func TestDTrmmLowerRight(t *testing.T) {
N := 563
K := 171
nofail := true
A := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(K, N)
B0 := cmat.NewMatrix(K, N)
C := cmat.NewMatrix(K, N)
ones := cmat.NewFloatConstSource(1.0)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean, cmat.LOWER)
B.SetFrom(ones)
B0.SetFrom(ones)
// B = B*A
blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.RIGHT)
blasd.Mult(C, B0, A, 1.0, 0.0, gomas.NONE)
ok := C.AllClose(B)
nofail = nofail && ok
t.Logf("trmm(B, A, R|L|N) == gemm(C, B, TriL(A)) : %v\n", ok)
B.SetFrom(ones)
// B = B*A.T
blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.RIGHT|gomas.TRANSA)
blasd.Mult(C, B0, A, 1.0, 0.0, gomas.TRANSB)
ok = C.AllClose(B)
nofail = nofail && ok
t.Logf("trmm(B, A, R|L|T) == gemm(C, B, TriL(A).T) : %v\n", ok)
}
func TestDTrmmLower(t *testing.T) {
N := 563
K := 171
nofail := true
A := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(N, K)
B0 := cmat.NewMatrix(N, K)
C := cmat.NewMatrix(N, K)
ones := cmat.NewFloatConstSource(1.0)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean, cmat.LOWER)
B.SetFrom(ones)
B0.SetFrom(ones)
// B = A*B
blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT)
blasd.Mult(C, A, B0, 1.0, 0.0, gomas.NONE)
ok := C.AllClose(B)
nofail = nofail && ok
t.Logf("trmm(B, A, L|L|N) == gemm(C, TriL(A), B) : %v\n", ok)
B.SetFrom(ones)
// B = A.T*B
blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT|gomas.TRANSA)
blasd.Mult(C, A, B0, 1.0, 0.0, gomas.TRANSA)
ok = C.AllClose(B)
nofail = nofail && ok
t.Logf("trmm(B, A, L|L|T) == gemm(C, TriL(A).T, B) : %v\n", ok)
}
func TestDTrmmUnitUpper(t *testing.T) {
var d cmat.FloatMatrix
N := 563
K := 171
A := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(N, K)
B0 := cmat.NewMatrix(N, K)
C := cmat.NewMatrix(N, K)
zeros := cmat.NewFloatConstSource(0.0)
ones := cmat.NewFloatConstSource(1.0)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean, cmat.UPPER|cmat.UNIT)
B.SetFrom(ones)
B0.SetFrom(ones)
// B = A*B
blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.LEFT|gomas.UNIT)
d.Diag(A).SetFrom(ones)
blasd.Mult(C, A, B0, 1.0, 0.0, gomas.NONE)
ok := C.AllClose(B)
t.Logf("trmm(B, A, L|U|N|U) == gemm(C, TriUU(A), B) : %v\n", ok)
B.SetFrom(ones)
// B = A.T*B
d.Diag(A).SetFrom(zeros)
blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.LEFT|gomas.TRANSA|gomas.UNIT)
d.Diag(A).SetFrom(ones)
blasd.Mult(C, A, B0, 1.0, 0.0, gomas.TRANSA)
ok = C.AllClose(B)
t.Logf("trmm(B, A, L|U|T|U) == gemm(C, TriUU(A).T, B) : %v\n", ok)
}
func TestDTrmmUnitUpperRight(t *testing.T) {
var d cmat.FloatMatrix
N := 563
K := 171
A := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(K, N)
B0 := cmat.NewMatrix(K, N)
C := cmat.NewMatrix(K, N)
zeros := cmat.NewFloatConstSource(0.0)
ones := cmat.NewFloatConstSource(1.0)
zeromean := cmat.NewFloatNormSource()
A.SetFrom(zeromean, cmat.UPPER|cmat.UNIT)
B.SetFrom(ones)
B0.SetFrom(ones)
// B = B*A
blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.RIGHT|gomas.UNIT)
