func TestLQFactor(t *testing.T) {
M := 611
N := 715
nb := 32
conf := gomas.NewConf()
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
tau := cmat.NewMatrix(M, 1)
A1 := cmat.NewCopy(A)
tau1 := cmat.NewCopy(tau)
conf.LB = 0
W := cmat.NewMatrix(M+N, 1)
lapackd.LQFactor(A, tau, W, conf)
conf.LB = nb
W1 := lapackd.Workspace(lapackd.LQFactorWork(A1, conf))
lapackd.LQFactor(A1, tau1, W1, conf)
blasd.Plus(A1, A, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(A1, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||blk.LQ(A) - unblk.LQ(A)||_1: %e\n", M, N, nrm)
}
// 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)
}
// test: min ||X|| s.t. A*X = B
func TestSolveLQ(t *testing.T) {
M := 743
N := 809
K := 281
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(N, K)
B0.SetFrom(src)
B := cmat.NewCopy(B0)
W := lapackd.Workspace(lapackd.LQFactorWork(A, conf))
lapackd.LQFactor(A, tau, W, conf)
lapackd.LQSolve(B, A, tau, W, gomas.NONE, conf)
var Bmin cmat.FloatMatrix
Bmin.SubMatrix(B0, 0, 0, M, K)
blasd.Mult(&Bmin, A0, B, 1.0, -1.0, gomas.NONE, conf)
nrm := lapackd.NormP(&Bmin, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||B - A*X||_1: %e\n", M, N, nrm)
}
func TestLQBuild(t *testing.T) {
var dc cmat.FloatMatrix
M := 877
N := 913
K := 831
lb := 48
conf := gomas.NewConf()
_ = lb
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
tau := cmat.NewMatrix(M, 1)
W := cmat.NewMatrix(M, 1)
C := cmat.NewMatrix(M, M)
dc.Diag(C)
conf.LB = lb
lapackd.LQFactor(A, tau, W, conf)
A1 := cmat.NewCopy(A)
conf.LB = 0
lapackd.LQBuild(A, tau, W, K, conf)
if N < 10 {
t.Logf("unblk.LQBuild Q:\n%v\n", A)
}
blasd.Mult(C, A, A, 1.0, 0.0, gomas.TRANSB, conf)
blasd.Add(&dc, -1.0)
n0 := lapackd.NormP(C, lapackd.NORM_ONE)
conf.LB = lb
W2 := lapackd.Workspace(lapackd.LQBuildWork(A, conf))
lapackd.LQBuild(A1, tau, W2, K, conf)
if N < 10 {
t.Logf("blk.LQBuild Q:\n%v\n", A1)
}
blasd.Mult(C, A1, A1, 1.0, 0.0, gomas.TRANSB, conf)
blasd.Add(&dc, -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.LQBuild(A) - blk.LQBuild(A)||_1 :%e\n", M, N, K, n2)
t.Logf("unblk M=%d, N=%d, K=%d ||I - Q*Q.T||_1 : %e\n", M, N, K, n0)
t.Logf(" blk M=%d, N=%d, K=%d ||I - Q*Q.T||_1 : %e\n", M, N, K, n1)
}
// test: ||C - Q*Q.T*C||_1 ~= 0;
// multipling from left requires: m(C) == n(A) [n(Q)]
func TestLQMultLeft(t *testing.T) {
M := 771
N := 813
nb := 16
conf := gomas.NewConf()
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
// C0 := A
C0 := cmat.NewCopy(A)
C1t := cmat.NewMatrix(N, M)
blasd.Transpose(C1t, C0)
C2t := cmat.NewCopy(C1t)
tau := cmat.NewMatrix(M, 1)
W := cmat.NewMatrix(M+N, 1)
conf.LB = 0
lapackd.LQFactor(A, tau, W, conf)
// A0 := Q.T*A0
conf.LB = 0
lapackd.LQMult(C2t, A, tau, W, gomas.LEFT, conf)
lapackd.LQMult(C2t, A, tau, W, gomas.LEFT|gomas.TRANS, conf)
// A0 := Q.T*A0
conf.LB = nb
W1 := lapackd.Workspace(lapackd.LQMultWork(C1t, gomas.LEFT, conf))
lapackd.LQMult(C1t, A, tau, W1, gomas.LEFT, conf)
lapackd.LQMult(C1t, A, tau, W1, gomas.LEFT|gomas.TRANS, conf)
blasd.Plus(C0, C1t, 1.0, -1.0, gomas.TRANSB)
nrm := lapackd.NormP(C0, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d, ||C - Q*Q*T*C||_1: %e\n", M, N, nrm)
blasd.Plus(C1t, C2t, 1.0, -1.0, gomas.NONE)
nrm = lapackd.NormP(C1t, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d, ||unblk(Q*Q.T*C) - blk(Q*Q*T*C)||_1: %e\n", M, N, nrm)
}
// test: ||A - A*Q*Q.T||_1 ~= 0
func TestLQMultRight(t *testing.T) {
M := 511
N := 627
nb := 24
conf := gomas.NewConf()
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
tau := cmat.NewMatrix(M, 1)
W := cmat.NewMatrix(M+N, 1)
A0 := cmat.NewCopy(A)
A1 := cmat.NewCopy(A)
A2 := cmat.NewCopy(A)
conf.LB = 0
lapackd.LQFactor(A, tau, W, conf)
// unblocked A1 := A1*Q*Q.T
conf.LB = 0
lapackd.LQMult(A1, A, tau, W, gomas.RIGHT, conf)
lapackd.LQMult(A1, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
// blocked A2 := A2*Q*Q.T
conf.LB = nb
W = lapackd.Workspace(lapackd.LQMultWork(A2, gomas.RIGHT, conf))
lapackd.LQMult(A2, A, tau, W, gomas.RIGHT, conf)
lapackd.LQMult(A2, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
// A1 - A0 == 0
blasd.Plus(A1, A0, 1.0, -1.0, gomas.NONE)
nrm := lapackd.NormP(A1, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d, unblk.||A - A*Q*Q.T||_1: %e\n", M, N, nrm)
// A2 - A0 == 0
blasd.Plus(A2, A0, 1.0, -1.0, gomas.NONE)
nrm = lapackd.NormP(A2, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d, nb=%d blk.||A - A*Q*Q.T||_1: %e\n", M, N, nb, nrm)
}
