M_NA

#define M_NA (0.0/0.0)

R_DIAG_MIN

#define R_DIAG_MIN 1.0e-8

enum GretlMatrixMod

typedef enum {
    GRETL_MOD_NONE = 0,
    GRETL_MOD_TRANSPOSE,
    GRETL_MOD_SQUARE,
    GRETL_MOD_CUMULATE,
    GRETL_MOD_DECREMENT
} GretlMatrixMod;

enum GretlMatrixStructure

typedef enum {
    GRETL_MATRIX_SQUARE = 1,
    GRETL_MATRIX_LOWER_TRIANGULAR,
    GRETL_MATRIX_UPPER_TRIANGULAR,
    GRETL_MATRIX_SYMMETRIC,
    GRETL_MATRIX_DIAGONAL,
    GRETL_MATRIX_IDENTITY,
    GRETL_MATRIX_SCALAR,
} GretlMatrixStructure;

gretl_matrix

typedef struct {
    int rows;
    int cols;
    int t1, t2;
    double *val;
} gretl_matrix;

gretl_vector

typedef struct _gretl_matrix gretl_vector;

gretl_matrix_block

typedef struct _gretl_matrix_block gretl_matrix_block;

gretl_matrix_get()

#define gretl_matrix_get(m,i,j) (m->val[(j)*m->rows+(i)])

gretl_vector_get()

#define gretl_vector_get(v,i) (v->val[i])

gretl_matrix_set()

#define gretl_matrix_set(m,i,j,x) ((m)->val[(j)*(m)->rows+(i)]=x)

Sets the i, j element of m to x.

gretl_vector_set()

#define gretl_vector_set(v,i,x) ((v)->val[i]=x)

Sets element i of v to x.

gretl_matrix_cols()

#define gretl_matrix_cols(m) ((m == NULL)? 0 : m->cols)

gretl_matrix_rows()

#define gretl_matrix_rows(m) ((m == NULL)? 0 : m->rows)

gretl_vector_get_length()

#define             gretl_vector_get_length(v)

gretl_vector_alloc()

#define gretl_vector_alloc(i) gretl_matrix_alloc(1,(i))

gretl_column_vector_alloc()

#define gretl_column_vector_alloc(i) gretl_matrix_alloc((i),1)

gretl_vector_free()

#define gretl_vector_free(v) gretl_matrix_free(v)

Frees the vector v and its associated storage.

gretl_matrix_is_scalar()

#define             gretl_matrix_is_scalar(m)

gretl_is_null_matrix()

#define gretl_is_null_matrix(m) (m == NULL || m->rows == 0 || m->cols == 0)

get_gretl_matrix_err ()

int                 get_gretl_matrix_err                (void);

clear_gretl_matrix_err ()

void                clear_gretl_matrix_err              (void);

gretl_matrix_print ()

void                gretl_matrix_print                  (const gretl_matrix *m,
                                                         const char *msg);

Prints the given matrix to stderr.

gretl_matrix_xna_check ()

int                 gretl_matrix_xna_check              (const gretl_matrix *m);

gretl_matrix_is_symmetric ()

int                 gretl_matrix_is_symmetric           (const gretl_matrix *m);

gretl_matrix_is_idempotent ()

int                 gretl_matrix_is_idempotent          (const gretl_matrix *m);

gretl_matrix_xtr_symmetric ()

void                gretl_matrix_xtr_symmetric          (gretl_matrix *m);

Computes the symmetric part of m by averaging its off-diagonal elements.

gretl_matrix_set_equals_tolerance ()

void                gretl_matrix_set_equals_tolerance   (double tol);

Sets the tolerance for judging whether or not a matrix is symmetric (see gretl_matrix_is_symmetric() and also gretl_invert_symmetric_matrix()). The tolerance is the maximum relative difference between corresponding off-diagonal elements that is acceptable in a supposedly "symmetric" matrix. The default value is 1.5e-12.

gretl_matrix_unset_equals_tolerance ()

void                gretl_matrix_unset_equals_tolerance (void);

Sets the tolerance for judging whether or not a matrix is symmetric to its default value. See also gretl_matrix_set_equals_tolerance().

gretl_matrix_alloc ()

gretl_matrix *      gretl_matrix_alloc                  (int rows,
                                                         int cols);

gretl_matrix_reuse ()

gretl_matrix *      gretl_matrix_reuse                  (gretl_matrix *m,
                                                         int rows,
                                                         int cols);

An "experts only" memory-conservation trick. If m is an already-allocated gretl matrix, you can "resize" it by specifying a new number of rows and columns. This works only if the product of rows and cols is less than or equal to the product of the number of rows and columns in the matrix as originally allocated; no actual reallocation of memory is performed. If you "reuse" with an excessive number of rows or columns you will surely crash your program or smash the stack. Note also that the matrix-pointer returned is not really new, and the when the matrix is to be freed, gretl_matrix_free() should be applied only once.

gretl_matrix_realloc ()

int                 gretl_matrix_realloc                (gretl_matrix *m,
                                                         int rows,
                                                         int cols);

Reallocates the storage in m to the specified dimensions.