d.Diag(A).SetFrom(ones)
blasd.Mult(C, B0, A, 1.0, 0.0, gomas.NONE)
ok := C.AllClose(B)
t.Logf("trmm(B, A, R|U|N|U) == gemm(C, B, TriUU(A)) : %v\n", ok)
B.SetFrom(ones)
// B = B*A.T
d.SetFrom(zeros)
blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.RIGHT|gomas.TRANSA|gomas.UNIT)
d.SetFrom(ones)
blasd.Mult(C, B0, A, 1.0, 0.0, gomas.TRANSB)
ok = C.AllClose(B)
t.Logf("trmm(B, A, R|U|T|U) == gemm(C, B, TriUU(A).T) : %v\n", ok)
}
// compute:
// Q.T*C = (I -Y*T*Y.T).T*C == C - Y*(C.T*Y*T).T
// or
// Q*C = (I -Y*T*Y.T)*C == C - Y*(C.T*Y*T.T).T
//
//
// where C = ( C2 ) Y = ( Y2 Y1 )
// ( C1 )
//
// C1 is nb*K, C2 is P*K, Y1 is nb*nb triuu, Y2 is nb*P, T is nb*nb
// W = K*nb
func updateLeftRQ(C1, C2, Y1t, Y2t, T, W *cmat.FloatMatrix, transpose bool, conf *gomas.Config) {
// W = C1.T
blasd.Plus(W, C1, 0.0, 1.0, gomas.TRANSB)
// W = C1.T*Y1.T
blasd.MultTrm(W, Y1t, 1.0, gomas.RIGHT|gomas.LOWER|gomas.UNIT|gomas.TRANSA, conf)
// W = W + C2.T*Y2.T
blasd.Mult(W, C2, Y2t, 1.0, 1.0, gomas.TRANSA|gomas.TRANSB, conf)
// --- here: W == C.T*Y == C1.T*Y1.T + C2.T*Y2.T ---
tflags := gomas.RIGHT | gomas.LOWER
if !transpose {
tflags |= gomas.TRANSA
}
// W = W*T or W*T.T
blasd.MultTrm(W, T, 1.0, tflags, conf)
// --- here: W == C.T*Y*T or C.T*Y*T.T ---
// C2 = C2 - Y2*W.T
blasd.Mult(C2, Y2t, W, -1.0, 1.0, gomas.TRANSA|gomas.TRANSB, conf)
// W = Y1*W.T ==> W.T = W*Y1
blasd.MultTrm(W, Y1t, 1.0, gomas.RIGHT|gomas.LOWER|gomas.UNIT, conf)
// C1 = C1 - W.T
blasd.Plus(C1, W, 1.0, -1.0, gomas.TRANSB)
// --- here: C = (I - Y*T*Y.T).T * C ---
}
// compute:
// C*Q.T = C*(I -Y*T*Y.T).T == C - C*Y*T.T*Y.T
// or
// C*Q = (I -Y*T*Y.T)*C == C - C*Y*T*Y.T
//
//
// where C = ( C2 C1 ), Y = ( Y2 Y1 )
//
// C1 is K*nb, C2 is K*P, Y1 is nb*nb triuu, Y2 is nb*P, T is nb*nb
// W = K*nb
func updateRightRQ(C1, C2, Y1t, Y2t, T, W *cmat.FloatMatrix, transpose bool, conf *gomas.Config) {
// -- compute: W = C*Y = C1*Y1 + C2*Y2
// W = C1
blasd.Plus(W, C1, 0.0, 1.0, gomas.NONE)
// W = C1*Y1t.T
blasd.MultTrm(W, Y1t, 1.0, gomas.RIGHT|gomas.LOWER|gomas.UNIT|gomas.TRANSA, conf)
// W = W + C2*Y2t.T
blasd.Mult(W, C2, Y2t, 1.0, 1.0, gomas.TRANSB, conf)
// --- here: W == C*Y ---
tflags := gomas.RIGHT | gomas.LOWER
if transpose {
tflags |= gomas.TRANSA
}
// W = W*T or W*T.T
blasd.MultTrm(W, T, 1.0, tflags, conf)
// --- here: W == C*Y*T or C*Y*T.T ---
// C2 = C2 - W*Y2t
blasd.Mult(C2, W, Y2t, -1.0, 1.0, gomas.NONE, conf)
// C1 = C1 - W*Y1t
// W = W*Y1
blasd.MultTrm(W, Y1t, 1.0, gomas.RIGHT|gomas.LOWER|gomas.UNIT, conf)
// C1 = C1 - W
blasd.Plus(C1, W, 1.0, -1.0, gomas.NONE)
// --- here: C = (I - Y*T*Y.T).T * C ---
}
func TestDTrsm1(t *testing.T) {
nofail := true
const N = 31
const K = 4
A := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(N, K)
B0 := cmat.NewMatrix(N, K)
ones := cmat.NewFloatConstSource(1.0)
zeromean := cmat.NewFloatUniformSource(1.0, -0.5)
A.SetFrom(zeromean, cmat.LOWER)
B.SetFrom(ones)
B0.Copy(B)
// B = A*B
blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT)
