// 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)
}
// m > n: A[m,n], I[m,m] --> A.T == A.T*I == A.T*Q*Q.T
func TestQRTMultRightIdent(t *testing.T) {
M := 511
N := 399
nb := 16
A := cmat.NewMatrix(M, N)
C := cmat.NewMatrix(N, M)
T := cmat.NewMatrix(nb, N)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
A0 := cmat.NewCopy(A)
C.Transpose(A)
conf := gomas.NewConf()
conf.LB = nb
// QR = A = Q*R
W := lapackd.Workspace(lapackd.QRTFactorWork(A, conf))
lapackd.QRTFactor(A, T, W, conf)
// C = A*Q
W = lapackd.Workspace(lapackd.QRTMultWork(C, T, gomas.RIGHT, conf))
err := lapackd.QRTMult(C, A, T, W, gomas.RIGHT, conf)
if err != nil {
t.Logf("err: %v\n", err)
}
// C = C*Q.T == A*Q*Q.T
err = lapackd.QRTMult(C, A, T, W, gomas.RIGHT|gomas.TRANS, conf)
if err != nil {
t.Logf("err: %v\n", err)
}
// A = A - (A.T*Q*Q.T).T
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 - (A.T*Q*Q.T).T||_1: %e\n", M, N, nrm)
}
// QR decompose A, then compute ||A - Q*R||_1, should be small
func TestMultQTLeft(t *testing.T) {
M := 513
N := 477
nb := 16
A := cmat.NewMatrix(M, N)
T := cmat.NewMatrix(nb, N)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean)
A0 := 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 = TriU(QR) = R
C := cmat.TriU(cmat.NewCopy(A), cmat.NONE)
//t.Logf("R:\n%v\n", C)
// C = Q*C
W = lapackd.Workspace(lapackd.QRTMultWork(C, T, gomas.LEFT, conf))
err := lapackd.QRTMult(C, A, T, 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)
}