# Try out NAG Library functions

Explore NAG maths and stats routines with interactive demos
Function ID
C09CAF
Name
nagf_wav_1d_sngl_fwd
Description
One-dimensional discrete wavelet transform
Keywords
discrete transform | wavelets | wavelets, one-dimensional
This example computes the one-dimensional discrete wavelet decomposition for $8$ values using the Daubechies wavelet, ${\mathbf{wavnam}}=\text{'DB4'}$, with zero end extension.
    Program c09cafe

!     C09CAF Example Program Text

!     Mark 26.1 Release. NAG Copyright 2016.

!     .. Use Statements ..
Use nag_library, Only: c09aaf, c09caf, c09cbf, nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Integer                          :: ifail, n, nf, nwc, nwl, ny
Character (12)                   :: mode, wavnam, wtrans
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: ca(:), cd(:), x(:), y(:)
Integer                          :: icomm(100)
!     .. Executable Statements ..
Write (nout,*) 'C09CAF Example Program Results'
!     Skip heading in data file
Allocate (x(n),y(n))

Write (nout,99999) wavnam, mode
Write (nout,*) 'Input Data      X :'
Write (nout,99997) x(1:n)
!     Query wavelet filter dimensions
wtrans = 'Single Level'

!     ifail: behaviour on error exit
!            =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call c09aaf(wavnam,wtrans,mode,n,nwl,nf,nwc,icomm,ifail)

Allocate (ca(nwc),cd(nwc))

ifail = 0
Call c09caf(n,x,nwc,ca,cd,icomm,ifail)

Write (nout,99998)
Write (nout,99997) ca(1:nwc)
Write (nout,99996)
Write (nout,99997) cd(1:nwc)

ny = n

ifail = 0
Call c09cbf(nwc,ca,cd,ny,y,icomm,ifail)

Write (nout,99995)
Write (nout,99997) y(1:ny)

99999 Format (1X,'DWT :: Wavelet: ',A,', End mode: ',A)
99998 Format (1X,'Approximation coefficients CA : ')
99997 Format (1X,8(F8.4,1X),:)
99996 Format (1X,'Detail coefficients        CD : ')
99995 Format (1X,'Reconstruction              Y : ')
End Program c09cafe

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