// ****************************************************************************
// Multiply a matrix A (size Arows rows by Acols columns) by a constant, and store the result in product.
// product must point to an allocated area of memory of the correct size. It is allowed to point to the same area of
// memory as A, and the contents of A will only be changed if this is the case.
// ****************************************************************************
void matrix_constant_multiply(double *A, long int Arows, long int Acols, double constant, double *product)
{
double *answer;
long int row, col;
if (A==NULL || Arows<1 || Acols <1 || product==NULL) quit_error((char*)"Illegal arguments to matrix_constant_multiply");
answer=(double *)malloc(sizeof(double)*Arows*Acols);
if (answer==NULL) quit_error((char*)"Out of memory");
for (row=0; row<Arows; row++)
{
for (col=0; col<Acols; col++)
{
answer[row*Acols+col]=constant*A[row*Acols+col];
}
}
for (row=0; row<Arows; row++)
{
for (col=0; col<Acols; col++)
{
product[row*Acols+col]=answer[row*Acols+col];
}
}
free(answer);
return;
}
// ****************************************************************************
// Calculates the Cholesky decomposition of N x N matrix A, such that A = L x transpose(L).
// This is only possible if matrix A is symmetric and positive definite (all eigenvalues
// positive).
// It is assumed that the memory required for this has already been allocated.
// The data in matrix A is not destroyed, unless the same address is supplied for L.
// (This case should be successfully handled also.)
// The function returns -1 if the matrix is not symmetric or not positive definite.
// ****************************************************************************
int matrix_cholesky(double *A, double *L, long int N)
{
long int row, col;
double *p, *backup;
int result;
if (A==NULL || L==NULL || N<1) quit_error((char*)"Bad input data to matrix_cholesky");
// Check that the A matrix is at least symmetric. (It also needs to be positive definite
// but that cannot be determined yet.)
for (row=0; row<N; row++)
{
for (col=row; col<N; col++)
{
if (fabs(A[row*N+col]-A[col*N+row])>DBL_EPSILON) return -1;
}
}
// Backup the A matrix so that manipulations can be performed here
// without damaging the original matrix.
backup=(double *)malloc(sizeof(double)*N*N);
if (backup==NULL) quit_error((char*)"Out of memory");
for (row=0; row<N; row++)
{
for (col=0; col<N; col++)
{
backup[row*N+col]=A[row*N+col];
}
}
// Create the vector for the results along the main diagonal
p=(double *)malloc(sizeof(double)*N);
if (p==NULL) quit_error((char*)"Out of memory");
// Calculate the Cholesky decomposition
result=choldc(backup, N, p);
// Assemble the answer in a nicer format
for (row=0; row<N; row++)
{
for (col=0; col<N; col++)
{
if (row<col) // Upper
{
L[row*N+col]=0.0;
}
else if (row>col) // Lower
{
L[row*N+col]=backup[row*N+col];
}
else L[row*N+col]=p[row]; // Diagonal
}
}
free(p);
free(backup);
return result;
}
// ****************************************************************************
// Invert the matrix A (size N by N) and store the result in Ainv, using the Cholesky
// decomposition. This is more numerically stable than standard inversion methods
// like Gauss-Jordan elimination but will only work if the matrix is symmetric
// and positive definite.
// ****************************************************************************
int matrix_cholesky_invert(double *A, double *Ainv, long int N)
{
double *L, *y, *z;
int result;
long int col, row, sum_count;
double sum;
L=(double *)malloc(sizeof(double)*N*N);
if (L==NULL) quit_error((char*)"Out of memory");
y=(double *)malloc(sizeof(double)*N);
if (y==NULL) quit_error((char*)"Out of memory");
z=(double *)malloc(sizeof(double)*N);
if (z==NULL) quit_error((char*)"Out of memory");
result=matrix_cholesky(A, L, N);
// Generate the inverse matrix one column at a time
for (col=0; col<N; col++)
{
// Create the y vector
for (row=0; row<N; row++)
{
if (row==col) y[row]=1.0;
else y[row]=0.0;
}
// Solve for the z vector
for (row=0; row<N; row++)
{
sum=0.0;
for (sum_count=0; sum_count<row; sum_count++)
{
sum+=L[row*N+sum_count]*z[sum_count];
}
z[row]=(y[row]-sum)/L[row*N+row];
}
// Solve for the solution vector - which is the next column
// of Ainv.
