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dsp/fourier/internal/fftpack: fix formatting
This commit is contained in:
Dan Kortschak
@@ -18,20 +18,20 @@ import (
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// tabulation of the trigonometric functions are computed and
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// tabulation of the trigonometric functions are computed and
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// stored in work.
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// stored in work.
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//
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//
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// input parameter
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// Input parameter:
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//
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//
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// n The length of the sequence to be transformed.
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// n The length of the sequence to be transformed.
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//
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//
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// Output parameters:
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// Output parameters:
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//
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//
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// work A work array which must be dimensioned at least 4*n.
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// work A work array which must be dimensioned at least 4*n.
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// the same work array can be used for both Cfftf and Cfftb
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// the same work array can be used for both Cfftf and Cfftb
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// as long as n remains unchanged. Different work arrays
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// as long as n remains unchanged. Different work arrays
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// are required for different values of n. The contents of
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// are required for different values of n. The contents of
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// work must not be changed between calls of Cfftf or Cfftb.
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// work must not be changed between calls of Cfftf or Cfftb.
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//
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//
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// ifac A work array containing the factors of n. ifac must have
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// ifac A work array containing the factors of n. ifac must have
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// length 15.
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// length 15.
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func Cffti(n int, work []float64, ifac []int) {
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func Cffti(n int, work []float64, ifac []int) {
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if len(work) < 4*n {
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if len(work) < 4*n {
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panic("fourier: short work")
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panic("fourier: short work")
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@@ -121,46 +121,46 @@ outer:
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// Fourier coefficients of a complex periodic sequence. The
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// Fourier coefficients of a complex periodic sequence. The
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// transform is defined below at output parameter c.
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// transform is defined below at output parameter c.
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//
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//
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// Input parameters:
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// Input parameters:
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//
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//
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// n The length of the array c to be transformed. The method
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// n The length of the array c to be transformed. The method
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// is most efficient when n is a product of small primes.
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// is most efficient when n is a product of small primes.
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// n may change so long as different work arrays are provided.
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// n may change so long as different work arrays are provided.
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//
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//
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// c A complex array of length n which contains the sequence
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// c A complex array of length n which contains the sequence
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// to be transformed.
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// to be transformed.
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//
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//
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// work A real work array which must be dimensioned at least 4*n.
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// work A real work array which must be dimensioned at least 4*n.
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// in the program that calls Cfftf. The work array must be
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// in the program that calls Cfftf. The work array must be
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// initialized by calling subroutine Cffti(n,work,ifac) and a
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// initialized by calling subroutine Cffti(n,work,ifac) and a
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// different work array must be used for each different
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// different work array must be used for each different
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// value of n. This initialization does not have to be
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// value of n. This initialization does not have to be
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// repeated so long as n remains unchanged thus subsequent
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// repeated so long as n remains unchanged thus subsequent
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// transforms can be obtained faster than the first.
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// transforms can be obtained faster than the first.
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// the same work array can be used by Cfftf and Cfftb.
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// the same work array can be used by Cfftf and Cfftb.
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//
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//
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// ifac A work array containing the factors of n. ifac must have
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// ifac A work array containing the factors of n. ifac must have
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// length of at least 15.
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// length of at least 15.
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//
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//
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// Output parameters:
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// Output parameters:
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//
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//
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// c for j=0, ..., n-1
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// c for j=0, ..., n-1
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// c[j]=the sum from k=0, ..., n-1 of
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// c[j]=the sum from k=0, ..., n-1 of
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// c[k]*exp(-i*j*k*2*pi/n)
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// c[k]*exp(-i*j*k*2*pi/n)
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//
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//
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// where i=sqrt(-1)
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// where i=sqrt(-1)
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//
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//
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// This transform is unnormalized since a call of Cfftf
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// This transform is unnormalized since a call of Cfftf
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// followed by a call of Cfftb will multiply the input
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// followed by a call of Cfftb will multiply the input
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// sequence by n.
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// sequence by n.
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//
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//
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// The n elements of c are represented in n pairs of real
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// The n elements of c are represented in n pairs of real
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// values in r where c[j] = r[j*2]+r[j*2+1]i.
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// values in r where c[j] = r[j*2]+r[j*2+1]i.
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//
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//
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// work Contains results which must not be destroyed between
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// work Contains results which must not be destroyed between
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// calls of Cfftf or Cfftb.
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// calls of Cfftf or Cfftb.
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// ifac Contains results which must not be destroyed between
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// ifac Contains results which must not be destroyed between
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// calls of Cfftf or Cfftb.
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// calls of Cfftf or Cfftb.
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func Cfftf(n int, r, work []float64, ifac []int) {
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func Cfftf(n int, r, work []float64, ifac []int) {
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if len(r) < 2*n {
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if len(r) < 2*n {
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panic("fourier: short sequence")
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panic("fourier: short sequence")
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@@ -182,46 +182,46 @@ func Cfftf(n int, r, work []float64, ifac []int) {
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// a complex periodic sequence from its Fourier coefficients. The
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// a complex periodic sequence from its Fourier coefficients. The
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// transform is defined below at output parameter c.
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// transform is defined below at output parameter c.
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//
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//
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// Input parameters:
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// Input parameters:
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//
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//
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// n The length of the array c to be transformed. The method
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// n The length of the array c to be transformed. The method
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// is most efficient when n is a product of small primes.
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// is most efficient when n is a product of small primes.
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// n may change so long as different work arrays are provided.
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// n may change so long as different work arrays are provided.
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//
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//
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// c A complex array of length n which contains the sequence
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// c A complex array of length n which contains the sequence
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// to be transformed.
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// to be transformed.
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//
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//
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// work A real work array which must be dimensioned at least 4*n.
