# Matrix API

Source: https://sh4zam.com/api/matrix/

> In-memory matrix manipulation for 4x4 and smaller matrices

These types and their corresponding functions are for working with matrices stored within memory, as opposed to being preloaded within the XMTRX back-bank of FP registers. Typically this is desirable for one-off operations where there is no batching of matrix operations, especially when clobbering XMTRX is undesirable. Matrices are column-major, as with GL, and `shz_mat4x4_t` must be aligned on 8-byte boundaries unless you use an `_unaligned` routine. Beware that some of these routines clobber the matrix currently loaded as the active 4x4 matrix, XMTRX.

- **C header:** `#include <sh4zam/shz_matrix.h>`
- **C++ header:** `#include <sh4zam/shz_matrix.hpp>`
- **C++ types:** [`shz::mat4x4`](https://sh4zam.com/api/cpp/mat4x4/)
- **Symbols:** 120

## Verb model

For most transform types this API offers several versions of the same operation. Using translation as the example:

| Verb | Meaning |
| --- | --- |
| `init_*` | **Initializes** the whole matrix to the given transform, setting the other components to identity. |
| `set_*` | **Sets** only the values corresponding to the given transform, leaving the others alone. |
| `apply_*` | **Applies** the transform, updating only the affected values based on their current values (additively for translation, multiplicatively for scaling and rotation). |
| `translate / scale / rotate_*` | **GL-style**: multiplies and accumulates the matrix by a matrix initialized to the given transform. The most general form. |
| `load_* / store_*` | Moves a matrix between memory and XMTRX. `load_apply_*` and `load_apply_store_*` are fused combinations. |
| `transform_*` | Transforms vectors or points. For `vec3` variants, `transform_point*` implies w = 1 and `transform_vec*` implies w = 0. |

## Suffixes

Suffixes used in this module. The full list is in [Naming and Suffixes](https://sh4zam.com/concepts/naming-and-suffixes/).

- `_unaligned`: Works on matrix data that is not 8-byte aligned, passed as a plain `float[16]`. The default routines use 64-bit paired `FMOV` loads that need 8-byte alignment.
- `_transpose`: Operates with the transposed matrix (row-major input, or inverse-rotation use).
- `_wxyz`: Register/column permutation so that `FTRV` yields W first (cycle 4 instead of 7), which helps perspective division.
- `_safe`: Guards degenerate input (zero-length vectors, zero denominators) at a small cost.

## Initialization

Routines for fully initializing a matrix.