for (row=N-1; row>=0; row--)
{
sum=0.0;
for (sum_count=row+1; sum_count<N; sum_count++)
{
sum+=L[sum_count*N+row]*Ainv[sum_count*N+col];
}
Ainv[row*N+col]=(z[row]-sum)/L[row*N+row];
}
}
free(z);
free(y);
free(L);
return result;
}
// ****************************************************************************
// Same as the previous function, but does not return D and V
// ****************************************************************************
long int find_null_space_decomposition(double *A, long int rows, long int cols, double tolerance)
{
double *Utemp, *Dtemp, *Vtemp, max_val, temp_val;
long int nullity=cols, i, ii, max_loc=0;
Utemp=(double *)malloc(sizeof(double)*rows*cols);
if (Utemp==NULL) quit_error((char*)"Out of memory");
Dtemp=(double *)malloc(sizeof(double)*cols*cols);
if (Dtemp==NULL) quit_error((char*)"Out of memory");
Vtemp=(double *)malloc(sizeof(double)*cols*cols);
if (Vtemp==NULL) quit_error((char*)"Out of memory");
// Calculate the Singular Value Decomposition
svd(A, rows, cols, Utemp, Dtemp, Vtemp);
// Transpose Vtemp
matrix_transpose(Vtemp, cols, cols);
// Sort the singular values into the correct order
for (i=0; i<cols; i++)
{
// Find the maximum singular value in the remainder of the list
max_val=-1.0;
for (ii=i; ii<cols; ii++)
{
if (fabs(Dtemp[ii+cols*ii])>max_val)
{
max_val=fabs(Dtemp[ii+cols*ii]);
max_loc=ii;
}
}
// Update the nullity
if (max_val>fabs(tolerance)) nullity--;
// Swap the singular values
temp_val=Dtemp[max_loc+cols*max_loc];
Dtemp[max_loc+cols*max_loc]=Dtemp[i+cols*i];
Dtemp[i+cols*i]=temp_val;
// Swap the corresponding singular vectors
single_swap_row(i, max_loc, Vtemp, cols);
}
// Return the stuff that is required and throw away the rest
free(Utemp);
free(Dtemp);
free(Vtemp);
return nullity;
}
//-------------------------------------------------------------------------
InputData_t::InputData_t()
{
ParamListHead_t param_list_head;
param_list_head.get_params_from_file((char*)"snapshot_pod.in");
param_list_head.print_params();
temporal_correlation_type = param_list_head.get_string_param((char*)"temporal_correlation_type");
normalisation = param_list_head.get_string_param((char*)"normalisation");
snapshot_list_filename = param_list_head.get_string_param((char*)"snapshot_list_filename");
snapshot_dir = param_list_head.get_string_param((char*)"snapshot_dir");
file_name_with_cell_volumes = param_list_head.get_string_param((char*)"file_name_with_cell_volumes");
dt = param_list_head.get_double_param((char*)"dt");
char *test_orthogonality_char;
test_orthogonality_char = param_list_head.get_string_param((char*)"test_orthogonality");
if (strcmp(test_orthogonality_char,"true")==0) {
test_orthogonality = true;
} else if (strcmp(test_orthogonality_char,"false")==0) {
test_orthogonality = false;
} else {
quit_error((char*)"<test_reconstruction> = 'true' or 'false'\n");
}
char *check_eigensolution_char;
check_eigensolution_char = param_list_head.get_string_param((char*)"check_eigensolution");
if (strcmp(check_eigensolution_char,"true")==0) {
check_eigensolution = true;
} else if (strcmp(check_eigensolution_char,"false")==0) {
check_eigensolution = false;
} else {
quit_error((char*)"<check_eigensolution> = 'true' or 'false'\n");
}
restart = param_list_head.get_string_param((char*)"restart");
threshhold_energy = param_list_head.get_double_param((char*)"threshhold_energy");
min_number_of_eigenvalues = param_list_head.get_int_param((char*)"min_number_of_eigenvalues");
max_number_of_eigenvalues = param_list_head.get_int_param((char*)"max_number_of_eigenvalues");
two_dimensional = param_list_head.get_string_param((char*)"two_dimensional");
x_min = param_list_head.get_double_param((char*) "x_min");
x_max = param_list_head.get_double_param((char*) "x_max");
y_min = param_list_head.get_double_param((char*) "y_min");
y_max = param_list_head.get_double_param((char*) "y_max");
z_min = param_list_head.get_double_param((char*) "z_min");
z_max = param_list_head.get_double_param((char*) "z_max");
}
// ****************************************************************************
// Row reduce matrix A (size: rows x cols).