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// work A real work array which must be dimensioned at least 4*n.
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// in the program that calls Cfftb. The work array must be
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// in the program that calls Cfftb. The work array must be
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// initialized by calling subroutine Cffti(n,work,ifac) and a
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// initialized by calling subroutine Cffti(n,work,ifac) and a
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// different work array must be used for each different
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// different work array must be used for each different
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// value of n. This initialization does not have to be
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// value of n. This initialization does not have to be
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// repeated so long as n remains unchanged thus subsequent
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// repeated so long as n remains unchanged thus subsequent
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// transforms can be obtained faster than the first.
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// transforms can be obtained faster than the first.
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// The same work array can be used by Cfftf and Cfftb.
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// The same work array can be used by Cfftf and Cfftb.
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//
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//
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// ifac A work array containing the factors of n. ifac must have
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// ifac A work array containing the factors of n. ifac must have
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// length of at least 15.
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// length of at least 15.
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//
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//
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// Output parameters:
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// Output parameters:
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//
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//
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// c for j=0, ..., n-1
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// c for j=0, ..., n-1
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// c[j]=the sum from k=0, ..., n-1 of
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// c[j]=the sum from k=0, ..., n-1 of
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// c[k]*exp(i*j*k*2*pi/n)
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// c[k]*exp(i*j*k*2*pi/n)
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//
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//
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// where i=sqrt(-1)
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// where i=sqrt(-1)
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//
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//
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// This transform is unnormalized since a call of Cfftf
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// This transform is unnormalized since a call of Cfftf
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// followed by a call of Cfftb will multiply the input
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// followed by a call of Cfftb will multiply the input
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// sequence by n.
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// sequence by n.
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//
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//
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// The n elements of c are represented in n pairs of real
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// The n elements of c are represented in n pairs of real
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// values in r where c[j] = r[j*2]+r[j*2+1]i.
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// values in r where c[j] = r[j*2]+r[j*2+1]i.
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//
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//
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// work Contains results which must not be destroyed between
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// work Contains results which must not be destroyed between
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// calls of Cfftf or Cfftb.
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// calls of Cfftf or Cfftb.
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// ifac Contains results which must not be destroyed between
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// ifac Contains results which must not be destroyed between
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// calls of Cfftf or Cfftb.
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// calls of Cfftf or Cfftb.
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func Cfftb(n int, c, work []float64, ifac []int) {
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func Cfftb(n int, c, work []float64, ifac []int) {
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if len(c) < 2*n {
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if len(c) < 2*n {
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panic("fourier: short sequence")
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panic("fourier: short sequence")
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@@ -15,20 +15,20 @@ import "math"
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// tabulation of the trigonometric functions are computed and
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// tabulation of the trigonometric functions are computed and
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// stored in work.
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// stored in work.
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//
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//
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// Input parameter
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// Input parameter:
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//
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//
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// n The length of the sequence to be transformed. the method
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// n The length of the sequence to be transformed. the method
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// is most efficient when n+1 is a product of small primes.
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// is most efficient when n+1 is a product of small primes.
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//
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//
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// Output parameters
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// Output parameters:
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//
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//
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// work A work array which must be dimensioned at least 3*n.
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// work A work array which must be dimensioned at least 3*n.
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// The same work array can be used for both Cosqf and Cosqb
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// The same work array can be used for both Cosqf and Cosqb
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// as long as n remains unchanged. Different work arrays
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// as long as n remains unchanged. Different work arrays
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// are required for different values of n. The contents of
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// are required for different values of n. The contents of
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// work must not be changed between calls of Cosqf or Cosqb.
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// work must not be changed between calls of Cosqf or Cosqb.
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//
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//
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// ifac An integer work array of length at least 15.
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// ifac An integer work array of length at least 15.
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func Cosqi(n int, work []float64, ifac []int) {
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func Cosqi(n int, work []float64, ifac []int) {
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if len(work) < 3*n {
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if len(work) < 3*n {
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panic("fourier: short work")
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panic("fourier: short work")
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@@ -55,36 +55,36 @@ func Cosqi(n int, work []float64, ifac []int) {
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// The array work which is used by subroutine Cosqf must be
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// The array work which is used by subroutine Cosqf must be
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// initialized by calling subroutine Cosqi(n,work).
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// initialized by calling subroutine Cosqi(n,work).
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//
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//
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// Input parameters
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// Input parameters:
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//
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//
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||||||
// n The length of the array x to be transformed. The method
|
// n The length of the array x to be transformed. The method
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// is most efficient when n is a product of small primes.
|
// is most efficient when n is a product of small primes.
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//
|
//
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// x An array which contains the sequence to be transformed.
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// x An array which contains the sequence to be transformed.
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//
|
//
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||||||
// work A work array which must be dimensioned at least 3*n
|
// work A work array which must be dimensioned at least 3*n
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// in the program that calls Cosqf. The work array must be
|
// in the program that calls Cosqf. The work array must be
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// initialized by calling subroutine Cosqi(n,work) and a
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// initialized by calling subroutine Cosqi(n,work) and a
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// different work array must be used for each different
|
// different work array must be used for each different
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// value of n. This initialization does not have to be
|
// value of n. This initialization does not have to be
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||||||
// repeated so long as n remains unchanged thus subsequent
|
// repeated so long as n remains unchanged thus subsequent
|
||||||
// transforms can be obtained faster than the first.
|
// transforms can be obtained faster than the first.
|
||||||
//
|
//
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||||||
// ifac An integer work array of length at least 15.
|
// ifac An integer work array of length at least 15.