| Symbol | Description |
| --- | --- |
| [`shz_mat4x4_init_identity`](https://sh4zam.com/api/matrix/shz_mat4x4_init_identity/) | Initializes the given matrix to the 4x4 identity matrix. |
| [`shz_mat4x4_init_identity_safe`](https://sh4zam.com/api/matrix/shz_mat4x4_init_identity_safe/) | Safely initializes the given matrix to the 4x4 identity matrix. |
| [`shz_mat4x4_init_zero`](https://sh4zam.com/api/matrix/shz_mat4x4_init_zero/) | Initializes the given matrix with all 0s for its element values. |
| [`shz_mat4x4_init_one`](https://sh4zam.com/api/matrix/shz_mat4x4_init_one/) | Initializes the given matrix with all 1s for its element values. |
| [`shz_mat4x4_init_fill`](https://sh4zam.com/api/matrix/shz_mat4x4_init_fill/) | Initializes the given matrix with all elements assigned to the given value. |
| [`shz_mat4x4_init_translation`](https://sh4zam.com/api/matrix/shz_mat4x4_init_translation/) | Initializes the given matrix to a 3D translation matrix with the given coordinates. |
| [`shz_mat4x4_init_scale`](https://sh4zam.com/api/matrix/shz_mat4x4_init_scale/) | Initializes the given matrix to a 3D scaling matrix with the given dimensions. |
| [`shz_mat4x4_init_rotation_x`](https://sh4zam.com/api/matrix/shz_mat4x4_init_rotation_x/) | Initializes the given matrix to a 3D rotation matrix by `xAngle` radians over the X-axis. |
| [`shz_mat4x4_init_rotation_y`](https://sh4zam.com/api/matrix/shz_mat4x4_init_rotation_y/) | Initializes the given matrix to a 3D rotation matrix by `yAngle` radians over the Y-axis. |
| [`shz_mat4x4_init_rotation_z`](https://sh4zam.com/api/matrix/shz_mat4x4_init_rotation_z/) | Initializes the given matrix to a 3D rotation matrix by `zAngle` radians over the Z-axis. |
| [`shz_mat4x4_init_rotation_xyz`](https://sh4zam.com/api/matrix/shz_mat4x4_init_rotation_xyz/) | Initializes the given matrix to a 3D rotation matrix from the intrinsic rotation created by the given Tait-Bryan X-Y-Z angles. |
| [`shz_mat4x4_init_rotation_zyx`](https://sh4zam.com/api/matrix/shz_mat4x4_init_rotation_zyx/) | Initializes the given matrix to a 3D rotation matrix from the intrinsic rotation created by the given Tait-Bryan Z-Y-X angles. |
| [`shz_mat4x4_init_rotation_zxy`](https://sh4zam.com/api/matrix/shz_mat4x4_init_rotation_zxy/) | Initializes the given matrix to a 3D rotation matrix from the intrinsic rotation created by the given Tait-Bryan Z-X-Y angles. |
| [`shz_mat4x4_init_rotation_yxz`](https://sh4zam.com/api/matrix/shz_mat4x4_init_rotation_yxz/) | Initializes the given matrix to a 3D rotation matrix from the intrinsic rotation created by the given Tait-Bryan Y-X-Z angles. |
| [`shz_mat4x4_init_rotation`](https://sh4zam.com/api/matrix/shz_mat4x4_init_rotation/) | Initializes the given 4x4 matrix to a 3D rotation matrix of `angle` radians about the vector with the given components. |
| [`shz_mat4x4_init_rotation_dir`](https://sh4zam.com/api/matrix/shz_mat4x4_init_rotation_dir/) | Initializes the given 4x4 matrix to contain a 3D rotation matrix of `angle` radians about the given direction. |
| [`shz_mat4x4_init_rotation_quat`](https://sh4zam.com/api/matrix/shz_mat4x4_init_rotation_quat/) | Initializes the given matrix to a 3D rotation matrix with its orientation given by a quaternion. |
| [`shz_mat4x4_init_diagonal`](https://sh4zam.com/api/matrix/shz_mat4x4_init_diagonal/) | Initializes the given matrix to a diagonal matrix with the given 4 values. |
| [`shz_mat4x4_init_upper_triangular`](https://sh4zam.com/api/matrix/shz_mat4x4_init_upper_triangular/) | Initializes the given matrix to an upper triangular matrix whose nonzero entries have the given value. |
| [`shz_mat4x4_init_lower_triangular`](https://sh4zam.com/api/matrix/shz_mat4x4_init_lower_triangular/) | Initializes the given matrix to a lower triangular matrix whose nonzero entries have the given value. |
| [`shz_mat4x4_init_symmetric_skew`](https://sh4zam.com/api/matrix/shz_mat4x4_init_symmetric_skew/) | Initializes the given matrix to be the symmetric skew of the given 3D vector components. |
| [`shz_mat4x4_init_outer_product`](https://sh4zam.com/api/matrix/shz_mat4x4_init_outer_product/) | Initializes the given matrix to be the result from taking the outer product of the two given 4D vectors. |
| [`shz_mat4x4_init_permutation_wxyz`](https://sh4zam.com/api/matrix/shz_mat4x4_init_permutation_wxyz/) | Initializes the matrix to to a permutation matrix, which reorders the components of transformed vectors to be in WXYZ order. |
| [`shz_mat4x4_init_permutation_yzwx`](https://sh4zam.com/api/matrix/shz_mat4x4_init_permutation_yzwx/) | Initializes the matrix to to a permutation matrix, which reorders the components of transformed vectors to be in YZWX order. |
| [`shz_mat4x4_init_screen`](https://sh4zam.com/api/matrix/shz_mat4x4_init_screen/) | Initializes the given matrix to the viewport matrix with the given dimenions. |
| [`shz_mat4x4_init_lookat`](https://sh4zam.com/api/matrix/shz_mat4x4_init_lookat/) | Initializes the given matrix to a "lookAt" view matrix. |
| [`shz_mat4x4_init_ortho`](https://sh4zam.com/api/matrix/shz_mat4x4_init_ortho/) | Initializes the given matrix to an orthographic projection matrix. |
| [`shz_mat4x4_init_frustum`](https://sh4zam.com/api/matrix/shz_mat4x4_init_frustum/) | Initializes the given matrix to a frustum projection matrix. |
| [`shz_mat4x4_init_perspective`](https://sh4zam.com/api/matrix/shz_mat4x4_init_perspective/) | Initializes the given matrix to a perspective projection matrix. |

