# Source: mat2.js

    import * as glMatrix from "./common.js"

    /**
     * 2x2 Matrix
     * @module mat2
     */

    /**
     * Creates a new identity mat2
     *
     * @returns {mat2} a new 2x2 matrix
     */
    export function create() {
      let out = new glMatrix.ARRAY_TYPE(4);
      out[0] = 1;
      out[1] = 0;
      out[2] = 0;
      out[3] = 1;
      return out;
    }

    /**
     * Creates a new mat2 initialized with values from an existing matrix
     *
     * @param {mat2} a matrix to clone
     * @returns {mat2} a new 2x2 matrix
     */
    export function clone(a) {
      let out = new glMatrix.ARRAY_TYPE(4);
      out[0] = a[0];
      out[1] = a[1];
      out[2] = a[2];
      out[3] = a[3];
      return out;
    }

    /**
     * Copy the values from one mat2 to another
     *
     * @param {mat2} out the receiving matrix
     * @param {mat2} a the source matrix
     * @returns {mat2} out
     */
    export function copy(out, a) {
      out[0] = a[0];
      out[1] = a[1];
      out[2] = a[2];
      out[3] = a[3];
      return out;
    }

    /**
     * Set a mat2 to the identity matrix
     *
     * @param {mat2} out the receiving matrix
     * @returns {mat2} out
     */
    export function identity(out) {
      out[0] = 1;
      out[1] = 0;
      out[2] = 0;
      out[3] = 1;
      return out;
    }

    /**
     * Create a new mat2 with the given values
     *
     * @param {Number} m00 Component in column 0, row 0 position (index 0)
     * @param {Number} m01 Component in column 0, row 1 position (index 1)
     * @param {Number} m10 Component in column 1, row 0 position (index 2)
     * @param {Number} m11 Component in column 1, row 1 position (index 3)
     * @returns {mat2} out A new 2x2 matrix
     */
    export function fromValues(m00, m01, m10, m11) {
      let out = new glMatrix.ARRAY_TYPE(4);
      out[0] = m00;
      out[1] = m01;
      out[2] = m10;
      out[3] = m11;
      return out;
    }

    /**
     * Set the components of a mat2 to the given values
     *
     * @param {mat2} out the receiving matrix
     * @param {Number} m00 Component in column 0, row 0 position (index 0)
     * @param {Number} m01 Component in column 0, row 1 position (index 1)
     * @param {Number} m10 Component in column 1, row 0 position (index 2)
     * @param {Number} m11 Component in column 1, row 1 position (index 3)
     * @returns {mat2} out
     */
    export function set(out, m00, m01, m10, m11) {
      out[0] = m00;
      out[1] = m01;
      out[2] = m10;
      out[3] = m11;
      return out;
    }

    /**
     * Transpose the values of a mat2
     *
     * @param {mat2} out the receiving matrix
     * @param {mat2} a the source matrix
     * @returns {mat2} out
     */
    export function transpose(out, a) {
      // If we are transposing ourselves we can skip a few steps but have to cache
      // some values
      if (out === a) {
        let a1 = a[1];
        out[1] = a[2];
        out[2] = a1;
      } else {
        out[0] = a[0];
        out[1] = a[2];
        out[2] = a[1];
        out[3] = a[3];
      }

      return out;
    }

    /**
     * Inverts a mat2
     *
     * @param {mat2} out the receiving matrix
     * @param {mat2} a the source matrix
     * @returns {mat2} out
     */
    export function invert(out, a) {
      let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];

      // Calculate the determinant
      let det = a0 * a3 - a2 * a1;

      if (!det) {
        return null;
      }
      det = 1.0 / det;

      out[0] =  a3 * det;
      out[1] = -a1 * det;
      out[2] = -a2 * det;
      out[3] =  a0 * det;

      return out;
    }

    /**
     * Calculates the adjugate of a mat2
     *
     * @param {mat2} out the receiving matrix
     * @param {mat2} a the source matrix
     * @returns {mat2} out
     */
    export function adjoint(out, a) {
      // Caching this value is nessecary if out == a
      let a0 = a[0];
      out[0] =  a[3];
      out[1] = -a[1];
      out[2] = -a[2];
      out[3] =  a0;

      return out;
    }

    /**
     * Calculates the determinant of a mat2
     *
     * @param {mat2} a the source matrix
     * @returns {Number} determinant of a
     */
    export function determinant(a) {
      return a[0] * a[3] - a[2] * a[1];
    }

    /**
     * Multiplies two mat2's
     *
     * @param {mat2} out the receiving matrix
     * @param {mat2} a the first operand
     * @param {mat2} b the second operand
     * @returns {mat2} out
     */
    export function multiply(out, a, b) {
      let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];
      let b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
      out[0] = a0 * b0 + a2 * b1;
      out[1] = a1 * b0 + a3 * b1;
      out[2] = a0 * b2 + a2 * b3;
      out[3] = a1 * b2 + a3 * b3;
      return out;
    }

    /**
     * Rotates a mat2 by the given angle
     *
     * @param {mat2} out the receiving matrix
     * @param {mat2} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat2} out
     */
    export function rotate(out, a, rad) {
      let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];
      let s = Math.sin(rad);
      let c = Math.cos(rad);
      out[0] = a0 *  c + a2 * s;
      out[1] = a1 *  c + a3 * s;
      out[2] = a0 * -s + a2 * c;
      out[3] = a1 * -s + a3 * c;
      return out;
    }

