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strsyl.c
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#include "relapack.h"
static void RELAPACK_strsyl_rec(const char *, const char *, const blasint *,
const blasint *, const blasint *, const float *, const blasint *, const float *,
const blasint *, float *, const blasint *, float *, blasint *);
/** STRSYL solves the real Sylvester matrix equation.
*
* This routine is functionally equivalent to LAPACK's strsyl.
* For details on its interface, see
* http://www.netlib.org/lapack/explore-html/d4/d7d/strsyl_8f.html
* */
void RELAPACK_strsyl(
const char *tranA, const char *tranB, const blasint *isgn,
const blasint *m, const blasint *n,
const float *A, const blasint *ldA, const float *B, const blasint *ldB,
float *C, const blasint *ldC, float *scale,
blasint *info
) {
// Check arguments
const blasint notransA = LAPACK(lsame)(tranA, "N");
const blasint transA = LAPACK(lsame)(tranA, "T");
const blasint ctransA = LAPACK(lsame)(tranA, "C");
const blasint notransB = LAPACK(lsame)(tranB, "N");
const blasint transB = LAPACK(lsame)(tranB, "T");
const blasint ctransB = LAPACK(lsame)(tranB, "C");
*info = 0;
if (!transA && !ctransA && !notransA)
*info = -1;
else if (!transB && !ctransB && !notransB)
*info = -2;
else if (*isgn != 1 && *isgn != -1)
*info = -3;
else if (*m < 0)
*info = -4;
else if (*n < 0)
*info = -5;
else if (*ldA < MAX(1, *m))
*info = -7;
else if (*ldB < MAX(1, *n))
*info = -9;
else if (*ldC < MAX(1, *m))
*info = -11;
if (*info) {
const blasint minfo = -*info;
LAPACK(xerbla)("STRSYL", &minfo, strlen("STRSYL"));
return;
}
if (*m == 0 || *n == 0) {
*scale = 1.;
return;
}
// Clean char * arguments
const char cleantranA = notransA ? 'N' : (transA ? 'T' : 'C');
const char cleantranB = notransB ? 'N' : (transB ? 'T' : 'C');
// Recursive kernel
RELAPACK_strsyl_rec(&cleantranA, &cleantranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
}
/** strsyl's recursive compute kernel */
static void RELAPACK_strsyl_rec(
const char *tranA, const char *tranB, const blasint *isgn,
const blasint *m, const blasint *n,
const float *A, const blasint *ldA, const float *B, const blasint *ldB,
float *C, const blasint *ldC, float *scale,
blasint *info
) {
if (*m <= MAX(CROSSOVER_STRSYL, 1) && *n <= MAX(CROSSOVER_STRSYL, 1)) {
// Unblocked
RELAPACK_strsyl_rec2(tranA, tranB, isgn, m, n, A, ldA, B, ldB, C, ldC, scale, info);
return;
}
// Constants
const float ONE[] = { 1. };
const float MONE[] = { -1. };
const float MSGN[] = { -*isgn };
const blasint iONE[] = { 1 };
// Outputs
float scale1[] = { 1. };
float scale2[] = { 1. };
blasint info1[] = { 0 };
blasint info2[] = { 0 };
if (*m > *n) {
// Splitting
blasint m1 = SREC_SPLIT(*m);
if (A[m1 + *ldA * (m1 - 1)])
m1++;
const blasint m2 = *m - m1;
// A_TL A_TR
// 0 A_BR
const float *const A_TL = A;
const float *const A_TR = A + *ldA * m1;
const float *const A_BR = A + *ldA * m1 + m1;
// C_T
// C_B
float *const C_T = C;
float *const C_B = C + m1;
if (*tranA == 'N') {
// recusion(A_BR, B, C_B)
RELAPACK_strsyl_rec(tranA, tranB, isgn, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, scale1, info1);
// C_T = C_T - A_TR * C_B
BLAS(sgemm)("N", "N", &m1, n, &m2, MONE, A_TR, ldA, C_B, ldC, scale1, C_T, ldC);
// recusion(A_TL, B, C_T)
RELAPACK_strsyl_rec(tranA, tranB, isgn, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, scale2, info2);
// apply scale
if (scale2[0] != 1)
LAPACK(slascl)("G", iONE, iONE, ONE, scale2, &m2, n, C_B, ldC, info);
} else {
// recusion(A_TL, B, C_T)
RELAPACK_strsyl_rec(tranA, tranB, isgn, &m1, n, A_TL, ldA, B, ldB, C_T, ldC, scale1, info1);
// C_B = C_B - A_TR' * C_T
BLAS(sgemm)("C", "N", &m2, n, &m1, MONE, A_TR, ldA, C_T, ldC, scale1, C_B, ldC);
// recusion(A_BR, B, C_B)
RELAPACK_strsyl_rec(tranA, tranB, isgn, &m2, n, A_BR, ldA, B, ldB, C_B, ldC, scale2, info2);
// apply scale
if (scale2[0] != 1)
LAPACK(slascl)("G", iONE, iONE, ONE, scale2, &m1, n, C_B, ldC, info);
}
} else {
// Splitting
blasint n1 = SREC_SPLIT(*n);
if (B[n1 + *ldB * (n1 - 1)])
n1++;
const blasint n2 = *n - n1;
// B_TL B_TR
// 0 B_BR
const float *const B_TL = B;
const float *const B_TR = B + *ldB * n1;
const float *const B_BR = B + *ldB * n1 + n1;
// C_L C_R
float *const C_L = C;
float *const C_R = C + *ldC * n1;
if (*tranB == 'N') {
// recusion(A, B_TL, C_L)
RELAPACK_strsyl_rec(tranA, tranB, isgn, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, scale1, info1);
// C_R = C_R -/+ C_L * B_TR
BLAS(sgemm)("N", "N", m, &n2, &n1, MSGN, C_L, ldC, B_TR, ldB, scale1, C_R, ldC);
// recusion(A, B_BR, C_R)
RELAPACK_strsyl_rec(tranA, tranB, isgn, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, scale2, info2);
// apply scale
if (scale2[0] != 1)
LAPACK(slascl)("G", iONE, iONE, ONE, scale2, m, &n1, C_L, ldC, info);
} else {
// recusion(A, B_BR, C_R)
RELAPACK_strsyl_rec(tranA, tranB, isgn, m, &n2, A, ldA, B_BR, ldB, C_R, ldC, scale1, info1);
// C_L = C_L -/+ C_R * B_TR'
BLAS(sgemm)("N", "C", m, &n1, &n2, MSGN, C_R, ldC, B_TR, ldB, scale1, C_L, ldC);
// recusion(A, B_TL, C_L)
RELAPACK_strsyl_rec(tranA, tranB, isgn, m, &n1, A, ldA, B_TL, ldB, C_L, ldC, scale2, info2);
// apply scale
if (scale2[0] != 1)
LAPACK(slascl)("G", iONE, iONE, ONE, scale2, m, &n2, C_R, ldC, info);
}
}
*scale = scale1[0] * scale2[0];
*info = info1[0] || info2[0];
}