// This function WILL NOT handle the case when rows > cols.
// false is returned if the matrix does not have the maximum possible rank, true otherwise.
// tolerance is the largest number which can be considered to be equal to zero, for the purposes of pivoting.
// ****************************************************************************
int matrix_row_reduce(double *A, long int rows, long int cols, double tolerance)
{
long int r, i, pivot_row, col_offset;
double pivot_val;
if (A==NULL || rows<1 || cols<1) quit_error((char*)"Bad arguments to matrix_row_reduce");
if (rows>cols) quit_error((char*)"matrix_row_reduce is limited to cases where rows<=cols");
col_offset=0;
for (i=0; i<rows; i++)
{
// Find the row with the best pivot and swap it
pivot_val=fabs(tolerance);
pivot_row=-1;
while (pivot_row<0)
{
for (r=i; r<rows; r++)
{
if (fabs(A[r*cols+i+col_offset])>fabs(pivot_val))
{
pivot_val=A[r*cols+i+col_offset];
pivot_row=r;
}
}
if (pivot_row<0)
{
col_offset++;
if (i+col_offset>=cols) return false;
}
}
if (pivot_row>=0 && pivot_row<rows)
{
if (pivot_row!=i) single_swap_row(pivot_row, i, A, cols);
single_multiply_row(i, 1.0/pivot_val, A, cols);
for (r=0; r<rows; r++)
{
if (r!=i)
{
single_add_multiple_row(-A[r*cols+i+col_offset], i, r, A, cols);
}
}
}
}
return true;
}
// ****************************************************************************
// Calculate the determinant of a square matrix
// ****************************************************************************
double matrix_determinant(double *A, long int N)
{
double *backup;
double result;
long int max_pivot;
double max_value;
if (N<1) quit_error((char*)"Attempt to calculate determinant of invalid matrix");
if (A==NULL) quit_error((char*)"Attempt to calculate determinant of invalid matrix");
// Copy the data to a place where it can safely be destroyed
backup=(double *)malloc(sizeof(double)*N*N);
if (backup==NULL) quit_error((char*)"Out of memory");
for (long int row=0; row<N; row++)
for (long int col=0; col<N; col++)
backup[row*N+col]=A[row*N+col];
result=1.0;
// Go through the matrix, diagonalising to form an upper triangular matrix.
// As part of this process, the rows are normalised to make the values along the diagonal
// equal to one. As factors are pulled out, they are multiplied onto result to keep track
// of the value of the determinant.
for (long int i=0; i<N; i++) {
// Find the element in this column which has the largest absolute value
max_pivot=-1;
max_value=0.0;
for (long int row=i; row<N; row++) {
if (fabs(backup[row*N+i])>fabs(max_value)) {
max_pivot=row;
max_value=backup[row*N+i];
}
}
if (max_pivot<0) return 0.0;
if (max_pivot!=i) {
single_swap_row(max_pivot, i, backup, N);
result*=-1.0;
}
result*=backup[i*N+i];
single_multiply_row(i, 1.0/backup[i*N+i], backup, N);
for (long int row=i+1; row<N; row++) single_add_multiple_row(-backup[row*N+i], i, row, backup, N);
}
free(backup);
return result;
}
char
*misc_bindir(void)
{
char *path;
char *tmp;
size_t len;
len = sizeof(char) * PATH_MAX;
if ((path = malloc(len)) == NULL)
{
quit_error(POUTOFMEM);
}
#ifdef FreeBSD
int32_t mib[4];
mib[0] = CTL_KERN;
mib[1] = KERN_PROC;
mib[2] = KERN_PROC_PATHNAME;
mib[3] = -1;
sysctl(mib, 4, path, &len, NULL, 0);
#elif __linux__
readlink("/proc/self/exe", path, len);
#endif
tmp = dirname(path);
misc_strlcpy(path, tmp, len);
return path;
}
void
hashmap_add(hashmap *map, const char *key, void *data, boolean is_alias)
{
hashnode *node;
uint16_t bucket;
assert(map);
assert(key);
assert(data);
if ((node = malloc(sizeof(hashnode))) == NULL)
{
quit_error(POUTOFMEM);
}
node->key = key;
node->data = data;
node->hash = hashmap_hash(key);
node->is_alias = is_alias;
bucket = node->hash % map->buckets;
if (!map->data[bucket])
{
map->data[bucket] = darray_create();
darray_push(map->data[bucket], node);
}
else
{
darray_push(map->data[bucket], node);
}
}
// ****************************************************************************
// Adds matrix A (Arows by Acols) to matrix B (Brows by Bcols) and stores the result in sum.