blasd.SolveTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT)
ok := B0.AllClose(B)
nofail = nofail && ok
t.Logf("B == trsm(trmm(B, A, L|L|N), A, L|L|N) : %v\n", ok)
if !ok {
t.Logf("B|B0:\n%v\n", cmat.NewJoin(cmat.AUGMENT, B, B0))
}
B.Copy(B0)
// B = A.T*B
blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT|gomas.TRANSA)
blasd.SolveTrm(B, A, 1.0, gomas.LOWER|gomas.LEFT|gomas.TRANSA)
ok = B0.AllClose(B)
nofail = nofail && ok
t.Logf("B == trsm(trmm(B, A, L|L|T), A, L|L|T) : %v\n", ok)
}
func TestDTrsm3(t *testing.T) {
const N = 31
const K = 4
A := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(N, K)
B0 := cmat.NewMatrix(N, K)
ones := cmat.NewFloatConstSource(1.0)
zeromean := cmat.NewFloatUniformSource(1.0, -0.5)
A.SetFrom(zeromean, cmat.UPPER)
B.SetFrom(ones)
B0.Copy(B)
// B = A*B
blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.LEFT)
blasd.SolveTrm(B, A, 1.0, gomas.UPPER|gomas.LEFT)
ok := B0.AllClose(B)
t.Logf("B == trsm(trmm(B, A, L|U|N), A, L|U|N) : %v\n", ok)
B.Copy(B0)
// B = A.T*B
blasd.MultTrm(B, A, 1.0, gomas.UPPER|gomas.LEFT|gomas.TRANSA)
blasd.SolveTrm(B, A, 1.0, gomas.UPPER|gomas.LEFT|gomas.TRANSA)
ok = B0.AllClose(B)
t.Logf("B == trsm(trmm(B, A, L|U|T), A, L|U|T) : %v\n", ok)
}
func TestDTrms2(t *testing.T) {
const N = 31
const K = 4
nofail := true
A := cmat.NewMatrix(N, N)
B := cmat.NewMatrix(K, N)
B0 := cmat.NewMatrix(K, N)
ones := cmat.NewFloatConstSource(1.0)
zeromean := cmat.NewFloatUniformSource(1.0, -0.5)
A.SetFrom(zeromean, cmat.LOWER)
B.SetFrom(ones)
B0.Copy(B)
// B = B*A
blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.RIGHT)
blasd.SolveTrm(B, A, 1.0, gomas.LOWER|gomas.RIGHT)
ok := B0.AllClose(B)
nofail = nofail && ok
t.Logf("B == trsm(trmm(B, A, R|L|N), A, R|L|N) : %v\n", ok)
B.Copy(B0)
// B = B*A.T
blasd.MultTrm(B, A, 1.0, gomas.LOWER|gomas.RIGHT|gomas.TRANSA)
blasd.SolveTrm(B, A, 1.0, gomas.LOWER|gomas.RIGHT|gomas.TRANSA)
ok = B0.AllClose(B)
nofail = nofail && ok
t.Logf("B == trsm(trmm(B, A, R|L|T), A, R|L|T) : %v\n", ok)
}
// update T: T = -T1*Y1.T*Y2*T2
// Y1 = /Y10\ Y2 = /Y11\
// \Y20/ \Y21/
//
// T = -T1 * [Y10.T*Y11 + Y20.T*Y21]*T2
//
// T1 is K*K triangular upper matrix
// T2 is nb*nb triangular upper matrix
// T is K*nb block matrix
// Y10 is nb*K block matrix
// Y20 is M-K-nb*K block matrix
// Y11 is nb*nb triangular lower unit diagonal matrix
// Y21 is M-K-nb*nb block matrix
//
func updateQRTReflector(T, Y10, Y20, Y11, Y21, T1, T2 *cmat.FloatMatrix, conf *gomas.Config) {
// T = Y10.T
if n(Y10) == 0 {
return
}
// T = Y10.T
blasd.Plus(T, Y10, 0.0, 1.0, gomas.TRANSB)
// T = Y10.T*Y11
blasd.MultTrm(T, Y11, 1.0, gomas.LOWER|gomas.UNIT|gomas.RIGHT, conf)
// T = T + Y20.T*Y21
blasd.Mult(T, Y20, Y21, 1.0, 1.0, gomas.TRANSA, conf)
// -- here: T == Y1.T*Y2
// T = -T1*T
blasd.MultTrm(T, T1, -1.0, gomas.UPPER, conf)
// T = T*T2
blasd.MultTrm(T, T2, 1.0, gomas.UPPER|gomas.RIGHT, conf)
}
/*
* Blocked version of Hessenberg reduction algorithm as presented in (1). This
* version uses compact-WY transformation.