gretl_matrix_block_destroy ()

void                gretl_matrix_block_destroy          (gretl_matrix_block *B);

gretl_matrix_block_new ()

gretl_matrix_block * gretl_matrix_block_new             (gretl_matrix **pm,
                                                         ...);

gretl_identity_matrix_new ()

gretl_matrix *      gretl_identity_matrix_new           (int n);

gretl_DW_matrix_new ()

gretl_matrix *      gretl_DW_matrix_new                 (int n);

gretl_zero_matrix_new ()

gretl_matrix *      gretl_zero_matrix_new               (int r,
                                                         int c);

gretl_unit_matrix_new ()

gretl_matrix *      gretl_unit_matrix_new               (int r,
                                                         int c);

gretl_null_matrix_new ()

gretl_matrix *      gretl_null_matrix_new               (void);

gretl_matrix_seq ()

gretl_matrix *      gretl_matrix_seq                    (int start,
                                                         int end,
                                                         int step,
                                                         int *err);

gretl_matrix_copy ()

gretl_matrix *      gretl_matrix_copy                   (const gretl_matrix *m);

gretl_matrix_copy_row ()

int                 gretl_matrix_copy_row               (gretl_matrix *dest,
                                                         int di,
                                                         const gretl_matrix *src,
                                                         int si);

Copies the values from row si of src into row di of dest, provided src and dest have the same number of columns.

gretl_matrix_inscribe_I ()

int                 gretl_matrix_inscribe_I             (gretl_matrix *m,
                                                         int row,
                                                         int col,
                                                         int n);

Writes an n x n identity matrix into matrix m, the top left-hand corner of the insertion being given by row and col (which are 0-based).

gretl_matrix_copy_transpose ()

gretl_matrix *      gretl_matrix_copy_transpose         (const gretl_matrix *m);

gretl_matrix_reverse_rows ()

gretl_matrix *      gretl_matrix_reverse_rows           (const gretl_matrix *m);

gretl_matrix_reverse_cols ()

gretl_matrix *      gretl_matrix_reverse_cols           (const gretl_matrix *m);

gretl_matrix_get_diagonal ()

gretl_matrix *      gretl_matrix_get_diagonal           (const gretl_matrix *m,
                                                         int *err);

gretl_matrix_trace ()

double              gretl_matrix_trace                  (const gretl_matrix *m,
                                                         int *err);

gretl_matrix_random_fill ()

int                 gretl_matrix_random_fill            (gretl_matrix *m,
                                                         int dist);

Fills m with pseudo-random values from either the uniform or the standard normal distribution.

gretl_random_matrix_new ()

gretl_matrix *      gretl_random_matrix_new             (int r,
                                                         int c,
                                                         int dist);

Creates a new $r x c matrix and filles it with pseudo-random values from either the uniform or the standard normal distribution.

gretl_matrix_resample ()

gretl_matrix *      gretl_matrix_resample               (const gretl_matrix *m,
                                                         int *err);

gretl_matrix_block_resample ()

gretl_matrix *      gretl_matrix_block_resample         (const gretl_matrix *m,
                                                         int blocklen,
                                                         int *err);

gretl_vector_mean ()

double              gretl_vector_mean                   (const gretl_vector *v);

gretl_vector_variance ()

double              gretl_vector_variance               (const gretl_vector *v);

gretl_matrix_zero ()

void                gretl_matrix_zero                   (gretl_matrix *m);

Sets all elements of m to zero.

gretl_matrix_zero_upper ()

int                 gretl_matrix_zero_upper             (gretl_matrix *m);

Sets the elements of m outside of the lower triangle to zero.

gretl_matrix_zero_lower ()

int                 gretl_matrix_zero_lower             (gretl_matrix *m);

Sets the elements of m outside of the upper triangle to zero.

gretl_matrix_fill ()

void                gretl_matrix_fill                   (gretl_matrix *m,
                                                         double x);

Sets all entries in m to the value x.

gretl_matrix_multiply_by_scalar ()

void                gretl_matrix_multiply_by_scalar     (gretl_matrix *m,
                                                         double x);

Multiplies all elements of m by x.

gretl_matrix_divide_by_scalar ()

int                 gretl_matrix_divide_by_scalar       (gretl_matrix *m,
                                                         double x);

Divides all elements of m by x.

gretl_matrix_switch_sign ()

void                gretl_matrix_switch_sign            (gretl_matrix *m);

Changes the sign of each element of m.

gretl_matrix_dot_op ()

gretl_matrix *      gretl_matrix_dot_op                 (const gretl_matrix *a,
                                                         const gretl_matrix *b,
                                                         int op,
                                                         int *err);

gretl_matrix_complex_multiply ()

gretl_matrix *      gretl_matrix_complex_multiply       (const gretl_matrix *a,
                                                         const gretl_matrix *b,
                                                         int *err);

Computes the complex product of a and b. The first column in these matrices is assumed to contain real values, and the second column (if present) imaginary coefficients.

gretl_matrix_complex_divide ()

gretl_matrix *      gretl_matrix_complex_divide         (const gretl_matrix *a,
                                                         const gretl_matrix *b,
                                                         int *err);

Computes the complex division of a over b. The first column in these matrices is assumed to contain real values, and the second column (if present) imaginary coefficients.

gretl_matrix_exp ()

gretl_matrix *      gretl_matrix_exp                    (const gretl_matrix *m,
                                                         int *err);

Calculates the matrix exponential of m, using algorithm 11.3.1 from Golub and Van Loan, "Matrix Computations", 3e.

gretl_matrix_polroots ()

gretl_matrix *      gretl_matrix_polroots               (const gretl_matrix *a,
                                                         int *err);

Calculates the roots of the polynomial with coefficients given by a. If the degree of the polynomial is p, then a should contain p + 1 coefficients in ascending order, i.e. starting with the constant and ending with the coefficient on x^p.

gretl_matrix_raise ()

void                gretl_matrix_raise                  (gretl_matrix *m,
                                                         double x);

Raises each element of m to the power x.

gretl_matrix_free ()

void                gretl_matrix_free                   (gretl_matrix *m);

