Exemplo n.º 1
0
func blockedInverseUpper(A *matrix.FloatMatrix, flags Flags, nb int) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, A01, A02, A11, A12, A22 matrix.FloatMatrix

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)

	for ATL.Rows() < A.Rows() {
		repartition2x2to3x3(&ATL,
			&A00, &A01, &A02,
			nil, &A11, &A12,
			nil, nil, &A22, A, nb, pBOTTOMRIGHT)
		// -------------------------------------------------
		// libflame, variant 1

		// A01 = A00*A01
		MultTrm(&A01, &A00, 1.0, flags)
		// A01 = -A01 / triu(A11)
		SolveTrm(&A01, &A11, -1.0, flags|RIGHT)
		// A11 = inv(A11)
		if flags&UNIT != 0 {
			unblockedInverseUnitUpper(&A11)
		} else {
			unblockedInverseUpper(&A11)
		}
		// -------------------------------------------------
		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &A11, &A22, A, pBOTTOMRIGHT)
	}
	return
}
Exemplo n.º 2
0
// 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
}
Exemplo n.º 3
0
func trmvTest(t *testing.T, A *matrix.FloatMatrix, flags Flags, nb int) bool {
	N := A.Cols()
	//S := 0
	//E := A.Cols()
	X0 := matrix.FloatWithValue(A.Rows(), 1, 2.0)
	X1 := X0.Copy()

	trans := linalg.OptNoTrans
	if flags&TRANS != 0 {
		trans = linalg.OptTrans
	}
	diag := linalg.OptNonUnit
	if flags&UNIT != 0 {
		diag = linalg.OptUnit
	}
	uplo := linalg.OptUpper
	if flags&LOWER != 0 {
		uplo = linalg.OptLower
	}

	blas.TrmvFloat(A, X0, uplo, diag, trans)

	Ar := A.FloatArray()
	Xr := X1.FloatArray()
	if nb == 0 {
		DTrimvUnblkMV(Xr, Ar, flags, 1, A.LeadingIndex(), N)
	}
	result := X0.AllClose(X1)
	t.Logf("   X0 == X1: %v\n", result)
	if !result && A.Rows() < 8 {
		t.Logf("  BLAS TRMV X0:\n%v\n", X0)
		t.Logf("  DTrmv X1:\n%v\n", X1)
	}
	return result
}
Exemplo n.º 4
0
// 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
}
Exemplo n.º 5
0
func runRefTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {

	var mintime time.Duration

	N := A.Rows()
	ipiv := make([]int32, N, N)
	lopt := linalg.OptLower
	if testUpper {
		lopt = linalg.OptUpper
	}

	fnc := func() {
		ERRlapack = lapack.Sytrf(A, ipiv, lopt)
	}

	A0 := A.Copy()
	for n := 0; n < ntest; n++ {
		if n > 0 {
			// restore original A
			A0.CopyTo(A)
		}
		mperf.FlushCache()
		time0 := mperf.Timeit(fnc)
		if n == 0 || time0 < mintime {
			mintime = time0
		}
	}
	return mintime
}
Exemplo n.º 6
0
// Inverse NON-UNIT diagonal tridiagonal matrix
func unblockedInverseUpper(A *matrix.FloatMatrix) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a01, A02, a11, a12t, A22 matrix.FloatMatrix

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)

	for ATL.Rows() < A.Rows() {
		repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			nil, &a11, &a12t,
			nil, nil, &A22, A, 1, pBOTTOMRIGHT)
		// -------------------------------------------------
		aval := a11.Float()

		// a12 = -a12/a11
		InvScale(&a12t, -aval)
		// A02 = A02 + a01*a12
		MVRankUpdate(&A02, &a01, &a12t, 1.0)
		// a01 = a01/a11
		InvScale(&a01, aval)
		// a11 = 1.0/a11
		a11.SetAt(0, 0, 1.0/aval)

		// -------------------------------------------------
		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pBOTTOMRIGHT)
	}
	return
}
Exemplo n.º 7
0
func runRefTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {

	var flags matops.Flags
	var mintime time.Duration

	N := A.Rows()
	ipiv := make([]int, N, N)
	flags = matops.LOWER
	if testUpper {
		flags = matops.UPPER
	}

	W := matrix.FloatZeros(A.Rows(), LB+2)
	fnc := func() {
		_, ERRref = matops.DecomposeLDL(A, W, ipiv, flags, 0)
	}