## Decomposition

Routines for decomposing a matrix into its constituent transforms.

| Symbol | Description |
| --- | --- |
| [`shz_mat4x4_decompose`](https://sh4zam.com/api/matrix/shz_mat4x4_decompose/) | Decomposes a 4x4 transform matrix into translation, rotation, and scale. |

## Getting

Routines for getting specific values within a matrix.

| Symbol | Description |
| --- | --- |
| [`shz_mat4x4_row`](https://sh4zam.com/api/matrix/shz_mat4x4_row/) | Extracts the `row` index as a 4D row vector from the given matrix. |
| [`shz_mat4x4_col`](https://sh4zam.com/api/matrix/shz_mat4x4_col/) | Extracts the `col` index as a 4D column vector from the given matrix. |
| [`shz_mat4x4_get_translation`](https://sh4zam.com/api/matrix/shz_mat4x4_get_translation/) | Returns the translational components from the 4th column as a 3D vector. |
| [`shz_mat4x4_get_scale`](https://sh4zam.com/api/matrix/shz_mat4x4_get_scale/) | Exracts the 3D scale factors from the given 4x4 matrix. |
| [`shz_mat4x4_determinant`](https://sh4zam.com/api/matrix/shz_mat4x4_determinant/) | Returns the determinant of the given 4x4 matrix. |
| [`shz_mat4x4_trace`](https://sh4zam.com/api/matrix/shz_mat4x4_trace/) | Returns the trace of the given 4x4 matrix. |
| [`shz_mat4x4_3x3`](https://sh4zam.com/api/matrix/shz_mat4x4_3x3/) | Extracts the top-left 3x3 of the given 4D matrix. |
| [`shz_mat4x4_3x3_inverse_unscaled`](https://sh4zam.com/api/matrix/shz_mat4x4_3x3_inverse_unscaled/) | Extracts and inverts the top-level, unscaled 3x3 of the given 4x4 matrix. |
| [`shz_mat4x4_3x3_inverse`](https://sh4zam.com/api/matrix/shz_mat4x4_3x3_inverse/) | Extracts and inverts the top-level 3x3 (which may be scaled) of the given 4x4 matrix. |
| [`shz_mat4x4_3x3_determinant`](https://sh4zam.com/api/matrix/shz_mat4x4_3x3_determinant/) | Returns the determinant of the given 4x4 matrix's internal top-level 3x3 matrix. |