// sum must point to an allocated area of memory of the correct size. It is allowed to point to the same area of
// memory as A and/or B, and the contents of A and/or B will only be changed if this is the case.
// ****************************************************************************
void matrix_add(double *A, long int Arows, long int Acols, double *B, long int Brows, long int Bcols, double *sum)
{
double *answer;
long int row, col;
if (A==NULL || Arows<1 || Acols <1 || B==NULL || Brows<1 || Bcols <1 || sum==NULL || Arows!=Brows || Acols!=Bcols) quit_error((char*)"Illegal arguments to matrix_add");
answer=(double *)malloc(sizeof(double)*Arows*Acols);
if (answer==NULL) quit_error((char*)"Out of memory");
for (row=0; row<Arows; row++)
{
for (col=0; col<Acols; col++)
{
answer[row*Acols+col]=A[row*Acols+col]+B[row*Acols+col];
}
}
for (row=0; row<Arows; row++)
{
for (col=0; col<Acols; col++)
{
sum[row*Acols+col]=answer[row*Acols+col];
}
}
free(answer);
return;
}
// ****************************************************************************
// Multplies one row of both matricies A and B (each of size N x N)
// by a certain factor
// ****************************************************************************
void multiply_row(long int row, double factor, double *A, double *B, long int N)
{
if (A==NULL || B==NULL || N<1 || row<0 || row>=N || fabs(factor)<DBL_EPSILON) quit_error((char*)"Bad input data to multiply_row");
for (long int col=0; col<N; col++) {
A[row*N+col]*=factor;
B[row*N+col]*=factor;
}
}
// ****************************************************************************
// Adds factor times row srow to row drow, in both matricies A and B
// (each of size N x N)
// ****************************************************************************
void add_multiple_row(double factor, long int srow, long int drow, double *A, double *B, long int N)
{
if (A==NULL || B==NULL || N<1 || srow<0 || srow>=N || drow<0 || drow>=N) quit_error((char*)"Bad input data to add_multiple_row");
for (long int col=0; col<N; col++) {
A[drow*N+col]+=factor*A[srow*N+col];
B[drow*N+col]+=factor*B[srow*N+col];
}
}
// ****************************************************************************
// Copies the contents of matrix A (R rows by C columns) onto the
// block of memory pointed to by Cp. It is assumed that sufficient
// memory has been allocated to do this.
// ****************************************************************************
void matrix_copy(double *A, long int R, long int C, double *Cp)
{
if (A==NULL || Cp==NULL || R<1 || C<1) quit_error((char*)"Bad input to matrix_copy");
for (long int row=0; row<R; row++)
for (long int col=0; col<C; col++)
Cp[row*C+col]=A[row*C+col];
}
double *dvector(long nl, long nh)
/* allocate a double vector with subscript range v[nl..nh] */
{
double *v;
v=(double *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(double)));
if (!v) quit_error((char*)"allocation failure in dvector()");
return v-nl+NR_END;
}
// ****************************************************************************
// Swaps rows row1 and row2 of matrix A (of size N x N)
// ****************************************************************************
void single_swap_row(long int row1, long int row2, double *A, long int N)
{
if (A==NULL || N<1 || row1<0 || row1>=N || row2<0 || row2>=N) quit_error((char*)"Bad input data to single_swap_row");
double temp;
for (long int col=0; col<N; col++) {
temp=A[row1*N+col];
A[row1*N+col]=A[row2*N+col];
A[row2*N+col]=temp;
}
}
void
misc_rmkdir(const char *dir)
{
char *p;
char tmp[PATH_MAX];
size_t len;
misc_strlcpy(tmp, dir, sizeof(tmp));
len = strlen(tmp);
if (tmp[len - 1] == '/')
{
tmp[len - 1] = 0;
}
for (p = tmp + 1; *p; p++)
{
if (*p == '/')
{
*p = 0;
if ((mkdir(tmp, 0700)) != 0)
{
if (errno != EEXIST)
{
quit_error(PCOULDNTCREATEDIR);
}
}
*p = '/';
}
}
if ((mkdir(tmp, 0700)) != 0)
{
if (errno != EEXIST)
{
quit_error(PCOULDNTCREATEDIR);
}
}
}
// ****************************************************************************
// Multiplies matrix A (Arows x Acols) by matrix B (Brows x Bcols) and writes the result to product.
