/*
* 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 Update2Sym(Cc, A, B *cmat.FloatMatrix, alpha, beta float64, bits int, confs ...*gomas.Config) *gomas.Error {
conf := gomas.DefaultConf()
if len(confs) > 0 {
conf = confs[0]
}
ok := true
cr, cc := Cc.Size()
ar, ac := A.Size()
br, bc := B.Size()
if cr*cc == 0 {
return nil
}
P := ac
E := cr
if bits&gomas.TRANS != 0 && bits&gomas.TRANSA == 0 {
bits |= gomas.TRANSA
}
switch {
case bits&gomas.TRANSA != 0:
ok = cr == cc && cr == ac && bc == ac && br == ar
P = ar
default:
ok = cr == cc && cr == ar && br == ar && bc == ac
}
if !ok {
return gomas.NewError(gomas.ESIZE, "Update2Sym")
}
if conf.NProc == 1 || conf.WB <= 0 || E <= conf.WB {
syr2k(Cc, A, B, alpha, beta, bits, P, 0, E, conf)
return nil
}
// parallelized
wait := make(chan int, 4)
_, nN := blocking(0, E, conf.WB)
nT := 0
for j := 0; j < nN; j++ {
jS := blockIndex(j, nN, conf.WB, E)
jE := blockIndex(j+1, nN, conf.WB, E)
task := func(q chan int) {
syr2k(Cc, A, B, alpha, beta, bits, P, jS, jE, conf)
q <- 1
}
conf.Sched.Schedule(gomas.NewTask(task, wait))
nT += 1
}
for nT > 0 {
<-wait
nT -= 1
}
return nil
}
/*
* 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
}
/*
* Compute an LU factorization of a general M-by-N matrix without pivoting.
*
* Arguments:
* A On entry, the M-by-N matrix to be factored. On exit the factors
* L and U from factorization A = P*L*U, the unit diagonal elements
* of L are not stored.
*
* nb Blocking factor for blocked invocations. If bn == 0 or
* min(M,N) < nb unblocked algorithm is used.
*
* Returns:
* LU factorization and error indicator.
*
* Compatible with lapack.DGETRF
*/
func luFactorNoPiv(A *cmat.FloatMatrix, confs ...*gomas.Config) *gomas.Error {
var err *gomas.Error = nil
conf := gomas.DefaultConf()
if len(confs) > 0 {
conf = confs[0]
}
mlen := imin(m(A), n(A))
if mlen <= conf.LB || conf.LB == 0 {
err = unblockedLUnoPiv(A, conf)
} else {
err = blockedLUnoPiv(A, conf.LB, conf)
}
return err
}
func TestLU(t *testing.T) {
N := 119
K := 41
nb := 0
A := cmat.NewMatrix(N, N)
A0 := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(N, K)
X := cmat.NewMatrix(N, K)
unitrand := cmat.NewFloatUniformSource()
A.SetFrom(unitrand)
A0.Copy(A)
B.SetFrom(unitrand)
X.Copy(B)
piv := lapackd.NewPivots(N)
conf := gomas.DefaultConf()
conf.LB = nb
// R = lu(A) = P*L*U
lapackd.LUFactor(A, piv, conf)
// X = A.-1*B = U.-1*(L.-1*B)
lapackd.LUSolve(X, A, piv, gomas.NONE)
// B = B - A*X
blasd.Mult(B, A0, X, -1.0, 1.0, gomas.NONE)
nrm := lapackd.NormP(B, lapackd.NORM_ONE)
t.Logf("Unblocked decomposition: nb=%d\n", conf.LB)
t.Logf("N=%d ||B - A*X||_1: %e\n", N, nrm)
// blocked
conf.LB = 16
A.Copy(A0)
B.SetFrom(unitrand)
X.Copy(B)
// lu(A) = P*L*U
lapackd.LUFactor(A, piv, conf)
// X = A.-1*B = U.-1*(L.-1*B)
lapackd.LUSolve(X, A, piv, gomas.NONE)
// B = B - A*X
blasd.Mult(B, A0, X, -1.0, 1.0, gomas.NONE)
nrm = lapackd.NormP(B, lapackd.NORM_ONE)
t.Logf("Blocked decomposition: nb=%d\n", conf.LB)
t.Logf("N=%d ||B - A*X||_1: %e\n", N, nrm)
}
/*
* Compute the Cholesky factorization of a symmetric positive definite
* N-by-N matrix A.
*
* Arguments:
* A On entry, the symmetric matrix A. If flags&UPPER the upper triangular part
* of A contains the upper triangular part of the matrix A, and strictly
* lower part A is not referenced. If flags&LOWER the lower triangular part
* of a contains the lower triangular part of the matrix A. Likewise, the
* strictly upper part of A is not referenced. On exit, factor U or L from the
* Cholesky factorization A = U.T*U or A = L*L.T
*
* flags The matrix structure indicator, UPPER for upper tridiagonal and LOWER for
* lower tridiagonal matrix.