	A0 := A.Copy()
	for n := 0; n < ntest; n++ {
		if n > 0 {
			// restore original A
			A0.CopyTo(A)
		}
		mperf.FlushCache()
		time0 := mperf.Timeit(fnc)
		if n == 0 || time0 < mintime {
			mintime = time0
		}
	}
	return mintime
}
Exemplo n.º 8
0
func runTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {

	var flags matops.Flags
	var mintime time.Duration

	N := A.Rows()
	ipiv := make([]int, N, N)
	flags = matops.LOWER
	if testUpper {
		flags = matops.UPPER
	}

	W := matrix.FloatZeros(A.Rows(), LB+2)
	fnc := func() {
		_, ERRmatops = matops.DecomposeBK(A, W, ipiv, flags, LB)
	}

	A0 := A.Copy()
	for n := 0; n < ntest; n++ {
		if n > 0 {
			// restore original A
			A0.CopyTo(A)
		}
		mperf.FlushCache()
		time0 := mperf.Timeit(fnc)
		if n == 0 || time0 < mintime {
			mintime = time0
		}
		if verbose {
			fmt.Printf("%.4f ms\n", time0.Seconds()*1000.0)
		}
	}
	return mintime
}
Exemplo n.º 9
0
// Inverse UNIT diagonal tridiagonal matrix
func unblockedInverseUnitLower(A *matrix.FloatMatrix) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a10t, a11, A20, a21, A22 matrix.FloatMatrix

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)

	for ATL.Rows() < A.Rows() {
		repartition2x2to3x3(&ATL,
			&A00, nil, nil,
			&a10t, &a11, nil,
			&A20, &a21, &A22, A, 1, pBOTTOMRIGHT)
		// -------------------------------------------------

		// a21 = -a21
		Scale(&a21, -1.0)
		// A20 = A20 + a21*a10.t
		MVRankUpdate(&A20, &a21, &a10t, 1.0)

		// -------------------------------------------------
		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pBOTTOMRIGHT)
	}
	return
}
Exemplo n.º 10
0
func runTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {

	var mintime time.Duration

	M := A.Rows()
	N := A.Cols()
	nN := N
	if M < N {
		nN = M
	}
	ipiv := make([]int, nN, nN)

	fnc := func() {
		_, ERRmatops = matops.DecomposeLU(A, ipiv, LB)
	}

	A0 := A.Copy()
	for n := 0; n < ntest; n++ {
		if n > 0 {
			// restore original A
			A0.CopyTo(A)
		}
		mperf.FlushCache()
		time0 := mperf.Timeit(fnc)
		if n == 0 || time0 < mintime {
			mintime = time0
		}
		if verbose {
			fmt.Printf("%.4f ms\n", time0.Seconds()*1000.0)
		}
	}
	return mintime
}
Exemplo n.º 11
0
/*
 *  ( A11  a12 )   ( U11 u12 )( D1  0  )( U11.t 0 )
 *  ( a21  a22 )   (  0   1  )(  0  d2 )( u12.t 1 )
 *
 *   a22  =   d2
 *   a01  =   u12*d2                       => u12 = a12/d2
 *   A11  =   u12*d2*u12.t + U11*D1*U11.t  => U11 = A11 - u12*d2*u12.t
 */
func unblkUpperLDLnoPiv(A *matrix.FloatMatrix) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a01, A02, a11, a12, A22 matrix.FloatMatrix

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pBOTTOMRIGHT)

	for ATL.Rows() > 0 {
		repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			nil, &a11, &a12,
			nil, nil, &A22, A, 1, pTOPLEFT)

		// --------------------------------------------------------

		// A00 = A00 - u01*d11*u01.T = A00 - a01*a01.T/a11; triangular update
		err = MVUpdateTrm(&A00, &a01, &a01, -1.0/a11.Float(), UPPER)

		// u01 = a01/a11
		InvScale(&a01, a11.Float())
		// ---------------------------------------------------------

		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pTOPLEFT)
	}
	return
}
Exemplo n.º 12
0
func runTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {
	var W *matrix.FloatMatrix = nil
	var mintime time.Duration

	N := A.Cols()
	tau := matrix.FloatZeros(N, 1)
	if LB > 0 {
		W = matrix.FloatZeros(A.Rows(), LB)
	}
	fnc := func() {
		_, ERRmatops = matops.DecomposeQR(A, tau, W, LB)
	}

