OpenBLAS/lapack/laed3/laed3_parallel.c

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#include <stdio.h>
#include "common.h"

#define max(a,b) ((a) > (b) ? (a) : (b))
#define copysign(x,y) ((y) < 0 ? ((x) < 0 ? (x) : -(x)) : ((x) < 0 ? -(x) : (x)))

#if defined(DOUBLE)
#define LAMC3  BLASFUNC(dlamc3)
#define LAED4  BLASFUNC(dlaed4)
#define GEMM   BLASFUNC(dgemm)
#define NRM2   BLASFUNC(dnrm2)
#define COPY   BLASFUNC(dcopy)
#define LACPY  BLASFUNC(dlacpy)
#define LASET  BLASFUNC(dlaset)
#else
#define LAMC3  BLASFUNC(slamc3)
#define LAED4  BLASFUNC(slaed4)
#define GEMM   BLASFUNC(sgemm)
#define NRM2   BLASFUNC(snrm2)
#define COPY   BLASFUNC(scopy)
#define LACPY  BLASFUNC(slacpy)
#define LASET  BLASFUNC(slaset)
#endif

FLOAT LAMC3(FLOAT *, FLOAT *);
void LAED4(blasint *, blasint *, FLOAT *, FLOAT *, FLOAT *, FLOAT *, FLOAT *, blasint *);
void LACPY(char *, blasint *, blasint *, FLOAT *, blasint *, FLOAT *, blasint *);
void LASET(char *, blasint *, blasint *, FLOAT *, FLOAT *, FLOAT *, blasint *);

/* Table of constant values */
static blasint c1 = 1;
static FLOAT c1f = 1.;
static FLOAT c0f = 0.;

static void inner_laed4_thread(blas_arg_t *args, BLASLONG *range_m, BLASLONG *range_n, FLOAT *sa, FLOAT *sb, BLASLONG mypos){
  blasint kval = args -> m;
  blasint j, j_from, j_to;
  FLOAT *dlamda = (FLOAT *)args -> a;
  FLOAT *w = (FLOAT *)args -> b;
  FLOAT *q = (FLOAT *)args -> c;
  BLASLONG qdim = args -> ldc;
  FLOAT *d = (FLOAT *)args -> d;
  FLOAT rho = *(FLOAT *)args -> alpha;
  blasint *info = &((blasint*)args -> beta)[mypos];

  j_from = range_m[0] + 1;
  j_to   = range_m[1];

  for (j = j_from; j <= j_to; j++) {
    LAED4(&kval, &j, dlamda, w, &q[(j - 1) * qdim], &rho, &d[j - 1], info);
    if(*info != 0) break;
  }
}

static void inner_wloop_thread(blas_arg_t *args, BLASLONG *range_m, BLASLONG *range_n, FLOAT *sa, FLOAT *sb, BLASLONG mypos){
  blasint kval = args -> m;
  blasint i, j, i_from, i_to;
  FLOAT *dlamda = (FLOAT *)args -> a;
  FLOAT *w = (FLOAT *)args -> b;
  FLOAT *q = (FLOAT *)args -> c;
  BLASLONG qdim = args -> ldc;
  i_from = range_m[0];
  i_to   = range_m[1];
  for (j = 0; j < kval; j++) {
    for (i = i_from; i < i_to; i++) {
      if (i != j) w[i] *= q[j * qdim + i] / (dlamda[i] - dlamda[j]);
    }
  }
}

/* ===================================================================== */
blasint CNAME(blasint *k, blasint *n, blasint *n1, FLOAT *d, 
        FLOAT *q, blasint *ldq, FLOAT *rho, FLOAT *dlamda,
        FLOAT *q2, blasint *indx, blasint *ctot, FLOAT *w, 
        FLOAT *s, blasint *info)
{
  FLOAT temp;
  blasint kval, qdim;
  blasint i, j, itmp;
  blasint n2, n12, ii, n23, iq2;
  blas_queue_t queue[MAX_CPU_NUMBER];
  blas_arg_t args;
  BLASLONG range[MAX_CPU_NUMBER + 1];
  blasint infoarray[MAX_CPU_NUMBER];
  int width, num_cpu, mode, nthreads;

  qdim = *ldq;
  kval = *k;

