Golang cmat.NewMatrix函數代碼示例

// test: min ||X|| s.t A.T*X = B
func TestSolveQR(t *testing.T) {
	M := 799
	N := 711
	K := 241
	nb := 32
	conf := gomas.NewConf()
	conf.LB = nb

	tau := cmat.NewMatrix(N, 1)
	A := cmat.NewMatrix(M, N)
	src := cmat.NewFloatNormSource()
	A.SetFrom(src)
	A0 := cmat.NewCopy(A)
	B0 := cmat.NewMatrix(M, K)
	B0.SetFrom(src)
	B := cmat.NewCopy(B0)

	W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
	lapackd.QRFactor(A, tau, W, conf)

	lapackd.QRSolve(B, A, tau, W, gomas.TRANS, conf)

	var Bmin cmat.FloatMatrix
	Bmin.SubMatrix(B0, 0, 0, N, K)
	blasd.Mult(&Bmin, A0, B, 1.0, -1.0, gomas.TRANSA, conf)

	nrm := lapackd.NormP(&Bmin, lapackd.NORM_ONE)
	t.Logf("M=%d, N=%d ||B - A.T*X||_1: %e\n", M, N, nrm)
}

func TestDTrmmLower(t *testing.T) {
	N := 563
	K := 171
	nofail := true

	A := cmat.NewMatrix(N, N)
	B := cmat.NewMatrix(N, K)
	B0 := cmat.NewMatrix(N, K)
	C := cmat.NewMatrix(N, K)

	ones := cmat.NewFloatConstSource(1.0)
	zeromean := cmat.NewFloatNormSource()

	A.SetFrom(zeromean, cmat.LOWER)
	B.SetFrom(ones)
	B0.SetFrom(ones)
	// B = A*B
	blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT)
	blasd.Mult(C, A, B0, 1.0, 0.0, gomas.NONE)
	ok := C.AllClose(B)
	nofail = nofail && ok
	t.Logf("trmm(B, A, L|L|N) == gemm(C, TriL(A), B)   : %v\n", ok)

	B.SetFrom(ones)
	// B = A.T*B
	blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT|gomas.TRANSA)
	blasd.Mult(C, A, B0, 1.0, 0.0, gomas.TRANSA)
	ok = C.AllClose(B)
	nofail = nofail && ok
	t.Logf("trmm(B, A, L|L|T) == gemm(C, TriL(A).T, B) : %v\n", ok)
}

func __TestZeroQLSweep(t *testing.T) {

	N := 5
	D0 := cmat.NewMatrix(1, N)
	E0 := cmat.NewMatrix(1, N-1)
	D1 := cmat.NewMatrix(1, N)
	E1 := cmat.NewMatrix(1, N-1)

	for k := 0; k < N; k++ {
		D0.SetAt(N-k-1, float64(k+1))
		D1.SetAt(N-k-1, float64(k+1))
		if k < N-1 {
			E0.SetAt(k, 1.0)
			E1.SetAt(k, 1.0)
		}
	}

	f := D0.GetAt(4)
	g := E0.GetAt(3)
	lapackd.BDQLsweep(D0, E0, f, g)
	lapackd.BDQLzero(D1, E1)
	t.Logf("D0.std :%v\n", D0)
	t.Logf("D1.zero:%v\n", D1)
	t.Logf("E0.std :%v\n", E0)
	t.Logf("E1.zero:%v\n", E1)
}

func __TestSweep(t *testing.T) {

	N := 5
	D0 := cmat.NewMatrix(1, N)
	E0 := cmat.NewMatrix(1, N-1)
	D1 := cmat.NewMatrix(1, N)
	E1 := cmat.NewMatrix(1, N-1)

	for k := 0; k < N; k++ {
		D0.SetAt(k, float64(k+1))
		D1.SetAt(N-1-k, float64(k+1))
		if k < N-1 {
			E0.SetAt(k, 1.0)
			E1.SetAt(k, 1.0)
		}
	}

	f := 0.5
	g := -0.45
	lapackd.BDQRsweep(D0, E0, f, g)
	lapackd.BDQLsweep(D1, E1, f, g)
	t.Logf("D0:%v\n", D0)
	t.Logf("D1:%v\n", D1)
	t.Logf("E0:%v\n", E0)
	t.Logf("E1:%v\n", E1)
}

