matrix_ops.c

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/*************************************************************************
 * Copyright (c) 2011 AT&T Intellectual Property 
 * All rights reserved. This program and the accompanying materials
 * are made available under the terms of the Eclipse Public License v1.0
 * which accompanies this distribution, and is available at
 * https://www.eclipse.org/legal/epl-v10.html
 *
 * Contributors: Details at https://graphviz.org
 *************************************************************************/
 
#include <neatogen/matrix_ops.h>
#include <stdbool.h>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <util/alloc.h>
 
static const double p_iteration_threshold = 1e-3;
 
bool power_iteration(double *const *square_mat, int n, int neigs, double **eigs) {
    /* compute the 'neigs' top eigenvectors of 'square_mat' using power iteration */
 
    int i;
    double *tmp_vec = gv_calloc(n, sizeof(double));
    double *last_vec = gv_calloc(n, sizeof(double));
    double angle;
    int iteration = 0;
    const int Max_iterations = 30 * n;
 
    double tol = 1 - p_iteration_threshold;
 
    if (neigs >= n) {
        neigs = n;
    }
 
    double *const evals = gv_calloc(neigs, sizeof(evals[0]));
    for (i = 0; i < neigs; i++) {
        double *const curr_vector = eigs[i];
        /* guess the i-th eigen vector */
      choose:
        for (int j = 0; j < n; j++)
            curr_vector[j] = rand() % 100;
        /* orthogonalize against higher eigenvectors */
        for (int j = 0; j < i; j++) {
            const double alpha = -vectors_inner_product(n, eigs[j], curr_vector);
            scadd(curr_vector, n - 1, alpha, eigs[j]);
        }
        double len = norm(curr_vector, n - 1);
        if (len < 1e-10) {
            // we have chosen a vector colinear with previous ones
            goto choose;
        }
        vectors_scalar_mult(n, curr_vector, 1.0 / len, curr_vector);
        iteration = 0;
        do {
            iteration++;
            copy_vector(n, curr_vector, last_vec);
 
            right_mult_with_vector_d(square_mat, n, n, curr_vector,
                                     tmp_vec);
            copy_vector(n, tmp_vec, curr_vector);
 
            /* orthogonalize against higher eigenvectors */
            for (int j = 0; j < i; j++) {
                const double alpha = -vectors_inner_product(n, eigs[j], curr_vector);
                scadd(curr_vector, n - 1, alpha, eigs[j]);
            }
            len = norm(curr_vector, n - 1);
            if (len < 1e-10 || iteration > Max_iterations) {
                /* We have reached the null space (e.vec. associated with e.val. 0) */
                goto exit;
            }
 
            vectors_scalar_mult(n, curr_vector, 1.0 / len, curr_vector);
            angle = vectors_inner_product(n, curr_vector, last_vec);
        } while (fabs(angle) < tol);
        evals[i] = angle * len; /* this is the Rayleigh quotient (up to errors due to orthogonalization):
                                   u*(A*u)/||A*u||)*||A*u||, where u=last_vec, and ||u||=1
                                 */
    }
  exit:
    for (; i < neigs; i++) {
        /* compute the smallest eigenvector, which are  */
        /* probably associated with eigenvalue 0 and for */
        /* which power-iteration is dangerous */
        double *const curr_vector = eigs[i];
        /* guess the i-th eigen vector */
        for (int j = 0; j < n; j++)
            curr_vector[j] = rand() % 100;
        /* orthogonalize against higher eigenvectors */
        for (int j = 0; j < i; j++) {
            const double alpha = -vectors_inner_product(n, eigs[j], curr_vector);
            scadd(curr_vector, n - 1, alpha, eigs[j]);
        }
        const double len = norm(curr_vector, n - 1);
        vectors_scalar_mult(n, curr_vector, 1.0 / len, curr_vector);
        evals[i] = 0;
 
    }
 
    /* sort vectors by their evals, for overcoming possible mis-convergence: */
    for (i = 0; i < neigs - 1; i++) {
        int largest_index = i;
        double largest_eval = evals[largest_index];
        for (int j = i + 1; j < neigs; j++) {
            if (largest_eval < evals[j]) {
                largest_index = j;
                largest_eval = evals[largest_index];
            }
        }
        if (largest_index != i) {       /* exchange eigenvectors: */
            copy_vector(n, eigs[i], tmp_vec);
            copy_vector(n, eigs[largest_index], eigs[i]);
            copy_vector(n, tmp_vec, eigs[largest_index]);
 
            evals[largest_index] = evals[i];
            evals[i] = largest_eval;
        }
    }
 
    free(evals);
    free(tmp_vec);
    free(last_vec);
 
    return iteration <= Max_iterations;
}
 
void
mult_dense_mat(double **A, float **B, int dim1, int dim2, int dim3,
               float ***CC)
{
  // A is dim1 × dim2, B is dim2 × dim3, C = A × B
 