|
||||||
//
|
//
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// Output parameters
|
// Output parameters:
|
||||||
//
|
//
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// x for i=0, ..., n-1
|
// x for i=0, ..., n-1
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// x[i] = x[i] + the sum from k=0 to k=n-2 of
|
// x[i] = x[i] + the sum from k=0 to k=n-2 of
|
||||||
// 2*x[k]*cos((2*i+1)*k*pi/(2*n))
|
// 2*x[k]*cos((2*i+1)*k*pi/(2*n))
|
||||||
//
|
//
|
||||||
// A call of Cosqf followed by a call of
|
// A call of Cosqf followed by a call of
|
||||||
// Cosqb will multiply the sequence x by 4*n.
|
// Cosqb will multiply the sequence x by 4*n.
|
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// Therefore Cosqb is the unnormalized inverse
|
// Therefore Cosqb is the unnormalized inverse
|
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// of Cosqf.
|
// of Cosqf.
|
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//
|
//
|
||||||
// work Contains initialization calculations which must not
|
// work Contains initialization calculations which must not
|
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// be destroyed between calls of Cosqf or Cosqb.
|
// be destroyed between calls of Cosqf or Cosqb.
|
||||||
func Cosqf(n int, x, work []float64, ifac []int) {
|
func Cosqf(n int, x, work []float64, ifac []int) {
|
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if len(x) < n {
|
if len(x) < n {
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panic("fourier: short sequence")
|
panic("fourier: short sequence")
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@@ -142,37 +142,36 @@ func cosqf1(n int, x, w, xh []float64, ifac []int) {
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// The array work which is used by subroutine Cosqb must be
|
// The array work which is used by subroutine Cosqb must be
|
||||||
// initialized by calling subroutine Cosqi(n,work).
|
// initialized by calling subroutine Cosqi(n,work).
|
||||||
//
|
//
|
||||||
|
// Input parameters:
|
||||||
//
|
//
|
||||||
// Input parameters
|
// n The length of the array x to be transformed. The method
|
||||||
|
// is most efficient when n is a product of small primes.
|
||||||
//
|
//
|
||||||
// n The length of the array x to be transformed. The method
|
// x An array which contains the sequence to be transformed.
|
||||||
// is most efficient when n is a product of small primes.
|
|
||||||
//
|
//
|
||||||
// x An array which contains the sequence to be transformed.
|
// work A work array which must be dimensioned at least 3*n
|
||||||
|
// in the program that calls Cosqb. The work array must be
|
||||||
|
// initialized by calling subroutine Cosqi(n,work) and a
|
||||||
|
// different work array must be used for each different
|
||||||
|
// value of n. This initialization does not have to be
|
||||||
|
// repeated so long as n remains unchanged thus subsequent
|
||||||
|
// transforms can be obtained faster than the first.
|
||||||
//
|
//
|
||||||
// work A work array which must be dimensioned at least 3*n
|
// ifac An integer work array of length at least 15.
|
||||||
// in the program that calls Cosqb. The work array must be
|
|
||||||
// initialized by calling subroutine Cosqi(n,work) and a
|
|
||||||
// different work array must be used for each different
|
|
||||||
// value of n. This initialization does not have to be
|
|
||||||
// repeated so long as n remains unchanged thus subsequent
|
|
||||||
// transforms can be obtained faster than the first.
|
|
||||||
//
|
//
|
||||||
// ifac An integer work array of length at least 15.
|
// Output parameters:
|
||||||
//
|
//
|
||||||
// Output parameters
|
// x for i=0, ..., n-1
|
||||||
|
// x[i]= the sum from k=0 to k=n-1 of
|
||||||
|
// 4*x[k]*cos((2*k+1)*i*pi/(2*n))
|
||||||
//
|
//
|
||||||
// x for i=0, ..., n-1
|
// A call of Cosqb followed by a call of
|
||||||
// x[i]= the sum from k=0 to k=n-1 of
|
// Cosqf will multiply the sequence x by 4*n.
|
||||||
// 4*x[k]*cos((2*k+1)*i*pi/(2*n))
|
// Therefore Cosqf is the unnormalized inverse
|
||||||
|
// of Cosqb.
|
||||||
//
|
//
|
||||||
// A call of Cosqb followed by a call of
|
// work Contains initialization calculations which must not
|
||||||
// Cosqf will multiply the sequence x by 4*n.
|
// be destroyed between calls of Cosqb or Cosqf.
|
||||||
// Therefore Cosqf is the unnormalized inverse
|
|
||||||
// of Cosqb.
|
|
||||||
//
|
|
||||||
// work Contains initialization calculations which must not
|
|
||||||
// be destroyed between calls of Cosqb or Cosqf.
|
|
||||||
func Cosqb(n int, x, work []float64, ifac []int) {
|
func Cosqb(n int, x, work []float64, ifac []int) {
|
||||||
if len(x) < n {
|
if len(x) < n {
|
||||||
panic("fourier: short sequence")
|
panic("fourier: short sequence")
|
||||||
|
|||||||
@@ -14,19 +14,19 @@ import "math"
|
|||||||
// Cost. The prime factorization of n together with a tabulation
|
// Cost. The prime factorization of n together with a tabulation
|
||||||
// of the trigonometric functions are computed and stored in work.
|
// of the trigonometric functions are computed and stored in work.
|
||||||
//
|
//
|
||||||
// Input parameter
|
// Input parameter:
|
||||||
//
|
//
|
||||||
// n The length of the sequence to be transformed. The method
|
// n The length of the sequence to be transformed. The method
|
||||||
// is most efficient when n-1 is a product of small primes.
|
// is most efficient when n-1 is a product of small primes.
|
||||||
//
|
//
|
||||||
// Output parameters
|
// Output parameters:
|
||||||
//
|
//
|
||||||
// work A work array which must be dimensioned at least 3*n.
|
// work A work array which must be dimensioned at least 3*n.
