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ctgsyl.c
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#include "relapack.h"
#include <math.h>
static void RELAPACK_ctgsyl_rec(const char *, const blasint *, const blasint *,
const blasint *, const float *, const blasint *, const float *, const blasint *,
float *, const blasint *, const float *, const blasint *, const float *,
const blasint *, float *, const blasint *, float *, float *, float *, blasint *);
/** CTGSYL solves the generalized Sylvester equation.
*
* This routine is functionally equivalent to LAPACK's ctgsyl.
* For details on its interface, see
* http://www.netlib.org/lapack/explore-html/d7/de7/ctgsyl_8f.html
* */
void RELAPACK_ctgsyl(
const char *trans, const blasint *ijob, const blasint *m, const blasint *n,
const float *A, const blasint *ldA, const float *B, const blasint *ldB,
float *C, const blasint *ldC,
const float *D, const blasint *ldD, const float *E, const blasint *ldE,
float *F, const blasint *ldF,
float *scale, float *dif,
float *Work, const blasint *lWork, blasint *iWork, blasint *info
) {
// Parse arguments
const blasint notran = LAPACK(lsame)(trans, "N");
const blasint tran = LAPACK(lsame)(trans, "C");
// Compute work buffer size
blasint lwmin = 1;
if (notran && (*ijob == 1 || *ijob == 2))
lwmin = MAX(1, 2 * *m * *n);
*info = 0;
// Check arguments
if (!tran && !notran)
*info = -1;
else if (notran && (*ijob < 0 || *ijob > 4))
*info = -2;
else if (*m <= 0)
*info = -3;
else if (*n <= 0)
*info = -4;
else if (*ldA < MAX(1, *m))
*info = -6;
else if (*ldB < MAX(1, *n))
*info = -8;
else if (*ldC < MAX(1, *m))
*info = -10;
else if (*ldD < MAX(1, *m))
*info = -12;
else if (*ldE < MAX(1, *n))
*info = -14;
else if (*ldF < MAX(1, *m))
*info = -16;
else if (*lWork < lwmin && *lWork != -1)
*info = -20;
if (*info) {
const blasint minfo = -*info;
LAPACK(xerbla)("CTGSYL", &minfo, strlen("CTGSYL"));
return;
}
if (*lWork == -1) {
// Work size query
*Work = lwmin;
return;
}
if ( *m == 0 || *n == 0) {
*scale = 1.;
if (notran && (*ijob != 0))
*dif = 0.;
return;
}
// Clean char * arguments
const char cleantrans = notran ? 'N' : 'C';
// Constant
const float ZERO[] = { 0., 0. };
blasint isolve = 1;
blasint ifunc = 0;
if (notran) {
if (*ijob >= 3) {
ifunc = *ijob - 2;
LAPACK(claset)("F", m, n, ZERO, ZERO, C, ldC);
LAPACK(claset)("F", m, n, ZERO, ZERO, F, ldF);
} else if (*ijob >= 1)
isolve = 2;
}
float scale2;
blasint iround;
for (iround = 1; iround <= isolve; iround++) {
*scale = 1;
float dscale = 0;
float dsum = 1;
RELAPACK_ctgsyl_rec(&cleantrans, &ifunc, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, &dsum, &dscale, info);
if (dscale != 0) {
if (*ijob == 1 || *ijob == 3)
*dif = sqrt(2 * *m * *n) / (dscale * sqrt(dsum));
else
*dif = sqrt(*m * *n) / (dscale * sqrt(dsum));
}
if (isolve == 2) {
if (iround == 1) {
if (notran)
