// Compute
// Y = alpha*A*X + beta*Y
// Y = alpha*A.T*X + beta*Y ; flags = TRANSA
//
// A is M*N or N*M generic matrix,
// X is row or column vector of length N
// Y is row or column vector of legth M.
//
// MVMult is vector orientation agnostic. It does not matter if Y, X are row or
// column vectors, they are always handled as if they were column vectors.
func MVMult(Y, A, X *matrix.FloatMatrix, alpha, beta float64, flags Flags) error {
if A.Rows() == 0 || A.Cols() == 0 {
return nil
}
if Y.Rows() != 1 && Y.Cols() != 1 {
return errors.New("Y not a vector.")
}
if X.Rows() != 1 && X.Cols() != 1 {
return errors.New("X not a vector.")
}
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Yr := Y.FloatArray()
incY := 1
lenY := Y.NumElements()
if Y.Rows() == 1 {
// row vector
incY = Y.LeadingIndex()
}
Xr := X.FloatArray()
incX := 1
lenX := X.NumElements()
if X.Rows() == 1 {
// row vector
incX = X.LeadingIndex()
}
// NOTE: This could diveded to parallel tasks by rows.
calgo.DMultMV(Yr, Ar, Xr, alpha, beta, calgo.Flags(flags), incY, ldA, incX,
0, lenX, 0, lenY, vpLen, mB)
return nil
}
// Calculate C = alpha*A*B.T + beta*C, C is M*N, A is M*P and B is N*P
func MMMultTransB(C, A, B *matrix.FloatMatrix, alpha, beta float64) error {
psize := int64(C.NumElements() * A.Cols())
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Br := B.FloatArray()
ldB := B.LeadingIndex()
Cr := C.FloatArray()
ldC := C.LeadingIndex()
if nWorker <= 1 || psize <= limitOne {
calgo.DMult(Cr, Ar, Br, alpha, beta, calgo.TRANSB, ldC, ldA, ldB,
B.Rows(), 0, C.Cols(), 0, C.Rows(), vpLen, nB, mB)
return nil
}
// here we have more than one worker available
worker := func(cstart, cend, rstart, rend int, ready chan int) {
calgo.DMult(Cr, Ar, Br, alpha, beta, calgo.TRANSB, ldC, ldA, ldB, B.Rows(),
cstart, cend, rstart, rend, vpLen, nB, mB)
ready <- 1
}
colworks, rowworks := divideWork(C.Rows(), C.Cols(), nWorker)
scheduleWork(colworks, rowworks, C.Cols(), C.Rows(), worker)
//scheduleWork(colworks, rowworks, worker)
return nil
}
// Y := alpha * X + Y
func Axpy(Y, X *matrix.FloatMatrix, alpha float64) {
if X == nil || Y == nil {
return
}
if !isVector(X) {
return
}
if !isVector(Y) {
return
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
Yr := Y.FloatArray()
incY := 1
if Y.Cols() != 1 {
// Row vector
incY = Y.LeadingIndex()
}
calgo.DAxpy(Xr, Yr, alpha, incX, incY, X.NumElements())
return
}
func Mult0(C, A, B *matrix.FloatMatrix, alpha, beta float64, flags Flags) error {
if A.Cols() != B.Rows() {
return errors.New("A.cols != B.rows: size mismatch")
}
psize := int64(C.NumElements()) * int64(A.Cols())
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Br := B.FloatArray()
ldB := B.LeadingIndex()
Cr := C.FloatArray()
ldC := C.LeadingIndex()
if nWorker <= 1 || psize <= limitOne {
calgo.DMult0(Cr, Ar, Br, alpha, beta, calgo.Flags(flags), ldC, ldA, ldB, B.Rows(),
0, C.Cols(), 0, C.Rows(),
vpLen, nB, mB)
return nil
}
// here we have more than one worker available
worker := func(cstart, cend, rstart, rend int, ready chan int) {
calgo.DMult0(Cr, Ar, Br, alpha, beta, calgo.Flags(flags), ldC, ldA, ldB, B.Rows(),
cstart, cend, rstart, rend, vpLen, nB, mB)
ready <- 1
}
colworks, rowworks := divideWork(C.Rows(), C.Cols(), nWorker)
scheduleWork(colworks, rowworks, C.Cols(), C.Rows(), worker)
return nil
}
// Calculate C = alpha*A*B + beta*C, C is M*N, A is M*M and B is M*N
func MMSymmUpper(C, A, B *matrix.FloatMatrix, alpha, beta float64) error {
if A.Rows() != A.Cols() {
return errors.New("A matrix not square matrix.")