|
||||||
// Different work arrays are required for different values
|
// Different work arrays are required for different values
|
||||||
// of n. The contents of work must not be changed between
|
// of n. The contents of work must not be changed between
|
||||||
// calls of Cost.
|
// calls of Cost.
|
||||||
//
|
//
|
||||||
// ifac An integer work array of length at least 15.
|
// ifac An integer work array of length at least 15.
|
||||||
func Costi(n int, work []float64, ifac []int) {
|
func Costi(n int, work []float64, ifac []int) {
|
||||||
if len(work) < 3*n {
|
if len(work) < 3*n {
|
||||||
panic("fourier: short work")
|
panic("fourier: short work")
|
||||||
@@ -56,40 +56,40 @@ func Costi(n int, work []float64, ifac []int) {
|
|||||||
// The array work which is used by subroutine Cost must be
|
// The array work which is used by subroutine Cost must be
|
||||||
// initialized by calling subroutine Costi(n,work).
|
// initialized by calling subroutine Costi(n,work).
|
||||||
//
|
//
|
||||||
// Input parameters
|
// Input parameters:
|
||||||
//
|
//
|
||||||
// n The length of the sequence x. n must be greater than 1.
|
// n The length of the sequence x. n must be greater than 1.
|
||||||
// The method is most efficient when n-1 is a product of
|
// The method is most efficient when n-1 is a product of
|
||||||
// small primes.
|
// small primes.
|
||||||
//
|
//
|
||||||
// x An array which contains the sequence to be transformed.
|
// x An array which contains the sequence to be transformed.
|
||||||
//
|
//
|
||||||
// work A work array which must be dimensioned at least 3*n
|
// work A work array which must be dimensioned at least 3*n
|
||||||
// in the program that calls Cost. The work array must be
|
// in the program that calls Cost. The work array must be
|
||||||
// initialized by calling subroutine Costi(n,work) and a
|
// initialized by calling subroutine Costi(n,work) and a
|
||||||
// different work array must be used for each different
|
// different work array must be used for each different
|
||||||
// value of n. This initialization does not have to be
|
// value of n. This initialization does not have to be
|
||||||
// repeated so long as n remains unchanged thus subsequent
|
// repeated so long as n remains unchanged thus subsequent
|
||||||
// transforms can be obtained faster than the first.
|
// transforms can be obtained faster than the first.
|
||||||
//
|
//
|
||||||
// ifac An integer work array of length at least 15.
|
// ifac An integer work array of length at least 15.
|
||||||
//
|
//
|
||||||
// Output parameters
|
// Output parameters:
|
||||||
//
|
//
|
||||||
// x for i=1,...,n
|
// x for i=1,...,n
|
||||||
// x(i) = x(1)+(-1)**(i-1)*x(n)
|
// x(i) = x(1)+(-1)**(i-1)*x(n)
|
||||||
// + the sum from k=2 to k=n-1
|
// + the sum from k=2 to k=n-1
|
||||||
// 2*x(k)*cos((k-1)*(i-1)*pi/(n-1))
|
// 2*x(k)*cos((k-1)*(i-1)*pi/(n-1))
|
||||||
//
|
//
|
||||||
// A call of Cost followed by another call of
|
// A call of Cost followed by another call of
|
||||||
// Cost will multiply the sequence x by 2*(n-1).
|
// Cost will multiply the sequence x by 2*(n-1).
|
||||||
// Hence Cost is the unnormalized inverse
|
// Hence Cost is the unnormalized inverse
|
||||||
// of itself.
|
// of itself.
|
||||||
//
|
//
|
||||||
// work Contains initialization calculations which must not be
|
// work Contains initialization calculations which must not be
|
||||||
// destroyed between calls of Cost.
|
// destroyed between calls of Cost.
|
||||||
//
|
//
|
||||||
// ifac An integer work array of length at least 15.
|
// ifac An integer work array of length at least 15.
|
||||||
func Cost(n int, x, work []float64, ifac []int) {
|
func Cost(n int, x, work []float64, ifac []int) {
|
||||||
if len(x) < n {
|
if len(x) < n {
|
||||||
panic("fourier: short sequence")
|
panic("fourier: short sequence")
|
||||||
|
|||||||
@@ -18,20 +18,20 @@ import (
|
|||||||
// tabulation of the trigonometric functions are computed and
|
// tabulation of the trigonometric functions are computed and
|
||||||
// stored in work.
|
// stored in work.
|
||||||
//
|
//
|
||||||
// Input parameter:
|
// Input parameter:
|
||||||
//
|
//
|
||||||
// n The length of the sequence to be transformed.
|
// n The length of the sequence to be transformed.
|
||||||
//
|
//
|
||||||
// Output parameters:
|
// Output parameters:
|
||||||
//
|
//
|
||||||
// work A work array which must be dimensioned at least 2*n.
|
// work A work array which must be dimensioned at least 2*n.
|
||||||
// The same work array can be used for both Rfftf and Rfftb
|
// The same work array can be used for both Rfftf and Rfftb
|
||||||
// as long as n remains unchanged. different work arrays
|
// as long as n remains unchanged. different work arrays
|
||||||
// are required for different values of n. The contents of
|
// are required for different values of n. The contents of
|
||||||
// work must not be changed between calls of Rfftf or Rfftb.
|
// work must not be changed between calls of Rfftf or Rfftb.
|
||||||
//
|
//
|
||||||
// ifac A work array containing the factors of n. ifac must have
|
// ifac A work array containing the factors of n. ifac must have
|
||||||
// length of at least 15.
|
// length of at least 15.