## Setting

Routines for setting specific values within a matrix

| Symbol | Description |
| --- | --- |
| [`shz_mat4x4_set_row`](https://sh4zam.com/api/matrix/shz_mat4x4_set_row/) | Sets the values of `mat` at the given `row` to those of the 4D vector, `vec`. |
| [`shz_mat4x4_set_col`](https://sh4zam.com/api/matrix/shz_mat4x4_set_col/) | Sets the values of `mat` at the given `col` to those of the 4D vector, `vec`. |
| [`shz_mat4x4_swap_rows`](https://sh4zam.com/api/matrix/shz_mat4x4_swap_rows/) | Swaps the 4D row vectors located at `row1` and `row2` within `mat`. |
| [`shz_mat4x4_swap_cols`](https://sh4zam.com/api/matrix/shz_mat4x4_swap_cols/) | Swaps the 4D column vectors located at `col1` and `col2` within `mat`. |
| [`shz_mat4x4_set_translation`](https://sh4zam.com/api/matrix/shz_mat4x4_set_translation/) | Assigns only the 3D translation-related elements of the given matrix to the given values. |
| [`shz_mat4x4_set_scale`](https://sh4zam.com/api/matrix/shz_mat4x4_set_scale/) | Assigns only the 3D scale-related elements of the given matrix to the given values. |
| [`shz_mat4x4_set_rotation_quat`](https://sh4zam.com/api/matrix/shz_mat4x4_set_rotation_quat/) | Sets just the rotational component of the matrix to the orientation given by a quaternion, keeping the other elements in-tact. |
| [`shz_mat4x4_set_diagonal`](https://sh4zam.com/api/matrix/shz_mat4x4_set_diagonal/) | Assigns only the 4 elements along the diagonal of the given matrix to the given values. |

## Applying

Routines for multiplying and accumulating onto the given matrix.

| Symbol | Description |
| --- | --- |
| [`shz_mat4x4_apply`](https://sh4zam.com/api/matrix/shz_mat4x4_apply/) | Multiplies and accumulates the `src` 4x4 matrix onto the `dst` 4x4 matrix. |
| [`shz_mat4x4_apply_unaligned`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_unaligned/) | Multiplies and accumulates the unaligned `src` 4x4 matrix onto the `dst` 4x4 matrix. |
| [`shz_mat4x4_apply_transpose`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_transpose/) | Multiplies and accumulates the transposed `src` 4x4 matrix onto the `dst` 4x4 matrix. |
| [`shz_mat4x4_apply_transpose_unaligned`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_transpose_unaligned/) | Multiplies and accumulates the transposed unaligned `src` 4x4 matrix onto the `dst` 4x4 matrix. |
| [`shz_mat4x4_apply_translation`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_translation/) | Adds the given 3D vector components to the translational values of the given matrix. |
| [`shz_mat4x4_apply_scale`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_scale/) | Multiplies and accumulates the scale-related elements of the given matrix by the given 3D components. |
| [`shz_mat4x4_apply_rotation_x`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_rotation_x/) | Multiplies and accumulates a rotation matrix by `xAngle` radians about the X-axis onto the given matrix. |
| [`shz_mat4x4_apply_rotation_y`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_rotation_y/) | Multiplies and accumulates a rotation matrix by `yAngle` radians about the Y-axis onto the given matrix. |
| [`shz_mat4x4_apply_rotation_z`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_rotation_z/) | Multiplies and accumulates a rotation matrix by `zAngle` radians about the Z-axis onto the given matrix. |
| [`shz_mat4x4_apply_rotation_xyz`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_rotation_xyz/) | Rotates the given transform matrix about the X axis, then the Y axis, then the Z axis by the given angles in radians. |
| [`shz_mat4x4_apply_rotation_zyx`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_rotation_zyx/) | Rotates the given transform matrix about the Z axis, then the Y axis, then the X axis by the given angles in radians. |
| [`shz_mat4x4_apply_rotation_zxy`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_rotation_zxy/) | Rotates the given transform matrix about the Z axis, then the X axis, then the Y axis by the given angles in radians. |
| [`shz_mat4x4_apply_rotation_yxz`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_rotation_yxz/) | Rotates the given transform matrix about the Y axis, then the X axis, then the Z axis by the given angles in radians. |
| [`shz_mat4x4_apply_rotation`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_rotation/) | Rotates the given transform matrix about the arbitrary axis given by a 3D direction vector and angle of rotation in radians. |
| [`shz_mat4x4_apply_rotation_quat`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_rotation_quat/) | Multiplies and accumulates the given matrix with a rotation matrix whose orientation is given by a quaternion. |
| [`shz_mat4x4_apply_lookat`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_lookat/) | Applies the 3D "lookAt" matrix constructed with the given vector components onto the given matrix. |
| [`shz_mat4x4_apply_ortho`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_ortho/) | Multiplies and accumulates the ortho matrix constructed from the given values onto the given matrix. |
| [`shz_mat4x4_apply_frustum`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_frustum/) | Multiplies and accumulates the frustum matrix constructed from the given values onto the given matrix. |
| [`shz_mat4x4_apply_perspective`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_perspective/) | Multiplies and accumulates the perspective matrix constructed from the given values onto the given matrix. |
| [`shz_mat4x4_apply_screen`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_screen/) | Multiplies and accumulates the viewport matrix created with the given components ont othe given matrix. |
| [`shz_mat4x4_apply_symmetric_skew`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_symmetric_skew/) | Multiplies and accumulates the given matrix with a symmetric skew matrix formed from the given 3D vector components. |
| [`shz_mat4x4_apply_permutation_wxyz`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_permutation_wxyz/) | Multiplies and accumulates a permutation matrix, which reorders the components of transformed vectors to be in WXYZ order. |
| [`shz_mat4x4_apply_permutation_yzwx`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_permutation_yzwx/) | Multiplies and accumulates a permutation matrix, which reorders the components of transformed vectors to be in YZWX order. |
| [`shz_mat4x4_apply_self`](https://sh4zam.com/api/matrix/shz_mat4x4_apply_self/) | Multiplies and accumulates the given matrix onto itself. |

