zgsvj1 function
void
zgsvj1()
Implementation
void zgsvj1(
final String JOBV,
final int M,
final int N,
final int N1,
final Matrix<Complex> A_,
final int LDA,
final Array<Complex> D_,
final Array<double> SVA_,
final int MV,
final Matrix<Complex> V_,
final int LDV,
final double EPS,
final double SFMIN,
final double TOL,
final int NSWEEP,
final Array<Complex> WORK_,
final int LWORK,
final Box<int> INFO,
) {
final A = A_.having(ld: LDA);
final V = V_.having(ld: LDV);
final D = D_.having(length: N);
final SVA = SVA_.having(length: N);
final WORK = WORK_.having(length: LWORK);
const ZERO = 0.0, HALF = 0.5, ONE = 1.0;
Complex AAPQ, OMPQ;
double AAPP0,
AAPQ1,
APOAQ,
AQOAP,
BIG,
BIGTHETA,
CS,
MXAAPQ = 0,
MXSINJ = 0,
ROOTBIG,
ROOTEPS,
ROOTSFMIN,
ROOTTOL,
SMALL,
SN,
TEMP1,
THETA,
THSIGN;
int BLSKIP,
EMPTSW,
i,
ibr,
igl = 0,
IJBLSK,
ISWROT = 0,
jbc,
jgl,
KBL,
MVL = 0,
NOTROT,
NBLC,
NBLR,
p,
PSKIPPED,
q,
ROWSKIP,
SWBAND;
bool APPLV, ROTOK, RSVEC;
final IERR = Box(0);
final AAPP = Box(0.0), AAQQ = Box(0.0), T = Box(0.0);
// Test the input parameters.
APPLV = lsame(JOBV, 'A');
RSVEC = lsame(JOBV, 'V');
if (!(RSVEC || APPLV || lsame(JOBV, 'N'))) {
INFO.value = -1;
} else if (M < 0) {
INFO.value = -2;
} else if ((N < 0) || (N > M)) {
INFO.value = -3;
} else if (N1 < 0) {
INFO.value = -4;
} else if (LDA < M) {
INFO.value = -6;
} else if ((RSVEC || APPLV) && (MV < 0)) {
INFO.value = -9;
} else if ((RSVEC && (LDV < N)) || (APPLV && (LDV < MV))) {
INFO.value = -11;
} else if (TOL <= EPS) {
INFO.value = -14;
} else if (NSWEEP < 0) {
INFO.value = -15;
} else if (LWORK < M) {
INFO.value = -17;
} else {
INFO.value = 0;
}
if (INFO.value != 0) {
xerbla('ZGSVJ1', -INFO.value);
return;
}
if (RSVEC) {
MVL = N;
} else if (APPLV) {
MVL = MV;
}
RSVEC = RSVEC || APPLV;
ROOTEPS = sqrt(EPS);
ROOTSFMIN = sqrt(SFMIN);
SMALL = SFMIN / EPS;
BIG = ONE / SFMIN;
ROOTBIG = ONE / ROOTSFMIN;
// LARGE = BIG / sqrt( (M*N) )
BIGTHETA = ONE / ROOTEPS;
ROOTTOL = sqrt(TOL);
// Initialize the right singular vector matrix
// RSVEC = lsame( JOBV, 'Y' )
EMPTSW = N1 * (N - N1);
NOTROT = 0;
// Row-cyclic pivot strategy with de Rijk's pivoting
KBL = min(8, N);
NBLR = N1 ~/ KBL;
if ((NBLR * KBL) != N1) NBLR++;
// the tiling is NBLR-by-NBLC [tiles]
NBLC = (N - N1) ~/ KBL;
if ((NBLC * KBL) != (N - N1)) NBLC++;
BLSKIP = pow(KBL, 2).toInt() + 1;
// [TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL.
ROWSKIP = min(5, KBL);
// [TP] ROWSKIP is a tuning parameter.
