// 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)
}
// 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)
}