// test: C = C*Q.T
func TestQLMultRightTrans(t *testing.T) {
var d, di0, di1 cmat.FloatMatrix
M := 891
N := 853
lb := 36
conf := gomas.NewConf()
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
C0 := cmat.NewMatrix(N, M)
d.Diag(C0, M-N)
ones := cmat.NewFloatConstSource(1.0)
d.SetFrom(ones)
C1 := cmat.NewCopy(C0)
I0 := cmat.NewMatrix(N, N)
I1 := cmat.NewCopy(I0)
di0.Diag(I0)
di1.Diag(I1)
tau := cmat.NewMatrix(N, 1)
W := cmat.NewMatrix(lb*(M+N), 1)
conf.LB = lb
lapackd.QLFactor(A, tau, W, conf)
conf.LB = 0
lapackd.QLMult(C0, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
// I = Q*Q.T - I
blasd.Mult(I0, C0, C0, 1.0, 0.0, gomas.TRANSB, conf)
blasd.Add(&di0, -1.0)
n0 := lapackd.NormP(I0, lapackd.NORM_ONE)
conf.LB = lb
lapackd.QLMult(C1, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
// I = Q*Q.T - I
blasd.Mult(I1, C1, C1, 1.0, 0.0, gomas.TRANSB, conf)
blasd.Add(&di1, -1.0)
n1 := lapackd.NormP(I1, lapackd.NORM_ONE)
if N < 10 {
t.Logf("unblk C0*Q:\n%v\n", C0)
t.Logf("blk. C2*Q:\n%v\n", C1)
}
blasd.Plus(C0, C1, 1.0, -1.0, gomas.NONE)
n2 := lapackd.NormP(C0, lapackd.NORM_ONE)
t.Logf("M=%d, N=%d ||unblk.QLMult(C) - blk.QLMult(C)||_1: %e\n", M, N, n2)
t.Logf("unblk M=%d, N=%d ||I - Q*Q.T||_1: %e\n", M, N, n0)
t.Logf("blk M=%d, N=%d ||I - Q*Q.T||_1: %e\n", M, N, n1)
}
func TestQLBuildwithK(t *testing.T) {
var dc cmat.FloatMatrix
M := 711
N := 707
K := 691
lb := 36
conf := gomas.NewConf()
A := cmat.NewMatrix(M, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src)
tau := cmat.NewMatrix(N, 1)
W := cmat.NewMatrix(M+N, 1)
C := cmat.NewMatrix(N, N)
conf.LB = lb
lapackd.QLFactor(A, tau, W, conf)
A1 := cmat.NewCopy(A)
conf.LB = 0
lapackd.QLBuild(A, tau, W, K, conf)
blasd.Mult(C, A, A, 1.0, 0.0, gomas.TRANSA, conf)
dc.Diag(C)
blasd.Add(&dc, -1.0)
if N < 10 {
t.Logf("unblk.QLBuild Q:\n%v\n", A)
t.Logf("unblk.QLBuild Q.T*Q:\n%v\n", C)
}
n0 := lapackd.NormP(C, lapackd.NORM_ONE)
conf.LB = lb
W1 := lapackd.Workspace(lapackd.QLBuildWork(A1, conf))
lapackd.QLBuild(A1, tau, W1, K, conf)
if N < 10 {
t.Logf("blk.QLBuild Q:\n%v\n", A1)
}
// compute: I - Q.T*Q
blasd.Mult(C, A1, A1, 1.0, 0.0, gomas.TRANSA, 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.QLBuild(A) - blk.QLBuild(A)||_1 :%e\n", M, N, K, n2)
t.Logf("unblk M=%d, N=%d, K=%d ||Q.T*Q - I||_1 : %e\n", M, N, K, n0)
t.Logf("blk M=%d, N=%d, K=%d ||Q.T*Q - I||_1 : %e\n", M, N, K, n1)
}
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)
}
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)
}
/*
* Unblocked code for generating M by N matrix Q with orthogonal columns which
* are defined as the first N columns of the product of K first elementary
* reflectors.
*
* Parameters nk = n(A)-K, mk = m(A)-K define the initial partitioning of
* matrix A.
*
* Q = H(k)H(k-1)...H(1) , 0 < k <= M, where H(i) = I - tau*v*v.T
*
* Computation is ordered as H(k)*H(k-1)...*H(1)*I ie. from bottom to top.
*
* If k < M rows k+1:M are cleared and diagonal entries [k+1:M,k+1:M] are
* set to unit. Then the matrix Q is generated by right multiplying elements below
* of i'th elementary reflector H(i).