}
psize := int64(C.NumElements() * A.Cols())
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Br := B.FloatArray()
ldB := B.LeadingIndex()
Cr := C.FloatArray()
ldC := C.LeadingIndex()
if nWorker <= 1 || psize <= limitOne {
calgo.DMultSymm(Cr, Ar, Br, alpha, beta, calgo.LEFT|calgo.UPPER, ldC, ldA, ldB,
A.Cols(), 0, C.Cols(), 0, C.Rows(), vpLen, nB, mB)
return nil
}
// here we have more than one worker available
worker := func(cstart, cend, rstart, rend int, ready chan int) {
calgo.DMultSymm(Cr, Ar, Br, alpha, beta, calgo.LEFT|calgo.UPPER, ldC, ldA, ldB,
A.Cols(), cstart, cend, rstart, rend, vpLen, nB, mB)
ready <- 1
}
colworks, rowworks := divideWork(C.Rows(), C.Cols(), nWorker)
scheduleWork(colworks, rowworks, C.Cols(), C.Rows(), worker)
return nil
}
// Generic matrix-matrix multpily. (blas.GEMM). Calculates
// C = beta*C + alpha*A*B (default)
// C = beta*C + alpha*A.T*B flags&TRANSA
// C = beta*C + alpha*A*B.T flags&TRANSB
// C = beta*C + alpha*A.T*B.T flags&(TRANSA|TRANSB)
//
// C is M*N, A is M*P or P*M if flags&TRANSA. B is P*N or N*P if flags&TRANSB.
//
func Mult(C, A, B *matrix.FloatMatrix, alpha, beta float64, flags Flags) error {
var ok, empty bool
// error checking must take in account flag values!
ar, ac := A.Size()
br, bc := B.Size()
cr, cc := C.Size()
switch flags & (TRANSA | TRANSB) {
case TRANSA | TRANSB:
empty = ac == 0 || br == 0
ok = cr == ac && cc == br && ar == bc
case TRANSA:
empty = ac == 0 || bc == 0
ok = cr == ac && cc == bc && ar == br
case TRANSB:
empty = ar == 0 || br == 0
ok = cr == ar && cc == br && ac == bc
default:
empty = ar == 0 || bc == 0
ok = cr == ar && cc == bc && ac == br
}
if empty {
return nil
}
if !ok {
return errors.New("Mult: size mismatch")
}
psize := int64(C.NumElements()) * int64(A.Cols())
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Br := B.FloatArray()
ldB := B.LeadingIndex()
Cr := C.FloatArray()
ldC := C.LeadingIndex()
// matrix A, B common dimension
P := A.Cols()
if flags&TRANSA != 0 {
P = A.Rows()
}
if nWorker <= 1 || psize <= limitOne {
calgo.DMult(Cr, Ar, Br, alpha, beta, calgo.Flags(flags), ldC, ldA, ldB, P,
0, C.Cols(), 0, C.Rows(),
vpLen, nB, mB)
return nil
}
// here we have more than one worker available
worker := func(cstart, cend, rstart, rend int, ready chan int) {
calgo.DMult(Cr, Ar, Br, alpha, beta, calgo.Flags(flags), ldC, ldA, ldB, P,
cstart, cend, rstart, rend, vpLen, nB, mB)
ready <- 1
}
colworks, rowworks := divideWork(C.Rows(), C.Cols(), nWorker)
scheduleWork(colworks, rowworks, C.Cols(), C.Rows(), worker)
return nil
}
/*
Returns x' * J * y, where J = [1, 0; 0, -I].