	A0 := A.Copy()
	for n := 0; n < ntest; n++ {
		if n > 0 {
			// restore original A
			A0.CopyTo(A)
			tau.Scale(0.0)
		}
		mperf.FlushCache()
		time0 := mperf.Timeit(fnc)
		if n == 0 || time0 < mintime {
			mintime = time0
		}
		if verbose {
			fmt.Printf("%.4f ms\n", time0.Seconds()*1000.0)
		}
	}
	return mintime
}
Exemplo n.º 13
0
func runRefTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {

	var mintime time.Duration

	M := A.Rows()
	N := A.Cols()
	nN := N
	if M < N {
		nN = M
	}
	ipiv := make([]int32, nN, nN)

	fnc := func() {
		ERRlapack = lapack.Getrf(A, ipiv)
	}

	A0 := A.Copy()
	for n := 0; n < ntest; n++ {
		if n > 0 {
			// restore original A
			A0.CopyTo(A)
		}
		mperf.FlushCache()
		time0 := mperf.Timeit(fnc)
		if n == 0 || time0 < mintime {
			mintime = time0
		}
	}
	return mintime
}
Exemplo n.º 14
0
// unblocked LU decomposition w/o pivots, FLAME LU nopivots variant 5
func unblockedLUnoPiv(A *matrix.FloatMatrix) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a01, A02, a10, a11, a12, A20, a21, A22 matrix.FloatMatrix

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)

	for ATL.Rows() < A.Rows() {
		repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			&a10, &a11, &a12,
			&A20, &a21, &A22, A, 1, pBOTTOMRIGHT)

		// a21 = a21/a11
		//a21.Scale(1.0/a11.Float())
		InvScale(&a21, a11.Float())
		// A22 = A22 - a21*a12
		err = MVRankUpdate(&A22, &a21, &a12, -1.0)

		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pBOTTOMRIGHT)
	}
	return
}
Exemplo n.º 15
0
// blocked LU decomposition w/o pivots, FLAME LU nopivots variant 5
func blockedLUnoPiv(A *matrix.FloatMatrix, nb int) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, A01, A02, A10, A11, A12, A20, A21, A22 matrix.FloatMatrix

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)

	for ATL.Rows() < A.Rows() {
		repartition2x2to3x3(&ATL,
			&A00, &A01, &A02,
			&A10, &A11, &A12,
			&A20, &A21, &A22, A, nb, pBOTTOMRIGHT)

		// A00 = LU(A00)
		unblockedLUnoPiv(&A11)
		// A12 = trilu(A00)*A12.-1  (TRSM)
		SolveTrm(&A12, &A11, 1.0, LEFT|LOWER|UNIT)
		// A21 = A21.-1*triu(A00) (TRSM)
		SolveTrm(&A21, &A11, 1.0, RIGHT|UPPER)
		// A22 = A22 - A21*A12
		Mult(&A22, &A21, &A12, -1.0, 1.0, NOTRANS)

		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &A11, &A22, A, pBOTTOMRIGHT)
	}
	return
}
Exemplo n.º 16
0
// Matrix-vector triangular update A = A + alpha*X*Y.T
//   A is N*N matrix,
//   X is row or column vector of length N
//   Y is row or column vector of legth N.
//   flags is UPPER or LOWER
func MVUpdateTrm(A, X, Y *matrix.FloatMatrix, alpha 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
	if Y.Rows() == 1 {
		// row vector
		incY = Y.LeadingIndex()
	}
	Xr := X.FloatArray()
	incX := 1
	if X.Rows() == 1 {
		// row vector
		incX = X.LeadingIndex()
	}
	// NOTE: This could diveded to parallel tasks like matrix-matrix multiplication
	calgo.DTrmUpdMV(Ar, Xr, Yr, alpha, calgo.Flags(flags), ldA, incX, incY, 0, A.Cols(), nB)
	return nil
}
Exemplo n.º 17
0
/*
 *  ( a11  a12 )   ( 1   0   )( d1  0   )( l  l21.t )
 *  ( a21  A22 )   ( l21 L22 )(  0  A22 )( 0  L22.t )
 *
 *   a11  =   d1
 *   a21  =   l21*d1                       => l21 = a21/d1
 *   A22  =   l21*d1*l21.t + L22*D2*L22.t  => L22 = A22 - l21*d1*l21t
 */
func unblkLowerLDLnoPiv(A *matrix.FloatMatrix) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a10, a11, A20, a21, A22 matrix.FloatMatrix