*
* confs Optional blocking configuration. If not provided default blocking configuration
* will be used.
*
* Compatible with lapack.DPOTRF
*/
func CHOLFactor(A *cmat.FloatMatrix, 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()
if ac != ar {
return gomas.NewError(gomas.ENOTSQUARE, "DecomposeCHOL")
}
if ac < conf.LB || conf.LB == 0 {
if flags&gomas.UPPER != 0 {
err = unblockedUpperCHOL(A, flags, 0)
} else {
err = unblockedLowerCHOL(A, flags, 0)
}
} else {
err = blockedCHOL(A, flags, conf)
}
return err
}
/*
* Solves a system system of linear equations A*X = B with symmetric positive
* definite matrix A using the Cholesky factorization A = U.T*U or A = L*L.T
* computed by DecomposeCHOL().
*
* Arguments:
* B On entry, the right hand side matrix B. On exit, the solution
* matrix X.
*
* A The triangular factor U or L from Cholesky factorization as computed by
* DecomposeCHOL().
*
* flags Indicator of which factor is stored in A. If flags&UPPER then upper
* triangle of A is stored. If flags&LOWER then lower triangle of A is
* stored.
*
* Compatible with lapack.DPOTRS.
*/
func CHOLSolve(B, A *cmat.FloatMatrix, flags int, confs ...*gomas.Config) *gomas.Error {
// A*X = B; X = A.-1*B == (LU).-1*B == U.-1*L.-1*B == U.-1*(L.-1*B)
conf := gomas.DefaultConf()
if len(confs) > 0 {
conf = confs[0]
}
ar, ac := A.Size()
br, _ := B.Size()
if ac != br || ar != ac {
return gomas.NewError(gomas.ESIZE, "SolveCHOL")
}
if flags&gomas.UPPER != 0 {
// X = (U.T*U).-1*B => U.-1*(U.-T*B)
blasd.SolveTrm(B, A, 1.0, gomas.UPPER|gomas.TRANSA, conf)
blasd.SolveTrm(B, A, 1.0, gomas.UPPER, conf)
} else if flags&gomas.LOWER != 0 {
// X = (L*L.T).-1*B = L.-T*(L.1*B)
blasd.SolveTrm(B, A, 1.0, gomas.LOWER, conf)
blasd.SolveTrm(B, A, 1.0, gomas.LOWER|gomas.TRANSA, conf)
}
return nil
}
/*
* General matrix-matrix multiplication.
*
* Computes C = beta*C + alpha*op(A)*op(B), where op is optional transpose operation
* encoded in bits argument. Operand A is transposed if gomas.TRANSA bit is set in
* bits. And operand B is transposed if gomas.TRANSB bit is set.
*
* Optional Config block defines blocking parameters for computation.
*/
func Mult(Cc, A, B *cmat.FloatMatrix, alpha, beta float64, bits int, confs ...*gomas.Config) *gomas.Error {
conf := gomas.DefaultConf()
if len(confs) > 0 {
conf = confs[0]
}
if A.Len() == 0 || B.Len() == 0 {
return nil
}
ok := true
cr, cc := Cc.Size()
ar, ac := A.Size()
br, bc := B.Size()
P := ac
L := cc
E := cr
switch bits & (gomas.TRANSA | gomas.TRANSB) {
case gomas.TRANSA | gomas.TRANSB:
ok = cr == ac && cc == br && ar == bc
P = ar
case gomas.TRANSA:
ok = cr == ac && cc == bc && ar == br
P = ar
case gomas.TRANSB:
ok = cr == ar && cc == br && ac == bc
P = ac
default:
ok = cr == ar && cc == bc && ac == br
}
if !ok {
return gomas.NewError(gomas.ESIZE, "Mult")
}
// single threaded
if conf.NProc == 1 || conf.WB <= 0 || Cc.Len() < conf.WB*conf.WB {
gemm(Cc, A, B, alpha, beta, bits, P, 0, L, 0, E, conf)
return nil
}
// parallelized
wait := make(chan int, 4)
nM, nN := blocking(cr, cc, conf.WB)
nT := int64(0)
for j := 0; j < nN; j++ {
jS := blockIndex(j, nN, conf.WB, cc)
jL := blockIndex(j+1, nN, conf.WB, cc)
for i := 0; i < nM; i++ {
iR := blockIndex(i, nM, conf.WB, cr)
iE := blockIndex(i+1, nM, conf.WB, cr)
task := func(q chan int) {
gemm(Cc, A, B, alpha, beta, bits, P, jS, jL, iR, iE, conf)
q <- 1
}
nT += 1
conf.Sched.Schedule(gomas.NewTask(task, wait))
}
}
