Functions

Create a matrix of zeros.

Create a matrix of zeros.

Create a matrix of ones.

Create a matrix of ones.

Create a matrix of uniformly distributed on [0, 1) interval random values.

Create a matrix of normally distibuted random values.

Create a matrix with ones on the main diagonal and zeros elsewhere.

Create a square matrix with specified values on the main diagonal and zeros elsewhere.

Create a square matrix with specified values on the main diagonal and zeros elsewhere.

Create a matrix with specified values on the main diagonal and zeros elsewhere.

Create a matrix with specified values on the main diagonal and zeros elsewhere.

Vertically stack (top-to-bottom) rows in matrices.

Precondition: All matrices need the same number of columns.

Horizontally stack (left-to-right) columns in matrices.

Precondition: All matrices need the same number of rows.

Insert row to matrix at specified position.

Insert rows to matrix at specified position.

Append row to matrix.

Append row to matrix.

Alternatively, append(m, row: row) can be executed with m === row.

Append row to matrix constructed from scalar value.

Alternatively, append(m, row: row) can be executed with m === row.

Append rows to matrix.

Alternatively, append(m, rows: rows) can be executed with m === rows.

Append rows to matrix.

Append row to matrix constructed from scalar value.

Alternatively, m === row can be executed with append(m, row: row).

Append row to matrix.

Alternatively, m === row can be executed with append(m, row: row).

Prepend row to matrix.

Prepend row to matrix.

Alternatively, prepend(m, row: row) can be executed with row === m.

Prepend row to matrix constructed from scalar value.

Alternatively, prepend(m, row: row) can be executed with row === m.

Prepend rows to matrix.

Alternatively, prepend(m, rows: rows) can be executed with rows === m.

Prepend rows to matrix.

Prepend row to matrix constructed from scalar value.

Alternatively, row === m can be executed with prepend(m, row: row).

Prepend row to matrix.

Alternatively, row === m can be executed with prepend(m, row: row).

Horizontally concatenate two matrices. It is similar to appending rhs as rows to lhs

Alternatively, lhs === rhs can be executed with append(lhs, rows: rhs).

Insert column to matrix at specified position.

Insert columns to matrix at specified position.

Append column to matrix.

Append column to matrix.

Alternatively, append(m, col: col) can be executed with m ||| col.

Append column to matrix constructed from scalar value.

Alternatively, append(m, col: col) can be executed with m ||| col.

Append columns to matrix.

Alternatively, append(m, cols: cols) can be executed with m ||| cols.

Append columns to matrix.

Append column to matrix constructed from scalar value.

Alternatively, m ||| col can be executed with append(m, col: col).

Append column to matrix.

Alternatively, m ||| col can be executed with append(m, col: col).

Prepend column to matrix.

Prepend column to matrix.

Alternatively, prepend(m, col: col) can be executed with col ||| m.

Prepend column to matrix constructed from scalar value.

Alternatively, prepend(m, col: col) can be executed with col ||| m.

Prepend columns to matrix.

Alternatively, prepend(m, cols: cols) can be executed with cols ||| m.

Prepend columns to matrix.

Prepend column to matrix constructed from scalar value.

Alternatively, col ||| m can be executed with prepend(m, col: col).

Prepend column to matrix.

Alternatively, col ||| m can be executed with prepend(m, col: col).

Vertically concatenate two matrices. It is similar to appending rhs as columns to lhs

Alternatively, lhs ||| rhs can be executed with append(lhs, cols: rhs).

Construct new matrix from source using specified extractor

Alternatively, slice(m, e) can be executed with m ?? e or m[e].

Construct new matrix from source using specified extractor.

Alternatively, m ?? e can be executed with slice(m, e) or m[e].

Map all elements of source matrix to new matrix using specified function.

Map all elements of source matrix to new matrix using specified function which operates on vectors.

Perform reduce operation on a matrix using specified function within the specified dimension.

Check if two matrices are equal using Double value approximate comparison

Check if two matrices are not equal using Double value approximate comparison

Check if one matrix is greater than another using Double value approximate comparison

Check if one matrix is less than another using Double value approximate comparison

Check if one matrix is greater than or equal to another using Double value approximate comparison

Check if one matrix is less than or equal to another using Double value approximate comparison

Compute the trace of a matrix.

Transpose matrix.

Alternatively, transpose(A) can be executed with A′.

Transpose matrix.

Alternatively, A′ can be executed with transpose(A).

Perform matrix multiplication.

Alternatively, mtimes(A, B) can be executed with A * B.

Perform matrix multiplication.

Alternatively, A * B can be executed with mtimes(A, B).

Raise matrix to specified power (integer value).

If power is 1, source matrix is returned If power is -1, inverted matrix is returned If power is > 1, continuous matrix product result is returned (eg mpower(A, 2) = mtimes(A, A)) If power is < -1, continuous matrix product of inverted matrix result is returned All other values are invalid

Alternatively, mpower(A, p) can be executed with A ^ p.

Raise matrix to specified power (integer value).