ifunc = *ijob;
scale2 = *scale;
LAPACK(clacpy)("F", m, n, C, ldC, Work, m);
LAPACK(clacpy)("F", m, n, F, ldF, Work + 2 * *m * *n, m);
LAPACK(claset)("F", m, n, ZERO, ZERO, C, ldC);
LAPACK(claset)("F", m, n, ZERO, ZERO, F, ldF);
} else {
LAPACK(clacpy)("F", m, n, Work, m, C, ldC);
LAPACK(clacpy)("F", m, n, Work + 2 * *m * *n, m, F, ldF);
*scale = scale2;
}
}
}
}
/** ctgsyl's recursive vompute kernel */
static void RELAPACK_ctgsyl_rec(
const char *trans, const blasint *ifunc, const blasint *m, const blasint *n,
const float *A, const blasint *ldA, const float *B, const blasint *ldB,
float *C, const blasint *ldC,
const float *D, const blasint *ldD, const float *E, const blasint *ldE,
float *F, const blasint *ldF,
float *scale, float *dsum, float *dscale,
blasint *info
) {
if (*m <= MAX(CROSSOVER_CTGSYL, 1) && *n <= MAX(CROSSOVER_CTGSYL, 1)) {
// Unblocked
LAPACK(ctgsy2)(trans, ifunc, m, n, A, ldA, B, ldB, C, ldC, D, ldD, E, ldE, F, ldF, scale, dsum, dscale, info);
return;
}
// Constants
const float ONE[] = { 1., 0. };
const float MONE[] = { -1., 0. };
const blasint iONE[] = { 1 };
// Outputs
float scale1[] = { 1., 0. };
float scale2[] = { 1., 0. };
blasint info1[] = { 0 };
blasint info2[] = { 0 };
if (*m > *n) {
// Splitting
const blasint m1 = CREC_SPLIT(*m);
const blasint m2 = *m - m1;
// A_TL A_TR
// 0 A_BR
const float *const A_TL = A;
const float *const A_TR = A + 2 * *ldA * m1;
const float *const A_BR = A + 2 * *ldA * m1 + 2 * m1;
// C_T
// C_B
float *const C_T = C;
float *const C_B = C + 2 * m1;
// D_TL D_TR
// 0 D_BR
const float *const D_TL = D;
const float *const D_TR = D + 2 * *ldD * m1;
const float *const D_BR = D + 2 * *ldD * m1 + 2 * m1;
// F_T
// F_B
float *const F_T = F;
float *const F_B = F + 2 * m1;
if (*trans == 'N') {
// recursion(A_BR, B, C_B, D_BR, E, F_B)
RELAPACK_ctgsyl_rec(trans, ifunc, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, D_BR, ldD, E, ldE, F_B, ldF, scale1, dsum, dscale, info1);
// C_T = C_T - A_TR * C_B
BLAS(cgemm)("N", "N", &m1, n, &m2, MONE, A_TR, ldA, C_B, ldC, scale1, C_T, ldC);
// F_T = F_T - D_TR * C_B
BLAS(cgemm)("N", "N", &m1, n, &m2, MONE, D_TR, ldD, C_B, ldC, scale1, F_T, ldF);
// recursion(A_TL, B, C_T, D_TL, E, F_T)
RELAPACK_ctgsyl_rec(trans, ifunc, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, D_TL, ldD, E, ldE, F_T, ldF, scale2, dsum, dscale, info2);
// apply scale
if (scale2[0] != 1) {
LAPACK(clascl)("G", iONE, iONE, ONE, scale2, &m2, n, C_B, ldC, info);
LAPACK(clascl)("G", iONE, iONE, ONE, scale2, &m2, n, F_B, ldF, info);
}
} else {
// recursion(A_TL, B, C_T, D_TL, E, F_T)
RELAPACK_ctgsyl_rec(trans, ifunc, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, D_TL, ldD, E, ldE, F_T, ldF, scale1, dsum, dscale, info1);
// apply scale
if (scale1[0] != 1)
LAPACK(clascl)("G", iONE, iONE, ONE, scale1, &m2, n, F_B, ldF, info);