// test: min || B - A.T*X ||
func TestLeastSquaresLQ(t *testing.T) {
	M := 723
	N := 811
	K := 273
	nb := 32
	conf := gomas.NewConf()
	conf.LB = nb

	tau := cmat.NewMatrix(M, 1)
	A := cmat.NewMatrix(M, N)
	src := cmat.NewFloatNormSource()
	A.SetFrom(src)
	B0 := cmat.NewMatrix(M, K)
	B0.SetFrom(src)
	B := cmat.NewMatrix(N, K)

	// B = A.T*B0
	blasd.Mult(B, A, B0, 1.0, 0.0, gomas.TRANSA, conf)

	W := lapackd.Workspace(lapackd.LQFactorWork(A, conf))
	lapackd.LQFactor(A, tau, W, conf)

	// B' = A.-1*B
	lapackd.LQSolve(B, A, tau, W, gomas.TRANS, conf)

	// expect B[0:M,0:K] == B0[0:M,0:K], B[M:N,0:K] == 0
	var X cmat.FloatMatrix

	X.SubMatrix(B, 0, 0, M, K)
	blasd.Plus(&X, B0, 1.0, -1.0, gomas.NONE)
	nrm := lapackd.NormP(&X, lapackd.NORM_ONE)

	t.Logf("M=%d, N=%d  ||B0 - min( ||A.T*X - B0|| ) ||_1: %e\n", M, N, nrm)
}

func TestBlockedDecomposeCHOL(t *testing.T) {
	N := 119
	nb := 16

	conf := gomas.NewConf()
	conf.LB = nb

	Z := cmat.NewMatrix(N, N)
	AL := cmat.NewMatrix(N, N)
	AU := cmat.NewMatrix(N, N)

	unitrand := cmat.NewFloatUniformSource()
	Z.SetFrom(unitrand)

	blasd.Mult(AL, Z, Z, 1.0, 0.0, gomas.TRANSB)
	AU.Copy(AL)

	eu := lapackd.CHOLFactor(AU, gomas.UPPER, conf)
	el := lapackd.CHOLFactor(AL, gomas.LOWER, conf)
	_, _ = eu, el

	Z.Transpose(AU)
	if N < 10 {
		t.Logf("AU.T:\n%v\n", Z)
		t.Logf("AL:\n%v\n", AL)
	}
	ok := AL.AllClose(Z)
	t.Logf("Decompose(AL) == Decompose(AU).T: %v\n", ok)
}

// m > n: A[m,n], I[m,m] --> A == I*A == Q*Q.T*A
func TestQRTMultLeftIdent(t *testing.T) {
	M := 411
	N := 399
	nb := 16
	A := cmat.NewMatrix(M, N)
	T := cmat.NewMatrix(nb, N)

	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)
	A0 := cmat.NewCopy(A)
	C := cmat.NewCopy(A)
	conf := gomas.NewConf()
	conf.LB = nb
	//t.Logf("A0:\n%v\n", A0)

	// QR = A = Q*R
	W := lapackd.Workspace(lapackd.QRTFactorWork(A, conf))
	lapackd.QRTFactor(A, T, W, conf)
	//t.Logf("T:\n%v\n", T)

	// C = Q.T*A
	W = lapackd.Workspace(lapackd.QRTMultWork(C, T, gomas.LEFT, conf))
	lapackd.QRTMult(C, A, T, W, gomas.LEFT|gomas.TRANS, conf)

	// C = Q*C == Q*Q.T*A
	lapackd.QRTMult(C, A, T, W, gomas.LEFT, conf)
	//t.Logf("A*Q*Q.T:\n%v\n", C)

	// A = A - Q*Q.T*A
	blasd.Plus(A0, C, 1.0, -1.0, gomas.NONE)
	// ||A - Q*Q.T*A||_1
	nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
	t.Logf("M=%d,N=%d  ||A - Q*Q.T*A||_1: %e\n", M, N, nrm)
}

// test that unblocked and blocked QRT are equal
func TestDecomposeQRT(t *testing.T) {
	M := 615
	N := 591
	nb := 16

	conf := gomas.NewConf()
	conf.LB = nb

	A := cmat.NewMatrix(M, N)
	T := cmat.NewMatrix(nb, N)
	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)

	A0 := cmat.NewCopy(A)
	T0 := cmat.NewMatrix(N, N)

	// blocked: QR = A = Q*R
	W := lapackd.Workspace(lapackd.QRTFactorWork(A, conf))
	lapackd.QRTFactor(A, T, W, conf)

	conf.LB = 0
	lapackd.QRTFactor(A0, T0, W, conf)

	ok := A.AllClose(A0)
	t.Logf("blk.DecomposeQRT(A) == unblk.DecomposeQRT(A): %v\n", ok)