## GL Transformations

OpenGL-style 4x4 matrix transforms.

| Symbol | Description |
| --- | --- |
| [`shz_mat4x4_translate`](https://sh4zam.com/api/matrix/shz_mat4x4_translate/) | Multiplies and accumulates `mat` by a 3D translation matrix with the given components. |
| [`shz_mat4x4_scale`](https://sh4zam.com/api/matrix/shz_mat4x4_scale/) | Multiplies and accumulates `mat` by a 3D scaling matrix with the given components. |
| [`shz_mat4x4_rotate_x`](https://sh4zam.com/api/matrix/shz_mat4x4_rotate_x/) | Multiplies and accumulates `mat` by a 3D rotation matrix about the X axis. |
| [`shz_mat4x4_rotate_y`](https://sh4zam.com/api/matrix/shz_mat4x4_rotate_y/) | Multiplies and accumulates `mat` by a 3D rotation matrix about the Y axis. |
| [`shz_mat4x4_rotate_z`](https://sh4zam.com/api/matrix/shz_mat4x4_rotate_z/) | Multiplies and accumulates `mat` by a 3D rotation matrix about the Z axis. |
| [`shz_mat4x4_rotate_xyz`](https://sh4zam.com/api/matrix/shz_mat4x4_rotate_xyz/) | Multiplies and accumulates `mat` by 3D rotation matrices about the X then Y then Z axes. |
| [`shz_mat4x4_rotate_zyx`](https://sh4zam.com/api/matrix/shz_mat4x4_rotate_zyx/) | Multiplies and accumulates `mat` by 3D rotation matrices about the Z then Y then X axes. |
| [`shz_mat4x4_rotate_zxy`](https://sh4zam.com/api/matrix/shz_mat4x4_rotate_zxy/) | Multiplies and accumulates `mat` by 3D rotation matrices about the Z then X then Y axes. |
| [`shz_mat4x4_rotate_yxz`](https://sh4zam.com/api/matrix/shz_mat4x4_rotate_yxz/) | Multiplies and accumulates `mat` by 3D rotation matrices about the Y then X then Z axes. |
| [`shz_mat4x4_rotate`](https://sh4zam.com/api/matrix/shz_mat4x4_rotate/) | Multiplies and accumulates `mat` by the 3D rotation matrix formed by the given axis and angle. |

## Reverse GL Transformations

Pre-multiplication variants of OpenGL-style 4x4 matrix transforms.