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)

	for ATL.Rows() < A.Rows() {
		repartition2x2to3x3(&ATL,
			&A00, nil, nil,
			&a10, &a11, nil,
			&A20, &a21, &A22, A, 1, pBOTTOMRIGHT)

		// --------------------------------------------------------

		// d11 = a11; no-op

		// A22 = A22 - l21*d11*l21.T = A22 - a21*a21.T/a11; triangular update
		err = MVUpdateTrm(&A22, &a21, &a21, -1.0/a11.Float(), LOWER)

		// l21 = a21/a11
		InvScale(&a21, a11.Float())
		// ---------------------------------------------------------

		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pBOTTOMRIGHT)
	}
	return
}
Exemplo n.º 18
0
func updateBlas(t *testing.T, Y1, Y2, C1, C2, T, W *matrix.FloatMatrix) {
	if W.Rows() != C1.Cols() {
		panic("W.Rows != C1.Cols")
	}
	// W = C1.T
	ScalePlus(W, C1, 0.0, 1.0, TRANSB)
	//fmt.Printf("W = C1.T:\n%v\n", W)
	// W = C1.T*Y1
	blas.TrmmFloat(Y1, W, 1.0, linalg.OptLower, linalg.OptUnit, linalg.OptRight)
	t.Logf("W = C1.T*Y1:\n%v\n", W)
	// W = W + C2.T*Y2
	blas.GemmFloat(C2, Y2, W, 1.0, 1.0, linalg.OptTransA)
	t.Logf("W = W + C2.T*Y2:\n%v\n", W)

	// --- here: W == C.T*Y ---
	// W = W*T
	blas.TrmmFloat(T, W, 1.0, linalg.OptUpper, linalg.OptRight)
	t.Logf("W = C.T*Y*T:\n%v\n", W)

	// --- here: W == C.T*Y*T ---
	// C2 = C2 - Y2*W.T
	blas.GemmFloat(Y2, W, C2, -1, 1.0, linalg.OptTransB)
	t.Logf("C2 = C2 - Y2*W.T:\n%v\n", C2)
	//  W = Y1*W.T ==> W.T = W*Y1.T
	blas.TrmmFloat(Y1, W, 1.0, linalg.OptLower,
		linalg.OptUnit, linalg.OptRight, linalg.OptTrans)
	t.Logf("W.T = W*Y1.T:\n%v\n", W)

	// C1 = C1 - W.T
	ScalePlus(C1, W, 1.0, -1.0, TRANSB)
	//fmt.Printf("C1 = C1 - W.T:\n%v\n", C1)

	// --- here: C = (I - Y*T*Y.T).T * C ---
}
Exemplo n.º 19
0
func blockedBuildQ(A, tau, W *matrix.FloatMatrix, nb int) error {
	var err error = nil
	var ATL, ATR, ABL, ABR, AL matrix.FloatMatrix
	var A00, A01, A02, A10, A11, A12, A20, A21, A22 matrix.FloatMatrix
	var tT, tB matrix.FloatMatrix
	var t0, tau1, t2, Tw, Wrk matrix.FloatMatrix
	var mb int

	mb = A.Rows() - A.Cols()
	Twork := matrix.FloatZeros(nb, nb)

	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, mb, 0, pBOTTOMRIGHT)
	partition2x1(
		&tT,
		&tB, tau, 0, pBOTTOM)

	// clearing of the columns of the right and setting ABR to unit diagonal
	// (only if not applying all reflectors, kb > 0)

	for ATL.Rows() > 0 && ATL.Cols() > 0 {
		repartition2x2to3x3(&ATL,
			&A00, &A01, &A02,
			&A10, &A11, &A12,
			&A20, &A21, &A22, A, nb, pTOPLEFT)
		repartition2x1to3x1(&tT,
			&t0,
			&tau1,
			&t2, tau, nb, pTOP)

		// --------------------------------------------------------

		// build block reflector from current block
		merge2x1(&AL, &A11, &A21)
		Twork.SubMatrix(&Tw, 0, 0, A11.Cols(), A11.Cols())
		unblkQRBlockReflector(&Tw, &AL, &tau1)

		// update with current block reflector (I - Y*T*Y.T)*Atrailing
		W.SubMatrix(&Wrk, 0, 0, A12.Cols(), A11.Cols())
		updateWithQT(&A12, &A22, &A11, &A21, &Tw, &Wrk, nb, false)