// It is assumed that the required amount of memory will already be allocated.
// If the matricies are not of the correct dimensions for multiplication then an error is thrown.
// product is not allowed to point to the same area of memory as A or B
// ****************************************************************************
void matrix_multiply(double *A, long int Arows, long int Acols, double *B, long int Brows, long int Bcols, double *product)
{
if (A==NULL || B==NULL || product==NULL) quit_error((char*)"Bad input data to matrix_multiply");
if (Acols!=Brows) quit_error((char*)"Matricies are incompatible for multiplication");
double *temp = malloc_1d_array_double(Arows*Bcols);
for (long int row=0; row<Arows; row++) {
for (long int col=0; col<Bcols; col++) {
temp[row*Bcols+col]=0;
for (long int sum_point=0; sum_point<Acols; sum_point++) temp[row*Bcols+col]+=A[row*Acols+sum_point]*B[sum_point*Bcols+col];
}
}
for (long int row=0; row<Arows; row++)
for (long int col=0; col<Bcols; col++)
product[row*Bcols+col]=temp[row*Bcols+col];
free_1d_array_double(temp);
}
// ****************************************************************************
// Calculates the inverse of N x N matrix A and stores it in matrix Ainv.
// It is assumed that the memory required for this has already been allocated.
// The data in matrix A is not destroyed, unless the same address is supplied for Ainv.
// (This case should be successfully handled also.)
// The function returns -1 if the matrix is not invertible.
// ****************************************************************************
int matrix_invert(double *A, double *Ainv, long int N)
{
double *backup = malloc_1d_array_double(N*N);
double pivot, factor;
long int pivot_row;
if (A==NULL || Ainv==NULL || N<1) quit_error((char*)"Bad input data to matrix_invert");
// Backup the A matrix so that manipulations can be performed here
// without damaging the original matrix.
for (long int row=0; row<N; row++)
for (long int col=0; col<N; col++)
backup[row*N+col]=A[row*N+col];
// First, fill Ainv with the identity matrix
for (long int row=0; row<N; row++) {
for (long int col=0; col<N; col++) {
if (row==col) Ainv[row*N+col]=1;
else Ainv[row*N+col]=0;
}
}
// Calculate the inverse using Gauss-Jordan elimination
for (long int col=0; col<N; col++) {
//display_augmented(backup, Ainv, N);
pivot_row=-1;
pivot=0.0;
for (long int row=col; row<N; row++) {
if (fabs(backup[row*N+col])>fabs(pivot)) {
pivot_row=row;
pivot=backup[row*N+col];
}
}
//printf("Pivot: %lf\n\n", pivot);
if (pivot_row<0 || pivot_row>=N || fabs(pivot)<DBL_EPSILON) {
free_1d_array_double(backup);
return -1;
} else {
swap_row(col, pivot_row, backup, Ainv, N);
multiply_row(col, 1.0/pivot, backup, Ainv, N);
for (long int elim_row=0; elim_row<N; elim_row++) {
if (elim_row!=col) {
factor=-backup[elim_row*N+col];
add_multiple_row(factor, col, elim_row, backup, Ainv, N);
}
}
}
}
free_1d_array_double(backup);
return 0;
}
// ****************************************************************************
// This function finds the nullity of matrix A.
// Note that A is a matrix of size rows x cols
// The rank deficit (nullity) is returned (0 if matrix is full rank, 1 if matrix has one singular value, etc).
// tolerance defines how small a singular value must be in order to be considered a "zero".