*
* Compatible to lapack.xORG2L subroutine.
*/
func unblkBuildLQ(A, Tvec, W *cmat.FloatMatrix, mk, nk int, mayClear bool) {
var ATL, ATR, ABL, ABR cmat.FloatMatrix
var A00, a10, a11, a12, a21, A22 cmat.FloatMatrix
var tT, tB cmat.FloatMatrix
var t0, tau1, t2, w12, D cmat.FloatMatrix
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, mk, nk, util.PBOTTOMRIGHT)
util.Partition2x1(
&tT,
&tB, Tvec, mk, util.PBOTTOM)
// zero the bottom part
if mk > 0 && mayClear {
blasd.Scale(&ABL, 0.0)
blasd.Scale(&ABR, 0.0)
D.Diag(&ABR)
blasd.Add(&D, 1.0)
}
for m(&ATL) > 0 && n(&ATL) > 0 {
util.Repartition2x2to3x3(&ATL,
&A00, nil, nil,
&a10, &a11, &a12,
nil, &a21, &A22, A, 1, util.PTOPLEFT)
util.Repartition2x1to3x1(&tT,
&t0,
&tau1,
&t2, Tvec, 1, util.PTOP)
// ------------------------------------------------------
w12.SubMatrix(W, 0, 0, a21.Len(), 1)
applyHouseholder2x1(&tau1, &a12, &a21, &A22, &w12, gomas.RIGHT)
blasd.Scale(&a12, -tau1.Get(0, 0))
a11.Set(0, 0, 1.0-tau1.Get(0, 0))
// zero
blasd.Scale(&a10, 0.0)
// ------------------------------------------------------
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &a11, &A22, A, util.PTOPLEFT)
util.Continue3x1to2x1(
&tT,
&tB, &t0, &tau1, Tvec, util.PTOP)
}
}
/*
* Unblocked code for generating M by N matrix Q with orthogonal columns which
* are defined as the last N columns of the product of K first elementary
* reflectors.
*
* Parameter nk is last nk elementary reflectors that are not used in computing
* the matrix Q. Parameter mk length of the first unused elementary reflectors
* First nk columns are zeroed and subdiagonal mk-nk is set to unit.
*
* Compatible with lapack.DORG2L subroutine.
*/
func unblkBuildQL(A, Tvec, W *cmat.FloatMatrix, mk, nk int, mayClear bool) {
var ATL, ATR, ABL, ABR cmat.FloatMatrix
var A00, a01, a10, a11, a21, A22 cmat.FloatMatrix
var tT, tB cmat.FloatMatrix
var t0, tau1, t2, w12, D cmat.FloatMatrix
// (mk, nk) = (rows, columns) of upper left partition
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, mk, nk, util.PTOPLEFT)
util.Partition2x1(
&tT,
&tB, Tvec, nk, util.PTOP)
// zero the left side
if nk > 0 && mayClear {
blasd.Scale(&ABL, 0.0)
blasd.Scale(&ATL, 0.0)
D.Diag(&ATL, nk-mk)
blasd.Add(&D, 1.0)
}
for m(&ABR) > 0 && n(&ABR) > 0 {
util.Repartition2x2to3x3(&ATL,
&A00, &a01, nil,
&a10, &a11, nil,
nil, &a21, &A22, A, 1, util.PBOTTOMRIGHT)
util.Repartition2x1to3x1(&tT,
&t0,
&tau1,
&t2, Tvec, 1, util.PBOTTOM)
// ------------------------------------------------------
w12.SubMatrix(W, 0, 0, a10.Len(), 1)
applyHouseholder2x1(&tau1, &a01, &a10, &A00, &w12, gomas.LEFT)
blasd.Scale(&a01, -tau1.Get(0, 0))
a11.Set(0, 0, 1.0-tau1.Get(0, 0))
// zero bottom elements
blasd.Scale(&a21, 0.0)
// ------------------------------------------------------
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &a11, &A22, A, util.PBOTTOMRIGHT)
util.Continue3x1to2x1(
&tT,
&tB, &t0, &tau1, Tvec, util.PBOTTOM)
}
}
func testEigen(N int, bits int, t *testing.T) {
var A, A0, W, D, V *cmat.FloatMatrix
var sD cmat.FloatMatrix
var s string = "lower"