*/
func jdot(x, y *matrix.FloatMatrix, n, offsetx, offsety int) float64 {
if n <= 0 {
n = x.NumElements()
}
a := blas.DotFloat(x, y, &la_.IOpt{"n", n - 1}, &la_.IOpt{"offsetx", offsetx + 1},
&la_.IOpt{"offsety", offsety + 1})
return x.GetIndex(offsetx)*y.GetIndex(offsety) - a
}
// Symmetric matrix multiply. (blas.SYMM)
// C = beta*C + alpha*A*B (default)
// C = beta*C + alpha*A.T*B flags&TRANSA
// C = beta*C + alpha*A*B.T flags&TRANSB
// C = beta*C + alpha*A.T*B.T flags&(TRANSA|TRANSB)
//
// C is N*P, A is N*N symmetric matrix. B is N*P or P*N if flags&TRANSB.
//
func MultSym(C, A, B *matrix.FloatMatrix, alpha, beta float64, flags Flags) error {
var ok, empty bool
ar, ac := A.Size()
br, bc := B.Size()
cr, cc := C.Size()
switch flags & (TRANSA | TRANSB) {
case TRANSA | TRANSB:
empty = ac == 0 || br == 0
ok = ar == ac && cr == ac && cc == br && ar == bc
case TRANSA:
empty = ac == 0 || bc == 0
ok = ar == ac && cr == ac && cc == bc && ar == br
case TRANSB:
empty = ar == 0 || br == 0
ok = ar == ac && cr == ar && cc == br && ac == bc
default:
empty = ar == 0 || bc == 0
ok = ar == ac && cr == ar && cc == bc && ac == br
}
if empty {
return nil
}
if !ok {
return errors.New("MultSym: size mismatch")
}
/*
if A.Rows() != A.Cols() {
return errors.New("A matrix not square matrix.");
}
if A.Cols() != B.Rows() {
return errors.New("A.cols != B.rows: size mismatch")
}
*/
psize := int64(C.NumElements()) * int64(A.Cols())
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Br := B.FloatArray()
ldB := B.LeadingIndex()
Cr := C.FloatArray()
ldC := C.LeadingIndex()
if nWorker <= 1 || psize <= limitOne {
calgo.DMultSymm(Cr, Ar, Br, alpha, beta, calgo.Flags(flags), ldC, ldA, ldB,
A.Cols(), 0, C.Cols(), 0, C.Rows(), vpLen, nB, mB)
return nil
}
// here we have more than one worker available
worker := func(cstart, cend, rstart, rend int, ready chan int) {
calgo.DMultSymm(Cr, Ar, Br, alpha, beta, calgo.Flags(flags), ldC, ldA, ldB,
A.Cols(), cstart, cend, rstart, rend, vpLen, nB, mB)
ready <- 1
}
colworks, rowworks := divideWork(C.Rows(), C.Cols(), nWorker)
scheduleWork(colworks, rowworks, C.Cols(), C.Rows(), worker)
return nil
}
/*
Returns sqrt(x' * J * x) where J = [1, 0; 0, -I], for a vector
x in a second order cone.
*/
func jnrm2(x *matrix.FloatMatrix, n, offset int) float64 {
/*DEBUGGED*/
if n <= 0 {
n = x.NumElements()
}
if offset < 0 {
offset = 0
}
a := blas.Nrm2Float(x, &la_.IOpt{"n", n - 1}, &la_.IOpt{"offset", offset + 1})
fst := x.GetIndex(offset)
return math.Sqrt(fst-a) * math.Sqrt(fst+a)
}
// Scaling with scalar: X = alpha * X
func Scale(X *matrix.FloatMatrix, alpha float64) {
if X == nil || X.NumElements() == 0 {
return
}
if !isVector(X) {
return
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
calgo.DScal(Xr, alpha, incX, X.NumElements())
}
// index of max |x|
func IAMax(X *matrix.FloatMatrix) int {
if X == nil {
return -1
}
if !isVector(X) {
return -1
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
return calgo.DIAMax(Xr, incX, X.NumElements())
}
// sum(|x|)
func ASum(X *matrix.FloatMatrix) float64 {
if X == nil {
return math.NaN()
}
if !isVector(X) {
return math.NaN()
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
return calgo.DAsum(Xr, incX, X.NumElements())
}
// Swap X and Y.