// ****************************************************************************
long int matrix_nullity(double *A, long int rows, long int cols, double tolerance)
{
double *U, *D, *V, max_val, min_val;
long int i, rank_deficit;
U=(double *)malloc(sizeof(double)*rows*cols);
if (U==NULL) quit_error((char*)"Out of memory");
D=(double *)malloc(sizeof(double)*cols*cols);
if (D==NULL) quit_error((char*)"Out of memory");
V=(double *)malloc(sizeof(double)*cols*cols);
if (V==NULL) quit_error((char*)"Out of memory");
// Calculate the Singular Value Decomposition
svd(A, rows, cols, U, D, V);
// Find the maximum and minimum magnitude singular values
max_val=0.0;
min_val=DBL_MAX;
for (i=0; i<cols; i++)
{
if (fabs(D[i*cols+i])<fabs(min_val)) min_val=D[i*cols+i];
if (fabs(D[i*cols+i])>fabs(max_val)) max_val=D[i*cols+i];
}
// Count the rank deficit of the matrix, and extract
// relevant rows of the transpose(V) matrix.
rank_deficit=0;
for (i=0; i<cols; i++)
{
if (fabs(D[i*cols+i])<fabs(tolerance)) rank_deficit++;
}
free(V);
free(D);
free(U);
return rank_deficit;
}
// ****************************************************************************
// Finds the transpose of matrix A (R rows by C columns).
// This is done in place.
// The transposed matrix has C rows by R columns.
// ****************************************************************************
void matrix_transpose(double *A, long int R, long int C)
{
double *backup;
if (A==NULL || R<1 || C<1) quit_error((char*)"Bad input to matrix_transpose");
// Backup the A matrix so that manipulations can be performed here
// without damaging the original matrix.
backup=(double *)malloc(sizeof(double)*R*C);
if (backup==NULL) quit_error((char*)"Out of memory");
for (long int row=0; row<R; row++)
for (long int col=0; col<C; col++)
backup[row*C+col]=A[row*C+col];
// Calculate the transpose
for (long int row=0; row<C; row++)
for (long int col=0; col<R; col++)
A[row*R+col]=backup[col*C+row];
free(backup);
return;
}
bool queue_peek(Queue queue, void * p)
{
if ( queue_is_empty(queue) ) {
if ( queue->exit_on_error ) {
quit_error("gds library", "queue empty");
}
else {
log_error("gds library", "queue empty");
return false;
}
}
gdt_get_value(&queue->elements[queue->front], p);
return true;
}
bool queue_pop(Queue queue, void * p)
{
if ( queue_is_empty(queue) ) {
if ( queue->exit_on_error ) {
quit_error("gds library", "queue empty");
}
else {
log_error("gds library", "queue empty");
return false;
}
}
gdt_get_value(&queue->elements[queue->front++], p);
if ( queue->front == queue->capacity ) {
queue->front = 0;
}
queue->size -= 1;
return true;
}
bool queue_push(Queue queue, ...)
{
if ( queue_is_full(queue) ) {
if ( queue->resizable ) {
struct gdt_generic_datatype * new_elements;
const size_t new_capacity = queue->capacity * GROWTH;
new_elements = realloc(queue->elements,
sizeof *queue->elements * new_capacity);
if ( !new_elements ) {
if ( queue->exit_on_error ) {
quit_strerror("gds library", "memory allocation failed");
}
else {
log_strerror("gds library", "memory allocation failed");
return false;
}
}
queue->elements = new_elements;
if ( queue->back < queue->front ||
queue->size == queue->capacity ) {
/* If we get here, then the back of the queue
* is at a lower index than the front of it
* (or the queue is full and both the back and
* front are zero). Conceptually the queue is
* wrapping around the back of the array, and if
* we resize it, there'll be a gap unless we move
* those wrapped elements back into the new space.
* Note that because we always grow by a factor of
* at least two, there'll always be enough space to
* move all the wrapped elements. In fact, we here
* move the entire array from the start through to
* the front element, including any "empty" ones,
* which is not really necessary. */
/** \todo Rewrite to move only the required elements */
const size_t excess = new_capacity - queue->capacity;
const size_t nfelem = queue->capacity - queue->front;
struct gdt_generic_datatype * old_front, * new_front;
old_front = queue->elements + queue->front;
new_front = old_front + excess;
memmove(new_front, old_front, nfelem * sizeof *old_front);
queue->front += excess;
}
queue->capacity = new_capacity;
}
else if ( queue->exit_on_error ) {
quit_error("gds library", "queue full");
}
else {
log_error("gds library", "queue full");
return false;
}
}
va_list ap;
va_start(ap, queue);
gdt_set_value(&queue->elements[queue->back++], queue->type, NULL, ap);
va_end(ap);
if ( queue->back == queue->capacity ) {
queue->back = 0;
}
queue->size += 1;
return true;
}
// ****************************************************************************
// This function finds a set of vectors (P) such that, for each vector p:
// A.p = 0
// Note that A is a matrix of size rows x cols, P is a matrix of size cols x cols whose ROWS are the p vectors.