}

func TestDSyr1(t *testing.T) {

	const N = 911

	A := cmat.NewMatrix(N, N)
	X := cmat.NewMatrix(N, 1)
	B := cmat.NewMatrix(N, N)

	//ones := cmat.NewFloatConstSource(1.0)
	zeromean := cmat.NewFloatUniformSource(0.5, 2.0)

	A.SetFrom(zeromean, cmat.LOWER)
	X.SetFrom(zeromean)
	B.Copy(A)

	// B = A*B
	blasd.MVUpdate(B, X, X, 1.0)
	cmat.TriL(B, cmat.NONE)
	blasd.MVUpdateSym(A, X, 1.0, gomas.LOWER)
	ok := B.AllClose(A)
	t.Logf("MVUpdateSym(A, X, L) == TriL(MVUpdate(A, X, X)) : %v\n", ok)

	A.SetFrom(zeromean, cmat.UPPER)
	cmat.TriU(A, cmat.NONE)
	B.Copy(A)
	blasd.MVUpdate(B, X, X, 1.0)
	cmat.TriU(B, cmat.NONE)
	blasd.MVUpdateSym(A, X, 1.0, gomas.UPPER)
	ok = B.AllClose(A)
	t.Logf("MVUpdateSym(A, X, U) == TriU(MVUpdate(A, X, X)) : %v\n", ok)
}

func TestDTrmmUnitUpper(t *testing.T) {
	var d cmat.FloatMatrix
	N := 563
	K := 171

	A := cmat.NewMatrix(N, N)
	B := cmat.NewMatrix(N, K)
	B0 := cmat.NewMatrix(N, K)
	C := cmat.NewMatrix(N, K)

	zeros := cmat.NewFloatConstSource(0.0)
	ones := cmat.NewFloatConstSource(1.0)
	zeromean := cmat.NewFloatNormSource()

	A.SetFrom(zeromean, cmat.UPPER|cmat.UNIT)
	B.SetFrom(ones)
	B0.SetFrom(ones)
	// B = A*B
	blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.LEFT|gomas.UNIT)
	d.Diag(A).SetFrom(ones)
	blasd.Mult(C, A, B0, 1.0, 0.0, gomas.NONE)
	ok := C.AllClose(B)
	t.Logf("trmm(B, A, L|U|N|U) == gemm(C, TriUU(A), B)   : %v\n", ok)

	B.SetFrom(ones)
	// B = A.T*B
	d.Diag(A).SetFrom(zeros)
	blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.LEFT|gomas.TRANSA|gomas.UNIT)
	d.Diag(A).SetFrom(ones)
	blasd.Mult(C, A, B0, 1.0, 0.0, gomas.TRANSA)
	ok = C.AllClose(B)
	t.Logf("trmm(B, A, L|U|T|U) == gemm(C, TriUU(A).T, B) : %v\n", ok)
}

func TestSolveBKLowerBig(t *testing.T) {
	N := 427
	normsrc := cmat.NewFloatNormSource(5.0, 10.0)
	A := cmat.NewMatrix(N, N)
	A.SetFrom(normsrc, cmat.LOWER)

	X := cmat.NewMatrix(N, 2)
	X.SetFrom(normsrc)
	B := cmat.NewCopy(X)
	blasd.MultSym(B, A, X, 1.0, 0.0, gomas.LOWER|gomas.LEFT)

	ipiv := lapackd.NewPivots(N)

	conf := gomas.NewConf()
	conf.LB = 16
	W := lapackd.Workspace(lapackd.BKFactorWork(A, conf))
	lapackd.BKFactor(A, W, ipiv, gomas.LOWER, conf)

	lapackd.BKSolve(B, A, ipiv, gomas.LOWER, conf)
	ok := B.AllClose(X)
	t.Logf("N=%d unblk.BK(X) == A.-1*B : %v\n", N, ok)
	blasd.Plus(B, X, 1.0, -1.0, gomas.NONE)
	nrm := lapackd.NormP(B, lapackd.NORM_ONE)
	t.Logf("  ||X - A.-1*B||_1: %.4e\n", nrm)

}

func TestDTrmmUnitUpperRight(t *testing.T) {
	var d cmat.FloatMatrix
	N := 563
	K := 171

