Syntax

A = Diag(B,k)

Arguments

Name

Description

B

A vector or a matrix.

k

(optional)

An index indicating the diagonal of interest. k = 0 (default) indicates the main diagonal. k is negative for sub-diagonals and positive for super diagonals.

Outputs

Name

Description

A

A vector or a square matrix. When B is a vector, it will be placed on the diagonal of square matrix A indicated by k. When B is a matrix, the diagonal indicated by k will be extracted as vector A.

Example 1

Create a 3 by 3 matrix with 1,2,3 on the main diagonal.

Syntax

A = Diag([1,2,3])

Results

            1               0               0

            0               2               0

            0               0               3

Example 2

Extract the first super diagonal from a matrix.

Syntax

A = Diag([1,2,3;4,5,6],1)

Results

            2

            6

See Also:

Ones

Zeros

Syntax

r = Eye()

r = Eye(m)

r = Eye(m, n)

r = Eye(Size(A))

Arguments

Name

Description

m

A scalar.

n

A scalar.

A

A matrix.

Outputs

Name

Description

r

An identity matrix.

Example

Syntax

A = Eye(3, 5);

print('A = ', A);

Comments

r = Eye(n) returns an n-by-n identity matrix.

r = Eye(m, n) or r = Eye([m n]) returns an m-by-n identity matrix.

r = Eye(Size(A)) returns an identity matrix with the same size as .

r = Eye() with no arguments is the scalar 1.

r = Eye() is equivalent to Eye(1, 1).

The size inputs m or n should be non-negative integers.

Negative integers are treated as 0.

See Also:

Ones

Zeros

Syntax

y = linspace(x1, x2)

y = linspace(x1, x2,n)

Arguments

Name

Description

x1

Real or complex scalars.

x2

Real or complex scalars.

n

Integer: the number of requested values (default value = 100).

Outputs

Name

Description

y

Real or complex row vector.

Example

Syntax

A = linspace(1, 50);

print('A = ', A);

A2 = linspace(1, 6, 2);

print('A2 = ', A2);

A3 = linspace(1, 4, 10);

print('A3 = ', A3);

A4 = linspace(1 + i, 2 + 2 * i,10);

print('A4 = ', A4);

Comments

linspace(x1, x2) computes spaced samples over the interval [x1, x2].

See Also:

Eye

logspace

Zeros

Syntax

y = logspace(x1, x2)

y = logspace(x1, x2, n)

Arguments

Name

Description

x1

Real or complex scalars.

x2

Real or complex scalars.

n

An integer; the number of requested values (default value = 50).

Outputs

Name

Description

y

A real or complex row vector.

Example

Syntax

A = logspace(1, 2, 10);

print(A)

Comments

logspace(x1, x2) computes spaced samples on a log scale.

In this case, where x2 is equal to PI, the values of the points computed are between 10x1 and the PI value.

See Also:

Eye

linspace

Zeros

Syntax

r = Ones()

r = Ones(m)

r = Ones(m, n)

r = Ones(Size(A))

Arguments

Name

Description

m

A scalar.

n

A scalar.

A

A matrix.

Outputs

Name

Description

r

A matrix of ones.

Example

Syntax

A = Ones(3, 5);

print('A = ', A);

Comments

r = Ones(n) returns an n-by-n matrix of ones.

r = Ones(m, n) or r = Ones([m n]) returns an m-by-n matrix of ones.

r = Ones(Size(A)) returns an array of ones that is the same size as A.

r = Ones() with no arguments is the scalar 1.

r = Ones() is equivalent to Ones(1, 1).

The size inputs m or n should be non-negative integers.

Negative integers are treated as 0.

For large matrices, HML scripts may execute faster if the ones function is used to set aside storage for a matrix whose elements are to be generated one at a time, or a row or column at a time.

For example:

N = 1e5;

t1 = CpuTime();

x = Ones(1,N);

t2 = CpuTime();

t3 = CpuTime();

x = [];

for k = 1,N do x(k) = 1; end

t4 = CpuTime();

print('Ones: t2 - t1 = ', t2 - t1)

print('loop: t4 - t3 = ', t4 - t3)

If you need to create a matrix whose values are all the same, you should use an expression like:

A = ones(m, n);

B = scalarvalue * A;

See Also:

Eye

Zeros

Syntax

B = Reshape(A,m,n)

B = Reshape(A,[m,n])

Arguments

Name

Description

A

A matrix to be reshaped.

m

The number of rows of the new matrix.

n

The number of columns of the new matrix.

Outputs

Name

Description

B

The output matrix. It must have the same size as A.

Example 1

Change the shape of [1,3,5;2,4,6].

Syntax

B = Reshape([1,3,5;2,4,6], 3, 2)

Results

B =  1   4

    2   5

    3   6

Comments

A must contain m*n elements.

Syntax

A = Tril(B,k)

Arguments

Name

Description

B

A matrix.

k

(optional)

An index indicating the uppermost diagonal of the input matrix to be preserved in the output matrix. k = 0 (default) indicates main diagonal. k is negative for sub diagonals and positive for super diagonals.

Outputs

Name

Description

A

A lower triangular matrix.

Example

Create a lower triangular matrix from a 3 by 3 matrix.

Syntax

A = Tril([1,2,3;4,5,6;7,8,9])

Results

A = [1,0,0

    4,5,0

    7,8,9]

See Also:

Diag

Triu

Syntax

A = Triu(B,k)

Arguments

Name

Description

B

A matrix.

k

(optional)

An index indicating the lowest diagonal of the input matrix to be preserved in the output matrix. k = 0 (default) indicates main diagonal. k is negative for sub diagonals and positive for super diagonals.

Outputs

Name

Description

A

An upper triangular matrix.

Example

Create an upper triangular matrix from a 3 by 3 matrix.

Syntax

A = Triu([1,2,3;4,5,6;7,8,9])

Results

A = [1,2,3

    0,5,6

    0,0,9]

See Also:

Diag

Tril

Syntax

r = Zeros()

r = Zeros(m)

r = Zeros(m, n)

r = Zeros(Size(A))

Arguments

Name

Description

m

A scalar.

n

A scalar.

A

A matrix.

Outputs

Name

Description

r

A matrix of zeros.

Example

Syntax

A = Zeros(3, 5);

print('A = ', A);

Comments

r = Zeros(n) returns an n-by-n matrix of zeros.

r = Zeros(m, n) or r = Zeros([m n]) returns an m-by-n matrix of zeros.

r = Zeros(Size(A)) returns an array of zeros that is the same size as A.

r = Zeros() with no arguments is the scalar 0.

r = Zeros() is equivalent to Zeros(1, 1).

The size inputs m or n should be nonnegative integers.

Negative integers are treated as 0.

For large matrices, HML scripts may execute faster if the zeros function is used to set aside storage for a matrix whose elements are to be generated one at a time, or a row or column at a time.

For example:

N = 1e5;

t1 = CpuTime();

x = Zeros(1,N);

t2 = CpuTime();

t3 = CpuTime();

x = [];

for k = 1,N do x(k) = 0; end

t4 = CpuTime();

print('Zeros: t2 - t1 = ', t2 - t1)

print('loop: t4 - t3 = ', t4 - t3)    

See Also:

Eye

Ones