Frees the allocated storage in m, then m itself.

gretl_matrix_steal_data ()

double *            gretl_matrix_steal_data             (gretl_matrix *m);

"Steals" the allocated data from m, which is left with a NULL data pointer.

gretl_vector_copy_values ()

int                 gretl_vector_copy_values            (gretl_vector *targ,
                                                         const gretl_vector *src);

Copies the elements of src into the corresponding elements of targ.

gretl_matrix_copy_values ()

int                 gretl_matrix_copy_values            (gretl_matrix *targ,
                                                         const gretl_matrix *src);

Copies the elements of src into the corresponding elements of targ.

gretl_matrix_copy_values_shaped ()

int                 gretl_matrix_copy_values_shaped     (gretl_matrix *targ,
                                                         const gretl_matrix *src);

Copies the elements of src into targ, column by column.

gretl_matrix_add_to ()

int                 gretl_matrix_add_to                 (gretl_matrix *targ,
                                                         const gretl_matrix *src);

Adds the elements of src to the corresponding elements of targ.

gretl_matrix_add_transpose_to ()

int                 gretl_matrix_add_transpose_to       (gretl_matrix *targ,
                                                         const gretl_matrix *src);

Adds the elements of src, transposed, to the corresponding elements of targ.

gretl_matrix_subtract_from ()

int                 gretl_matrix_subtract_from          (gretl_matrix *targ,
                                                         const gretl_matrix *src);

Subtracts the elements of src from the corresponding elements of targ.

gretl_matrix_subtract_reversed ()

int                 gretl_matrix_subtract_reversed      (const gretl_matrix *a,
                                                         gretl_matrix *b);

Operates on b such that b_{ij} = a_{ij} - b_{ij}.

gretl_matrix_I_minus ()

int                 gretl_matrix_I_minus                (gretl_matrix *m);

Rewrites m as (I - m), where I is the n x n identity matrix.

gretl_matrix_transpose_in_place ()

int                 gretl_matrix_transpose_in_place     (gretl_matrix *m);

Tranposes m in place.

gretl_matrix_transpose ()

int                 gretl_matrix_transpose              (gretl_matrix *targ,
                                                         const gretl_matrix *src);

Fills out targ (which must be pre-allocated and of the right dimensions) with the transpose of src.

gretl_square_matrix_transpose ()

int                 gretl_square_matrix_transpose       (gretl_matrix *m);

Transposes the matrix m.

gretl_matrix_add_self_transpose ()

int                 gretl_matrix_add_self_transpose     (gretl_matrix *m);

Adds the transpose of m to m itself, yielding a symmetric matrix.

gretl_matrix_vectorize ()

int                 gretl_matrix_vectorize              (gretl_matrix *targ,
                                                         const gretl_matrix *src);

Writes into targ vec(src), that is, a column vector formed by stacking the columns of src.

gretl_matrix_unvectorize ()

int                 gretl_matrix_unvectorize            (gretl_matrix *targ,
                                                         const gretl_matrix *src);

Writes successive blocks of length m from src into the successive columns of targ (that is, performs the inverse of the vec() operation).

gretl_matrix_vectorize_h ()

int                 gretl_matrix_vectorize_h            (gretl_matrix *targ,
                                                         const gretl_matrix *src);

Writes into targ vech(src), that is, a column vector containing the lower-triangular elements of src. This is only useful for symmetric matrices, but for the sake of performance we don't check for that.

gretl_matrix_unvectorize_h ()

int                 gretl_matrix_unvectorize_h          (gretl_matrix *targ,
                                                         const gretl_matrix *src);

Rearranges successive blocks of decreasing length from src into the successive columns of targ (that is, performs the inverse of the vech() operation): targ comes out symmetric.

gretl_matrix_inscribe_matrix ()

int                 gretl_matrix_inscribe_matrix        (gretl_matrix *targ,
                                                         const gretl_matrix *src,
                                                         int row,
                                                         int col,
                                                         GretlMatrixMod mod);

Writes src into targ, starting at offset row, col. The targ matrix must be large enough to sustain the inscription of src at the specified point. If mod is GRETL_MOD_TRANSPOSE it is in fact the transpose of src that is written into targ.

gretl_matrix_extract_matrix ()

int                 gretl_matrix_extract_matrix         (gretl_matrix *targ,
                                                         const gretl_matrix *src,
                                                         int row,
                                                         int col,
                                                         GretlMatrixMod mod);

Writes into targ a sub-matrix of src, taken from the offset row, col. The targ matrix must be large enough to provide a sub-matrix of the dimensions of src. If mod is GRETL_MOD_TRANSPOSE it is in fact the transpose of the sub-matrix that that is written into targ.

gretl_matrix_multiply_mod ()

int                 gretl_matrix_multiply_mod           (const gretl_matrix *a,
                                                         GretlMatrixMod amod,
                                                         const gretl_matrix *b,
                                                         GretlMatrixMod bmod,
                                                         gretl_matrix *c,
                                                         GretlMatrixMod cmod);

Multiplies a (or a-transpose) into b (or b transpose), with the result written into c.

gretl_matrix_multiply ()

int                 gretl_matrix_multiply               (const gretl_matrix *a,
                                                         const gretl_matrix *b,
                                                         gretl_matrix *c);

Multiplies a into b, with the result written into c.

gretl_matrix_multiply_new ()

gretl_matrix *      gretl_matrix_multiply_new           (const gretl_matrix *a,
                                                         const gretl_matrix *b,
                                                         int *err);

Multiplies a into b, with the result written into a newly allocated matrix.

