// 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)
}
// 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)
}
// 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)
}
// 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)
}
// 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)
}
// 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)
}
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)
}
// 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)
}