func Swap(X, Y *matrix.FloatMatrix) {
if X == nil || Y == nil {
return
}
if X.NumElements() == 0 || Y.NumElements() == 0 {
return
}
if !isVector(X) {
return
}
if !isVector(Y) {
return
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
Yr := Y.FloatArray()
incY := 1
if Y.Cols() != 1 {
// Row vector
incY = Y.LeadingIndex()
}
calgo.DSwap(Xr, Yr, incX, incY, X.NumElements())
}
// Add inner product: Z[index] = beta*Z[index] + alpha * X * Y
func AddDot(Z, X, Y *matrix.FloatMatrix, alpha, beta float64, index int) {
if X == nil || Y == nil {
return
}
if X.NumElements() == 0 || Y.NumElements() == 0 {
return
}
if !isVector(X) {
return
}
if !isVector(Y) {
return
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
Yr := Y.FloatArray()
incY := 1
if Y.Cols() != 1 {
// Row vector
incY = Y.LeadingIndex()
}
Zr := Z.FloatArray()
incZ := 1
if Z.Cols() != 1 {
// Row vector
incZ = Z.LeadingIndex()
}
calgo.DDotSum(Zr[incZ*index:], Xr, Yr, alpha, beta, incZ, incX, incY, X.NumElements())
}
func _TestPartition2D(t *testing.T) {
var ATL, ATR, ABL, ABR, As matrix.FloatMatrix
var A00, a01, A02, a10, a11, a12, A20, a21, A22 matrix.FloatMatrix
A := matrix.FloatZeros(6, 6)
As.SubMatrixOf(A, 1, 1, 4, 4)
As.SetIndexes(1.0)
partition2x2(&ATL, &ATR, &ABL, &ABR, &As, 0)
t.Logf("ATL:\n%v\n", &ATL)
for ATL.Rows() < As.Rows() {
repartition2x2to3x3(&ATL,
&A00, &a01, &A02,
&a10, &a11, &a12,
&A20, &a21, &A22, &As, 1)
t.Logf("m(a12)=%d [%d], m(a11)=%d\n", a12.Cols(), a12.NumElements(), a11.NumElements())
a11.Add(1.0)
a21.Add(-2.0)
continue3x3to2x2(&ATL, &ATR, &ABL, &ABR, &A00, &a11, &A22, &As)
}
t.Logf("A:\n%v\n", A)
}
// Inner product: alpha * X * Y
func Dot(X, Y *matrix.FloatMatrix, alpha float64) float64 {
if X == nil || Y == nil {
return math.NaN()
}
if !isVector(X) {
return math.NaN()
}
if !isVector(Y) {
return math.NaN()
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
Yr := Y.FloatArray()
incY := 1
if Y.Cols() != 1 {
// Row vector
incY = Y.LeadingIndex()
}
return calgo.DDot(Xr, Yr, alpha, incX, incY, X.NumElements())
}
/*
* Generic rank update of diagonal matrix.
* diag(D) = diag(D) + alpha * x * y.T
*
* Arguments:
* D N element column or row vector or N-by-N matrix
*
* x, y N element vectors
*
* alpha scalar
*/
func MVUpdateDiag(D, x, y *matrix.FloatMatrix, alpha float64) error {
var d *matrix.FloatMatrix
var dvec matrix.FloatMatrix
if !isVector(x) || !isVector(y) {
return errors.New("x, y not vectors")
}
if D.Rows() > 0 && D.Cols() == D.Rows() {
D.Diag(&dvec)
d = &dvec
} else if isVector(D) {
d = D
} else {
return errors.New("D not a diagonal")
}
N := d.NumElements()
for k := 0; k < N; k++ {
val := d.GetIndex(k)
val += x.GetIndex(k) * y.GetIndex(k) * alpha
d.SetIndex(k, val)
}
return nil
}