gretl_matrix_kronecker_product ()

int                 gretl_matrix_kronecker_product      (const gretl_matrix *A,
                                                         const gretl_matrix *B,
                                                         gretl_matrix *K);

Writes the Kronecker product of A and B into K.

gretl_matrix_kronecker_product_new ()

gretl_matrix *      gretl_matrix_kronecker_product_new  (const gretl_matrix *A,
                                                         const gretl_matrix *B,
                                                         int *err);

gretl_matrix_I_kronecker ()

int                 gretl_matrix_I_kronecker            (int p,
                                                         const gretl_matrix *B,
                                                         gretl_matrix *K);

Writes the Kronecker product of the identity matrix of order r and B into K.

gretl_matrix_I_kronecker_new ()

gretl_matrix *      gretl_matrix_I_kronecker_new        (int p,
                                                         const gretl_matrix *B,
                                                         int *err);

Writes the Kronecker product of the identity matrix of order r and B into a newly allocated matrix.

gretl_matrix_kronecker_I ()

int                 gretl_matrix_kronecker_I            (const gretl_matrix *A,
                                                         int r,
                                                         gretl_matrix *K);

Writes the Kronecker product of A and the identity matrix of order r into K.

gretl_matrix_kronecker_I_new ()

gretl_matrix *      gretl_matrix_kronecker_I_new        (const gretl_matrix *A,
                                                         int r,
                                                         int *err);

Writes into a newl allocated matrix the Kronecker product of A and the identity matrix of order r.

gretl_matrix_pow ()

gretl_matrix *      gretl_matrix_pow                    (const gretl_matrix *A,
                                                         int s,
                                                         int *err);

Calculates the matrix A^k using Golub and Van Loan's Algorithm 11.2.2 ("Binary Powering").

gretl_matrix_dot_product ()

double              gretl_matrix_dot_product            (const gretl_matrix *a,
                                                         GretlMatrixMod amod,
                                                         const gretl_matrix *b,
                                                         GretlMatrixMod bmod,
                                                         int *errp);

gretl_vector_dot_product ()

double              gretl_vector_dot_product            (const gretl_vector *a,
                                                         const gretl_vector *b,
                                                         int *errp);

gretl_matrix_row_sum ()

gretl_matrix *      gretl_matrix_row_sum                (const gretl_matrix *m,
                                                         int *err);

gretl_matrix_column_sum ()

gretl_matrix *      gretl_matrix_column_sum             (const gretl_matrix *m,
                                                         int *err);

gretl_matrix_row_mean ()

gretl_matrix *      gretl_matrix_row_mean               (const gretl_matrix *m,
                                                         int *err);

gretl_matrix_column_mean ()

gretl_matrix *      gretl_matrix_column_mean            (const gretl_matrix *m,
                                                         int *err);

gretl_matrix_column_sd ()

gretl_matrix *      gretl_matrix_column_sd              (const gretl_matrix *m,
                                                         int *err);

gretl_matrix_row_i_mean ()

double              gretl_matrix_row_i_mean             (const gretl_matrix *m,
                                                         int row);

gretl_matrix_column_j_mean ()

double              gretl_matrix_column_j_mean          (const gretl_matrix *m,
                                                         int col);

gretl_matrix_demean_by_row ()

void                gretl_matrix_demean_by_row          (gretl_matrix *m);

For each row of m, subtracts the row mean from each element on the row.

gretl_matrix_demean_by_column ()

void                gretl_matrix_demean_by_column       (gretl_matrix *m);

For each column of m, subtracts the column mean from each element in the column.

gretl_matrix_vcv ()

gretl_matrix *      gretl_matrix_vcv                    (gretl_matrix *m);

Forms a variance-covariance matrix based on m, thus: (1) subtract the column means from the column elements of m; (2) multiply m-transpose into m; and (3) divide the elements of the product by the number of rows in m.

gretl_matrix_quantiles ()

gretl_matrix *      gretl_matrix_quantiles              (const gretl_matrix *m,
                                                         double p,
                                                         int *err);

gretl_matrix_determinant ()

double              gretl_matrix_determinant            (gretl_matrix *a,
                                                         int *err);

Compute the determinant of the square matrix a using the LU factorization. Matrix a is not preserved: it is overwritten by the factorization.

gretl_matrix_log_determinant ()

double              gretl_matrix_log_determinant        (gretl_matrix *a,
                                                         int *err);

Compute the log of the determinant of the square matrix a using LU factorization. Matrix a is not preserved: it is overwritten by the factorization.

gretl_matrix_log_abs_determinant ()

double              gretl_matrix_log_abs_determinant    (gretl_matrix *a,
                                                         int *err);

Compute the log of the absolute value of the determinant of the square matrix a using LU factorization. Matrix a is not preserved: it is overwritten by the factorization.

gretl_vcv_log_determinant ()

double              gretl_vcv_log_determinant           (const gretl_matrix *m);

Compute the log determinant of the symmetric positive-definite matrix m using Cholesky decomposition.

gretl_matrix_one_norm ()

double              gretl_matrix_one_norm               (const gretl_matrix *m);

gretl_matrix_infinity_norm ()

double              gretl_matrix_infinity_norm          (const gretl_matrix *m);

gretl_LU_solve ()

int                 gretl_LU_solve                      (gretl_matrix *a,
                                                         gretl_matrix *b);

Solves ax = b for the unknown x, using LU decomposition. On exit, b is replaced by the solution and a is replaced by its LU decomposition.

gretl_cholesky_decomp_solve ()

int                 gretl_cholesky_decomp_solve         (gretl_matrix *a,
                                                         gretl_matrix *b);

Solves ax = b for the unknown vector x, using Cholesky decomposition via the lapack functions dpotrf and dpotrs.