		// use unblocked version to compute current block
		W.SubMatrix(&Wrk, 0, 0, 1, A11.Cols())
		unblockedBuildQ(&AL, &tau1, &Wrk, 0)

		// zero upper part
		A01.SetIndexes(0.0)

		// --------------------------------------------------------
		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &A11, &A22, A, pTOPLEFT)
		continue3x1to2x1(
			&tT,
			&tB, &t0, &tau1, tau, pTOP)
	}
	return err
}
Exemplo n.º 20
0
/*
 * like LAPACK/dlafrt.f
 *
 * Build block reflector T from HH reflector stored in TriLU(A) and coefficients
 * in tau.
 *
 * Q = I - Y*T*Y.T; Householder H = I - tau*v*v.T
 *
 * T = | T  z |   z = -tau*T*Y.T*v
 *     | 0  c |   c = tau
 *
 * Q = H(1)H(2)...H(k) building forward here.
 */
func unblkQRBlockReflector(T, A, tau *matrix.FloatMatrix) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a10, a11, A20, a21, A22 matrix.FloatMatrix
	var TTL, TTR, TBL, TBR matrix.FloatMatrix
	var T00, t01, T02, t11, t12, T22 matrix.FloatMatrix
	var tT, tB matrix.FloatMatrix
	var t0, tau1, t2 matrix.FloatMatrix

	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)
	partition2x2(
		&TTL, &TTR,
		&TBL, &TBR, T, 0, 0, pTOPLEFT)
	partition2x1(
		&tT,
		&tB, tau, 0, pTOP)

	for ABR.Rows() > 0 && ABR.Cols() > 0 {
		repartition2x2to3x3(&ATL,
			&A00, nil, nil,
			&a10, &a11, nil,
			&A20, &a21, &A22, A, 1, pBOTTOMRIGHT)
		repartition2x2to3x3(&TTL,
			&T00, &t01, &T02,
			nil, &t11, &t12,
			nil, nil, &T22, T, 1, pBOTTOMRIGHT)
		repartition2x1to3x1(&tT,
			&t0,
			&tau1,
			&t2, tau, 1, pBOTTOM)
		// --------------------------------------------------

		// t11 := tau
		tauval := tau1.GetAt(0, 0)
		if tauval != 0.0 {
			t11.SetAt(0, 0, tauval)

			// t01 := a10.T + &A20.T*a21
			a10.CopyTo(&t01)
			MVMult(&t01, &A20, &a21, -tauval, -tauval, TRANSA)
			// t01 := T00*t01
			MVMultTrm(&t01, &T00, UPPER)
			//t01.Scale(-tauval)
		}