// wait for subtask to complete
for nT > 0 {
<-wait
nT -= 1
}
return nil
}
func UpdateTrm(Cc, A, B *cmat.FloatMatrix, alpha, beta float64, bits int, confs ...*gomas.Config) *gomas.Error {
conf := gomas.DefaultConf()
if len(confs) > 0 {
conf = confs[0]
}
if A.Len() == 0 || B.Len() == 0 {
return nil
}
ok := true
cr, cc := Cc.Size()
ar, ac := A.Size()
br, bc := B.Size()
P := ac
L := cc
E := cr
switch bits & (gomas.TRANSA | gomas.TRANSB) {
case gomas.TRANSA | gomas.TRANSB:
ok = cr == ac && cc == br && ar == bc
P = ar
case gomas.TRANSA:
ok = cr == ac && cc == bc && ar == br
P = ar
case gomas.TRANSB:
ok = cr == ar && cc == br && ac == bc
default:
ok = cr == ar && cc == bc && ac == br
}
if !ok {
return gomas.NewError(gomas.ESIZE, "UpdateTrm")
}
// single threaded
if conf.NProc == 1 || conf.WB <= 0 || Cc.Len() < conf.WB*conf.WB {
updtrm(Cc, A, B, alpha, beta, bits, P, 0, L, 0, E, conf)
return nil
}
// parallelized
wait := make(chan int, 4)
nM, nN := blocking(cr, cc, conf.WB)
nT := 0
if bits&gomas.UPPER != 0 {
// by rows; upper trapezoidial
for j := 0; j < nM; j++ {
iR := blockIndex(j, nM, conf.WB, cr)
iE := blockIndex(j+1, nM, conf.WB, cr)
task := func(q chan int) {
updtrm(Cc, A, B, alpha, beta, bits, P, iR, L, iR, iE, conf)
q <- 1
}
conf.Sched.Schedule(gomas.NewTask(task, wait))
nT += 1
}
} else {
// by columns; lower trapezoidial
for j := 0; j < nN; j++ {
jS := blockIndex(j, nN, conf.WB, cc)
jL := blockIndex(j+1, nN, conf.WB, cc)
task := func(q chan int) {
updtrm(Cc, A, B, alpha, beta, bits, P, jS, jL, jS, E, conf)
q <- 1
}
conf.Sched.Schedule(gomas.NewTask(task, wait))
nT += 1
}
}
// wait for subtasks to complete
for nT > 0 {
<-wait
nT -= 1
}
return nil
}
/*
* UpdateSym performs symmetric rank-k update C = beta*C + alpha*A*A.T or
* C = beta*C + alpha*A.T*A if gomas.TRANS bit is set.
*/
func UpdateSym(c, a *cmat.FloatMatrix, alpha, beta float64, bits int, confs ...*gomas.Config) *gomas.Error {
conf := gomas.DefaultConf()
if len(confs) > 0 {
conf = confs[0]
}
ok := true
cr, cc := c.Size()
ar, ac := a.Size()
if cr*cc == 0 {
return nil
}
P := ac
E := cr
if bits&gomas.TRANS != 0 && bits&gomas.TRANSA == 0 {
bits |= gomas.TRANSA
}
switch {
case bits&gomas.TRANSA != 0:
ok = cr == cc && cr == ac
P = ar
default:
ok = cr == cc && cr == ar
}
if !ok {
return gomas.NewError(gomas.ESIZE, "UpdateSym")
}
if conf.NProc == 1 || conf.WB <= 0 || E <= conf.WB {
syrk(c, a, alpha, beta, bits, P, 0, E, conf)
return nil
}
// parallelized
var sbits int = 0
wait := make(chan int, 4)
nM, nN := blocking(E, E, conf.WB)
nT := 0
if bits&gomas.TRANS != 0 {
sbits |= gomas.TRANSA
} else {
sbits |= gomas.TRANSB
}
if bits&gomas.LOWER != 0 {
sbits |= gomas.LOWER
for j := 0; j < nN; j++ {
jS := blockIndex(j, nN, conf.WB, E)
jL := blockIndex(j+1, nN, conf.WB, E)
// update lower trapezoidal/triangular blocks
task := func(q chan int) {
updtrm(c, a, a, alpha, beta, sbits, P, jS, jL, jS, E, conf)
//syrk(c, a, alpha, beta, bits, P, jS, jL, conf)
q <- 1
}
conf.Sched.Schedule(gomas.NewTask(task, wait))
nT += 1
}
} else {
sbits |= gomas.UPPER
for j := 0; j < nM; j++ {
jS := blockIndex(j, nM, conf.WB, E)
jL := blockIndex(j+1, nM, conf.WB, E)
// update upper trapezoidal/triangular blocks
task := func(q chan int) {
updtrm(c, a, a, alpha, beta, sbits, P, jS, E, jS, jL, conf)
//syrk(c, a, alpha, beta, bits, P, jS, jL, conf)
q <- 1
}
conf.Sched.Schedule(gomas.NewTask(task, wait))
nT += 1
}
}
for nT > 0 {
<-wait
nT -= 1
}
return nil
}