SWBAND = 0;
// [TP] SWBAND is a tuning parameter. It is meaningful and effective
// if ZGESVJ is used as a computational routine in the preconditioned
// Jacobi SVD algorithm ZGEJSV.
// | * * * [x] [x] [x]|
// | * * * [x] [x] [x]| Row-cycling in the NBLR-by-NBLC [x] blocks.
// | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block.
// |[x] [x] [x] * * * |
// |[x] [x] [x] * * * |
// |[x] [x] [x] * * * |
var exhausted = true;
for (i = 1; i <= NSWEEP; i++) {
MXAAPQ = ZERO;
MXSINJ = ZERO;
ISWROT = 0;
NOTROT = 0;
PSKIPPED = 0;
// Each sweep is unrolled using KBL-by-KBL tiles over the pivot pairs
// 1 <= p < q <= N. This is the first step toward a blocked implementation
// of the rotations. New implementation, based on block transformations,
// is under development.
for (ibr = 1; ibr <= NBLR; ibr++) {
igl = (ibr - 1) * KBL + 1;
// go to the off diagonal blocks
igl = (ibr - 1) * KBL + 1;
jbcLoop:
for (jbc = 1; jbc <= NBLC; jbc++) {
jgl = (jbc - 1) * KBL + N1 + 1;
// doing the block at ( ibr, jbc )
IJBLSK = 0;
for (p = igl; p <= min(igl + KBL - 1, N1); p++) {
AAPP.value = SVA[p];
if (AAPP.value > ZERO) {
PSKIPPED = 0;
for (q = jgl; q <= min(jgl + KBL - 1, N); q++) {
AAQQ.value = SVA[q];
if (AAQQ.value > ZERO) {
AAPP0 = AAPP.value;
// M x 2 Jacobi SVD
// Safe Gram matrix computation
if (AAQQ.value >= ONE) {
if (AAPP.value >= AAQQ.value) {
ROTOK = (SMALL * AAPP.value) <= AAQQ.value;
} else {
ROTOK = (SMALL * AAQQ.value) <= AAPP.value;
}
if (AAPP.value < (BIG / AAQQ.value)) {
AAPQ =
(zdotc(M, A(1, p).asArray(), 1, A(1, q).asArray(), 1) /
AAQQ.value.toComplex()) /
AAPP.value.toComplex();
} else {
zcopy(M, A(1, p).asArray(), 1, WORK, 1);
zlascl('G', 0, 0, AAPP.value, ONE, M, 1, WORK.asMatrix(LDA),
LDA, IERR);
AAPQ = zdotc(M, WORK, 1, A(1, q).asArray(), 1) /
AAQQ.value.toComplex();
}
} else {
if (AAPP.value >= AAQQ.value) {
ROTOK = AAPP.value <= (AAQQ.value / SMALL);
} else {
ROTOK = AAQQ.value <= (AAPP.value / SMALL);
}
if (AAPP.value > (SMALL / AAQQ.value)) {
AAPQ =
(zdotc(M, A(1, p).asArray(), 1, A(1, q).asArray(), 1) /
max(AAQQ.value, AAPP.value).toComplex()) /
min(AAQQ.value, AAPP.value).toComplex();
} else {
zcopy(M, A(1, q).asArray(), 1, WORK, 1);
zlascl('G', 0, 0, AAQQ.value, ONE, M, 1, WORK.asMatrix(LDA),
LDA, IERR);
AAPQ = zdotc(M, A(1, p).asArray(), 1, WORK, 1) /
AAPP.value.toComplex();
}
}
// AAPQ *= CONJG(CWORK(p))*CWORK(q)
AAPQ1 = -AAPQ.abs();
MXAAPQ = max(MXAAPQ, -AAPQ1);
// TO rotate or NOT to rotate, THAT is the question .