// C_B = C_B - A_TR^H * C_T
BLAS(cgemm)("C", "N", &m2, n, &m1, MONE, A_TR, ldA, C_T, ldC, scale1, C_B, ldC);
// C_B = C_B - D_TR^H * F_T
BLAS(cgemm)("C", "N", &m2, n, &m1, MONE, D_TR, ldD, F_T, ldC, ONE, C_B, ldC);
// recursion(A_BR, B, C_B, D_BR, E, F_B)
RELAPACK_ctgsyl_rec(trans, ifunc, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, D_BR, ldD, E, ldE, F_B, ldF, scale2, dsum, dscale, info2);
// apply scale
if (scale2[0] != 1) {
LAPACK(clascl)("G", iONE, iONE, ONE, scale2, &m1, n, C_T, ldC, info);
LAPACK(clascl)("G", iONE, iONE, ONE, scale2, &m1, n, F_T, ldF, info);
}
}
} else {
// Splitting
const blasint n1 = CREC_SPLIT(*n);
const blasint n2 = *n - n1;
// B_TL B_TR
// 0 B_BR
const float *const B_TL = B;
const float *const B_TR = B + 2 * *ldB * n1;
const float *const B_BR = B + 2 * *ldB * n1 + 2 * n1;
// C_L C_R
float *const C_L = C;
float *const C_R = C + 2 * *ldC * n1;
// E_TL E_TR
// 0 E_BR
const float *const E_TL = E;
const float *const E_TR = E + 2 * *ldE * n1;
const float *const E_BR = E + 2 * *ldE * n1 + 2 * n1;
// F_L F_R
float *const F_L = F;
float *const F_R = F + 2 * *ldF * n1;
if (*trans == 'N') {
// recursion(A, B_TL, C_L, D, E_TL, F_L)
RELAPACK_ctgsyl_rec(trans, ifunc, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, D, ldD, E_TL, ldE, F_L, ldF, scale1, dsum, dscale, info1);
// C_R = C_R + F_L * B_TR
BLAS(cgemm)("N", "N", m, &n2, &n1, ONE, F_L, ldF, B_TR, ldB, scale1, C_R, ldC);
// F_R = F_R + F_L * E_TR
BLAS(cgemm)("N", "N", m, &n2, &n1, ONE, F_L, ldF, E_TR, ldE, scale1, F_R, ldF);
// recursion(A, B_BR, C_R, D, E_BR, F_R)
RELAPACK_ctgsyl_rec(trans, ifunc, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, D, ldD, E_BR, ldE, F_R, ldF, scale2, dsum, dscale, info2);
// apply scale
if (scale2[0] != 1) {
LAPACK(clascl)("G", iONE, iONE, ONE, scale2, m, &n1, C_L, ldC, info);
LAPACK(clascl)("G", iONE, iONE, ONE, scale2, m, &n1, F_L, ldF, info);
}
} else {
// recursion(A, B_BR, C_R, D, E_BR, F_R)
RELAPACK_ctgsyl_rec(trans, ifunc, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, D, ldD, E_BR, ldE, F_R, ldF, scale1, dsum, dscale, info1);
// apply scale
if (scale1[0] != 1)
LAPACK(clascl)("G", iONE, iONE, ONE, scale1, m, &n1, C_L, ldC, info);
// F_L = F_L + C_R * B_TR
BLAS(cgemm)("N", "C", m, &n1, &n2, ONE, C_R, ldC, B_TR, ldB, scale1, F_L, ldF);
// F_L = F_L + F_R * E_TR
BLAS(cgemm)("N", "C", m, &n1, &n2, ONE, F_R, ldF, E_TR, ldB, ONE, F_L, ldF);
// recursion(A, B_TL, C_L, D, E_TL, F_L)
RELAPACK_ctgsyl_rec(trans, ifunc, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, D, ldD, E_TL, ldE, F_L, ldF, scale2, dsum, dscale, info2);
// apply scale
if (scale2[0] != 1) {
LAPACK(clascl)("G", iONE, iONE, ONE, scale2, m, &n2, C_R, ldC, info);
LAPACK(clascl)("G", iONE, iONE, ONE, scale2, m, &n2, F_R, ldF, info);
}
}
}
*scale = scale1[0] * scale2[0];
*info = info1[0] || info2[0];
}