|
||||||
func Rffti(n int, work []float64, ifac []int) {
|
func Rffti(n int, work []float64, ifac []int) {
|
||||||
if len(work) < 2*n {
|
if len(work) < 2*n {
|
||||||
panic("fourier: short work")
|
panic("fourier: short work")
|
||||||
@@ -117,50 +117,50 @@ outer:
|
|||||||
// (Fourier analysis). The transform is defined below at output
|
// (Fourier analysis). The transform is defined below at output
|
||||||
// parameter r.
|
// parameter r.
|
||||||
//
|
//
|
||||||
// Input parameters:
|
// Input parameters:
|
||||||
//
|
//
|
||||||
// n The length of the array r to be transformed. The method
|
// n The length of the array r to be transformed. The method
|
||||||
// is most efficient when n is a product of small primes.
|
// is most efficient when n is a product of small primes.
|
||||||
// n may change so long as different work arrays are provided.
|
// n may change so long as different work arrays are provided.
|
||||||
//
|
//
|
||||||
// r A real array of length n which contains the sequence
|
// r A real array of length n which contains the sequence
|
||||||
// to be transformed.
|
// to be transformed.
|
||||||
//
|
//
|
||||||
// work a work array which must be dimensioned at least 2*n.
|
// work a work array which must be dimensioned at least 2*n.
|
||||||
// in the program that calls Rfftf. the work array must be
|
// in the program that calls Rfftf. the work array must be
|
||||||
// initialized by calling subroutine rffti(n,work,ifac) and a
|
// initialized by calling subroutine rffti(n,work,ifac) and a
|
||||||
// different work array must be used for each different
|
// different work array must be used for each different
|
||||||
// value of n. This initialization does not have to be
|
// value of n. This initialization does not have to be
|
||||||
// repeated so long as n remains unchanged. Thus subsequent
|
// repeated so long as n remains unchanged. Thus subsequent
|
||||||
// transforms can be obtained faster than the first.
|
// transforms can be obtained faster than the first.
|
||||||
// The same work array can be used by Rfftf and Rfftb.
|
// The same work array can be used by Rfftf and Rfftb.
|
||||||
//
|
//
|
||||||
// ifac A work array containing the factors of n. ifac must have
|
// ifac A work array containing the factors of n. ifac must have
|
||||||
// length of at least 15.
|
// length of at least 15.
|
||||||
//
|
//
|
||||||
// Output parameters:
|
// Output parameters:
|
||||||
//
|
//
|
||||||
// r r[0] = the sum from i=0 to i=n-1 of r[i]
|
// r r[0] = the sum from i=0 to i=n-1 of r[i]
|
||||||
//
|
//
|
||||||
// if n is even set l=n/2, if n is odd set l = (n+1)/2
|
// if n is even set l=n/2, if n is odd set l = (n+1)/2
|
||||||
// then for k = 1, ..., l-1
|
// then for k = 1, ..., l-1
|
||||||
// r[2*k-1] = the sum from i = 0 to i = n-1 of
|
// r[2*k-1] = the sum from i = 0 to i = n-1 of
|
||||||
// r[i]*cos(k*i*2*pi/n)
|
// r[i]*cos(k*i*2*pi/n)
|
||||||
// r[2*k] = the sum from i = 0 to i = n-1 of
|
// r[2*k] = the sum from i = 0 to i = n-1 of
|
||||||
// -r[i]*sin(k*i*2*pi/n)
|
// -r[i]*sin(k*i*2*pi/n)
|
||||||
//
|
//
|
||||||
// if n is even
|
// if n is even
|
||||||
// r[n-1] = the sum from i = 0 to i = n-1 of
|
// r[n-1] = the sum from i = 0 to i = n-1 of
|
||||||
// (-1)^i*r[i]
|
// (-1)^i*r[i]
|
||||||
//
|
//
|
||||||
// This transform is unnormalized since a call of Rfftf
|
// This transform is unnormalized since a call of Rfftf
|
||||||
// followed by a call of Rfftb will multiply the input
|
// followed by a call of Rfftb will multiply the input
|
||||||
// sequence by n.
|
// sequence by n.
|
||||||
//
|
//
|
||||||
// work contains results which must not be destroyed between
|
// work contains results which must not be destroyed between
|
||||||
// calls of Rfftf or Rfftb.
|
// calls of Rfftf or Rfftb.
|
||||||
// ifac contains results which must not be destroyed between
|
// ifac contains results which must not be destroyed between
|
||||||
// calls of Rfftf or Rfftb.
|
// calls of Rfftf or Rfftb.
|
||||||
func Rfftf(n int, r, work []float64, ifac []int) {
|
func Rfftf(n int, r, work []float64, ifac []int) {
|
||||||
if len(r) < n {
|
if len(r) < n {
|
||||||
panic("fourier: short sequence")
|
panic("fourier: short sequence")
|
||||||
@@ -592,48 +592,48 @@ func radfg(ido, ip, l1, idl1 int, cc, c1, c2, ch, ch2, wa []float64) {
|
|||||||
// coefficients (Fourier synthesis). The transform is defined
|
// coefficients (Fourier synthesis). The transform is defined
|
||||||
// below at output parameter r.
|
// below at output parameter r.
|
||||||
//
|
//
|
||||||
// Input parameters
|
// Input parameters
|
||||||
//
|
//
|
||||||
// n The length of the array r to be transformed. The method
|
// n The length of the array r to be transformed. The method
|
||||||
// is most efficient when n is a product of small primes.
|
// is most efficient when n is a product of small primes.
|
||||||
// n may change so long as different work arrays are provided.
|
// n may change so long as different work arrays are provided.
|
||||||
//
|
//
|
||||||
// r A real array of length n which contains the sequence
|
// r A real array of length n which contains the sequence
|
||||||
// to be transformed.
|
// to be transformed.
|
||||||
//
|
//
|
||||||
// work A work array which must be dimensioned at least 2*n.