*
* Some notes:
*
* Elementary reflectors stored in [A11; A21].T are not on diagonal of A11. Update of
* a block aligned with A11; A21 is as follow
*
* 1. Update from left Q(k)*C:
* c0 0 c0
* (I - Y*T*Y.T).T*C = C - Y*(C.T*Y)*T.T = C1 - Y1 * (C1.T.Y1+C2.T*Y2)*T.T = C1-Y1*W
* C2 Y2 C2-Y2*W
*
* where W = (C1.T*Y1+C2.T*Y2)*T.T and first row of C is not affected by update
*
* 2. Update from right C*Q(k):
* 0
* C - C*Y*T*Y.T = c0;C1;C2 - c0;C1;C2 * Y1 *T*(0;Y1;Y2) = c0; C1-W*Y1; C2-W*Y2
* Y2
* where W = (C1*Y1 + C2*Y2)*T and first column of C is not affected
*
*/
func blkHessGQvdG(A, Tvec, W *cmat.FloatMatrix, nb int, conf *gomas.Config) *gomas.Error {
var ATL, ATR, ABL, ABR cmat.FloatMatrix
var A00, A11, A12, A21, A22, A2 cmat.FloatMatrix
var tT, tB, td cmat.FloatMatrix
var t0, t1, t2, T cmat.FloatMatrix
var V, VT, VB /*V0, V1, V2,*/, Y1, Y2, W0 cmat.FloatMatrix
//fmt.Printf("blkHessGQvdG...\n")
T.SubMatrix(W, 0, 0, conf.LB, conf.LB)
V.SubMatrix(W, conf.LB, 0, m(A), conf.LB)
td.Diag(&T)
util.Partition2x2(
&ATL, &ATR,
&ABL, &ABR, A, 0, 0, util.PTOPLEFT)
util.Partition2x1(
&tT,
&tB, Tvec, 0, util.PTOP)
for m(&ABR) > nb+1 && n(&ABR) > nb {
util.Repartition2x2to3x3(&ATL,
&A00, nil, nil,
nil, &A11, &A12,
nil, &A21, &A22, A, nb, util.PBOTTOMRIGHT)
util.Repartition2x1to3x1(&tT,
&t0,
&t1,
&t2, Tvec, nb, util.PBOTTOM)
util.Partition2x1(
&VT,
&VB, &V, m(&ATL), util.PTOP)
// ------------------------------------------------------
unblkBuildHessGQvdG(&ABR, &T, &VB, nil)
blasd.Copy(&t1, &td)
// m(Y) == m(ABR)-1, n(Y) == n(A11)
Y1.SubMatrix(&ABR, 1, 0, n(&A11), n(&A11))
Y2.SubMatrix(&ABR, 1+n(&A11), 0, m(&A21)-1, n(&A11))
// [A01; A02] == ATR := ATR*(I - Y*T*Y.T)
updateHessRightWY(&ATR, &Y1, &Y2, &T, &VT, conf)
// A2 = [A12; A22].T
util.Merge2x1(&A2, &A12, &A22)
// A2 := A2 - VB*T*A21.T
be := A21.Get(0, -1)
A21.Set(0, -1, 1.0)
blasd.MultTrm(&VB, &T, 1.0, gomas.UPPER|gomas.RIGHT)
blasd.Mult(&A2, &VB, &A21, -1.0, 1.0, gomas.TRANSB, conf)
A21.Set(0, -1, be)
// A2 := (I - Y*T*Y.T).T * A2
W0.SubMatrix(&V, 0, 0, n(&A2), n(&Y2))
updateHessLeftWY(&A2, &Y1, &Y2, &T, &W0, conf)
// ------------------------------------------------------
util.Continue3x3to2x2(
&ATL, &ATR,
&ABL, &ABR, &A00, &A11, &A22, A, util.PBOTTOMRIGHT)
util.Continue3x1to2x1(
&tT,
&tB, &t0, &t1, Tvec, util.PBOTTOM)
}
if m(&ABR) > 1 {
// do the rest with unblocked
util.Merge2x1(&A2, &ATR, &ABR)
W0.SetBuf(m(A), 1, m(A), W.Data())
unblkHessGQvdG(&A2, &tB, &W0, m(&ATR))
}
return nil
}