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|
/*
** Zabbix
** Copyright (C) 2001-2019 Zabbix SIA
**
** This program is free software; you can redistribute it and/or modify
** it under the terms of the GNU General Public License as published by
** the Free Software Foundation; either version 2 of the License, or
** (at your option) any later version.
**
** This program is distributed in the hope that it will be useful,
** but WITHOUT ANY WARRANTY; without even the implied warranty of
** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
** GNU General Public License for more details.
**
** You should have received a copy of the GNU General Public License
** along with this program; if not, write to the Free Software
** Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
**/
#include "common.h"
#include "log.h"
#include "zbxalgo.h"
#define DB_INFINITY (1e12 - 1e-4)
#define ZBX_MATH_EPSILON (1e-6)
#define ZBX_IS_NAN(x) ((x) != (x))
#define ZBX_VALID_MATRIX(m) (0 < (m)->rows && 0 < (m)->columns && NULL != (m)->elements)
#define ZBX_MATRIX_EL(m, row, col) ((m)->elements[(row) * (m)->columns + (col)])
#define ZBX_MATRIX_ROW(m, row) ((m)->elements + (row) * (m)->columns)
typedef struct
{
int rows;
int columns;
double *elements;
}
zbx_matrix_t;
static void zbx_matrix_struct_alloc(zbx_matrix_t **pm)
{
*pm = (zbx_matrix_t *)zbx_malloc(*pm, sizeof(zbx_matrix_t));
(*pm)->rows = 0;
(*pm)->columns = 0;
(*pm)->elements = NULL;
}
static int zbx_matrix_alloc(zbx_matrix_t *m, int rows, int columns)
{
if (0 >= rows || 0 >= columns)
goto error;
m->rows = rows;
m->columns = columns;
m->elements = (double *)zbx_malloc(m->elements, sizeof(double) * rows * columns);
return SUCCEED;
error:
THIS_SHOULD_NEVER_HAPPEN;
return FAIL;
}
static void zbx_matrix_free(zbx_matrix_t *m)
{
if (NULL != m)
zbx_free(m->elements);
zbx_free(m);
}
static int zbx_matrix_copy(zbx_matrix_t *dest, zbx_matrix_t *src)
{
if (!ZBX_VALID_MATRIX(src))
goto error;
if (SUCCEED != zbx_matrix_alloc(dest, src->rows, src->columns))
return FAIL;
memcpy(dest->elements, src->elements, sizeof(double) * src->rows * src->columns);
return SUCCEED;
error:
THIS_SHOULD_NEVER_HAPPEN;
return FAIL;
}
static int zbx_identity_matrix(zbx_matrix_t *m, int n)
{
int i, j;
if (SUCCEED != zbx_matrix_alloc(m, n, n))
return FAIL;
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
ZBX_MATRIX_EL(m, i, j) = (i == j ? 1.0 : 0.0);
return SUCCEED;
}
static int zbx_transpose_matrix(zbx_matrix_t *m, zbx_matrix_t *r)
{
int i, j;
if (!ZBX_VALID_MATRIX(m))
goto error;
if (SUCCEED != zbx_matrix_alloc(r, m->columns, m->rows))
return FAIL;
for (i = 0; i < r->rows; i++)
for (j = 0; j < r->columns; j++)
ZBX_MATRIX_EL(r, i, j) = ZBX_MATRIX_EL(m, j, i);
return SUCCEED;
error:
THIS_SHOULD_NEVER_HAPPEN;
return FAIL;
}
static void zbx_matrix_swap_rows(zbx_matrix_t *m, int r1, int r2)
{
double tmp;
int i;
for (i = 0; i < m->columns; i++)
{
tmp = ZBX_MATRIX_EL(m, r1, i);
ZBX_MATRIX_EL(m, r1, i) = ZBX_MATRIX_EL(m, r2, i);
ZBX_MATRIX_EL(m, r2, i) = tmp;
}
}
static void zbx_matrix_divide_row_by(zbx_matrix_t *m, int row, double denominator)
{
int i;
for (i = 0; i < m->columns; i++)
ZBX_MATRIX_EL(m, row, i) /= denominator;
}
static void zbx_matrix_add_rows_with_factor(zbx_matrix_t *m, int dest, int src, double factor)
{
int i;
for (i = 0; i < m->columns; i++)
ZBX_MATRIX_EL(m, dest, i) += ZBX_MATRIX_EL(m, src, i) * factor;
}
static int zbx_inverse_matrix(zbx_matrix_t *m, zbx_matrix_t *r)
{
zbx_matrix_t *l = NULL;