if bits&gomas.UPPER != 0 {
s = "upper"
}
wsize := N * N
if wsize < 100 {
wsize = 100
}
D = cmat.NewMatrix(N, 1)
A = cmat.NewMatrix(N, N)
V = cmat.NewMatrix(N, N)
src := cmat.NewFloatNormSource()
A.SetFrom(src, cmat.SYMM)
A0 = cmat.NewCopy(A)
W = cmat.NewMatrix(wsize, 1)
if err := lapackd.EigenSym(D, A, W, bits|gomas.WANTV); err != nil {
t.Errorf("EigenSym error: %v\n", err)
return
}
// ||I - V.T*V||
sD.Diag(V)
blasd.Mult(V, A, A, 1.0, 0.0, gomas.TRANSA)
blasd.Add(&sD, -1.0)
nrm1 := lapackd.NormP(V, lapackd.NORM_ONE)
// left vectors are M-by-N
V.Copy(A)
lapackd.MultDiag(V, D, gomas.RIGHT)
blasd.Mult(A0, V, A, -1.0, 1.0, gomas.TRANSB)
nrm2 := lapackd.NormP(A0, lapackd.NORM_ONE)
t.Logf("N=%d, [%s] ||A - V*D*V.T||_1 :%e\n", N, s, nrm2)
t.Logf(" ||I - V.T*V||_1 : %e\n", nrm1)
}
func blkBuildLQ(A, Tvec, Twork, W *cmat.FloatMatrix, K, lb int, conf *gomas.Config) {
var ATL, ATR, ABL, ABR, AL cmat.FloatMatrix
var A00, A10, A11, A12, A21, A22 cmat.FloatMatrix
var tT, tB cmat.FloatMatrix
var t0, tau, t2, Wrk, D, T cmat.FloatMatrix
nk := n(A) - K
mk := m(A) - K
uk := K % lb
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, mk+uk, nk+uk, util.PBOTTOMRIGHT)
util.Partition2x1(
&tT,
&tB, Tvec, mk+uk, util.PBOTTOM)
// zero the bottom part __CHECK HERE: nk? or mk?
if nk+uk > 0 {
blasd.Scale(&ABL, 0.0)
if uk > 0 {
// number of reflectors is not multiple of blocking factor
// do the first part with unblocked code.
unblkBuildLQ(&ABR, &tB, W, m(&ABR)-uk, n(&ABR)-uk, true)
} else {
// blocking factor is multiple of K
blasd.Scale(&ABR, 0.0)
D.Diag(&ABR)
blasd.Add(&D, 1.0)
}
}
for m(&ATL) > 0 && n(&ATL) > 0 {
util.Repartition2x2to3x3(&ATL,
&A00, nil, nil,
&A10, &A11, &A12,
nil, &A21, &A22, A, lb, util.PTOPLEFT)
util.Repartition2x1to3x1(&tT,
&t0,
&tau,
&t2, Tvec, lb, util.PTOP)
// ------------------------------------------------------
util.Merge1x2(&AL, &A11, &A12)
// build block reflector
T.SubMatrix(Twork, 0, 0, n(&A11), n(&A11))
unblkBlockReflectorLQ(&T, &AL, &tau)
// update A21 and A22 with (I - Y*T*Y.T) from right
ar, ac := A21.Size()
Wrk.SubMatrix(W, 0, 0, ar, ac)
updateRightLQ(&A21, &A22, &A11, &A12, &T, &Wrk, false, conf)
// update current block
unblkBuildLQ(&AL, &tau, W, 0, n(&A12), false)
// zero top rows
blasd.Scale(&A10, 0.0)
// ------------------------------------------------------
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &A11, &A22, A, util.PTOPLEFT)
util.Continue3x1to2x1(
&tT,
&tB, &t0, &tau, Tvec, util.PTOP)
}
}
// test: M < N, U=[m,m] and V=[m,n] or V=[n,n] (square)
func testWide(M, N int, square bool, t *testing.T) {
var A, A0, W, S, U, Uu, V, Vv *cmat.FloatMatrix
var sD cmat.FloatMatrix
var s string
wsize := M * N
if wsize < 100 {
wsize = 100
}
S = cmat.NewMatrix(M, 1)
A = cmat.NewMatrix(M, N)
U = cmat.NewMatrix(M, M)
Uu = cmat.NewMatrix(M, M)
if square {
V = cmat.NewMatrix(N, N)
Vv = cmat.NewMatrix(N, N)
} else {
V = cmat.NewMatrix(M, N)
Vv = cmat.NewMatrix(M, M)
}
src := cmat.NewFloatNormSource()
A.SetFrom(src)
A0 = cmat.NewCopy(A)
W = cmat.NewMatrix(wsize, 1)