If power is 1, source matrix is returned If power is -1, inverted matrix is returned If power is > 1, continuous matrix product result is returned (eg A ^ 2 = mtimes(A, A)) If power is < -1, continuous matrix product of inverted matrix result is returned All other values are invalid

Alternatively, A ^ p can be executed with mpower(A, p).

Compute the inverse of a given square matrix.

A precondition error is thrown if the given matrix is singular or algorithm fails to converge.

Compute eigen values and vectors of a given square matrix.

A precondition error is thrown if the algorithm fails to converge.

Perform a singular value decomposition of a given matrix.

Perform a generalized singular value decomposition of 2 given matrices.

Compute the Cholesky factorization of a real symmetric positive definite matrix.

A precondition error is thrown if the algorithm fails to converge.

Return the upper/lower triangular part of a given matrix.

Compute the determinant of a given square matrix.

A precondition error is thrown if the given matrix is singular or algorithm fails to converge.

Return the result of convolving the given matrix with the provided kernel.

Perform matrix addition.

Alternatively, plus(A, B) can be executed with A + B.

Perform matrix addition.

Alternatively, A + B can be executed with plus(A, B).

Perform matrix substraction.

Alternatively, minus(A, B) can be executed with A - B.

Perform matrix substraction.

Alternatively, A - B can be executed with minus(A, B).

Perform matrix multiplication.

Alternatively, times(A, B) can be executed with A .* B.

Perform matrix multiplication.

Alternatively, A .* B can be executed with times(A, B).

Perform matrix right division.

Alternatively, rdivide(A, B) can be executed with A ./ B.

Perform matrix right division.

Alternatively, A ./ B can be executed with rdivide(A, B).

Perform matrix left division.

Alternatively, ldivide(A, B) can be executed with A ./. B.

Perform matrix left division.

Alternatively, A ./. B can be executed with ldivide(A, B).

Perform matrix and scalar addition.

Scalar value expands to matrix dimensions and elementwise matrix addition is performed.

Alternatively, plus(A, b) can be executed with A + b.

Perform matrix and scalar addition.

Scalar value expands to matrix dimensions and elementwise matrix addition is performed.

Alternatively, A + b can be executed with plus(A, b).

Perform scalar and matrix addition.

Scalar value expands to matrix dimensions and elementwise matrix addition is performed.

Alternatively, plus(a, B) can be executed with a + B.

Perform scalar and matrix addition.

Scalar value expands to matrix dimensions and elementwise matrix addition is performed.

Alternatively, a + B can be executed with plus(a, B).

Perform matrix and scalar substraction.

Scalar value expands to matrix dimensions and elementwise matrix substraction is performed.

Alternatively, minus(A, b) can be executed with A - b.

Perform matrix and scalar substraction.

Scalar value expands to matrix dimensions and elementwise matrix substraction is performed.

Alternatively, A - b can be executed with minus(A, b).

Perform scalar and matrix substraction.

Scalar value expands to matrix dimensions and elementwise matrix addition is performed.

Alternatively, minus(a, B) can be executed with a - B.

Perform scalar and matrix substraction.

Scalar value expands to matrix dimensions and elementwise matrix addition is performed.

Alternatively, a - B can be executed with minus(a, B).

Perform matrix and scalar multiplication.

Scalar value expands to matrix dimensions and elementwise matrix multiplication is performed.

Alternatively, times(A, b) can be executed with A .* b.

Perform matrix and scalar multiplication.

Scalar value expands to matrix dimensions and elementwise matrix multiplication is performed.

Alternatively, A .* b can be executed with times(A, b).

Perform scalar and matrix multiplication.

Scalar value expands to matrix dimensions and elementwise matrix multiplication is performed.

Alternatively, times(a, B) can be executed with a .* B.

Perform scalar and matrix multiplication.

Scalar value expands to matrix dimensions and elementwise matrix multiplication is performed.

Alternatively, a .* B can be executed with times(a, B).

Perform matrix and scalar right division.

Scalar value expands to matrix dimensions and elementwise matrix right division is performed.

Alternatively, rdivide(A, b) can be executed with A ./ b.

Perform matrix and scalar right division.

Scalar value expands to matrix dimensions and elementwise matrix right division is performed.

Alternatively, A ./ b can be executed with rdivide(A, b).

Perform scalar and matrix right division.

Scalar value expands to matrix dimensions and elementwise matrix right division is performed.

Alternatively, rdivide(a, B) can be executed with a ./ B.

Perform scalar and matrix right division.

Scalar value expands to matrix dimension and elementwise matrix right division is performed.

Alternatively, a ./ B can be executed with rdivide(a, B).

Perform matrix and scalar left division.

Scalar value expands to matrix dimensions and elementwise matrix left division is performed.

Alternatively, ldivide(A, b) can be executed with A ./. b.

Perform scalar and matrix left division.

Scalar value expands to matrix dimensions and elementwise matrix left division is performed.

Alternatively, ldivide(a, B) can be executed with a ./. B.

Perform matrix and vector addition.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, plus(A, b) can be executed with A + b.

Perform matrix and vector addition.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, A + b can be executed with plus(A, b).

Perform vector and matrix addition.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, plus(a, B) can be executed with a + B.