    float *storage = gv_calloc(dim1 * dim3, sizeof(storage[0]));
    float **const C = *CC = gv_calloc(dim1, sizeof(C[0]));
 
    for (int i = 0; i < dim1; i++) {
        C[i] = storage;
        storage += dim3;
    }
 
    for (int i = 0; i < dim1; i++) {
        for (int j = 0; j < dim3; j++) {
            double sum = 0;
            for (int k = 0; k < dim2; k++) {
                sum += A[i][k] * B[k][j];
            }
            C[i][j] = (float)sum;
        }
    }
}
 
void
mult_dense_mat_d(double **A, float **B, int dim1, int dim2, int dim3,
                 double ***CC)
{
  // A is dim1 × dim2, B is dim2 × dim3, C = A × B
 
    int i, j, k;
    double sum;
 
    double *storage = gv_calloc(dim1 * dim3, sizeof(double));
    double **C = *CC = gv_calloc(dim1, sizeof(double *));
 
    for (i = 0; i < dim1; i++) {
        C[i] = storage;
        storage += dim3;
    }
 
    for (i = 0; i < dim1; i++) {
        for (j = 0; j < dim3; j++) {
            sum = 0;
            for (k = 0; k < dim2; k++) {
                sum += A[i][k] * B[k][j];
            }
            C[i][j] = sum;
        }
    }
}
 
void
mult_sparse_dense_mat_transpose(vtx_data * A, double **B, int dim1,
                                int dim2, float ***CC)
{
  // A is dim1 × dim1 and sparse, B is dim2 × dim1, C = A × B
 
    int i, j;
    double sum;
    float *ewgts;
    int *edges;
    float *storage = gv_calloc(dim1 * dim2, sizeof(A[0]));
    float **C = *CC = gv_calloc(dim1, sizeof(A));
 
    for (i = 0; i < dim1; i++) {
        C[i] = storage;
        storage += dim2;
    }
 
    for (i = 0; i < dim1; i++) {
        edges = A[i].edges;
        ewgts = A[i].ewgts;
        const size_t nedges = A[i].nedges;
        for (j = 0; j < dim2; j++) {
            sum = 0;
            for (size_t k = 0; k < nedges; k++) {
                sum += ewgts[k] * B[j][edges[k]];
            }
            C[i][j] = (float) (sum);
        }
    }
}
 
/* Scaled add - fills double vec1 with vec1 + alpha*vec2 over range*/
void scadd(double *vec1, int end, double fac, double *vec2) {
    int i;
 
    for (i = end + 1; i; i--) {
        (*vec1++) += fac * (*vec2++);
    }
}
 
/* Returns 2-norm of a double n-vector over range. */
double norm(double *vec, int end) {
  return sqrt(vectors_inner_product(end + 1, vec, vec));
}
 
void orthog1(int n, double *vec /* vector to be orthogonalized against 1 */
    )
{
    int i;
    double *pntr;
    double sum;
 
    sum = 0.0;
    pntr = vec;
    for (i = n; i; i--) {
        sum += *pntr++;
    }
    sum /= n;
    pntr = vec;
    for (i = n; i; i--) {
        *pntr++ -= sum;
    }
}
 
#define RANGE 500
 
void init_vec_orth1(int n, double *vec)
{
    /* randomly generate a vector orthogonal to 1 (i.e., with mean 0) */
    int i;
 
    for (i = 0; i < n; i++)
        vec[i] = rand() % RANGE;
 
    orthog1(n, vec);
}
 
void
right_mult_with_vector(vtx_data * matrix, int n, double *vector,
                       double *result)
{
    int i;
 
    double res;
    for (i = 0; i < n; i++) {
        res = 0;
        for (size_t j = 0; j < matrix[i].nedges; j++)
            res += matrix[i].ewgts[j] * vector[matrix[i].edges[j]];
        result[i] = res;
    }
}
 
void
right_mult_with_vector_f(float **matrix, int n, double *vector,
                         double *result)
{
    int i, j;
 
    double res;
    for (i = 0; i < n; i++) {
        res = 0;
        for (j = 0; j < n; j++)
            res += matrix[i][j] * vector[j];
        result[i] = res;
    }
}
 
void
vectors_subtraction(int n, double *vector1, double *vector2,
                    double *result)
{
    int i;
    for (i = 0; i < n; i++) {
        result[i] = vector1[i] - vector2[i];
    }
}
 
void
vectors_addition(int n, double *vector1, double *vector2, double *result)
{
    int i;
    for (i = 0; i < n; i++) {
        result[i] = vector1[i] + vector2[i];
    }
}
 
void vectors_scalar_mult(int n, const double *vector, double alpha,
                         double *result) {
    int i;
    for (i = 0; i < n; i++) {
        result[i] = vector[i] * alpha;
    }
}
 
void copy_vector(int n, const double *restrict source, double *restrict dest) {
    int i;
    for (i = 0; i < n; i++)
        dest[i] = source[i];
}
 