On exit, b is replaced by the solution and a is replaced by its Cholesky decomposition.

gretl_cholesky_solve ()

int                 gretl_cholesky_solve                (const gretl_matrix *a,
                                                         gretl_vector *b);

Solves ax = b for the unknown vector x, using the pre-computed Cholesky decomposition of a. On exit, b is replaced by the solution.

gretl_toeplitz_solve ()

gretl_vector *      gretl_toeplitz_solve                (const gretl_vector *c,
                                                         const gretl_vector *r,
                                                         const gretl_vector *b,
                                                         int *err);

Solves Tx = b for the unknown vector x, where T is a Toeplitz matrix, that is (zero-based)

T_{ij} = c_{i-j} for i <= j T_{ij} = r_{i-j} for i > j

Note that c[0] should equal r[0].

gretl_matrix_XTX_new ()

gretl_matrix *      gretl_matrix_XTX_new                (const gretl_matrix *X);

gretl_inverse_from_cholesky_decomp ()

int                 gretl_inverse_from_cholesky_decomp  (gretl_matrix *targ,
                                                         const gretl_matrix *src);

Computes in targ the inverse of a symmetric positive definite matrix, on the assumption that the original matrix this has already been Cholesky-decomposed in src.

gretl_invert_general_matrix ()

int                 gretl_invert_general_matrix         (gretl_matrix *a);

Computes the inverse of a general matrix using LU factorization. On exit a is overwritten with the inverse. Uses the lapack functions dgetrf and dgetri.

gretl_invert_symmetric_indef_matrix ()

int                 gretl_invert_symmetric_indef_matrix (gretl_matrix *a);

Computes the inverse of a real symmetric matrix via the Bunch-Kaufman diagonal pivoting method. Uses the lapack functions dsytrf and dsytri. On exit a is overwritten with the inverse.

gretl_invert_symmetric_matrix ()

int                 gretl_invert_symmetric_matrix       (gretl_matrix *a);

Computes the inverse of a symmetric positive definite matrix using Cholesky factorization. On exit a is overwritten with the inverse. Uses the lapack functions dpotrf and dpotri.

gretl_invert_symmetric_matrix2 ()

int                 gretl_invert_symmetric_matrix2      (gretl_matrix *a,
                                                         double *ldet);

Computes the inverse of a symmetric positive definite matrix using Cholesky factorization, computing the log-determinant in the process. On exit a is overwritten with the inverse and if ldet is not NULL the log-determinant is written to that location. Uses the lapack functions dpotrf and dpotri.

gretl_invert_packed_symmetric_matrix ()

int                 gretl_invert_packed_symmetric_matrix
                                                        (gretl_matrix *v);

Computes the inverse of a symmetric positive definite matrix, stored in vech form, using Cholesky factorization. On exit v is overwritten with the lower triangle of the inverse. Uses the lapack functions dpptrf and dpptri.

gretl_invert_triangular_matrix ()

int                 gretl_invert_triangular_matrix      (gretl_matrix *a,
                                                         char uplo);

Computes the inverse of a triangular matrix. On exit a is overwritten with the inverse. Uses the lapack function dtrtri.

gretl_invert_diagonal_matrix ()

int                 gretl_invert_diagonal_matrix        (gretl_matrix *a);

Computes the inverse of a diagonal matrix. On exit a is overwritten with the inverse.

gretl_invert_matrix ()

int                 gretl_invert_matrix                 (gretl_matrix *a);

Computes the inverse of matrix a: on exit a is overwritten with the inverse. If a is diagonal or symmetric, appropriate simple inversion routines are called.

gretl_matrix_moore_penrose ()

int                 gretl_matrix_moore_penrose          (gretl_matrix *A);

Computes the generalized inverse of matrix a via its SVD factorization, with the help of the lapack function dgesvd. On exit the original matrix is overwritten by the inverse.

gretl_SVD_invert_matrix ()

int                 gretl_SVD_invert_matrix             (gretl_matrix *a);

Computes the inverse (or generalized inverse) of a general square matrix using SVD factorization, with the help of the lapack function dgesvd. If any of the singular values of a are less than 1.0e-9 the Moore-Penrose generalized inverse is computed instead of the standard inverse. On exit the original matrix is overwritten by the inverse.

gretl_invpd ()

int                 gretl_invpd                         (gretl_matrix *a);

Computes the inverse of a symmetric positive definite matrix using Cholesky factorization. On exit a is overwritten with the inverse. Uses the lapack functions dpotrf and dpotri. Little checking is done, for speed: we assume the caller knows what he's doing.

gretl_maybe_invpd ()

int                 gretl_maybe_invpd                   (gretl_matrix *a);

Attempts to computes the inverse of a matrix which may be positive definite. On exit a is overwritten with the inverse. Uses the lapack functions dpotrf and dpotri. Little checking is done, for speed: we assume the caller knows what he's doing. Unlike gretl_invpd() this function does not sump error messages to stderr in case the matrix is not in fact positive definite.

gretl_matrix_SVD ()

int                 gretl_matrix_SVD                    (const gretl_matrix *a,
                                                         gretl_matrix **pu,
                                                         gretl_vector **ps,
                                                         gretl_matrix **pvt);

Computes SVD factorization of a general matrix using the lapack function dgesvd. A = u * diag(s) * vt.

gretl_symmetric_matrix_rcond ()

double              gretl_symmetric_matrix_rcond        (const gretl_matrix *m,
                                                         int *err);

Estimates the reciprocal condition number of the real symmetric positive definite matrix m (in the 1-norm), using the lapack functions dpotrf and dpocon.

