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- Function:
*int***gsl_linalg_tri_upper_invert***(gsl_matrix **`T`) - Function:
*int***gsl_linalg_tri_lower_invert***(gsl_matrix **`T`) - Function:
*int***gsl_linalg_tri_upper_unit_invert***(gsl_matrix **`T`) - Function:
*int***gsl_linalg_tri_lower_unit_invert***(gsl_matrix **`T`) These functions calculate the in-place inverse of the triangular matrix

`T`. When the`upper`

prefix is specified, then the upper triangle of`T`is used, and when the`lower`

prefix is specified, the lower triangle is used. If the`unit`

prefix is specified, then the diagonal elements of the matrix`T`are taken as unity and are not referenced. Otherwise the diagonal elements are used in the inversion.

- Function:
*int***gsl_linalg_tri_upper_rcond***(const gsl_matrix **`T`, double *`rcond`, gsl_vector *`work`) - Function:
*int***gsl_linalg_tri_lower_rcond***(const gsl_matrix **`T`, double *`rcond`, gsl_vector *`work`) These functions estimate the reciprocal condition number, in the 1-norm, of the upper or lower

*N*-by-*N*triangular matrix`T`. The reciprocal condition number is stored in`rcond`on output, and is defined by*1 / (||T||_1 \cdot ||T^{-1}||_1)*. Additional workspace of size*3 N*is required in`work`.