double pivot, factor, det;
int i, j, k, n, res;
if (!ZBX_VALID_MATRIX(m) || m->rows != m->columns)
goto error;
n = m->rows;
if (1 == n)
{
if (SUCCEED != zbx_matrix_alloc(r, 1, 1))
return FAIL;
if (0.0 == ZBX_MATRIX_EL(m, 0, 0))
{
zabbix_log(LOG_LEVEL_DEBUG, "matrix is singular");
res = FAIL;
goto out;
}
ZBX_MATRIX_EL(r, 0, 0) = 1.0 / ZBX_MATRIX_EL(m, 0, 0);
return SUCCEED;
}
if (2 == n)
{
if (SUCCEED != zbx_matrix_alloc(r, 2, 2))
return FAIL;
if (0.0 == (det = ZBX_MATRIX_EL(m, 0, 0) * ZBX_MATRIX_EL(m, 1, 1) -
ZBX_MATRIX_EL(m, 0, 1) * ZBX_MATRIX_EL(m, 1, 0)))
{
zabbix_log(LOG_LEVEL_DEBUG, "matrix is singular");
res = FAIL;
goto out;
}
ZBX_MATRIX_EL(r, 0, 0) = ZBX_MATRIX_EL(m, 1, 1) / det;
ZBX_MATRIX_EL(r, 0, 1) = -ZBX_MATRIX_EL(m, 0, 1) / det;
ZBX_MATRIX_EL(r, 1, 0) = -ZBX_MATRIX_EL(m, 1, 0) / det;
ZBX_MATRIX_EL(r, 1, 1) = ZBX_MATRIX_EL(m, 0, 0) / det;
return SUCCEED;
}
if (SUCCEED != zbx_identity_matrix(r, n))
return FAIL;
zbx_matrix_struct_alloc(&l);
if (SUCCEED != (res = zbx_matrix_copy(l, m)))
goto out;
/* Gauss-Jordan elimination with partial (row) pivoting */
for (i = 0; i < n; i++)
{
k = i;
pivot = ZBX_MATRIX_EL(l, i, i);
for (j = i; j < n; j++)
{
if (fabs(ZBX_MATRIX_EL(l, j, i)) > fabs(pivot))
{
k = j;
pivot = ZBX_MATRIX_EL(l, j, i);
}
}
if (0.0 == pivot)
{
zabbix_log(LOG_LEVEL_DEBUG, "matrix is singular");
res = FAIL;
goto out;
}
if (k != i)
{
zbx_matrix_swap_rows(l, i, k);
zbx_matrix_swap_rows(r, i, k);
}
for (j = i + 1; j < n; j++)
{
if (0.0 != (factor = -ZBX_MATRIX_EL(l, j, i) / ZBX_MATRIX_EL(l, i, i)))
{
zbx_matrix_add_rows_with_factor(l, j, i, factor);
zbx_matrix_add_rows_with_factor(r, j, i, factor);
}
}
}
for (i = n - 1; i > 0; i--)
{
for (j = 0; j < i; j++)
{
if (0.0 != (factor = -ZBX_MATRIX_EL(l, j, i) / ZBX_MATRIX_EL(l, i, i)))
{
zbx_matrix_add_rows_with_factor(l, j, i, factor);
zbx_matrix_add_rows_with_factor(r, j, i, factor);
}
}
}
for (i = 0; i < n; i++)
zbx_matrix_divide_row_by(r, i, ZBX_MATRIX_EL(l, i, i));
res = SUCCEED;
out:
zbx_matrix_free(l);
return res;
error:
THIS_SHOULD_NEVER_HAPPEN;
return FAIL;
}
static int zbx_matrix_mult(zbx_matrix_t *left, zbx_matrix_t *right, zbx_matrix_t *result)
{
double element;
int i, j, k;
if (!ZBX_VALID_MATRIX(left) || !ZBX_VALID_MATRIX(right) || left->columns != right->rows)
goto error;
if (SUCCEED != zbx_matrix_alloc(result, left->rows, right->columns))
return FAIL;
for (i = 0; i < result->rows; i++)
{
for (j = 0; j < result->columns; j++)
{
element = 0;
for (k = 0; k < left->columns; k++)
element += ZBX_MATRIX_EL(left, i, k) * ZBX_MATRIX_EL(right, k, j);
ZBX_MATRIX_EL(result, i, j) = element;
}
}
return SUCCEED;
error:
THIS_SHOULD_NEVER_HAPPEN;
return FAIL;
}
static int zbx_least_squares(zbx_matrix_t *independent, zbx_matrix_t *dependent, zbx_matrix_t *coefficients)
{
/* |<----------to_be_inverted---------->| */
/* coefficients = inverse( transpose( independent ) * independent ) * transpose( independent ) * dependent */
/* |<------------------left_part------------------>| |<-----------right_part----------->| */
/* we change order of matrix multiplication to reduce operation count and memory usage */
zbx_matrix_t *independent_transposed = NULL, *to_be_inverted = NULL, *left_part = NULL, *right_part = NULL;
int res;
zbx_matrix_struct_alloc(&independent_transposed);
zbx_matrix_struct_alloc(&to_be_inverted);
zbx_matrix_struct_alloc(&left_part);
zbx_matrix_struct_alloc(&right_part);
if (SUCCEED != (res = zbx_transpose_matrix(independent, independent_transposed)))
goto out;