|
// work A work array which must be dimensioned at least 2*n.
|
||||||
// in the program that calls Rfftb. The work array must be
|
// in the program that calls Rfftb. The work array must be
|
||||||
// initialized by calling subroutine rffti(n,work,ifac) and a
|
// initialized by calling subroutine rffti(n,work,ifac) and a
|
||||||
// different work array must be used for each different
|
// different work array must be used for each different
|
||||||
// value of n. This initialization does not have to be
|
// value of n. This initialization does not have to be
|
||||||
// repeated so long as n remains unchanged thus subsequent
|
// repeated so long as n remains unchanged thus subsequent
|
||||||
// transforms can be obtained faster than the first.
|
// transforms can be obtained faster than the first.
|
||||||
// The same work array can be used by Rfftf and Rfftb.
|
// The same work array can be used by Rfftf and Rfftb.
|
||||||
//
|
//
|
||||||
// ifac A work array containing the factors of n. ifac must have
|
// ifac A work array containing the factors of n. ifac must have
|
||||||
// length of at least 15.
|
// length of at least 15.
|
||||||
//
|
//
|
||||||
// output parameters
|
// output parameters
|
||||||
//
|
//
|
||||||
// r for n even and for i = 0, ..., n
|
// r for n even and for i = 0, ..., n
|
||||||
// r[i] = r[0]+(-1)^i*r[n-1]
|
// r[i] = r[0]+(-1)^i*r[n-1]
|
||||||
// plus the sum from k=1 to k=n/2-1 of
|
// plus the sum from k=1 to k=n/2-1 of
|
||||||
// 2*r(2*k-1)*cos(k*i*2*pi/n)
|
// 2*r(2*k-1)*cos(k*i*2*pi/n)
|
||||||
// -2*r(2*k)*sin(k*i*2*pi/n)
|
// -2*r(2*k)*sin(k*i*2*pi/n)
|
||||||
//
|
//
|
||||||
// for n odd and for i = 0, ..., n-1
|
// for n odd and for i = 0, ..., n-1
|
||||||
// r[i] = r[0] plus the sum from k=1 to k=(n-1)/2 of
|
// r[i] = r[0] plus the sum from k=1 to k=(n-1)/2 of
|
||||||
// 2*r(2*k-1)*cos(k*i*2*pi/n)
|
// 2*r(2*k-1)*cos(k*i*2*pi/n)
|
||||||
// -2*r(2*k)*sin(k*i*2*pi/n)
|
// -2*r(2*k)*sin(k*i*2*pi/n)
|
||||||
//
|
//
|
||||||
// This transform is unnormalized since a call of Rfftf
|
// This transform is unnormalized since a call of Rfftf
|
||||||
// followed by a call of Rfftb will multiply the input
|
// followed by a call of Rfftb will multiply the input
|
||||||
// sequence by n.
|
// sequence by n.
|
||||||
//
|
//
|
||||||
// work Contains results which must not be destroyed between
|
// work Contains results which must not be destroyed between
|
||||||
// calls of Rfftf or Rfftb.
|
// calls of Rfftf or Rfftb.
|
||||||
// ifac Contains results which must not be destroyed between
|
// ifac Contains results which must not be destroyed between
|
||||||
// calls of Rfftf or Rfftb.
|
// calls of Rfftf or Rfftb.
|
||||||
func Rfftb(n int, r, work []float64, ifac []int) {
|
func Rfftb(n int, r, work []float64, ifac []int) {
|
||||||
if len(r) < n {
|
if len(r) < n {
|
||||||
panic("fourier: short sequence")
|
panic("fourier: short sequence")
|
||||||
|
|||||||
@@ -14,20 +14,20 @@ import "math"
|
|||||||
// Sinqb. The prime factorization of n together with a tabulation
|
// Sinqb. The prime factorization of n together with a tabulation
|
||||||
// of the trigonometric functions are computed and stored in work.
|
// of the trigonometric functions are computed and stored in work.
|
||||||
//
|
//
|
||||||
// Input parameter
|
// Input parameter:
|
||||||
//
|
//
|
||||||
// n The length of the sequence to be transformed. The method
|
// n The length of the sequence to be transformed. The method
|
||||||
// is most efficient when n+1 is a product of small primes.
|
// is most efficient when n+1 is a product of small primes.
|
||||||
//
|
//
|
||||||
// Output parameter
|
// Output parameter:
|
||||||
//
|
//
|
||||||
// work A work array which must be dimensioned at least 3*n.
|
// work A work array which must be dimensioned at least 3*n.
|
||||||
// The same work array can be used for both Sinqf and Sinqb
|
// The same work array can be used for both Sinqf and Sinqb
|
||||||
// as long as n remains unchanged. Different work arrays
|
// as long as n remains unchanged. Different work arrays
|
||||||
// are required for different values of n. The contents of
|
// are required for different values of n. The contents of
|
||||||
// work must not be changed between calls of Sinqf or Sinqb.
|
// work must not be changed between calls of Sinqf or Sinqb.
|
||||||
//
|
//
|
||||||
// ifac An integer work array of length at least 15.
|
// ifac An integer work array of length at least 15.
|
||||||
func Sinqi(n int, work []float64, ifac []int) {
|
func Sinqi(n int, work []float64, ifac []int) {
|
||||||
if len(work) < 3*n {
|
if len(work) < 3*n {
|
||||||
panic("fourier: short work")
|
panic("fourier: short work")
|
||||||
@@ -54,37 +54,37 @@ func Sinqi(n int, work []float64, ifac []int) {
|
|||||||
// The array work which is used by subroutine Sinqf must be
|
// The array work which is used by subroutine Sinqf must be
|
||||||
// initialized by calling subroutine Sinqi(n,work).