if (AAPQ1.abs() > TOL) {
OMPQ = AAPQ / AAPQ.abs().toComplex();
NOTROT = 0;
// [RTD] ROTATED++
PSKIPPED = 0;
ISWROT++;
if (ROTOK) {
AQOAP = AAQQ.value / AAPP.value;
APOAQ = AAPP.value / AAQQ.value;
THETA = -HALF * (AQOAP - APOAQ).abs() / AAPQ1;
if (AAQQ.value > AAPP0) THETA = -THETA;
if (THETA.abs() > BIGTHETA) {
T.value = HALF / THETA;
CS = ONE;
zrot(M, A(1, p).asArray(), 1, A(1, q).asArray(), 1, CS,
OMPQ.conjugate() * T.value.toComplex());
if (RSVEC) {
zrot(MVL, V(1, p).asArray(), 1, V(1, q).asArray(), 1,
CS, OMPQ.conjugate() * T.value.toComplex());
}
SVA[q] = AAQQ.value *
sqrt(max(ZERO, ONE + T.value * APOAQ * AAPQ1));
AAPP.value *=
sqrt(max(ZERO, ONE - T.value * AQOAP * AAPQ1));
MXSINJ = max(MXSINJ, T.value.abs());
} else {
// choose correct signum for THETA and rotate
THSIGN = -sign(ONE, AAPQ1);
if (AAQQ.value > AAPP0) THSIGN = -THSIGN;
T.value =
ONE / (THETA + THSIGN * sqrt(ONE + THETA * THETA));
CS = sqrt(ONE / (ONE + T.value * T.value));
SN = T.value * CS;
MXSINJ = max(MXSINJ, SN.abs());
SVA[q] = AAQQ.value *
sqrt(max(ZERO, ONE + T.value * APOAQ * AAPQ1));
AAPP.value *=
sqrt(max(ZERO, ONE - T.value * AQOAP * AAPQ1));
zrot(M, A(1, p).asArray(), 1, A(1, q).asArray(), 1, CS,
OMPQ.conjugate() * SN.toComplex());
if (RSVEC) {
zrot(MVL, V(1, p).asArray(), 1, V(1, q).asArray(), 1,
CS, OMPQ.conjugate() * SN.toComplex());
}
}
D[p] = -D[q] * OMPQ;
} else {
// have to use modified Gram-Schmidt like transformation
if (AAPP.value > AAQQ.value) {
zcopy(M, A(1, p).asArray(), 1, WORK, 1);
zlascl('G', 0, 0, AAPP.value, ONE, M, 1,
WORK.asMatrix(LDA), LDA, IERR);
zlascl(
'G', 0, 0, AAQQ.value, ONE, M, 1, A(1, q), LDA, IERR);
zaxpy(M, -AAPQ, WORK, 1, A(1, q).asArray(), 1);
zlascl(
'G', 0, 0, ONE, AAQQ.value, M, 1, A(1, q), LDA, IERR);
SVA[q] =
AAQQ.value * sqrt(max(ZERO, ONE - AAPQ1 * AAPQ1));
MXSINJ = max(MXSINJ, SFMIN);
} else {
zcopy(M, A(1, q).asArray(), 1, WORK, 1);
zlascl('G', 0, 0, AAQQ.value, ONE, M, 1,
WORK.asMatrix(LDA), LDA, IERR);
zlascl(
'G', 0, 0, AAPP.value, ONE, M, 1, A(1, p), LDA, IERR);
zaxpy(
M, -AAPQ.conjugate(), WORK, 1, A(1, p).asArray(), 1);
zlascl(
'G', 0, 0, ONE, AAPP.value, M, 1, A(1, p), LDA, IERR);
SVA[p] =
AAPP.value * sqrt(max(ZERO, ONE - AAPQ1 * AAPQ1));
MXSINJ = max(MXSINJ, SFMIN);
}
}
// END IF ROTOK THEN ... ELSE
// In the case of cancellation in updating SVA(q), SVA(p)
// recompute SVA(q), SVA(p)