if (SUCCEED != (res = zbx_matrix_mult(independent_transposed, independent, to_be_inverted)))
goto out;
if (SUCCEED != (res = zbx_inverse_matrix(to_be_inverted, left_part)))
goto out;
if (SUCCEED != (res = zbx_matrix_mult(independent_transposed, dependent, right_part)))
goto out;
if (SUCCEED != (res = zbx_matrix_mult(left_part, right_part, coefficients)))
goto out;
out:
zbx_matrix_free(independent_transposed);
zbx_matrix_free(to_be_inverted);
zbx_matrix_free(left_part);
zbx_matrix_free(right_part);
return res;
}
static int zbx_fill_dependent(double *x, int n, zbx_fit_t fit, zbx_matrix_t *m)
{
int i;
if (FIT_LINEAR == fit || FIT_POLYNOMIAL == fit || FIT_LOGARITHMIC == fit)
{
if (SUCCEED != zbx_matrix_alloc(m, n, 1))
return FAIL;
for (i = 0; i < n; i++)
ZBX_MATRIX_EL(m, i, 0) = x[i];
}
else if (FIT_EXPONENTIAL == fit || FIT_POWER == fit)
{
if (SUCCEED != zbx_matrix_alloc(m, n, 1))
return FAIL;
for (i = 0; i < n; i++)
{
if (0.0 >= x[i])
{
zabbix_log(LOG_LEVEL_DEBUG, "data contains negative or zero values");
return FAIL;
}
ZBX_MATRIX_EL(m, i, 0) = log(x[i]);
}
}
return SUCCEED;
}
static int zbx_fill_independent(double *t, int n, zbx_fit_t fit, int k, zbx_matrix_t *m)
{
double element;
int i, j;
if (FIT_LINEAR == fit || FIT_EXPONENTIAL == fit)
{
if (SUCCEED != zbx_matrix_alloc(m, n, 2))
return FAIL;
for (i = 0; i < n; i++)
{
ZBX_MATRIX_EL(m, i, 0) = 1.0;
ZBX_MATRIX_EL(m, i, 1) = t[i];
}
}
else if (FIT_LOGARITHMIC == fit || FIT_POWER == fit)
{
if (SUCCEED != zbx_matrix_alloc(m, n, 2))
return FAIL;
for (i = 0; i < n; i++)
{
ZBX_MATRIX_EL(m, i, 0) = 1.0;
ZBX_MATRIX_EL(m, i, 1) = log(t[i]);
}
}
else if (FIT_POLYNOMIAL == fit)
{
if (k > n - 1)
k = n - 1;
if (SUCCEED != zbx_matrix_alloc(m, n, k+1))
return FAIL;
for (i = 0; i < n; i++)
{
element = 1.0;
for (j = 0; j < k; j++)
{
ZBX_MATRIX_EL(m, i, j) = element;
element *= t[i];
}
ZBX_MATRIX_EL(m, i, k) = element;
}
}
return SUCCEED;
}
static int zbx_regression(double *t, double *x, int n, zbx_fit_t fit, int k, zbx_matrix_t *coefficients)
{
zbx_matrix_t *independent = NULL, *dependent = NULL;
int res;
zbx_matrix_struct_alloc(&independent);
zbx_matrix_struct_alloc(&dependent);
if (SUCCEED != (res = zbx_fill_independent(t, n, fit, k, independent)))
goto out;
if (SUCCEED != (res = zbx_fill_dependent(x, n, fit, dependent)))
goto out;
if (SUCCEED != (res = zbx_least_squares(independent, dependent, coefficients)))
goto out;
out:
zbx_matrix_free(independent);
zbx_matrix_free(dependent);
return res;
}
static double zbx_polynomial_value(double t, zbx_matrix_t *coefficients)
{
double pow = 1.0, res = 0.0;
int i;
for (i = 0; i < coefficients->rows; i++, pow *= t)
res += ZBX_MATRIX_EL(coefficients, i, 0) * pow;
return res;
}
static double zbx_polynomial_antiderivative(double t, zbx_matrix_t *coefficients)
{
double pow = t, res = 0.0;
int i;
for (i = 0; i < coefficients->rows; i++, pow *= t)
res += ZBX_MATRIX_EL(coefficients, i, 0) * pow / (i + 1);
return res;
}
static int zbx_derive_polynomial(zbx_matrix_t *polynomial, zbx_matrix_t *derivative)
{
int i;
if (!ZBX_VALID_MATRIX(polynomial))
goto error;
if (SUCCEED != zbx_matrix_alloc(derivative, (polynomial->rows > 1 ? polynomial->rows - 1 : 1), 1))
return FAIL;
for (i = 1; i < polynomial->rows; i++)
ZBX_MATRIX_EL(derivative, i - 1, 0) = ZBX_MATRIX_EL(polynomial, i, 0) * i;
if (1 == i)
ZBX_MATRIX_EL(derivative, 0, 0) = 0.0;
return SUCCEED;
error:
THIS_SHOULD_NEVER_HAPPEN;
return FAIL;
}
static int zbx_polynomial_roots(zbx_matrix_t *coefficients, zbx_matrix_t *roots)
{