// P must NOT point to any allocated memory prior to calling this function.
// The rank deficit (nullity) is returned (0 if matrix is full rank, 1 if matrix has one singular value, etc).
// tol defines how small a singular value must be in order to be considered a "zero".
// ****************************************************************************
long int find_null_space_vectors(double *A, long int rows, long int cols, double **P, double tolerance)
{
double *U, *D, *V, *R, max_val, min_val;
long int i, rank_deficit, c, r;
U=(double *)malloc(sizeof(double)*rows*cols);
if (U==NULL) quit_error((char*)"Out of memory");
D=(double *)malloc(sizeof(double)*cols*cols);
if (D==NULL) quit_error((char*)"Out of memory");
V=(double *)malloc(sizeof(double)*cols*cols);
if (V==NULL) quit_error((char*)"Out of memory");
// Calculate the Singular Value Decomposition
svd(A, rows, cols, U, D, V);
// Find the maximum and minimum magnitude singular values
max_val=0.0;
min_val=DBL_MAX;
for (i=0; i<cols; i++)
{
if (fabs(D[i*cols+i])<fabs(min_val)) min_val=fabs(D[i*cols+i]);
if (fabs(D[i*cols+i])>fabs(max_val)) max_val=fabs(D[i*cols+i]);
}
// Count the rank deficit of the matrix, and extract
// relevant rows of the transpose(V) matrix.
rank_deficit=0;
for (i=0; i<cols; i++)
{
if (fabs(D[i*cols+i])<tolerance) rank_deficit++;
}
// Transpose V
matrix_transpose(V, cols, cols);
// Generate a reduced version of transpose(V)
R=(double *)malloc(sizeof(double)*cols*(rank_deficit));
if (R==NULL) quit_error((char*)"Out of memory");
r=0;
for (i=0; i<cols; i++)
{
if (fabs(D[i*cols+i])<fabs(tolerance))
{
for (c=0; c<cols; c++)
{
R[r*cols+c]=V[i*cols+c];
}
r++;
}
}
// Row reduce R
matrix_row_reduce(R, rank_deficit, cols, tolerance);
*P=R;
free(V);
free(D);
free(U);
return rank_deficit;
}
/*
Given a matrix a[1..m][1..n], this routine computes its singular value decomposition,
A = U.W.transpose(V). The matrix U replaces a on output. The diagonal matrix of singular values
W is output as a vector w[1..n]. The matrix V (not its transpose) is output as v[1..n][1..n].
The matrix a must exist prior to calling this function (obviously), and so too must w and v.