| Symbol | Description |
| --- | --- |
| [`shz_mat4x4_translate_reverse`](https://sh4zam.com/api/matrix/shz_mat4x4_translate_reverse/) | Pre-multiplies and accumulates the given matrix onto the 3D translation matrix with the given components. |
| [`shz_mat4x4_scale_reverse`](https://sh4zam.com/api/matrix/shz_mat4x4_scale_reverse/) | Pre-multiplies and accumulates the given matrix onto the 3D scaling matrix with the given components. |

## Transforming

Routines for transforming vectors and points by a matrix.

| Symbol | Description |
| --- | --- |
| [`shz_mat4x4_mult`](https://sh4zam.com/api/matrix/shz_mat4x4_mult/) | Multiplies two 4x4 matrices together, storing the result into a third. |
| [`shz_mat4x4_mult_unaligned`](https://sh4zam.com/api/matrix/shz_mat4x4_mult_unaligned/) | Multiplies two 4x4 matrices together, with the right handed matrix being unaligned, storing the result into a third. |
| [`shz_mat4x4_mult_transpose`](https://sh4zam.com/api/matrix/shz_mat4x4_mult_transpose/) | Multiplies the regular matrix, `lhs`, by the transpose of the matrix, `rhs`, storing the result into `mat`. |
| [`shz_mat4x4_mult_transpose_unaligned`](https://sh4zam.com/api/matrix/shz_mat4x4_mult_transpose_unaligned/) | Multiplies the regular matrix, `lhs`, by the transpose of the unaligned matrix, `rhs`, storing the result into `mat`. |
| [`shz_mat4x4_transform_vec2`](https://sh4zam.com/api/matrix/shz_mat4x4_transform_vec2/) | Transforms a 2D vector by a 4x4 matrix. |
| [`shz_mat4x4_transform_vec3`](https://sh4zam.com/api/matrix/shz_mat4x4_transform_vec3/) | Transforms a 3D vector by a 4x4 matrix. |
| [`shz_mat4x4_transform_vec4`](https://sh4zam.com/api/matrix/shz_mat4x4_transform_vec4/) | Transforms a 4D vector by a 4x4 matrix. |
| [`shz_mat4x4_transform_vec2_transpose`](https://sh4zam.com/api/matrix/shz_mat4x4_transform_vec2_transpose/) | Transforms a 2D vector the the transpose of a 4x4 matrix. |
| [`shz_mat4x4_transform_vec3_transpose`](https://sh4zam.com/api/matrix/shz_mat4x4_transform_vec3_transpose/) | Transforms a 3D vector the the transpose of a 4x4 matrix. |
| [`shz_mat4x4_transform_vec4_transpose`](https://sh4zam.com/api/matrix/shz_mat4x4_transform_vec4_transpose/) | Transforms a 4D vector the the transpose of a 4x4 matrix. |
| [`shz_mat4x4_transform_point2`](https://sh4zam.com/api/matrix/shz_mat4x4_transform_point2/) | Transforms a 2D point by a 4x4 matrix. |
| [`shz_mat4x4_transform_point3`](https://sh4zam.com/api/matrix/shz_mat4x4_transform_point3/) | Transforms a 3D point by a 4x4 matrix. |
| [`shz_mat4x4_transform_point2_transpose`](https://sh4zam.com/api/matrix/shz_mat4x4_transform_point2_transpose/) | Transforms a 2D point by the transpose of a 4x4 matrix. |
| [`shz_mat4x4_transform_point3_transpose`](https://sh4zam.com/api/matrix/shz_mat4x4_transform_point3_transpose/) | Transforms a 3D point by the transpose of a 4x4 matrix. |