#define Re(z) (z)[0]
#define Im(z) (z)[1]
#define ZBX_COMPLEX_MULT(z1, z2, tmp) \
do \
{ \
Re(tmp) = Re(z1) * Re(z2) - Im(z1) * Im(z2); \
Im(tmp) = Re(z1) * Im(z2) + Im(z1) * Re(z2); \
Re(z1) = Re(tmp); \
Im(z1) = Im(tmp); \
} \
while(0)
#define ZBX_MAX_ITERATIONS 200
zbx_matrix_t *denominator_multiplicands = NULL, *updates = NULL;
double z[2], mult[2], denominator[2], zpower[2], polynomial[2], highest_degree_coefficient,
lower_bound, upper_bound, radius, max_update, min_distance, residual, temp;
int i, j, degree, first_nonzero, res, iteration = 0, roots_ok = 0, root_init = 0;
if (!ZBX_VALID_MATRIX(coefficients))
goto error;
degree = coefficients->rows - 1;
highest_degree_coefficient = ZBX_MATRIX_EL(coefficients, degree, 0);
while (0.0 == highest_degree_coefficient && 0 < degree)
highest_degree_coefficient = ZBX_MATRIX_EL(coefficients, --degree, 0);
if (0 == degree)
{
/* please check explicitly for an attempt to solve equation 0 == 0 */
if (0.0 == highest_degree_coefficient)
goto error;
return SUCCEED;
}
if (1 == degree)
{
if (SUCCEED != zbx_matrix_alloc(roots, 1, 2))
return FAIL;
Re(ZBX_MATRIX_ROW(roots, 0)) = -ZBX_MATRIX_EL(coefficients, 0, 0) / ZBX_MATRIX_EL(coefficients, 1, 0);
Im(ZBX_MATRIX_ROW(roots, 0)) = 0.0;
return SUCCEED;
}
if (2 == degree)
{
if (SUCCEED != zbx_matrix_alloc(roots, 2, 2))
return FAIL;
if (0.0 < (temp = ZBX_MATRIX_EL(coefficients, 1, 0) * ZBX_MATRIX_EL(coefficients, 1, 0) -
4 * ZBX_MATRIX_EL(coefficients, 2, 0) * ZBX_MATRIX_EL(coefficients, 0, 0)))
{
temp = (0 < ZBX_MATRIX_EL(coefficients, 1, 0) ?
-ZBX_MATRIX_EL(coefficients, 1, 0) - sqrt(temp) :
-ZBX_MATRIX_EL(coefficients, 1, 0) + sqrt(temp));
Re(ZBX_MATRIX_ROW(roots, 0)) = 0.5 * temp / ZBX_MATRIX_EL(coefficients, 2, 0);
Re(ZBX_MATRIX_ROW(roots, 1)) = 2.0 * ZBX_MATRIX_EL(coefficients, 0, 0) / temp;
Im(ZBX_MATRIX_ROW(roots, 0)) = Im(ZBX_MATRIX_ROW(roots, 1)) = 0.0;
}
else
{
Re(ZBX_MATRIX_ROW(roots, 0)) = Re(ZBX_MATRIX_ROW(roots, 1)) =
-0.5 * ZBX_MATRIX_EL(coefficients, 1, 0) / ZBX_MATRIX_EL(coefficients, 2, 0);
Im(ZBX_MATRIX_ROW(roots, 0)) = -(Im(ZBX_MATRIX_ROW(roots, 1)) = 0.5 * sqrt(-temp)) /
ZBX_MATRIX_EL(coefficients, 2, 0);
}
return SUCCEED;
}
zbx_matrix_struct_alloc(&denominator_multiplicands);
zbx_matrix_struct_alloc(&updates);
if (SUCCEED != zbx_matrix_alloc(roots, degree, 2) ||
SUCCEED != zbx_matrix_alloc(denominator_multiplicands, degree, 2) ||
SUCCEED != zbx_matrix_alloc(updates, degree, 2))
{
res = FAIL;
goto out;
}
/* if n lower coefficients are zeros, zero is a root of multiplicity n */
for (first_nonzero = 0; 0.0 == ZBX_MATRIX_EL(coefficients, first_nonzero, 0); first_nonzero++)
Re(ZBX_MATRIX_ROW(roots, first_nonzero)) = Im(ZBX_MATRIX_ROW(roots, first_nonzero)) = 0.0;
/* compute bounds for the roots */
upper_bound = lower_bound = 1.0;
for (i = first_nonzero; i < degree; i++)
{
if (upper_bound < fabs(ZBX_MATRIX_EL(coefficients, i, 0) / highest_degree_coefficient))
upper_bound = fabs(ZBX_MATRIX_EL(coefficients, i, 0) / highest_degree_coefficient);
if (lower_bound < fabs(ZBX_MATRIX_EL(coefficients, i + 1, 0) /
ZBX_MATRIX_EL(coefficients, first_nonzero, 0)))
lower_bound = fabs(ZBX_MATRIX_EL(coefficients, i + 1, 0) /
ZBX_MATRIX_EL(coefficients, first_nonzero, 0));
}
radius = lower_bound = 1.0 / lower_bound;
/* Weierstrass (Durand-Kerner) method */
while (ZBX_MAX_ITERATIONS >= ++iteration && !roots_ok)
{
if (0 == root_init)
{
if (radius <= upper_bound)
{
for (i = 0; i < degree - first_nonzero; i++)
{
Re(ZBX_MATRIX_ROW(roots, i)) = radius * cos((2.0 * M_PI * (i + 0.25)) /