	A := cmat.NewMatrix(N, N)
	B := cmat.NewMatrix(K, N)
	B0 := cmat.NewMatrix(K, N)
	C := cmat.NewMatrix(K, N)

	zeros := cmat.NewFloatConstSource(0.0)
	ones := cmat.NewFloatConstSource(1.0)
	zeromean := cmat.NewFloatNormSource()

	A.SetFrom(zeromean, cmat.UPPER|cmat.UNIT)
	B.SetFrom(ones)
	B0.SetFrom(ones)
	// B = B*A
	blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.RIGHT|gomas.UNIT)
	d.Diag(A).SetFrom(ones)
	blasd.Mult(C, B0, A, 1.0, 0.0, gomas.NONE)
	ok := C.AllClose(B)
	t.Logf("trmm(B, A, R|U|N|U) == gemm(C, B, TriUU(A))   : %v\n", ok)

	B.SetFrom(ones)
	// B = B*A.T
	d.SetFrom(zeros)
	blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.RIGHT|gomas.TRANSA|gomas.UNIT)
	d.SetFrom(ones)
	blasd.Mult(C, B0, A, 1.0, 0.0, gomas.TRANSB)
	ok = C.AllClose(B)
	t.Logf("trmm(B, A, R|U|T|U) == gemm(C, B, TriUU(A).T) : %v\n", ok)
}

// QR decompose A, then compute ||A - Q*R||_1, should be small
func TestUnblkQRMultLeft(t *testing.T) {
	M := 711
	N := 593
	A := cmat.NewMatrix(M, N)
	tau := cmat.NewMatrix(N, 1)

	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)
	A0 := cmat.NewCopy(A)

	conf := gomas.NewConf()
	conf.LB = 0

	// QR = A = Q*R
	W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
	lapackd.QRFactor(A, tau, W, conf)

	// C = TriU(QR) = R
	C := cmat.TriU(cmat.NewCopy(A), cmat.NONE)

	// C = Q*C
	W = lapackd.Workspace(lapackd.QRMultWork(C, gomas.LEFT, conf))
	err := lapackd.QRMult(C, A, tau, W, gomas.LEFT, conf)
	if err != nil {
		t.Logf("err: %v\n", err)
	}

	// A = A - QR
	blasd.Plus(A0, C, 1.0, -1.0, gomas.NONE)
	// ||A - Q*R||_1
	nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
	t.Logf("M=%d,N=%d  ||A - Q*R||_1: %e\n", M, N, nrm)
}

func TestDTrsm1(t *testing.T) {
	nofail := true

	const N = 31
	const K = 4

	A := cmat.NewMatrix(N, N)
	B := cmat.NewMatrix(N, K)
	B0 := cmat.NewMatrix(N, K)

	ones := cmat.NewFloatConstSource(1.0)
	zeromean := cmat.NewFloatUniformSource(1.0, -0.5)

	A.SetFrom(zeromean, cmat.LOWER)
	B.SetFrom(ones)
	B0.Copy(B)
	// B = A*B
	blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT)
	blasd.SolveTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT)
	ok := B0.AllClose(B)
	nofail = nofail && ok
	t.Logf("B == trsm(trmm(B, A, L|L|N), A, L|L|N) : %v\n", ok)
	if !ok {
		t.Logf("B|B0:\n%v\n", cmat.NewJoin(cmat.AUGMENT, B, B0))
	}

	B.Copy(B0)
	// B = A.T*B
	blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT|gomas.TRANSA)
	blasd.SolveTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT|gomas.TRANSA)
	ok = B0.AllClose(B)
	nofail = nofail && ok
	t.Logf("B == trsm(trmm(B, A, L|L|T), A, L|L|T) : %v\n", ok)
}

// test that unblocked QR and QRT are equal
func TestQRFactor(t *testing.T) {
	M := 411
	N := 375
	nb := 16

	conf := gomas.NewConf()
	conf.LB = nb

	A := cmat.NewMatrix(M, N)
	//W := cmat.NewMatrix(N, nb)
	tau := cmat.NewMatrix(N, 1)
	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)

	A0 := cmat.NewCopy(A)
	tau0 := cmat.NewCopy(tau)

	// blocked: QR = A = Q*R
	W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
	lapackd.QRFactor(A, tau, W, conf)

	conf.LB = 0
	lapackd.QRFactor(A0, tau0, W, conf)

	ok := A.AllClose(A0)
	t.Logf("blk.QRFactor(A) == unblk.QRFactor(A): %v\n", ok)

	ok = tau0.AllClose(tau)
	t.Logf("blk QR.tau == unblk QR.tau: %v\n", ok)
}