Perform vector and matrix addition.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, a + B can be executed with plus(a, B).

Perform matrix and vector substraction.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, minus(A, b) can be executed with A - b.

Perform matrix and vector substraction.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, A - b can be executed with minus(A, b).

Perform vector and matrix substraction.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, minus(a, B) can be executed with a - B.

Perform vector and matrix substraction.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, a - B can be executed with minus(a, B).

Perform matrix and vector multiplication.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, times(A, b) can be executed with A .* b.

Perform matrix and vector multiplication.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, A .* b can be executed with times(A, b).

Perform vector and matrix multiplication.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, times(a, B) can be executed with a .* B.

Perform vector and matrix multiplication.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, a .* B can be executed with times(a, B).

Perform matrix and vector right division.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, rdivide(A, b) can be executed with A ./ b.

Perform matrix and vector right division.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, A ./ b can be executed with rdivide(A, b).

Perform vector and matrix right division.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, rdivide(a, B) can be executed with a ./ B.

Perform vector and matrix right division.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, a ./ B can be executed with rdivide(a, B).

Perform matrix and vector left division.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, ldivide(A, b) can be executed with A ./. b.

Perform vector and matrix left division.

Vector value expands to matrix dimensions (by rows) and elementwise matrix addition is performed.

Alternatively, ldivide(a, B) can be executed with a ./. B.

Absolute value of matrix.

Negation of matrix.

Alternatively, uminus(A) can be executed with -A.

Negation of matrix.

Alternatively, -A can be executed with uminus(A).

Threshold function on matrix.

Exponentiation function, returning matrix raised to power.

Alternatively, power(A, p) can be executed with A .^ p.

Mathematically, power would return a complex number when base is negative and power is not an integral value. power can’t do that, so instead it signals domain error (returns ±NaN).

Exponentiation function, returning matrix raised to power.

Alternatively, A .^ p can be executed with power(A, p).

Mathematically, power would return a complex number when base is negative and power is not an integral value. power can’t do that, so instead it signals domain error (returns ±NaN).

Exponentiation function, returning matrix raised to power of 2.

Exponentiation function, returning square root of matrix.

Mathematically, sqrt would return a complex number when base is negative. sqrt can’t do that, so instead it signals domain error (returns ±NaN).

Compute e (the base of natural logarithms) raised to the power A.

If the magnitude of the result is too large to be representable, exp signals overflow (returns Inf).

Compute the natural logarithm of A where exp(log(A)) equals A, exactly in mathematics and approximately in C.

If x is negative, log signals a domain error (returns NaN). If x is zero, it returns negative infinity (-Inf); if x is too close to zero, it may signal overflow.

Return the base-2 logarithm of A, where log2(A) = log(A)/log(2).

Return the base-10 logarithm of A, where log10(A) = log(A)/log(10).

Compute the least squares solution to the overdetermined linear system A*X = B with full rank matrix A.

A precondition errors throw for mismatched matrix dimensions or if algorithm fails.

Requires M (rows of A) >= N (cols of A).

Return vector of largest elements of matrix in a specified dimension.

Return vector of indices of largest elements of matrix in a specified dimension.

Return vector of smallest elements of matrix in a specified dimension.

Return vector of indices of smallest elements of matrix in a specified dimension.

Return vector of mean values of matrix in a specified dimension.

Return vector of standard deviation values of matrix in a specified dimension.

Return normalized matrix (substract mean value and divide by standard deviation) in dpecified dimension.

Return vector of sums of values of matrix in a specified dimension.

Return vector of sums of squared values of matrix in a specified dimension.

Return the sine of A, where A is given in radians and the return value is in the range -1 to 1.

Return the cosine of A, where A is given in radians and the return value is in the range -1 to 1.

Return the tangent of A, where A is given in radians.

Mathematically, the tangent function has singularities at odd multiples of pi/2. If the argument x is too close to one of these singularities, tan will return extremely large value.

Return the arcsine of A, where return value is in the range -pi/2 to pi/2.

Return the arccosine of A, where return value is in the range 0 to pi.

Return the arctangent of a.

Create a vector of zeros.

Create a vector of ones.

Create a vector of uniformly distributed on [0, 1) interval random values.

Create a vector of normally distributed random values.

Check if two vectors are equal using Double value approximate comparison

Check if two vectors are not equal using Double value approximate comparison

Check if one vector is greater than another using Double value approximate comparison

Check if one vector is less than another using Double value approximate comparison

Check if one vector is greater than or equal to another using Double value approximate comparison

Check if one vector is less than or equal to another using Double value approximate comparison

Perform vector addition.

Alternatively, plus(a, b) can be executed with a + b.

Perform vector addition.

Alternatively, a + b can be executed with plus(a, b).

Perform vector substraction.

Alternatively, minus(a, b) can be executed with a - b.

Perform vector substraction.

Alternatively, a - b can be executed with minus(a, b).

Perform vector multiplication.

Alternatively, times(a, b) can be executed with a .* b.

Perform vector multiplication.

Alternatively, a .* b can be executed with times(a, b).