double vectors_inner_product(int n, const double *vector1,
                             const double *vector2) {
    int i;
    double result = 0;
    for (i = 0; i < n; i++) {
        result += vector1[i] * vector2[i];
    }
 
    return result;
}
 
double max_abs(int n, double *vector)
{
    double max_val = -1e50;
    int i;
    for (i = 0; i < n; i++)
        max_val = fmax(max_val, fabs(vector[i]));
 
    return max_val;
}
 
void
right_mult_with_vector_transpose(double **matrix,
                                 int dim1, int dim2,
                                 double *vector, double *result)
{
    // matrix is dim2 × dim1, vector has dim2 components,
    // result = matrixᵀ × vector
    int i, j;
 
    double res;
    for (i = 0; i < dim1; i++) {
        res = 0;
        for (j = 0; j < dim2; j++)
            res += matrix[j][i] * vector[j];
        result[i] = res;
    }
}
 
void right_mult_with_vector_d(double *const *matrix, int dim1, int dim2,
                              double *vector, double *result) {
    // matrix is dim1 × dim2, vector has dim2 components,
    // result = matrix × vector
    int i, j;
 
    double res;
    for (i = 0; i < dim1; i++) {
        res = 0;
        for (j = 0; j < dim2; j++)
            res += matrix[i][j] * vector[j];
        result[i] = res;
    }
}
 
/*****************************
** Single precision (float) **
** version                  **
*****************************/
 
void orthog1f(int n, float *vec)
{
    int i;
    float *pntr;
    float sum;
 
    sum = 0.0;
    pntr = vec;
    for (i = n; i; i--) {
        sum += *pntr++;
    }
    sum /= n;
    pntr = vec;
    for (i = n; i; i--) {
        *pntr++ -= sum;
    }
}
 
void right_mult_with_vector_ff
    (float *packed_matrix, int n, float *vector, float *result) {
    /* packed matrix is the upper-triangular part of a symmetric matrix arranged in a vector row-wise */
    int i, j, index;
    float vector_i;
 
    float res;
    for (i = 0; i < n; i++) {
        result[i] = 0;
    }
    for (index = 0, i = 0; i < n; i++) {
        res = 0;
        vector_i = vector[i];
        /* deal with main diag */
        res += packed_matrix[index++] * vector_i;
        /* deal with off diag */
        for (j = i + 1; j < n; j++, index++) {
            res += packed_matrix[index] * vector[j];
            result[j] += packed_matrix[index] * vector_i;
        }
        result[i] += res;
    }
}
 
void
vectors_subtractionf(int n, float *vector1, float *vector2, float *result)
{
    int i;
    for (i = 0; i < n; i++) {
        result[i] = vector1[i] - vector2[i];
    }
}
 
void
vectors_additionf(int n, float *vector1, float *vector2, float *result)
{
    int i;
    for (i = 0; i < n; i++) {
        result[i] = vector1[i] + vector2[i];
    }
}
 
void
vectors_mult_additionf(int n, float *vector1, float alpha, float *vector2)
{
    int i;
    for (i = 0; i < n; i++) {
        vector1[i] = vector1[i] + alpha * vector2[i];
    }
}
 
void copy_vectorf(int n, float *source, float *dest)
{
    int i;
    for (i = 0; i < n; i++)
        dest[i] = source[i];
}
 
double vectors_inner_productf(int n, float *vector1, float *vector2)
{
    int i;
    double result = 0;
    for (i = 0; i < n; i++) {
        result += vector1[i] * vector2[i];
    }
 
    return result;
}
 
void set_vector_val(int n, double val, double *result)
{
    int i;
    for (i = 0; i < n; i++)
        result[i] = val;
}
 
void set_vector_valf(int n, float val, float* result)
{
    int i;
    for (i = 0; i < n; i++)
        result[i] = val;
}
 
double max_absf(int n, float *vector)
{
    int i;
    float max_val = -1e30f;
    for (i = 0; i < n; i++)
        max_val = fmaxf(max_val, fabsf(vector[i]));
 
    return max_val;
}
 
void square_vec(int n, float *vec)
{
    int i;
    for (i = 0; i < n; i++) {
        vec[i] *= vec[i];
    }
}
 
void invert_vec(int n, float *vec)
{
    int i;
    for (i = 0; i < n; i++) {
        if (vec[i] != 0.0) {
            vec[i] = 1.0f / vec[i];
        }
    }
}
 
void sqrt_vecf(int n, float *source, float *target)
{
    int i;
    for (i = 0; i < n; i++) {
        if (source[i] >= 0.0) {
            target[i] = sqrtf(source[i]);
        }
    }
}
 
void invert_sqrt_vec(int n, float *vec)
{
    int i;
    for (i = 0; i < n; i++) {
        if (vec[i] > 0.0) {
            vec[i] = 1.0f / sqrtf(vec[i]);
        }
    }
}