|
// initialized by calling subroutine Sinqi(n,work).
|
||||||
//
|
//
|
||||||
// Input parameters
|
// Input parameters:
|
||||||
//
|
//
|
||||||
// n The length of the array x to be transformed. The method
|
// n The length of the array x to be transformed. The method
|
||||||
// is most efficient when n is a product of small primes.
|
// is most efficient when n is a product of small primes.
|
||||||
//
|
//
|
||||||
// x An array which contains the sequence to be transformed.
|
// x An array which contains the sequence to be transformed.
|
||||||
//
|
//
|
||||||
// work A work array which must be dimensioned at least 3*n.
|
// work A work array which must be dimensioned at least 3*n.
|
||||||
// in the program that calls Sinqf. The work array must be
|
// in the program that calls Sinqf. The work array must be
|
||||||
// initialized by calling subroutine Sinqi(n,work) and a
|
// initialized by calling subroutine Sinqi(n,work) and a
|
||||||
// different work array must be used for each different
|
// different work array must be used for each different
|
||||||
// value of n. This initialization does not have to be
|
// value of n. This initialization does not have to be
|
||||||
// repeated so long as n remains unchanged thus subsequent
|
// repeated so long as n remains unchanged thus subsequent
|
||||||
// transforms can be obtained faster than the first.
|
// transforms can be obtained faster than the first.
|
||||||
//
|
//
|
||||||
// ifac An integer work array of length at least 15.
|
// ifac An integer work array of length at least 15.
|
||||||
//
|
//
|
||||||
// Output parameters
|
// Output parameters:
|
||||||
//
|
//
|
||||||
// x for i=0, ..., n-1
|
// x for i=0, ..., n-1
|
||||||
// x[i] = (-1)^(i)*x[n-1]
|
// x[i] = (-1)^(i)*x[n-1]
|
||||||
// + the sum from k=0 to k=n-2 of
|
// + the sum from k=0 to k=n-2 of
|
||||||
// 2*x[k]*sin((2*i+1)*k*pi/(2*n))
|
// 2*x[k]*sin((2*i+1)*k*pi/(2*n))
|
||||||
//
|
//
|
||||||
// A call of Sinqf followed by a call of
|
// A call of Sinqf followed by a call of
|
||||||
// Sinqb will multiply the sequence x by 4*n.
|
// Sinqb will multiply the sequence x by 4*n.
|
||||||
// Therefore Sinqb is the unnormalized inverse
|
// Therefore Sinqb is the unnormalized inverse
|
||||||
// of Sinqf.
|
// of Sinqf.
|
||||||
//
|
//
|
||||||
// work Contains initialization calculations which must not
|
// work Contains initialization calculations which must not
|
||||||
// be destroyed between calls of Sinqf or Sinqb.
|
// be destroyed between calls of Sinqf or Sinqb.
|
||||||
func Sinqf(n int, x, work []float64, ifac []int) {
|
func Sinqf(n int, x, work []float64, ifac []int) {
|
||||||
if len(x) < n {
|
if len(x) < n {
|
||||||
panic("fourier: short sequence")
|
panic("fourier: short sequence")
|
||||||
@@ -120,36 +120,36 @@ func Sinqf(n int, x, work []float64, ifac []int) {
|
|||||||
// The array work which is used by subroutine Sinqb must be
|
// The array work which is used by subroutine Sinqb must be
|
||||||
// initialized by calling subroutine Sinqi(n,work).
|
// initialized by calling subroutine Sinqi(n,work).
|
||||||
//
|
//
|
||||||
// Input parameters
|
// Input parameters:
|
||||||
//
|
//
|
||||||
// n The length of the array x to be transformed. The method
|
// n The length of the array x to be transformed. The method
|
||||||
// is most efficient when n is a product of small primes.
|
// is most efficient when n is a product of small primes.
|
||||||
//
|
//
|
||||||
// x An array which contains the sequence to be transformed.
|
// x An array which contains the sequence to be transformed.
|
||||||
//
|
//
|
||||||
// work A work array which must be dimensioned at least 3*n.
|
// work A work array which must be dimensioned at least 3*n.
|
||||||
// in the program that calls Sinqb. The work array must be
|
// in the program that calls Sinqb. The work array must be
|
||||||
// initialized by calling subroutine Sinqi(n,work) and a
|
// initialized by calling subroutine Sinqi(n,work) and a
|
||||||
// different work array must be used for each different
|
// different work array must be used for each different
|
||||||
// value of n. This initialization does not have to be
|
// value of n. This initialization does not have to be
|
||||||
// repeated so long as n remains unchanged thus subsequent
|
// repeated so long as n remains unchanged thus subsequent
|
||||||
// transforms can be obtained faster than the first.
|
// transforms can be obtained faster than the first.
|
||||||
//
|
//
|
||||||
// ifac An integer work array of length at least 15.
|
// ifac An integer work array of length at least 15.
|
||||||
//
|
//
|
||||||
// Output parameters
|
// Output parameters:
|
||||||
//
|
//
|
||||||
// x for i=0, ..., n-1
|
// x for i=0, ..., n-1
|
||||||
// x[i]= the sum from k=0 to k=n-1 of
|
// x[i]= the sum from k=0 to k=n-1 of
|
||||||
// 4*x[k]*sin((2*k+1)*i*pi/(2*n))
|
// 4*x[k]*sin((2*k+1)*i*pi/(2*n))
|
||||||
//
|
//
|
||||||
// A call of Sinqb followed by a call of
|
// A call of Sinqb followed by a call of
|
||||||
// Sinqf will multiply the sequence x by 4*n.
|
// Sinqf will multiply the sequence x by 4*n.