gretl_matrix_rcond ()

double              gretl_matrix_rcond                  (const gretl_matrix *m,
                                                         int *err);

Estimates the reciprocal condition number of the real matrix m (in the 1-norm).

gretl_general_eigen_sort ()

int                 gretl_general_eigen_sort            (gretl_matrix *evals,
                                                         gretl_matrix *evecs,
                                                         int rank);

Sorts the real components of the eigenvalues in evals from largest to smallest, and rearranges the columns in evecs correspondingly. If rank is greater than zero and less than the number of columns in evecs, then on output evecs is shrunk so that it contains only the columns associated with the largest rank eigenvalues.

gretl_symmetric_eigen_sort ()

int                 gretl_symmetric_eigen_sort          (gretl_matrix *evals,
                                                         gretl_matrix *evecs,
                                                         int rank);

Sorts the eigenvalues in evals from largest to smallest, and rearranges the columns in evecs correspondingly. If rank is greater than zero and less than the number of columns in evecs, then on output evecs is shrunk so that it contains only the columns associated with the largest rank eigenvalues.

gretl_general_matrix_eigenvals ()

gretl_matrix *      gretl_general_matrix_eigenvals      (gretl_matrix *m,
                                                         int eigenvecs,
                                                         int *err);

Computes the eigenvalues of the general matrix m. If eigenvecs is non-zero, also compute the right eigenvectors of m, which are stored in m. Uses the lapack function dgeev.

gretl_symmetric_matrix_eigenvals ()

gretl_matrix *      gretl_symmetric_matrix_eigenvals    (gretl_matrix *m,
                                                         int eigenvecs,
                                                         int *err);

Computes the eigenvalues of the real symmetric matrix m. If eigenvecs is non-zero, also compute the orthonormal eigenvectors of m, which are stored in m. Uses the lapack function dsyev.

gretl_gensymm_eigenvals ()

gretl_matrix *      gretl_gensymm_eigenvals             (const gretl_matrix *A,
                                                         const gretl_matrix *B,
                                                         gretl_matrix *V,
                                                         int *err);

Solves the generalized eigenvalue problem | A - \lambda B | = 0 , where both A and B are symmetric and B is positive definite.

gretl_matrix_right_nullspace ()

gretl_matrix *      gretl_matrix_right_nullspace        (const gretl_matrix *M,
                                                         int *err);

Given an m x n matrix M, construct a conformable matrix R such that MR = 0 (that is, all the columns of R are orthogonal to the space spanned by the rows of M).

gretl_matrix_left_nullspace ()

gretl_matrix *      gretl_matrix_left_nullspace         (const gretl_matrix *M,
                                                         GretlMatrixMod mod,
                                                         int *err);

Given an m x n matrix M, construct a conformable matrix L such that LM = 0 (that is, all the columns of M are orthogonal to the space spanned by the rows of L).

gretl_matrix_row_concat ()

gretl_matrix *      gretl_matrix_row_concat             (const gretl_matrix *a,
                                                         const gretl_matrix *b,
                                                         int *err);

gretl_matrix_col_concat ()

gretl_matrix *      gretl_matrix_col_concat             (const gretl_matrix *a,
                                                         const gretl_matrix *b,
                                                         int *err);

gretl_matrix_inplace_colcat ()

int                 gretl_matrix_inplace_colcat         (gretl_matrix *a,
                                                         const gretl_matrix *b,
                                                         const char *mask);

Concatenates onto a the selected columns of b, if the two matrices are conformable.

gretl_matrix_cumcol ()

gretl_matrix *      gretl_matrix_cumcol                 (const gretl_matrix *m,
                                                         int *err);

gretl_matrix_diffcol ()

gretl_matrix *      gretl_matrix_diffcol                (const gretl_matrix *m,
                                                         double missval,
                                                         int *err);

gretl_matrix_lag ()

gretl_matrix *      gretl_matrix_lag                    (const gretl_matrix *m,
                                                         const gretl_vector *k,
                                                         double missval);

gretl_matrix_inplace_lag ()

int                 gretl_matrix_inplace_lag            (gretl_matrix *targ,
                                                         const gretl_matrix *src,
                                                         int k);

Fills out targ (if it is of the correct dimensions), with (columnwise) lags of src, using 0 for missing values.

gretl_matrix_cholesky_decomp ()

int                 gretl_matrix_cholesky_decomp        (gretl_matrix *a);

Computes the Cholesky factorization of the symmetric, positive definite matrix a. On exit the lower triangle of a is replaced by the factor L, as in a = LL', and the upper triangle is set to zero. Uses the lapack function dpotrf.

gretl_matrix_psd_root ()

int                 gretl_matrix_psd_root               (gretl_matrix *a);

Computes the LL' factorization of the symmetric, positive semidefinite matrix a. On successful exit the lower triangle of a is replaced by the factor L and the upper triangle is set to zero.

gretl_matrix_QR_decomp ()

int                 gretl_matrix_QR_decomp              (gretl_matrix *M,
                                                         gretl_matrix *R);

Computes the QR factorization of M. On successful exit the matrix M holds Q, and, if R is not NULL, the upper triangle of R holds R. Uses the lapack functions dgeqrf and dorgqr.

gretl_check_QR_rank ()

int                 gretl_check_QR_rank                 (const gretl_matrix *R,
                                                         int *err,
                                                         double *rcnd);

Checks the reciprocal condition number of R and calculates the rank of the matrix QR. If rcnd is not NULL it receives the reciprocal condition number.

gretl_matrix_rank ()

int                 gretl_matrix_rank                   (const gretl_matrix *a,
                                                         int *err);