    /**
     * Scales the mat2 by the dimensions in the given vec2
     *
     * @param {mat2} out the receiving matrix
     * @param {mat2} a the matrix to rotate
     * @param {vec2} v the vec2 to scale the matrix by
     * @returns {mat2} out
     **/
    export function scale(out, a, v) {
      let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];
      let v0 = v[0], v1 = v[1];
      out[0] = a0 * v0;
      out[1] = a1 * v0;
      out[2] = a2 * v1;
      out[3] = a3 * v1;
      return out;
    }

    /**
     * Creates a matrix from a given angle
     * This is equivalent to (but much faster than):
     *
     *     mat2.identity(dest);
     *     mat2.rotate(dest, dest, rad);
     *
     * @param {mat2} out mat2 receiving operation result
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat2} out
     */
    export function fromRotation(out, rad) {
      let s = Math.sin(rad);
      let c = Math.cos(rad);
      out[0] = c;
      out[1] = s;
      out[2] = -s;
      out[3] = c;
      return out;
    }

    /**
     * Creates a matrix from a vector scaling
     * This is equivalent to (but much faster than):
     *
     *     mat2.identity(dest);
     *     mat2.scale(dest, dest, vec);
     *
     * @param {mat2} out mat2 receiving operation result
     * @param {vec2} v Scaling vector
     * @returns {mat2} out
     */
    export function fromScaling(out, v) {
      out[0] = v[0];
      out[1] = 0;
      out[2] = 0;
      out[3] = v[1];
      return out;
    }

    /**
     * Returns a string representation of a mat2
     *
     * @param {mat2} a matrix to represent as a string
     * @returns {String} string representation of the matrix
     */
    export function str(a) {
      return 'mat2(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')';
    }

    /**
     * Returns Frobenius norm of a mat2
     *
     * @param {mat2} a the matrix to calculate Frobenius norm of
     * @returns {Number} Frobenius norm
     */
    export function frob(a) {
      return(Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2)))
    }

    /**
     * Returns L, D and U matrices (Lower triangular, Diagonal and Upper triangular) by factorizing the input matrix
     * @param {mat2} L the lower triangular matrix
     * @param {mat2} D the diagonal matrix
     * @param {mat2} U the upper triangular matrix
     * @param {mat2} a the input matrix to factorize
     */

    export function LDU(L, D, U, a) {
      L[2] = a[2]/a[0];
      U[0] = a[0];
      U[1] = a[1];
      U[3] = a[3] - L[2] * U[1];
      return [L, D, U];
    }

    /**
     * Adds two mat2's
     *
     * @param {mat2} out the receiving matrix
     * @param {mat2} a the first operand
     * @param {mat2} b the second operand
     * @returns {mat2} out
     */
    export function add(out, a, b) {
      out[0] = a[0] + b[0];
      out[1] = a[1] + b[1];
      out[2] = a[2] + b[2];
      out[3] = a[3] + b[3];
      return out;
    }

    /**
     * Subtracts matrix b from matrix a
     *
     * @param {mat2} out the receiving matrix
     * @param {mat2} a the first operand
     * @param {mat2} b the second operand
     * @returns {mat2} out
     */
    export function subtract(out, a, b) {
      out[0] = a[0] - b[0];
      out[1] = a[1] - b[1];
      out[2] = a[2] - b[2];
      out[3] = a[3] - b[3];
      return out;
    }

    /**
     * Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)
     *
     * @param {mat2} a The first matrix.
     * @param {mat2} b The second matrix.
     * @returns {Boolean} True if the matrices are equal, false otherwise.
     */
    export function exactEquals(a, b) {
      return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];
    }

    /**
     * Returns whether or not the matrices have approximately the same elements in the same position.
     *
     * @param {mat2} a The first matrix.
     * @param {mat2} b The second matrix.
     * @returns {Boolean} True if the matrices are equal, false otherwise.
     */
    export function equals(a, b) {
      let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];
      let b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
      return (Math.abs(a0 - b0) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a0), Math.abs(b0)) &&
              Math.abs(a1 - b1) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a1), Math.abs(b1)) &&
              Math.abs(a2 - b2) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a2), Math.abs(b2)) &&
              Math.abs(a3 - b3) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a3), Math.abs(b3)));
    }

    /**
     * Multiply each element of the matrix by a scalar.
     *
     * @param {mat2} out the receiving matrix
     * @param {mat2} a the matrix to scale
     * @param {Number} b amount to scale the matrix's elements by
     * @returns {mat2} out
     */
    export function multiplyScalar(out, a, b) {
      out[0] = a[0] * b;
      out[1] = a[1] * b;
      out[2] = a[2] * b;
      out[3] = a[3] * b;
      return out;
    }

    /**
     * Adds two mat2's after multiplying each element of the second operand by a scalar value.
     *
     * @param {mat2} out the receiving vector
     * @param {mat2} a the first operand
     * @param {mat2} b the second operand
     * @param {Number} scale the amount to scale b's elements by before adding
     * @returns {mat2} out
     */
    export function multiplyScalarAndAdd(out, a, b, scale) {
      out[0] = a[0] + (b[0] * scale);
      out[1] = a[1] + (b[1] * scale);
      out[2] = a[2] + (b[2] * scale);
      out[3] = a[3] + (b[3] * scale);
      return out;
    }

    /**
     * Alias for {@link mat2.multiply}
     * @function
     */
    export const mul = multiply;

    /**
     * Alias for {@link mat2.subtract}
     * @function
     */
    export const sub = subtract;