lc)
d.SubMatrix(AL, index, 0, 1, lc)
blasd.Swap(&s, &d)
// S2 -- D2
s.SubMatrix(AR, 1, 0, index-1, 1)
d.SubMatrix(AR, index, 1, 1, index-1)
blasd.Swap(&s, &d)
// S3 -- D3
s.SubMatrix(AR, index+1, 0, rr-index-1, 1)
d.SubMatrix(AR, index+1, index, rr-index-1, 1)
blasd.Swap(&s, &d)
// swap P1 and P3
p1 := AR.Get(0, 0)
p3 := AR.Get(index, index)
AR.Set(0, 0, p3)
AR.Set(index, index, p1)
return
}
if flags&gomas.UPPER != 0 {
// AL is merged from [ATL, ATR], AR is [ABR]; P1 is AR[0, 0]; P2 is AL[index, -1]
colno := lc - rc
// S1 -- D1; S1 is on the first row of AR
s.SubMatrix(AR, 0, 1, 1, rc-1)
d.SubMatrix(AL, index, colno+1, 1, rc-1)
blasd.Swap(&s, &d)
// S2 -- D2
s.SubMatrix(AL, index+1, colno, lr-index-2, 1)
d.SubMatrix(AL, index, index+1, 1, colno-index-1)
blasd.Swap(&s, &d)
// S3 -- D3
s.SubMatrix(AL, 0, index, index, 1)
d.SubMatrix(AL, 0, colno, index, 1)
blasd.Swap(&s, &d)
//fmt.Printf("3, AR=%v\n", AR)
// swap P1 and P3
p1 := AR.Get(0, 0)
p3 := AL.Get(index, index)
AR.Set(0, 0, p3)
AL.Set(index, index, p1)
return
}
}
func iamax(X *cmat.FloatMatrix, N int) int {
var x C.mvec_t
var ix C.int
xr, _ := X.Size()
x.md = (*C.double)(unsafe.Pointer(&X.Data()[0]))
x.inc = C.int(1)
if xr == 1 {
x.inc = C.int(X.Stride())
}
ix = C.__d_vec_iamax(
(*C.mvec_t)(unsafe.Pointer(&x)), C.int(N))
return int(ix)
}
/*
* Partition A to 1 by 2 blocks.
*
* A --> AL | AR
*
* Parameter nb is initial block size for AL (pLEFT) or AR (pRIGHT).
*/
func Partition1x2(AL, AR, A *cmat.FloatMatrix, nb int, side Direction) {
ar, ac := A.Size()
if nb > ac {
nb = ac
}
switch side {
case PLEFT:
AL.SubMatrix(A, 0, 0, ar, nb)
AR.SubMatrix(A, 0, nb, ar, ac-nb)
case PRIGHT:
AL.SubMatrix(A, 0, 0, ar, ac-nb)
AR.SubMatrix(A, 0, ac-nb, ar, nb)
}
}
func sum(X *cmat.FloatMatrix, N int) float64 {
var x C.mvec_t
var dc C.double
xr, _ := X.Size()
x.md = (*C.double)(unsafe.Pointer(&X.Data()[0]))
x.inc = C.int(1)
if xr == 1 {
x.inc = C.int(X.Stride())
}
dc = C.__d_vec_sum_recursive(
(*C.mvec_t)(unsafe.Pointer(&x)), C.int(N))
return float64(dc)
}