if (pow(SVA[q] / AAQQ.value, 2) <= ROOTEPS) {
if ((AAQQ.value < ROOTBIG) && (AAQQ.value > ROOTSFMIN)) {
SVA[q] = dznrm2(M, A(1, q).asArray(), 1);
} else {
T.value = ZERO;
AAQQ.value = ONE;
zlassq(M, A(1, q).asArray(), 1, T, AAQQ);
SVA[q] = T.value * sqrt(AAQQ.value);
}
}
if (pow(AAPP.value / AAPP0, 2) <= ROOTEPS) {
if ((AAPP.value < ROOTBIG) && (AAPP.value > ROOTSFMIN)) {
AAPP.value = dznrm2(M, A(1, p).asArray(), 1);
} else {
T.value = ZERO;
AAPP.value = ONE;
zlassq(M, A(1, p).asArray(), 1, T, AAPP);
AAPP.value = T.value * sqrt(AAPP.value);
}
SVA[p] = AAPP.value;
}
// end of OK rotation
} else {
NOTROT++;
// [RTD] SKIPPED++
PSKIPPED++;
IJBLSK++;
}
} else {
NOTROT++;
PSKIPPED++;
IJBLSK++;
}
if ((i <= SWBAND) && (IJBLSK >= BLSKIP)) {
SVA[p] = AAPP.value;
NOTROT = 0;
break jbcLoop;
}
if ((i <= SWBAND) && (PSKIPPED > ROWSKIP)) {
AAPP.value = -AAPP.value;
NOTROT = 0;
break;
}
}
// end of the q-loop
SVA[p] = AAPP.value;
} else {
if (AAPP.value == ZERO) {
NOTROT += min(jgl + KBL - 1, N).toInt() - jgl + 1;
}
if (AAPP.value < ZERO) NOTROT = 0;
}
}
// end of the p-loop
}
// end of the jbc-loop
// 2011 bailed out of the jbc-loop
for (p = igl; p <= min(igl + KBL - 1, N); p++) {
SVA[p] = SVA[p].abs();
}
}
// 2000 :: end of the ibr-loop
// update SVA(N)
if ((SVA[N] < ROOTBIG) && (SVA[N] > ROOTSFMIN)) {
SVA[N] = dznrm2(M, A(1, N).asArray(), 1);
} else {
T.value = ZERO;
AAPP.value = ONE;
zlassq(M, A(1, N).asArray(), 1, T, AAPP);
SVA[N] = T.value * sqrt(AAPP.value);
}
// Additional steering devices
if ((i < SWBAND) && ((MXAAPQ <= ROOTTOL) || (ISWROT <= N))) SWBAND = i;
if ((i > SWBAND + 1) &&
(MXAAPQ < sqrt(N) * TOL) &&
(N * MXAAPQ * MXSINJ < TOL)) {
exhausted = false;
break;
}
if (NOTROT >= EMPTSW) {
exhausted = false;
break;
}
}
// end i=1:NSWEEP loop
if (exhausted) {
// Reaching this point means that the procedure has not converged.
INFO.value = NSWEEP - 1;
} else {
// Reaching this point means numerical convergence after the i-th
// sweep.
INFO.value = 0;
// INFO = 0 confirms successful iterations.
}
// Sort the vector SVA() of column norms.
for (p = 1; p <= N - 1; p++) {
q = idamax(N - p + 1, SVA(p), 1) + p - 1;
if (p != q) {
TEMP1 = SVA[p];
SVA[p] = SVA[q];
SVA[q] = TEMP1;
AAPQ = D[p];
D[p] = D[q];
D[q] = AAPQ;
zswap(M, A(1, p).asArray(), 1, A(1, q).asArray(), 1);
if (RSVEC) zswap(MVL, V(1, p).asArray(), 1, V(1, q).asArray(), 1);
}
}
}