NumCosmoMathMatrix

If cm is not NULL, decreases its reference count by one and sets cm to NULL.

Allocates a matrix with every element zero.

Replaces *cm by a new reference to nm, releasing the previous one. With check_size, aborts if both are set and their shapes differ.

Adds cm2 to cm1; they must have the same shape.

Adds val to every element.

Sets $M_1 \to M_1 + a M_2$.

Adds val to the element ($i$, $j$).

Creates a view of all the elements of cm, row after row, holding a reference to cm. The tda of cm must equal its number of columns.

Computes the squared Mahalanobis distance of each column of cm from theta under the covariance $C = U^\intercal U$, $$\chi^2_p = (x_p - \theta)^\intercal C^{-1} (x_p - \theta),$$ and stores it in the first $n_p$ entries of chi2. The triangular solve $y_p = (x_p - \theta) U^{-1}$ and the norm $|y_p|^2$ are done in one pass, on blocks of $n_b$ columns, with work as the only scratch.

Replaces the UL triangle of the symmetric positive definite cm by its Cholesky factor, with LAPACK dpotrf.

Stores in decomp the Cholesky factor of cm, reading the UL triangle and leaving cm unchanged. If cm is not positive definite to rounding, the factor of the nearest positive definite matrix, from ncm_matrix_nearPD(), is stored instead.

Replaces the Cholesky factor in the UL triangle of cm, from ncm_matrix_cholesky_decomp(), by that triangle of the inverse of the original matrix, with LAPACK dpotri.

cm holds the Cholesky factor from ncm_matrix_cholesky_decomp(). The product of the diagonal is rescaled as it is accumulated, so it cannot overflow.

Solves $A x = b$ for the symmetric positive definite $A$ in cm, with LAPACK dposv: cm is replaced by the Cholesky factor in its UL triangle and b by $x$.

Solves $A x = b$ with the Cholesky factor of $A$ already in cm, from ncm_matrix_cholesky_decomp(), with LAPACK dpotrs; b is replaced by $x$.

Same as ncm_matrix_cmp() over the diagonal only.

Same as ncm_matrix_nrows().

Decreases the reference count of cm by one.

Copies the upper triangle of the square cm over the lower for UL ‘U’, or the lower over the upper for ‘L’. Aborts if cm is not square or UL is invalid.

Stores in cor the correlation matrix of the covariance cov; they may be the same object.

Sets $C \to \alpha\,\mathrm{op}(A)\,\mathrm{op}(B) + \beta C$.

Divides cm1 by cm2, element by element; they must have the same shape.

Sets $C \to \alpha A B + \beta C$, reading only the UL triangle of $A$. The three matrices are square and of the same size.

Sets $C \to \alpha A A^\intercal + \beta C$ for Trans ‘N’, or $C \to \alpha A^\intercal A + \beta C$ for ‘T’. Only the UL triangle of $C$ is written.

Sets $B \to \alpha\,\mathrm{op}(A)\,B$ for Side ‘L’, or $B \to \alpha B\,\mathrm{op}(A)$ for ‘R’. Only the UL triangle of $A$ is read, its diagonal taken as stored.

Sets $v \to \mathrm{op}(A)\,v$. Only the UL triangle of $A$ is read, its diagonal taken as stored.

Sets $B \to \alpha\,\mathrm{op}(A)^{-1} B$ for Side ‘L’, or $B \to \alpha B\,\mathrm{op}(A)^{-1}$ for ‘R’. Only the UL triangle of $A$ is read, its diagonal taken as stored.

Sets $v \to \mathrm{op}(A)^{-1} v$. Only the UL triangle of $A$ is read, its diagonal taken as stored.

Reads the data directly: the element ($i$, $j$) is at ij $= i\,\mathrm{tda} + j$.

Writes the data directly: the element ($i$, $j$) is at ij $= i\,\mathrm{tda} + j$.

Replaces cm by a random correlation matrix from the vine construction of Lewandowski, Kurowicka and Joe (2009): the partial correlations are drawn from Beta($\beta$, $\beta$) mapped to $[-1, 1]$, so a smaller cor_level gives stronger correlations.

Replaces cm by a random covariance matrix: the correlations of ncm_matrix_fill_rand_cor() and standard deviations drawn uniformly in [sigma_min, sigma_max].

Replaces cm by a random covariance matrix: the correlations of ncm_matrix_fill_rand_cor() and standard deviations $\sigma_k = |\mu_k| r_k$, or $r_k$ where $\mu_k = 0$, with $r_k$ drawn log-uniformly in [reltol_min, reltol_max].

Decreases the reference count of cm by one.

cm must have been created by ncm_matrix_new_array().

Creates a view of the column col, holding a reference to cm.

Reads the data of cm in column-major order.

Copies the diagonal of cm to the first entries of diag.

Creates a view of the row row, holding a reference to cm.

Creates a view of the nrows by ncols block of cm whose first element is (k1, k2), holding a reference to cm.

Aborts if cm is not square.

Logs the elements of cm, one row per line.

Copies cm2 into cm1; they must have the same shape.

Copies cm2 into cm1, writing the data of cm1 in column-major order; they must have the same shape.

Multiplies the column col_i by val.

Multiplies cm1 by cm2, element by element; they must have the same shape.

Multiplies the row row_i by val.

Replaces the symmetric cm, stored in its UL triangle, by the nearest positive definite matrix in the Frobenius norm, Higham (2002), iterating until its Cholesky decomposition succeeds or maxiter is reached.

Creates a GVariant of type aad sharing the data of cm, which must not change while the variant exists.

Increases the reference count of cm by one.

Same as ncm_matrix_ncols().

Multiplies every element by val.

Sets $M \to M\,\mathrm{diag}(s)$.

Sets $M \to \mathrm{diag}(s)\,M$.

Sets the element ($i$, $j$) to val.

Sets every element to val.

Copies cv into the column n; its length must be the number of rows.

Sets the element ($i$, $j$), in column-major order, to val.

Sets the diagonal of cm to the first entries of diag.

Sets the elements of cm; a must hold as many values as cm has elements.

Sets the elements of cm; data must hold as many values as cm has elements.

Sets the elements of cm to those of var. A matrix without elements is allocated with the shape of var. Aborts if var has another type or shape.

Sets cm, square or not, to one on the diagonal and zero elsewhere.

Copies cv into the row n; its length must be the number of columns.

Sets every element to zero.

Stores in the UL triangle of sym the symmetric $M M^\intercal$ for NT ‘N’, or $M^\intercal M$ for ‘T’.

Subtracts cm2 from cm1; they must have the same shape.

Sets $M_{ij} \to M_{ij} - v_j$, subtracting v from every row.

Computes the matrix exponential of cm from its eigendecomposition, and stores in exp_cm_dec the upper triangular $U$ with $\exp(M) = U^\intercal U$.

Stores in ln_cm the matrix logarithm $\ln M$, from the eigendecomposition of cm.

Sets $u \to \alpha M v + \beta u$, reading only the UL triangle of $M$.

Transposes the square cm in place.

Copies the transpose of src into cm, whose shape must be that of the transpose.

Stores in sym the symmetric $M^\intercal M$ for an upper triangular cm, or $M M^\intercal$ for a lower one. Unless zero is TRUE, the other triangle of cm must already be zero.

Sets $u \to \alpha\,\mathrm{op}(M)\,v + \beta u$; any NT other than ‘N’ transposes.

Sets to zero the strict lower triangle of the square cm for UL ‘U’, or its strict upper triangle for ‘L’. Factorizations leave the other triangle as it was, so a routine reading the whole matrix needs it cleared. Aborts if cm is not square or UL is invalid.