Computes the rank of a via its SV decomposition.

gretl_matrix_ols ()

int                 gretl_matrix_ols                    (const gretl_vector *y,
                                                         const gretl_matrix *X,
                                                         gretl_vector *b,
                                                         gretl_matrix *vcv,
                                                         gretl_vector *uhat,
                                                         double *s2);

Computes OLS estimates using Cholesky factorization by default, but with a fallback to QR decomposition if the data are highly ill-conditioned, and puts the coefficient estimates in b. Optionally, calculates the covariance matrix in vcv and the residuals in uhat.

gretl_matrix_multi_ols ()

int                 gretl_matrix_multi_ols              (const gretl_matrix *Y,
                                                         const gretl_matrix *X,
                                                         gretl_matrix *B,
                                                         gretl_matrix *E,
                                                         gretl_matrix **XTXi);

Computes OLS estimates using Cholesky decomposition by default, but with a fallback to QR decomposition if the data are highly ill-conditioned, and puts the coefficient estimates in B. Optionally, calculates the residuals in E.

gretl_matrix_multi_SVD_ols ()

int                 gretl_matrix_multi_SVD_ols          (const gretl_matrix *Y,
                                                         const gretl_matrix *X,
                                                         gretl_matrix *B,
                                                         gretl_matrix *E,
                                                         gretl_matrix **XTXi);

Computes OLS estimates using SVD decomposition, and puts the coefficient estimates in B. Optionally, calculates the residuals in E, (X'X)^{-1} in XTXi.

gretl_matrix_QR_ols ()

int                 gretl_matrix_QR_ols                 (const gretl_matrix *Y,
                                                         const gretl_matrix *X,
                                                         gretl_matrix *B,
                                                         gretl_matrix *E,
                                                         gretl_matrix **XTXi,
                                                         gretl_matrix **Qout);

Computes OLS estimates using QR decomposition, and puts the coefficient estimates in B. Optionally, calculates the residuals in E, (X'X)^{-1} in XTXi, and/or the matrix Q in Qout.

gretl_matrix_r_squared ()

double              gretl_matrix_r_squared              (const gretl_matrix *y,
                                                         const gretl_matrix *X,
                                                         const gretl_matrix *b,
                                                         int *err);

gretl_matrix_SVD_johansen_solve ()

int                 gretl_matrix_SVD_johansen_solve     (const gretl_matrix *R0,
                                                         const gretl_matrix *R1,
                                                         gretl_matrix *evals,
                                                         gretl_matrix *B,
                                                         gretl_matrix *A,
                                                         int jrank);

Solves the Johnsen generalized eigenvalue problem via SVD decomposition. See J. A. Doornik and R. J. O'Brien, "Numerically stable cointegration analysis", Computational Statistics and Data Analysis, 41 (2002), pp. 185-193, Algorithm 4.

If B is non-null it should be p1 x p on input; it will be trimmed to p1 x jrank on output if jrank < p. If A is non-null it should be p x p on input; it will be trimmed to p x jrank on output if jrank < p. evals should be a vector of length jrank.

gretl_matrix_restricted_ols ()

int                 gretl_matrix_restricted_ols         (const gretl_vector *y,
                                                         const gretl_matrix *X,
                                                         const gretl_matrix *R,
                                                         const gretl_vector *q,
                                                         gretl_vector *b,
                                                         gretl_matrix *vcv,
                                                         gretl_vector *uhat,
                                                         double *s2);

Computes OLS estimates restricted by R and q, using LU factorization, and puts the coefficient estimates in b. Optionally, calculates the covariance matrix in vcv.

gretl_matrix_SVD_ols ()

int                 gretl_matrix_SVD_ols                (const gretl_vector *y,
                                                         const gretl_matrix *X,
                                                         gretl_vector *b,
                                                         gretl_matrix *vcv,
                                                         gretl_vector *uhat,
                                                         double *s2);

Computes OLS estimates using SVD decomposition, and puts the coefficient estimates in b. Optionally, calculates the covariance matrix in vcv and the residuals in uhat.

gretl_matrix_qform ()

int                 gretl_matrix_qform                  (const gretl_matrix *A,
                                                         GretlMatrixMod amod,
                                                         const gretl_matrix *X,
                                                         gretl_matrix *C,
                                                         GretlMatrixMod cmod);

Computes either A * X * A' (if amod = GRETL_MOD_NONE) or A' * X * A (if amod = GRETL_MOD_TRANSPOSE), with the result written into C. The matrix X must be symmetric, but this is not checked, to save time. If you are in doubt on this point you can call gretl_matrix_is_symmetric() first.

gretl_scalar_qform ()

double              gretl_scalar_qform                  (const gretl_vector *b,
                                                         const gretl_matrix *X,
                                                         int *errp);

Computes the scalar product bXb', or b'Xb if b is a column vector. The content of errp is set to 0 on success, or a non-zero code on failure.

gretl_matrix_columnwise_product ()

int                 gretl_matrix_columnwise_product     (const gretl_matrix *A,
                                                         const gretl_matrix *B,
                                                         gretl_matrix *C);

gretl_matrix_diagonal_sandwich ()

int                 gretl_matrix_diagonal_sandwich      (const gretl_vector *d,
                                                         const gretl_matrix *X,
                                                         gretl_matrix *DXD);

Computes in DXD (which must be pre-allocated), the matrix product D * X * D, where D is a diagonal matrix with elements given by the vector d.

gretl_matrix_set_t1 ()

void                gretl_matrix_set_t1                 (gretl_matrix *m,
                                                         int t);

Sets an integer value on the t1 member of the gretl_matrix (used for internal information).