(degree - first_nonzero));
Im(ZBX_MATRIX_ROW(roots, i)) = radius * sin((2.0 * M_PI * (i + 0.25)) /
(degree - first_nonzero));
}
radius *= 2.0;
}
else
root_init = 1;
}
roots_ok = 1;
max_update = 0.0;
min_distance = HUGE_VAL;
for (i = first_nonzero; i < degree; i++)
{
Re(z) = Re(ZBX_MATRIX_ROW(roots, i));
Im(z) = Im(ZBX_MATRIX_ROW(roots, i));
/* subtract from z every one of denominator_multiplicands and multiplicate them */
Re(denominator) = highest_degree_coefficient;
Im(denominator) = 0.0;
for (j = first_nonzero; j < degree; j++)
{
if (j == i)
continue;
temp = (ZBX_MATRIX_EL(roots, i, 0) - ZBX_MATRIX_EL(roots, j, 0)) *
(ZBX_MATRIX_EL(roots, i, 0) - ZBX_MATRIX_EL(roots, j, 0)) +
(ZBX_MATRIX_EL(roots, i, 1) - ZBX_MATRIX_EL(roots, j, 1)) *
(ZBX_MATRIX_EL(roots, i, 1) - ZBX_MATRIX_EL(roots, j, 1));
if (temp < min_distance)
min_distance = temp;
Re(ZBX_MATRIX_ROW(denominator_multiplicands, j)) = Re(z) - Re(ZBX_MATRIX_ROW(roots, j));
Im(ZBX_MATRIX_ROW(denominator_multiplicands, j)) = Im(z) - Im(ZBX_MATRIX_ROW(roots, j));
ZBX_COMPLEX_MULT(denominator, ZBX_MATRIX_ROW(denominator_multiplicands, j), mult);
}
/* calculate complex value of polynomial for z */
Re(zpower) = 1.0;
Im(zpower) = 0.0;
Re(polynomial) = ZBX_MATRIX_EL(coefficients, first_nonzero, 0);
Im(polynomial) = 0.0;
for (j = first_nonzero + 1; j <= degree; j++)
{
ZBX_COMPLEX_MULT(zpower, z, mult);
Re(polynomial) += Re(zpower) * ZBX_MATRIX_EL(coefficients, j, 0);
Im(polynomial) += Im(zpower) * ZBX_MATRIX_EL(coefficients, j, 0);
}
/* check how good root approximation is */
residual = fabs(Re(polynomial)) + fabs(Im(polynomial));
roots_ok = roots_ok && (ZBX_MATH_EPSILON > residual);
/* divide polynomial value by denominator */
if (0.0 != (temp = Re(denominator) * Re(denominator) + Im(denominator) * Im(denominator)))
{
Re(ZBX_MATRIX_ROW(updates, i)) = (Re(polynomial) * Re(denominator) +
Im(polynomial) * Im(denominator)) / temp;
Im(ZBX_MATRIX_ROW(updates, i)) = (Im(polynomial) * Re(denominator) -
Re(polynomial) * Im(denominator)) / temp;
}
else /* Denominator is zero iff two or more root approximations are equal. */
/* Since root approximations are initially different their equality means that they */
/* converged to a multiple root (hopefully) and no updates are required in this case. */
{
Re(ZBX_MATRIX_ROW(updates, i)) = Im(ZBX_MATRIX_ROW(updates, i)) = 0.0;
}
temp = ZBX_MATRIX_EL(updates, i, 0) * ZBX_MATRIX_EL(updates, i, 0) +
ZBX_MATRIX_EL(updates, i, 1) * ZBX_MATRIX_EL(updates, i, 1);
if (temp > max_update)
max_update = temp;
}
if (max_update > radius * radius && 0 == root_init)
continue;
else
root_init = 1;
for (i = first_nonzero; i < degree; i++)
{
Re(ZBX_MATRIX_ROW(roots, i)) -= Re(ZBX_MATRIX_ROW(updates, i));
Im(ZBX_MATRIX_ROW(roots, i)) -= Im(ZBX_MATRIX_ROW(updates, i));
}
}
if (0 == roots_ok)
{
zabbix_log(LOG_LEVEL_DEBUG, "polynomial root finding problem is ill-defined");
res = FAIL;
}
else
res = SUCCEED;
out:
zbx_matrix_free(denominator_multiplicands);
zbx_matrix_free(updates);
return res;
error:
THIS_SHOULD_NEVER_HAPPEN;
return FAIL;
#undef ZBX_MAX_ITERATIONS
#undef Re
#undef Im
}
static int zbx_polynomial_minmax(double now, double time, zbx_mode_t mode, zbx_matrix_t *coefficients,
double *result)
{
zbx_matrix_t *derivative = NULL, *derivative_roots = NULL;
double min, max, tmp;
int i, res;
if (!ZBX_VALID_MATRIX(coefficients))
goto error;
zbx_matrix_struct_alloc(&derivative);
zbx_matrix_struct_alloc(&derivative_roots);