		// --------------------------------------------------
		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pBOTTOMRIGHT)
		continue3x3to2x2(
			&TTL, &TTR,
			&TBL, &TBR, &T00, &t11, &T22, T, pBOTTOMRIGHT)
		continue3x1to2x1(
			&tT,
			&tB, &t0, &tau1, tau, pBOTTOM)
	}
}
Exemplo n.º 21
0
/*
 * 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 *matrix.FloatMatrix, srcix, dstix int, flags Flags) {
	var s, d matrix.FloatMatrix
	if flags&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, AL.Cols())
		AL.SubMatrix(&d, dstix, 0, 1, AL.Cols())
		Swap(&s, &d)
		if srcix > 0 {
			AR.SubMatrix(&s, srcix, 0, 1, srcix)
			AR.SubMatrix(&d, dstix, 0, 1, srcix)
			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)
		Swap(&s, &d)
		// S3 -- D3
		AR.SubMatrix(&s, dstix+1, srcix, AR.Rows()-dstix-1, 1)
		AR.SubMatrix(&d, dstix+1, dstix, AR.Rows()-dstix-1, 1)
		Swap(&s, &d)
		// swap P1 and P3
		p1 := AR.GetAt(srcix, srcix)
		p3 := AR.GetAt(dstix, dstix)
		AR.SetAt(srcix, srcix, p3)
		AR.SetAt(dstix, dstix, p1)
		return
	}
	if flags&UPPER != 0 {
		// AL is ATL, AR is ATR; P1 is AL[srcix, srcix];
		// S1 -- D1;
		AR.SubMatrix(&s, srcix, 0, 1, AR.Cols())
		AR.SubMatrix(&d, dstix, 0, 1, AR.Cols())
		Swap(&s, &d)
		if srcix < AL.Cols()-1 {
			// not the corner element
			AL.SubMatrix(&s, srcix, srcix+1, 1, srcix)
			AL.SubMatrix(&d, dstix, srcix+1, 1, srcix)
			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)
		Swap(&s, &d)
		// S3 -- D3
		AL.SubMatrix(&s, 0, srcix, dstix, 1)
		AL.SubMatrix(&d, 0, dstix, dstix, 1)
		Swap(&s, &d)
		//fmt.Printf("3, AR=%v\n", AR)
		// swap P1 and P3
		p1 := AR.GetAt(0, 0)
		p3 := AL.GetAt(dstix, dstix)
		AR.SetAt(srcix, srcix, p3)
		AL.SetAt(dstix, dstix, p1)
		return
	}
}
Exemplo n.º 22
0
func swapCols(A *matrix.FloatMatrix, src, dst int) {
	var c0, c1 matrix.FloatMatrix
	if src == dst || A.Rows() == 0 {
		return
	}
	A.SubMatrix(&c0, 0, src, A.Rows(), 1)
	A.SubMatrix(&c1, 0, dst, A.Rows(), 1)
	Swap(&c0, &c1)
}
Exemplo n.º 23
0
/*
 *  ( A11  a12 )   ( U11 u12 )( D1  0  )( U11.t 0 )
 *  ( a21  a22 )   (  0   1  )(  0  d2 )( u12.t 1 )
 *
 *   a22  =   d2
 *   a01  =   u12*d2                       => u12 = a12/d2
 *   A11  =   u12*d2*u12.t + U11*D1*U11.t  => U11 = A11 - u12*d2*u12.t
 */
func unblkUpperLDL(A *matrix.FloatMatrix, p *pPivots) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a01, A02, a11, a12, A22 matrix.FloatMatrix
	var AL, AR, acol matrix.FloatMatrix
	var pT, pB, p0, p1, p2 pPivots

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pBOTTOMRIGHT)
	partitionPivot2x1(
		&pT,
		&pB, p, 0, pBOTTOM)

	for ATL.Rows() > 0 {
		repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			nil, &a11, &a12,
			nil, nil, &A22, A, 1, pTOPLEFT)
		repartPivot2x1to3x1(&pT,
			&p0, &p1, &p2 /**/, p, 1, pTOP)

		// --------------------------------------------------------
		// search diagonal; diag(A00;a11)
		ATL.Diag(&acol)
		//merge2x1(&acol, &a01, &a11)
		imax := IAMax(&acol)
		if imax < ATL.Rows()-1 {
			merge1x2(&AL, &ATL, &ATR)
			merge1x2(&AR, &a11, &a12)
			// pivot diagonal in symmetric matrix; will swap a11 and [imax,imax]
			applyPivotSym(&AL, &AR, imax, UPPER)
			p1.pivots[0] = imax + 1
		} else {
			p1.pivots[0] = 0
		}

		if a11.Float() == 0.0 {
			err = onError("zero on diagonal.")
			return
		}
		// A00 = A00 - u01*d11*u01.T = A00 - a01*a01.T/a11; triangular update
		err = MVUpdateTrm(&A00, &a01, &a01, -1.0/a11.Float(), UPPER)

		// u01 = a01/a11
		InvScale(&a01, a11.Float())
		// ---------------------------------------------------------

		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pTOPLEFT)
		contPivot3x1to2x1(
			&pT,
			&pB, &p0, &p1, p, pTOP)
	}
	return
}
Exemplo n.º 24
0
func blockedBuildQT(A, T, W *matrix.FloatMatrix, nb int) error {
	var err error = nil
	var ATL, ATR, ABL, ABR, AL matrix.FloatMatrix
	var A00, A01, A11, A12, A21, A22 matrix.FloatMatrix
	var TTL, TTR, TBL, TBR matrix.FloatMatrix
	var T00, T01, T02, T11, T12, T22 matrix.FloatMatrix
	var tau1, Wrk matrix.FloatMatrix
	var mb int

	mb = A.Rows() - A.Cols()

	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, mb, 0, pBOTTOMRIGHT)
	partition2x2(
		&TTL, &TTR,
		&TBL, &TBR, T, 0, 0, pBOTTOMRIGHT)

