Пример #1
0
// 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)
}
Пример #2
0
// 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)
}
Пример #3
0
// QR decompose A, then compute ||A - (R.T*Q.T).T||_1, should be small
func TestUnblkQRMultRight(t *testing.T) {
	M := 711
	N := 593
	A := cmat.NewMatrix(M, N)
	C := cmat.NewMatrix(N, M)
	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 = transpose(TriU(QR)) = R.T
	C.Transpose(cmat.TriU(cmat.NewCopy(A), cmat.NONE))

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

	// A = A - QR
	blasd.Plus(A0, C, 1.0, -1.0, gomas.TRANSB)
	// ||A - Q*R||_1
	nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
	t.Logf("M=%d,N=%d  ||A - (R.T*Q.T).T||_1: %e\n", M, N, nrm)
}
Пример #4
0
// 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)
}
Пример #5
0
// m > n: A[m,n], I[m,m] --> A.T == A.T*I == A.T*Q*Q.T
func TestBlockedQRMultRightIdent(t *testing.T) {
	M := 511
	N := 489
	A := cmat.NewMatrix(M, N)
	C := cmat.NewMatrix(N, M)
	tau := cmat.NewMatrix(N, 1)

	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)
	A0 := cmat.NewCopy(A)
	C.Transpose(A)
	conf := gomas.NewConf()
	conf.LB = 32

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

	// C = A.T*Q
	W = lapackd.Workspace(lapackd.QRMultWork(C, gomas.RIGHT, conf))
	lapackd.QRMult(C, A, tau, W, gomas.RIGHT, conf)

	// C = C*Q.T == A.T*Q*Q.T
	lapackd.QRMult(C, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
	//t.Logf("A*Q*Q.T:\n%v\n", C)

	// A = A - (A.T*Q*Q.T).T
	blasd.Plus(A0, C, 1.0, -1.0, gomas.TRANSB)
	// ||A - (A.T*Q*Q.T).T||_1
	nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
	t.Logf("M=%d,N=%d  ||A - (A.T*Q*Q.T).T||_1: %e\n", M, N, nrm)
}
Пример #6
0
// m > n: A[m,n], I[m,m] --> A == I*A == Q*Q.T*A
func TestBlkQRMultLeftIdent(t *testing.T) {
	M := 411
	N := 399
	A := cmat.NewMatrix(M, N)
	tau := cmat.NewMatrix(N, 1)

	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)
	A0 := cmat.NewCopy(A)
	C := cmat.NewCopy(A)
	conf := gomas.NewConf()
	conf.LB = 32

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

	// C = Q.T*A
	W = lapackd.Workspace(lapackd.QRMultWork(C, gomas.LEFT, conf))
	lapackd.QRMult(C, A, tau, W, gomas.LEFT|gomas.TRANS, conf)

	// C = Q*C == Q*Q.T*A
	lapackd.QRMult(C, A, tau, 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)
}
Пример #7
0
func main() {
	flag.Parse()

	M := N + N/10

	conf := gomas.CurrentConf()

	A := cmat.NewMatrix(M, N)
	A0 := cmat.NewCopy(A)
	tau := cmat.NewMatrix(N, 1)
	W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)

	cumtime := 0.0
	mintime := 0.0
	maxtime := 0.0
	for i := 0; i < count; i++ {
		flushCache()

		t1 := time.Now()
		// ----------------------------------------------

		lapackd.QRFactor(A, tau, W, conf)

		// ----------------------------------------------
		t2 := time.Now()
		tm := t2.Sub(t1)

		if mintime == 0.0 || tm.Seconds() < mintime {
			mintime = tm.Seconds()
		}
		if maxtime == 0.0 || tm.Seconds() > maxtime {
			maxtime = tm.Seconds()
		}
		cumtime += tm.Seconds()
		if verbose {
			fmt.Printf("%3d  %12.4f msec, %9.4f gflops\n",
				i, 1e+3*tm.Seconds(), gflops(M, N, tm.Seconds()))
		}
		blasd.Copy(A, A0)
	}
	cumtime /= float64(count)
	minflops := gflops(M, N, maxtime)
	avgflops := gflops(M, N, cumtime)
	maxflops := gflops(M, N, mintime)
	fmt.Printf("%5d %5d %3d %9.4f %9.4f %9.4f Gflops\n", M, N, conf.LB, minflops, avgflops, maxflops)
}
Пример #8
0
func TestQRBuild(t *testing.T) {
	var d cmat.FloatMatrix

	M := 911
	N := 899
	K := 873
	lb := 36
	conf := gomas.NewConf()

	A := cmat.NewMatrix(M, N)
	src := cmat.NewFloatNormSource()
	A.SetFrom(src)
	tau := cmat.NewMatrix(N, 1)
	W := cmat.NewMatrix(N+M, 1)

	C := cmat.NewMatrix(N, N)
	d.Diag(C)

	conf.LB = lb
	lapackd.QRFactor(A, tau, W, conf)
	A1 := cmat.NewCopy(A)

	conf.LB = 0
	lapackd.QRBuild(A, tau, W, K, conf)

	blasd.Mult(C, A, A, 1.0, 0.0, gomas.TRANSA, conf)
	blasd.Add(&d, -1.0)
	n0 := lapackd.NormP(C, lapackd.NORM_ONE)

	conf.LB = lb
	W2 := lapackd.Workspace(lapackd.QRBuildWork(A, conf))
	lapackd.QRBuild(A1, tau, W2, K, conf)

	blasd.Mult(C, A1, A1, 1.0, 0.0, gomas.TRANSA, conf)
	blasd.Add(&d, -1.0)
	n1 := lapackd.NormP(C, lapackd.NORM_ONE)

	blasd.Plus(A, A1, 1.0, -1.0, gomas.NONE)
	n2 := lapackd.NormP(A, lapackd.NORM_ONE)

	t.Logf("M=%d, N=%d, K=%d ||unblk.QRBuild(A) - blk.QRBuild(A)||_1 :%e\n", M, N, K, n2)
	t.Logf("unblk M=%d, N=%d, K=%d ||I - Q.T*Q||_1: %e\n", M, N, K, n0)
	t.Logf("  blk M=%d, N=%d, K=%d ||I - Q.T*Q||_1: %e\n", M, N, K, n1)
}
Пример #9
0
// test: min || B - A*X ||
func TestLeastSquaresQR(t *testing.T) {
	M := 811
	N := 723
	K := 311
	nb := 32
	conf := gomas.NewConf()
	conf.LB = nb

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

	// B = A*B0
	blasd.Mult(B, A, B0, 1.0, 0.0, gomas.NONE, conf)

	W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
	err := lapackd.QRFactor(A, tau, W, conf)
	if err != nil {
		t.Logf("DecomposeQR: %v\n", err)
	}

	// B' = A.-1*B
	err = lapackd.QRSolve(B, A, tau, W, gomas.NONE, conf)
	if err != nil {
		t.Logf("SolveQR: %v\n", err)
	}

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

	X.SubMatrix(B, 0, 0, N, 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*X - B0|| ) ||_1: %e\n", M, N, nrm)
}