if err := lapackd.SVD(S, U, V, A, W, gomas.WANTU|gomas.WANTV); err != nil {
t.Errorf("SVD error: %v\n", err)
return
}
// ||I - U.T*U||
sD.Diag(Uu)
blasd.Mult(Uu, U, U, 1.0, 0.0, gomas.TRANSA)
blasd.Add(&sD, -1.0)
nrm0 := lapackd.NormP(Uu, lapackd.NORM_ONE)
// ||I - V*V.T||
sD.Diag(Vv)
blasd.Mult(Vv, V, V, 1.0, 0.0, gomas.TRANSB)
blasd.Add(&sD, -1.0)
nrm1 := lapackd.NormP(Vv, lapackd.NORM_ONE)
if square {
// right vectors are N-by-N
Sg := cmat.NewMatrix(M, N)
A1 := cmat.NewMatrix(M, N)
sD.Diag(Sg)
blasd.Copy(&sD, S)
blasd.Mult(A1, Sg, V, 1.0, 0.0, gomas.NONE)
blasd.Mult(A0, U, A1, -1.0, 1.0, gomas.NONE)
s = "U=[m,m], V=[n,n]"
} else {
// right vectors are M-by-N
lapackd.MultDiag(V, S, gomas.LEFT)
blasd.Mult(A0, U, V, -1.0, 1.0, gomas.NONE)
s = "U=[m,m], V=[m,n]"
}
nrm2 := lapackd.NormP(A0, lapackd.NORM_ONE)
if N < 10 {
t.Logf("A - U*S*V.T:\n%v\n", A0)
}
t.Logf("M=%d, N=%d, %s ||A - U*S*V.T||_1 :%e\n", M, N, s, nrm2)
t.Logf(" ||I - U.T*U||_1 : %e\n", nrm0)
t.Logf(" ||I - V*V.T||_1 : %e\n", nrm1)
}
/*
* Blocked code for generating M by N matrix Q with orthogonal columns which
* are defined as the last N columns of the product of K first elementary
* reflectors.
*
* If the number K of elementary reflectors is not multiple of the blocking
* factor lb, then unblocked code is used first to generate the upper left corner
* of the matrix Q.
*
* Compatible with lapack.DORGQL subroutine.
*/
func blkBuildQL(A, Tvec, Twork, W *cmat.FloatMatrix, K, lb int, conf *gomas.Config) {
var ATL, ATR, ABL, ABR, AL cmat.FloatMatrix
var A00, A01, A10, A11, A21, A22 cmat.FloatMatrix
var tT, tB cmat.FloatMatrix
var t0, tau, t2, Wrk, D, T cmat.FloatMatrix
nk := n(A) - K
mk := m(A) - K
uk := K % lb
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, mk+uk, nk+uk, util.PTOPLEFT)
util.Partition2x1(
&tT,
&tB, Tvec, nk+uk, util.PTOP)
// zero the left side
if nk+uk > 0 {
blasd.Scale(&ABL, 0.0)
if uk > 0 {
// number of reflectors is not multiple of blocking factor
// do the first part with unblocked code.
unblkBuildQL(&ATL, &tT, W, m(&ATL)-uk, n(&ATL)-uk, true)
} else {
// blocking factor is multiple of K
blasd.Scale(&ATL, 0.0)
D.Diag(&ATL)
blasd.Add(&D, 1.0)
}
}
for m(&ABR) > 0 && n(&ABR) > 0 {
util.Repartition2x2to3x3(&ATL,
&A00, &A01, nil,
&A10, &A11, nil,
nil, &A21, &A22, A, lb, util.PBOTTOMRIGHT)
util.Repartition2x1to3x1(&tT,
&t0,
&tau,
&t2, Tvec, lb, util.PBOTTOM)
// ------------------------------------------------------
util.Merge2x1(&AL, &A01, &A11)
// build block reflector
T.SubMatrix(Twork, 0, 0, n(&A11), n(&A11))
unblkQLBlockReflector(&T, &AL, &tau)
// update left side i.e. A10 and A00 with (I - Y*T*Y.T)
ar, ac := A10.Size()
Wrk.SubMatrix(W, 0, 0, ac, ar)
updateQLLeft(&A10, &A00, &A11, &A01, &T, &Wrk, false, conf)
// update current block
unblkBuildQL(&AL, &tau, W, m(&A01), 0, false)
// zero bottom rows
blasd.Scale(&A21, 0.0)
// ------------------------------------------------------
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &A11, &A22, A, util.PBOTTOMRIGHT)
util.Continue3x1to2x1(
&tT,
&tB, &t0, &tau, Tvec, util.PBOTTOM)
}
}