	// clearing of the columns of the right and setting ABR to unit diagonal
	// (only if not applying all reflectors, kb > 0)

	for ATL.Rows() > 0 && ATL.Cols() > 0 {
		repartition2x2to3x3(&ATL,
			&A00, &A01, nil,
			nil, &A11, &A12,
			nil, &A21, &A22, A, nb, pTOPLEFT)
		repartition2x2to3x3(&TTL,
			&T00, &T01, &T02,
			nil, &T11, &T12,
			nil, nil, &T22, T, nb, pTOPLEFT)

		// --------------------------------------------------------

		// update with current block reflector (I - Y*T*Y.T)*Atrailing
		W.SubMatrix(&Wrk, 0, 0, A12.Cols(), A11.Cols())
		updateWithQT(&A12, &A22, &A11, &A21, &T11, &Wrk, nb, false)

		// use unblocked version to compute current block
		W.SubMatrix(&Wrk, 0, 0, 1, A11.Cols())
		// elementary scalar coefficients on the diagonal, column vector
		T11.Diag(&tau1)
		merge2x1(&AL, &A11, &A21)
		// do an unblocked update to current block
		unblockedBuildQ(&AL, &tau1, &Wrk, 0)

		// zero upper part
		A01.SetIndexes(0.0)
		// --------------------------------------------------------
		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &A11, &A22, A, pTOPLEFT)
		continue3x3to2x2(
			&TTL, &TTR,
			&TBL, &TBR, &T00, &T11, &T22, T, pTOPLEFT)
	}
	return err
}
Exemplo n.º 25
0
func swapRows(A *matrix.FloatMatrix, src, dst int) {
	var r0, r1 matrix.FloatMatrix
	if src == dst || A.Rows() == 0 {
		return
	}
	A.SubMatrix(&r0, src, 0, 1, A.Cols())
	A.SubMatrix(&r1, dst, 0, 1, A.Cols())
	Swap(&r0, &r1)
}
Exemplo n.º 26
0
// Find largest absolute value on column
func pivotIndex(A *matrix.FloatMatrix, p *pPivots) {
	max := math.Abs(A.GetAt(0, 0))
	for k := 1; k < A.Rows(); k++ {
		v := math.Abs(A.GetAt(k, 0))
		if v > max {
			p.pivots[0] = k
			max = v
		}
	}
}
Exemplo n.º 27
0
/*
 * 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 DecomposeLUnoPiv(A *matrix.FloatMatrix, nb int) (*matrix.FloatMatrix, error) {
	var err error
	mlen := imin(A.Rows(), A.Cols())
	if mlen <= nb || nb == 0 {
		err = unblockedLUnoPiv(A)
	} else {
		err = blockedLUnoPiv(A, nb)
	}
	return A, err
}
Exemplo n.º 28
0
/*
 * Build block reflector T from HH elementary reflectors stored in TriLU(A) and
 * scalar factors in tau.
 *
 * Q = I - Y*T*Y.T; Householder H = I - tau*v*v.T
 *
 * T = | T  z |   z = -tau*T*Y.T*v
 *     | 0  c |   c = tau
 *
 * Compatible with lapack.DLAFRT
 */
func BuildT(T, A, tau *matrix.FloatMatrix) (*matrix.FloatMatrix, error) {
	var err error = nil

	if T.Cols() < A.Cols() || T.Rows() < A.Cols() {
		return nil, errors.New("reflector matrix T too small")
	}

	unblkQRBlockReflector(T, A, tau)
	return T, err
}
Exemplo n.º 29
0
func columnDiffs(A, B *matrix.FloatMatrix) *matrix.FloatMatrix {
	var c matrix.FloatMatrix
	nrm := matrix.FloatZeros(A.Cols(), 1)
	A0 := A.Copy()
	A0.Minus(B)
	for k := 0; k < A.Cols(); k++ {
		A0.SubMatrix(&c, 0, k, A.Rows(), 1)
		nrm.SetAt(k, 0, matops.Norm2(&c))
	}
	return nrm
}
Exemplo n.º 30
0
func rowDiffs(A, B *matrix.FloatMatrix) *matrix.FloatMatrix {
	var r matrix.FloatMatrix
	nrm := matrix.FloatZeros(A.Rows(), 1)
	A0 := A.Copy()
	A0.Minus(B)
	for k := 0; k < A.Rows(); k++ {
		A0.SubMatrix(&r, k, 0, 1, A.Cols())
		nrm.SetAt(k, 0, matops.Norm2(&r))
	}
	return nrm
}