gretl_matrix_set_t2 ()

void                gretl_matrix_set_t2                 (gretl_matrix *m,
                                                         int t);

Sets an integer value on the t2 member of the gretl_matrix (used for internal information).

gretl_matrix_get_t1 ()

int                 gretl_matrix_get_t1                 (const gretl_matrix *m);

gretl_matrix_get_t2 ()

int                 gretl_matrix_get_t2                 (const gretl_matrix *m);

gretl_is_identity_matrix ()

int                 gretl_is_identity_matrix            (const gretl_matrix *m);

gretl_is_zero_matrix ()

int                 gretl_is_zero_matrix                (const gretl_matrix *m);

gretl_matrix_get_structure ()

int                 gretl_matrix_get_structure          (const gretl_matrix *m);

gretl_matrices_are_equal ()

int                 gretl_matrices_are_equal            (const gretl_matrix *a,
                                                         const gretl_matrix *b,
                                                         int *err);

gretl_covariance_matrix ()

gretl_matrix *      gretl_covariance_matrix             (const gretl_matrix *m,
                                                         int corr,
                                                         int *errp);

gretl_matrix_array_new ()

gretl_matrix **     gretl_matrix_array_new              (int n);

Allocates an array of n gretl matrix pointers. On successful allocation of the array, each element is initialized to NULL.

gretl_matrix_array_new_with_size ()

gretl_matrix **     gretl_matrix_array_new_with_size    (int n,
                                                         int rows,
                                                         int cols);

Allocates an array of n gretl matrix pointers, each one with size rows * cols.

gretl_matrix_array_free ()

void                gretl_matrix_array_free             (gretl_matrix **A,
                                                         int n);

Frees each of the n gretl matrices in the array A, and the array itself. See also gretl_matrix_array_alloc().

gretl_matrix_values ()

gretl_matrix *      gretl_matrix_values                 (const double *x,
                                                         int n,
                                                         int *err);

gretl_matrix_shape ()

gretl_matrix *      gretl_matrix_shape                  (const gretl_matrix *A,
                                                         int r,
                                                         int c);

Creates an (r x c) matrix containing the re-arranged values of A. Elements are read from A by column and written into the target, also by column. If A contains less elements than n = r*c, they are repeated cyclically; if A has more elements, only the first n are used.

gretl_matrix_trim_rows ()

gretl_matrix *      gretl_matrix_trim_rows              (const gretl_matrix *A,
                                                         int ttop,
                                                         int tbot,
                                                         int *err);

Creates a new matrix which is a copy of A with ttop rows trimmed from the top and tbot rows trimmed from the bottom.

gretl_matrix_minmax ()

gretl_matrix *      gretl_matrix_minmax                 (const gretl_matrix *A,
                                                         int mm,
                                                         int rc,
                                                         int idx,
                                                         int *err);

Creates a matrix holding the row or column mimima or maxima from A, either as values or as location indices. For example, if mm = 0, rc = 0, and idx = 0, the created matrix is m x 1 and holds the values of the row minima.

gretl_matrix_pca ()

gretl_matrix *      gretl_matrix_pca                    (const gretl_matrix *X,
                                                         int p,
                                                         int *err);

Carries out a Principal Components analysis of X and returns the first p components: the component corresponding to the largest eigenvalue of the correlation matrix of X is placed in column 1, and so on.

gretl_matrix_xtab ()

gretl_matrix *      gretl_matrix_xtab                   (int t1,
                                                         int t2,
                                                         const double *x,
                                                         const double *y,
                                                         int *err);

Computes the cross tabulation of the values contained in the vectors x (by row) and y (by column). These must be integer values.

matrix_matrix_xtab ()

gretl_matrix *      matrix_matrix_xtab                  (const gretl_matrix *x,
                                                         const gretl_matrix *y,
                                                         int *err);

Computes the cross tabulation of the values contained in the vectors x (by row) and y (by column). These must be integer values.

gretl_matrix_bool_sel ()

gretl_matrix *      gretl_matrix_bool_sel               (const gretl_matrix *A,
                                                         const gretl_matrix *sel,
                                                         int rowsel,
                                                         int *err);

If rowsel = 1, constructs a matrix which contains the rows of A corresponding to non-zero values in the vector sel; if rowsel = 0, does the same thing but column-wise.

gretl_matrix_sort_by_column ()

gretl_matrix *      gretl_matrix_sort_by_column         (const gretl_matrix *m,
                                                         int k,
                                                         int *err);

Produces a matrix which contains the rows of m, re- ordered by increasing value of the elements in column k.

gretl_matrix_covariogram ()

gretl_matrix *      gretl_matrix_covariogram            (const gretl_matrix *X,
                                                         const gretl_matrix *u,
                                                         const gretl_matrix *w,
                                                         int p,
                                                         int *err);

Produces the matrix covariogram,

\sum_{j=-p}^{p} \sum_j w_{|j|} (X_t' u_t u_{t-j} X_{t-j})

If u is not given the u terms are omitted, and if w is not given, all the weights are 1.0.

gretl_matrix_transcribe_obs_info ()

void                gretl_matrix_transcribe_obs_info    (gretl_matrix *targ,
                                                         const gretl_matrix *src);

If targ and src have the same number of rows, and if the rows of src are identified by observation stamps while those of targ are not so identified, copy the stamp information across to targ. (Or if the given conditions are not satified, do nothing.)

lapack_mem_free ()

void                lapack_mem_free                     (void);

set_blas_nmk_min ()

void                set_blas_nmk_min                    (int n);

get_blas_nmk_min ()

int                 get_blas_nmk_min                    (void);