## Miscellaneous

Other matrix-related operations and routines

| Symbol | Description |
| --- | --- |
| [`shz_mat4x4_to_quat`](https://sh4zam.com/api/matrix/shz_mat4x4_to_quat/) | Converts the given 4x4 orientation matrix into a quaternion. |
| [`shz_mat4x4_transpose`](https://sh4zam.com/api/matrix/shz_mat4x4_transpose/) | Stores the transpose of `mat` within `out`. |
| [`shz_mat4x4_inverse`](https://sh4zam.com/api/matrix/shz_mat4x4_inverse/) | Computes the inverse of a 4x4 matrix. |
| [`shz_mat4x4_inverse_block_triangular`](https://sh4zam.com/api/matrix/shz_mat4x4_inverse_block_triangular/) | Computes the inverse of a 4x4 matrix in block-triangular form. |
| [`shz_mat4x4_equal`](https://sh4zam.com/api/matrix/shz_mat4x4_equal/) | Returns true if the two matrices are equal, based on either absolute or relative tolerance. |
| [`shz_mat4x4_is_block_triangular`](https://sh4zam.com/api/matrix/shz_mat4x4_is_block_triangular/) | Returns true if the given matrix is in block-triangular form: having a bottom row in the form of `<0.0f, 0.0f, 0.0f, w>`. |
| [`shz_mat4x4_copy`](https://sh4zam.com/api/matrix/shz_mat4x4_copy/) | Copies the given `src` 4x4 matrix into the given `dst` 4x4 matrix. |
| [`shz_mat4x4_copy_unaligned`](https://sh4zam.com/api/matrix/shz_mat4x4_copy_unaligned/) | Copies the given unaligned `src` 4x4 matrix into the given `dst` 4x4 matrix. |
| [`shz_mat4x4_swap`](https://sh4zam.com/api/matrix/shz_mat4x4_swap/) | Swaps the contents of the two given matrices, `matA` and `matB`. |
| [`shz_mat4x4_blend`](https://sh4zam.com/api/matrix/shz_mat4x4_blend/) | Adds and accumulates a scaled 4x4 matrix into the given matrix. |

## Types

| Symbol | Description |
| --- | --- |
| [`shz_mat4x4_t`](https://sh4zam.com/api/matrix/shz_mat4x4_t/) | Structure representing a 4x4 column-major matrix. |
| [`shz_mat4x4`](https://sh4zam.com/api/matrix/shz_mat4x4/) | Alternate [`shz_mat4x4_t`](https://sh4zam.com/api/matrix/shz_mat4x4_t/) C typedef for those who hate POSIX style. |
| [`shz_mat2x2_t`](https://sh4zam.com/api/matrix/shz_mat2x2_t/) | Structure representing a 2x2 column-major matrix. |
| [`shz_mat3x3_t`](https://sh4zam.com/api/matrix/shz_mat3x3_t/) | Structure representing a 3x3 column-major matrix. |
| [`shz_mat3x4_t`](https://sh4zam.com/api/matrix/shz_mat3x4_t/) | Structure representing a 3x4 column-major matrix. |
| [`shz_mat4x3_t`](https://sh4zam.com/api/matrix/shz_mat4x3_t/) | Structure representing a 4x3 column-major matrix. |

## Functions

| Symbol | Description |
| --- | --- |
| [`shz_mat3x3_transpose`](https://sh4zam.com/api/matrix/shz_mat3x3_transpose/) | Stores the transpose of 3x3 matrix `mat` within `out`. |
| [`shz_mat3x3_inverse_unscaled`](https://sh4zam.com/api/matrix/shz_mat3x3_inverse_unscaled/) | Computes the inverse of an orthonormal 3x3 matrix. |
| [`shz_mat3x3_inverse`](https://sh4zam.com/api/matrix/shz_mat3x3_inverse/) | Computes the inverse of a 3x3 matrix. |
| [`shz_mat3x3_scale`](https://sh4zam.com/api/matrix/shz_mat3x3_scale/) | Uniformly scales each element within a 3x3 matrix by the given value. |
| [`shz_mat3x3_transform_vec3`](https://sh4zam.com/api/matrix/shz_mat3x3_transform_vec3/) | Transforms an input vector by a 3x3 matrix, returning the resulting vector. |
| [`shz_mat3x3_transform_vec3_transpose`](https://sh4zam.com/api/matrix/shz_mat3x3_transform_vec3_transpose/) | Transforms an input vector by the transpose of a 3x3 matrix, returning the resulting vector. |