if (SUCCEED != (res = zbx_derive_polynomial(coefficients, derivative)))
goto out;
if (SUCCEED != (res = zbx_polynomial_roots(derivative, derivative_roots)))
goto out;
/* choose min and max among now, now + time and derivative roots inbetween (these are potential local extrema) */
/* we ignore imaginary part of roots, this means that more calculations will be made, */
/* but result will not be affected and we wont need a boundary on minimal imaginary part that differs from zero */
min = zbx_polynomial_value(now, coefficients);
tmp = zbx_polynomial_value(now + time, coefficients);
if (tmp < min)
{
max = min;
min = tmp;
}
else
max = tmp;
for (i = 0; i < derivative_roots->rows; i++)
{
tmp = ZBX_MATRIX_EL(derivative_roots, i, 0);
if (tmp < now || tmp > now + time)
continue;
tmp = zbx_polynomial_value(tmp, coefficients);
if (tmp < min)
min = tmp;
else if (tmp > max)
max = tmp;
}
if (MODE_MAX == mode)
*result = max;
else if (MODE_MIN == mode)
*result = min;
else if (MODE_DELTA == mode)
*result = max - min;
else
THIS_SHOULD_NEVER_HAPPEN;
out:
zbx_matrix_free(derivative);
zbx_matrix_free(derivative_roots);
return res;
error:
THIS_SHOULD_NEVER_HAPPEN;
return FAIL;
}
static int zbx_polynomial_timeleft(double now, double threshold, zbx_matrix_t *coefficients, double *result)
{
zbx_matrix_t *shifted_coefficients = NULL, *roots = NULL;
double tmp;
int i, res, no_root = 1;
if (!ZBX_VALID_MATRIX(coefficients))
goto error;
zbx_matrix_struct_alloc(&shifted_coefficients);
zbx_matrix_struct_alloc(&roots);
if (SUCCEED != (res = zbx_matrix_copy(shifted_coefficients, coefficients)))
goto out;
ZBX_MATRIX_EL(shifted_coefficients, 0, 0) -= threshold;
if (SUCCEED != (res = zbx_polynomial_roots(shifted_coefficients, roots)))
goto out;
/* choose the closest root right from now or set result to -1 otherwise */
/* if zbx_polynomial_value(tmp) is not close enough to zero it must be a complex root and must be skipped */
for (i = 0; i < roots->rows; i++)
{
tmp = ZBX_MATRIX_EL(roots, i, 0);
if (no_root)
{
if (tmp > now && ZBX_MATH_EPSILON > fabs(zbx_polynomial_value(tmp, shifted_coefficients)))
{
no_root = 0;
*result = tmp;
}
}
else if (now < tmp && tmp < *result &&
ZBX_MATH_EPSILON > fabs(zbx_polynomial_value(tmp, shifted_coefficients)))
{
*result = tmp;
}
}
if (no_root)
*result = DB_INFINITY;
else
*result -= now;
out:
zbx_matrix_free(shifted_coefficients);
zbx_matrix_free(roots);
return res;
error:
THIS_SHOULD_NEVER_HAPPEN;
return FAIL;
}
static int zbx_calculate_value(double t, zbx_matrix_t *coefficients, zbx_fit_t fit, double *value)
{
if (!ZBX_VALID_MATRIX(coefficients))
goto error;
if (FIT_LINEAR == fit)
*value = ZBX_MATRIX_EL(coefficients, 0, 0) + ZBX_MATRIX_EL(coefficients, 1, 0) * t;
else if (FIT_POLYNOMIAL == fit)
*value = zbx_polynomial_value(t, coefficients);
else if (FIT_EXPONENTIAL == fit)
*value = exp(ZBX_MATRIX_EL(coefficients, 0, 0) + ZBX_MATRIX_EL(coefficients, 1, 0) * t);
else if (FIT_LOGARITHMIC == fit)
*value = ZBX_MATRIX_EL(coefficients, 0, 0) + ZBX_MATRIX_EL(coefficients, 1, 0) * log(t);
else if (FIT_POWER == fit)
*value = exp(ZBX_MATRIX_EL(coefficients, 0, 0) + ZBX_MATRIX_EL(coefficients, 1, 0) * log(t));
else
goto error;
return SUCCEED;
error:
THIS_SHOULD_NEVER_HAPPEN;
return FAIL;
}
int zbx_fit_code(char *fit_str, zbx_fit_t *fit, unsigned *k, char **error)
{
if ('\0' == *fit_str || 0 == strcmp(fit_str, "linear"))
{
*fit = FIT_LINEAR;
*k = 0;
}
else if (0 == strncmp(fit_str, "polynomial", strlen("polynomial")))
{
*fit = FIT_POLYNOMIAL;