/*     Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */
/*     be computed with high relative accuracy (barring over/underflow). */

  for (i = 0; i < kval; i++) {
    dlamda[i] = LAMC3(&dlamda[i], &dlamda[i]) - dlamda[i];
  }

  nthreads = num_cpu_avail(4);

#if defined(DOUBLE)
  mode  =  BLAS_DOUBLE  | BLAS_REAL;
#else
  mode  =  BLAS_SINGLE  | BLAS_REAL;
#endif
  args.m = kval;
  args.a = (void *)dlamda;
  args.b = (void *)w;
  args.c = (void *)q;
  args.ldc = qdim;
  args.d = (void *)d;
  args.alpha = (void *)rho;
  args.beta = (void *)infoarray;
  num_cpu = 0;
  range[0] = 0;
  i = kval;
  while (i > 0) {
    width  = blas_quickdivide(i + nthreads - num_cpu - 1, nthreads - num_cpu);
    range[num_cpu + 1] = range[num_cpu] + width;
    queue[num_cpu].range_m = &range[num_cpu];
    queue[num_cpu].range_n = NULL;
    queue[num_cpu].routine = inner_laed4_thread;
    queue[num_cpu].args  = &args;
    queue[num_cpu].sa    = NULL;
    queue[num_cpu].sb    = NULL;
    queue[num_cpu].mode  = mode;
    queue[num_cpu].next  = &queue[num_cpu + 1];
    infoarray[num_cpu] = 0;
    num_cpu ++;
    i -= width;
  }
  if (num_cpu) {
    queue[num_cpu - 1].next = NULL;
    exec_blas(num_cpu, queue);
  }
  for (i = 0; i < num_cpu; i++) {
    *info = max(infoarray[i], *info);
  }

/*   If the zero finder fails, the computation is terminated. */

  if (*info != 0) {
    return 0;
  }

  if (kval == 2) {
    for (j = 0; j < kval; j++) {
      w[0] = q[j * qdim];
      w[1] = q[j * qdim + 1];
      ii = indx[0] - 1;
      q[j * qdim] = w[ii];
      ii = indx[1] - 1;
      q[j * qdim + 1] = w[ii];
    }
  } else if (kval != 1) {

/*   Compute updated W. */

    COPY(k, w, &c1, s, &c1);

/*   Initialize W(I) = Q(I,I) */

    itmp = qdim + 1;
    COPY(k, q, &itmp, w, &c1);

    for (i = 0; i < num_cpu; i++) {
      queue[i].routine = inner_wloop_thread;
    }
    if (num_cpu) {
      exec_blas(num_cpu, queue);
    }
    for (i = 0; i < kval; i++) {
      temp = sqrt(-w[i]);
      w[i] = copysign(temp, s[i]);
    }

/*   Compute eigenvectors of the modified rank-1 modification. */

    for (j = 0; j < kval; j++) {
      for (i = 0; i < kval; i++) {
        s[i] = w[i] / q[j * qdim + i];
      }
      temp = NRM2(k, s, &c1);
      for (i = 0; i < kval; i++) {
        ii = indx[i] - 1;
        q[j * qdim + i] = s[ii] / temp;
      }
    }
  }

/*   Compute the updated eigenvectors. */

  n2 = *n - *n1;
  n12 = ctot[0] + ctot[1];
  n23 = ctot[1] + ctot[2];

  LACPY("A", &n23, k, &q[ctot[0]], ldq, s, &n23);
  iq2 = *n1 * n12;
  if (n23 != 0) {
    GEMM("N", "N", &n2, k, &n23, &c1f, &q2[iq2], &n2, s, &n23, &c0f, &q[*n1], ldq);
  } else {
    LASET("A", &n2, k, &c0f, &c0f, &q[*n1], ldq);
  }

  LACPY("A", &n12, k, q, ldq, s, &n12);
  if (n12 != 0) {
    GEMM("N", "N", n1, k, &n12, &c1f, q2, n1, s, &n12, &c0f, q, ldq);
  } else {
    LASET("A", n1, k, &c0f, &c0f, q, ldq);
  }

  return 0;
}