*/
void dsvdcmp(double **a, int m, int n, double w[], double **v)
{
int flag,i,its,j,jj,k,l=0,nm=0;
double anorm,c,f,g,h,s,scale,x,y,z,*rv1;
rv1=dvector(1,n);
g=scale=anorm=0.0;
for (i=1;i<=n;i++) {
l=i+1;
rv1[i]=scale*g;
g=s=scale=0.0;
if (i <= m) {
for (k=i;k<=m;k++) scale += fabs(a[k][i]);
if (scale) {
for (k=i;k<=m;k++) {
a[k][i] /= scale;
s += a[k][i]*a[k][i];
}
f=a[i][i];
g = -SIGN(sqrt(s),f);
h=f*g-s;
a[i][i]=f-g;
for (j=l;j<=n;j++) {
for (s=0.0,k=i;k<=m;k++) s += a[k][i]*a[k][j];
f=s/h;
for (k=i;k<=m;k++) a[k][j] += f*a[k][i];
}
for (k=i;k<=m;k++) a[k][i] *= scale;
}
}
w[i]=scale *g;
g=s=scale=0.0;
if (i <= m && i != n) {
for (k=l;k<=n;k++) scale += fabs(a[i][k]);
if (scale) {
for (k=l;k<=n;k++) {
a[i][k] /= scale;
s += a[i][k]*a[i][k];
}
f=a[i][l];
g = -SIGN(sqrt(s),f);
h=f*g-s;
a[i][l]=f-g;
for (k=l;k<=n;k++) rv1[k]=a[i][k]/h;
for (j=l;j<=m;j++) {
for (s=0.0,k=l;k<=n;k++) s += a[j][k]*a[i][k];
for (k=l;k<=n;k++) a[j][k] += s*rv1[k];
}
for (k=l;k<=n;k++) a[i][k] *= scale;
}
}
anorm=MAX(anorm,(fabs(w[i])+fabs(rv1[i])));
}
for (i=n;i>=1;i--) {
if (i < n) {
if (g) {
for (j=l;j<=n;j++) v[j][i]=(a[i][j]/a[i][l])/g;
for (j=l;j<=n;j++) {
for (s=0.0,k=l;k<=n;k++) s += a[i][k]*v[k][j];
for (k=l;k<=n;k++) v[k][j] += s*v[k][i];
}
}
for (j=l;j<=n;j++) v[i][j]=v[j][i]=0.0;
}
v[i][i]=1.0;
g=rv1[i];
l=i;
}
for (i=MIN(m,n);i>=1;i--) {
l=i+1;
g=w[i];
for (j=l;j<=n;j++) a[i][j]=0.0;
if (g) {
g=1.0/g;
for (j=l;j<=n;j++) {
for (s=0.0,k=l;k<=m;k++) s += a[k][i]*a[k][j];
f=(s/a[i][i])*g;
for (k=i;k<=m;k++) a[k][j] += f*a[k][i];
}
for (j=i;j<=m;j++) a[j][i] *= g;
} else for (j=i;j<=m;j++) a[j][i]=0.0;
++a[i][i];
}
for (k=n;k>=1;k--) {
for (its=1;its<=30;its++) {
flag=1;
for (l=k;l>=1;l--) {
nm=l-1;
if ((double)(fabs(rv1[l])+anorm) == anorm) {
flag=0;
break;
}
if ((double)(fabs(w[nm])+anorm) == anorm) break;
}
if (flag) {
c=0.0;
s=1.0;
for (i=l;i<=k;i++) {
f=s*rv1[i];
rv1[i]=c*rv1[i];
if ((double)(fabs(f)+anorm) == anorm) break;
g=w[i];
h=dpythag(f,g);
w[i]=h;
h=1.0/h;
c=g*h;
s = -f*h;
for (j=1;j<=m;j++) {
y=a[j][nm];
z=a[j][i];
a[j][nm]=y*c+z*s;
a[j][i]=z*c-y*s;
}
}
}
z=w[k];
if (l == k) {
if (z < 0.0) {
w[k] = -z;
for (j=1;j<=n;j++) v[j][k] = -v[j][k];
}
break;
}
if (its == 30) quit_error((char*)"no convergence in 30 dsvdcmp iterations");
x=w[l];
nm=k-1;
y=w[nm];
g=rv1[nm];
h=rv1[k];
f=((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y);
g=dpythag(f,1.0);
f=((x-z)*(x+z)+h*((y/(f+SIGN(g,f)))-h))/x;
c=s=1.0;
for (j=l;j<=nm;j++) {
i=j+1;
g=rv1[i];
y=w[i];
h=s*g;
g=c*g;
z=dpythag(f,h);
rv1[j]=z;
c=f/z;
s=h/z;
f=x*c+g*s;
g = g*c-x*s;
h=y*s;
y *= c;
for (jj=1;jj<=n;jj++) {
x=v[jj][j];
z=v[jj][i];
v[jj][j]=x*c+z*s;
v[jj][i]=z*c-x*s;
}
z=dpythag(f,h);
w[j]=z;
if (z) {
z=1.0/z;
c=f*z;
s=h*z;
}
f=c*g+s*y;
x=c*y-s*g;
for (jj=1;jj<=m;jj++) {
y=a[jj][j];
z=a[jj][i];
a[jj][j]=y*c+z*s;
a[jj][i]=z*c-y*s;
}
}
rv1[l]=0.0;
rv1[k]=f;
w[k]=x;
}
}
free_dvector(rv1,1,n);
return;
}