if (SUCCEED != is_uint_range(fit_str + strlen("polynomial"), k, 1, 6))
{
*error = zbx_strdup(*error, "polynomial degree is invalid");
return FAIL;
}
}
else if (0 == strcmp(fit_str, "exponential"))
{
*fit = FIT_EXPONENTIAL;
*k = 0;
}
else if (0 == strcmp(fit_str, "logarithmic"))
{
*fit = FIT_LOGARITHMIC;
*k = 0;
}
else if (0 == strcmp(fit_str, "power"))
{
*fit = FIT_POWER;
*k = 0;
}
else
{
*error = zbx_strdup(*error, "invalid 'fit' parameter");
return FAIL;
}
return SUCCEED;
}
int zbx_mode_code(char *mode_str, zbx_mode_t *mode, char **error)
{
if ('\0' == *mode_str || 0 == strcmp(mode_str, "value"))
{
*mode = MODE_VALUE;
}
else if (0 == strcmp(mode_str, "max"))
{
*mode = MODE_MAX;
}
else if (0 == strcmp(mode_str, "min"))
{
*mode = MODE_MIN;
}
else if (0 == strcmp(mode_str, "delta"))
{
*mode = MODE_DELTA;
}
else if (0 == strcmp(mode_str, "avg"))
{
*mode = MODE_AVG;
}
else
{
*error = zbx_strdup(*error, "invalid 'mode' parameter");
return FAIL;
}
return SUCCEED;
}
static void zbx_log_expression(double now, zbx_fit_t fit, int k, zbx_matrix_t *coeffs)
{
/* x is item value, t is time in seconds counted from now */
if (FIT_LINEAR == fit)
{
zabbix_log(LOG_LEVEL_DEBUG, "fitted expression is: x = (" ZBX_FS_DBL ") + (" ZBX_FS_DBL ") * (" ZBX_FS_DBL " + t)",
ZBX_MATRIX_EL(coeffs, 0, 0), ZBX_MATRIX_EL(coeffs, 1, 0), now);
}
else if (FIT_POLYNOMIAL == fit)
{
char *polynomial = NULL;
size_t alloc, offset;
while (0 <= k)
{
zbx_snprintf_alloc(&polynomial, &alloc, &offset, "(" ZBX_FS_DBL ") * (" ZBX_FS_DBL " + t) ^ %d",
ZBX_MATRIX_EL(coeffs, k, 0), now, k);
if (0 < k--)
zbx_snprintf_alloc(&polynomial, &alloc, &offset, " + ");
}
zabbix_log(LOG_LEVEL_DEBUG, "fitted expression is: x = %s", polynomial);
zbx_free(polynomial);
}
else if (FIT_EXPONENTIAL == fit)
{
zabbix_log(LOG_LEVEL_DEBUG, "fitted expression is: x = (" ZBX_FS_DBL ") * exp( (" ZBX_FS_DBL ") * (" ZBX_FS_DBL " + t) )",
exp(ZBX_MATRIX_EL(coeffs, 0, 0)), ZBX_MATRIX_EL(coeffs, 1, 0), now);
}
else if (FIT_LOGARITHMIC == fit)
{
zabbix_log(LOG_LEVEL_DEBUG, "fitted expression is: x = (" ZBX_FS_DBL ") + (" ZBX_FS_DBL ") * log(" ZBX_FS_DBL " + t)",
ZBX_MATRIX_EL(coeffs, 0, 0), ZBX_MATRIX_EL(coeffs, 1, 0), now);
}
else if (FIT_POWER == fit)
{
zabbix_log(LOG_LEVEL_DEBUG, "fitted expression is: x = (" ZBX_FS_DBL ") * (" ZBX_FS_DBL " + t) ^ (" ZBX_FS_DBL ")",
exp(ZBX_MATRIX_EL(coeffs, 0, 0)), now, ZBX_MATRIX_EL(coeffs, 1, 0));
}
else
THIS_SHOULD_NEVER_HAPPEN;
}
double zbx_forecast(double *t, double *x, int n, double now, double time, zbx_fit_t fit, unsigned k, zbx_mode_t mode)
{
zbx_matrix_t *coefficients = NULL;
double left, right, result;
int res;
if (1 == n)
{
if (MODE_VALUE == mode || MODE_MAX == mode || MODE_MIN == mode || MODE_AVG == mode)
return x[0];
if (MODE_DELTA == mode)
return 0.0;
THIS_SHOULD_NEVER_HAPPEN;
return ZBX_MATH_ERROR;
}
zbx_matrix_struct_alloc(&coefficients);
if (SUCCEED != (res = zbx_regression(t, x, n, fit, k, coefficients)))
goto out;
zbx_log_expression(now, fit, (int)k, coefficients);
if (MODE_VALUE == mode)
{
res = zbx_calculate_value(now + time, coefficients, fit, &result);
goto out;
}
if (0.0 == time)
{
if (MODE_MAX == mode || MODE_MIN == mode || MODE_AVG == mode)
{
res = zbx_calculate_value(now + time, coefficients, fit, &result);
}
else if (MODE_DELTA == mode)
{
result = 0.0;
res = SUCCEED;
}
else
{
THIS_SHOULD_NEVER_HAPPEN;
res = FAIL;
}
goto out;
}
if (FIT_LINEAR == fit || FIT_EXPONENTIAL == fit || FIT_LOGARITHMIC == fit || FIT_POWER == fit)
{
/* fit is monotone, therefore maximum and minimum are either at now or at now + time */
