Diag

This function creates a diagonal matrix.

The generic syntax is given below.

Diag syntax

diagMat = Diag(d)

• where, d denotes the main diagonal of the diagMat.
• d can be a vector of Real32, Real64, Int8, Int16, Int32, Int64
• The result is always n x n matrix of REAL(DFP).

܀ Example 1

In this example we show the usage of Diag function. We will form diagonal matrix in this example from REAL(DFP) vector.

program main
  use easifemBase

  real( DFP ), allocatable :: mat(:, :)
  real( DFP ), allocatable :: d(:)

  call reallocate(d, 5)
  call random_number(d)
  d = d * 10
  call display( MdEncode(d), "d = " )

  mat = Diag(d)
  call display( MdEncode(mat), "mat = " )

end program

Results

d =

8.2717	3.502	0.39168	0.51942	2.6892

mat =

8.2717	0	0	0	0
0	3.502	0	0	0
0	0	0.39168	0	0
0	0	0	0.51942	0
0	0	0	0	2.6892

܀ Example 2

In this example we show the usage of Diag function. We will form diagonal matrix in this example from REAL(Real32) vector.

header

program main
  use easifemBase

variables

  real( DFP ), allocatable :: mat(:, :)
  real( Real32 ), allocatable :: d(:)

form random diagonal

  call reallocate(d, 5)
  call random_number(d)
  d = d * 10
  call display( MdEncode(d), "d = " )

diagonal matrix

  mat = Diag(d)
  call display( MdEncode(mat), "mat = " )

cleanup

end program

Results

d =

5.165	2.5622	1.1153	1.0442	5.2306

mat =

5.165	0	0	0	0
0	2.5622	0	0	0
0	0	1.1153	0	0
0	0	0	1.0442	0
0	0	0	0	5.2306

↢ Close

info

We can also use Diag to access the diagonal of the matrix. The syntaxt is given below:

d = Diag(mat, diagNo)

where,

• mat is a two-dimensional square matrix
• diagNo is an integer, which stands for the diagonal
• diagNo == 0 denotes the main diagonal
• diagNo > 0 denotes the super-diagonal
• diagNo < 0 denotes the sub diagonal

܀ See example

In this example we show the usage of Diag function.

We will extract diagonals from a square matrix.

program main
  use easifemBase

  real( DFP ), allocatable :: mat(:, :)
  real( DFP ), allocatable :: d(:)

  call reallocate(mat, 5, 5)
  call random_number(mat)
  call display( MdEncode(mat), "mat = " )

mat =

0.68758	3.17016E-02	0.59785	4.6886E-02	0.61175
0.48573	0.67486	0.73655	0.52901	0.60769
0.17241	0.52752	0.79169	0.21098	0.94547
0.21998	0.67235	0.52645	0.32917	0.3067
0.50651	5.82701E-02	4.87607E-02	0.38279	0.11833

getting the main diagonal

  d = Diag(mat, 0)
  call display( MdEncode(d), "main diagonal = " )

main diagonal =

0.68758	0.67486	0.79169	0.32917	0.11833

getting the first super diagonal

  d = Diag(mat, 1)
  call display( MdEncode(d), "super diagonal 1= " )

super diagonal 1=

3.17016E-02	0.73655	0.21098	0.3067

getting the second super diagonal

  d = Diag(mat, 2)
  call display( MdEncode(d), "super diagonal 2= " )

super diagonal 2=

0.59785	0.52901	0.94547

getting the first sub diagonal

  d = Diag(mat, -1)
  call display( MdEncode(d), "subdiagonal 1= " )

subdiagonal 1=

0.48573	0.52752	0.52645	0.38279

getting the second subdiagonal

  d = Diag(mat, -2)
  call display( MdEncode(d), "subdiagonal 2= " )

subdiagonal 2=

0.17241	0.67235	4.87607E-02

cleanup

end program

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