|
||||||
// Therefore Sinqf is the unnormalized inverse
|
// Therefore Sinqf is the unnormalized inverse
|
||||||
// of Sinqb.
|
// of Sinqb.
|
||||||
//
|
//
|
||||||
// work Contains initialization calculations which must not
|
// work Contains initialization calculations which must not
|
||||||
// be destroyed between calls of Sinqb or Sinqf.
|
// be destroyed between calls of Sinqb or Sinqf.
|
||||||
func Sinqb(n int, x, work []float64, ifac []int) {
|
func Sinqb(n int, x, work []float64, ifac []int) {
|
||||||
if len(x) < n {
|
if len(x) < n {
|
||||||
panic("fourier: short sequence")
|
panic("fourier: short sequence")
|
||||||
|
|||||||
@@ -14,19 +14,19 @@ import "math"
|
|||||||
// The prime factorization of n together with a tabulation of the
|
// The prime factorization of n together with a tabulation of the
|
||||||
// trigonometric functions are computed and stored in work.
|
// trigonometric functions are computed and stored in work.
|
||||||
//
|
//
|
||||||
// Input parameter
|
// Input parameter:
|
||||||
//
|
//
|
||||||
// n The length of the sequence to be transformed. The method
|
// n The length of the sequence to be transformed. The method
|
||||||
// is most efficient when n+1 is a product of small primes.
|
// is most efficient when n+1 is a product of small primes.
|
||||||
//
|
//
|
||||||
// Output parameter
|
// Output parameter:
|
||||||
//
|
//
|
||||||
// work A work array with at least ceil(2.5*n) locations.
|
// work A work array with at least ceil(2.5*n) locations.
|
||||||
// Different work arrays are required for different values
|
// Different work arrays are required for different values
|
||||||
// of n. The contents of work must not be changed between
|
// of n. The contents of work must not be changed between
|
||||||
// calls of Sint.
|
// calls of Sint.
|
||||||
//
|
//
|
||||||
// ifac An integer work array of length at least 15.
|
// ifac An integer work array of length at least 15.
|
||||||
func Sinti(n int, work []float64, ifac []int) {
|
func Sinti(n int, work []float64, ifac []int) {
|
||||||
if len(work) < 5*(n+1)/2 {
|
if len(work) < 5*(n+1)/2 {
|
||||||
panic("fourier: short work")
|
panic("fourier: short work")
|
||||||
@@ -54,39 +54,39 @@ func Sinti(n int, work []float64, ifac []int) {
|
|||||||
// The array work which is used by subroutine Sint must be
|
// The array work which is used by subroutine Sint must be
|
||||||
// initialized by calling subroutine Sinti(n,work).
|
// initialized by calling subroutine Sinti(n,work).
|
||||||
//
|
//
|
||||||
// Input parameters
|
// Input parameters:
|
||||||
//
|
//
|
||||||
// n The length of the sequence to be transformed. The method
|
// n The length of the sequence to be transformed. The method
|
||||||
// is most efficient when n+1 is the product of small primes.
|
// is most efficient when n+1 is the product of small primes.
|
||||||
//
|
//
|
||||||
// x An array which contains the sequence to be transformed.
|
// x An array which contains the sequence to be transformed.
|
||||||
//
|
//
|
||||||
//
|
//
|
||||||
// work A work array with dimension at least ceil(2.5*n)
|
// work A work array with dimension at least ceil(2.5*n)
|
||||||
// in the program that calls Sint. The work array must be
|
// in the program that calls Sint. The work array must be
|
||||||
// initialized by calling subroutine Sinti(n,work) and a
|
// initialized by calling subroutine Sinti(n,work) and a
|
||||||
// different work array must be used for each different
|
// different work array must be used for each different
|
||||||
// value of n. This initialization does not have to be
|
// value of n. This initialization does not have to be
|
||||||
// repeated so long as n remains unchanged thus subsequent
|
// repeated so long as n remains unchanged thus subsequent
|
||||||
// transforms can be obtained faster than the first.
|
// transforms can be obtained faster than the first.
|
||||||
//
|
//
|
||||||
// ifac An integer work array of length at least 15.
|
// ifac An integer work array of length at least 15.
|
||||||
//
|
//
|
||||||
// Output parameters
|
// Output parameters:
|
||||||
//
|
//
|
||||||
// x for i=1,...,n
|
// x for i=1,...,n
|
||||||
// x(i)= the sum from k=1 to k=n
|
// x(i)= the sum from k=1 to k=n
|
||||||
// 2*x(k)*sin(k*i*pi/(n+1))
|
// 2*x(k)*sin(k*i*pi/(n+1))
|
||||||
//
|
//
|
||||||
// A call of Sint followed by another call of
|
// A call of Sint followed by another call of
|
||||||
// Sint will multiply the sequence x by 2*(n+1).
|
// Sint will multiply the sequence x by 2*(n+1).
|
||||||
// Hence Sint is the unnormalized inverse
|
// Hence Sint is the unnormalized inverse
|
||||||
// of itself.
|
// of itself.
|
||||||
//
|
//
|
||||||
// work Contains initialization calculations which must not be
|
// work Contains initialization calculations which must not be
|
||||||
// destroyed between calls of Sint.
|
// destroyed between calls of Sint.
|
||||||
// ifac Contains initialization calculations which must not be
|
// ifac Contains initialization calculations which must not be
|
||||||
// destroyed between calls of Sint.
|
// destroyed between calls of Sint.
|
||||||
func Sint(n int, x, work []float64, ifac []int) {
|
func Sint(n int, x, work []float64, ifac []int) {
|
||||||
if len(x) < n {
|
if len(x) < n {
|
||||||
panic("fourier: short sequence")
|
panic("fourier: short sequence")
|
||||||
|
|||||||
Reference in New Issue
Block a user