if (SUCCEED != zbx_calculate_value(now, coefficients, fit, &left) ||
SUCCEED != zbx_calculate_value(now + time, coefficients, fit, &right))
{
res = FAIL;
goto out;
}
if (MODE_MAX == mode)
{
result = (left > right ? left : right);
}
else if (MODE_MIN == mode)
{
result = (left < right ? left : right);
}
else if (MODE_DELTA == mode)
{
result = (left > right ? left - right : right - left);
}
else if (MODE_AVG == mode)
{
if (FIT_LINEAR == fit)
{
result = 0.5 * (left + right);
}
else if (FIT_EXPONENTIAL == fit)
{
result = (right - left) / time / ZBX_MATRIX_EL(coefficients, 1, 0);
}
else if (FIT_LOGARITHMIC == fit)
{
result = right + ZBX_MATRIX_EL(coefficients, 1, 0) *
(log(1.0 + time / now) * now / time - 1.0);
}
else if (FIT_POWER == fit)
{
if (-1.0 != ZBX_MATRIX_EL(coefficients, 1, 0))
result = (right * (now + time) - left * now) / time /
(ZBX_MATRIX_EL(coefficients, 1, 0) + 1.0);
else
result = exp(ZBX_MATRIX_EL(coefficients, 0, 0)) * log(1.0 + time / now) / time;
}
else
{
THIS_SHOULD_NEVER_HAPPEN;
res = FAIL;
goto out;
}
}
else
{
THIS_SHOULD_NEVER_HAPPEN;
res = FAIL;
goto out;
}
res = SUCCEED;
}
else if (FIT_POLYNOMIAL == fit)
{
if (MODE_MAX == mode || MODE_MIN == mode || MODE_DELTA == mode)
{
res = zbx_polynomial_minmax(now, time, mode, coefficients, &result);
}
else if (MODE_AVG == mode)
{
result = (zbx_polynomial_antiderivative(now + time, coefficients) -
zbx_polynomial_antiderivative(now, coefficients)) / time;
res = SUCCEED;
}
else
{
THIS_SHOULD_NEVER_HAPPEN;
res = FAIL;
}
}
else
{
THIS_SHOULD_NEVER_HAPPEN;
res = FAIL;
}
out:
zbx_matrix_free(coefficients);
if (SUCCEED != res)
{
result = ZBX_MATH_ERROR;
}
else if (ZBX_IS_NAN(result))
{
zabbix_log(LOG_LEVEL_DEBUG, "numerical error");
result = ZBX_MATH_ERROR;
}
else if (DB_INFINITY < result)
{
result = DB_INFINITY;
}
else if (-DB_INFINITY > result)
{
result = -DB_INFINITY;
}
return result;
}
double zbx_timeleft(double *t, double *x, int n, double now, double threshold, zbx_fit_t fit, unsigned k)
{
zbx_matrix_t *coefficients = NULL;
double current, result;
int res;
if (1 == n)
return (x[0] == threshold ? 0.0 : DB_INFINITY);
zbx_matrix_struct_alloc(&coefficients);
if (SUCCEED != (res = zbx_regression(t, x, n, fit, k, coefficients)))
goto out;
zbx_log_expression(now, fit, (int)k, coefficients);
if (SUCCEED != (res = zbx_calculate_value(now, coefficients, fit, ¤t)))
{
goto out;
}
else if (current == threshold)
{
result = 0.0;
goto out;
}
if (FIT_LINEAR == fit)
{
result = (threshold - ZBX_MATRIX_EL(coefficients, 0, 0)) / ZBX_MATRIX_EL(coefficients, 1, 0) - now;
}
else if (FIT_POLYNOMIAL == fit)
{
res = zbx_polynomial_timeleft(now, threshold, coefficients, &result);
}
else if (FIT_EXPONENTIAL == fit)
{
result = (log(threshold) - ZBX_MATRIX_EL(coefficients, 0, 0)) / ZBX_MATRIX_EL(coefficients, 1, 0) - now;
}
else if (FIT_LOGARITHMIC == fit)
{
result = exp((threshold - ZBX_MATRIX_EL(coefficients, 0, 0)) / ZBX_MATRIX_EL(coefficients, 1, 0)) - now;
}
else if (FIT_POWER == fit)
{
result = exp((log(threshold) - ZBX_MATRIX_EL(coefficients, 0, 0)) / ZBX_MATRIX_EL(coefficients, 1, 0))
- now;
}
else
{
THIS_SHOULD_NEVER_HAPPEN;
res = FAIL;
}
out:
if (SUCCEED != res)
{
result = ZBX_MATH_ERROR;
}
else if (ZBX_IS_NAN(result))
{
zabbix_log(LOG_LEVEL_DEBUG, "numerical error");
result = ZBX_MATH_ERROR;
}
else if (0.0 > result || DB_INFINITY < result)
{
result = DB_INFINITY;
}
zbx_matrix_free(coefficients);
return result;
}
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