CCOR1D(3S)CCOR1D(3S)NAME
CCOR1D, ZCOR1D, SCOR1D, DCOR1D - Compute the one-dimensional (1D)
correlation of two sequences.
SYNOPSIS
Single precision complex
Fortran:
CALL CCOR1D (x, incx, ix0, nx, h, inch, ih0, nh, y, incy, iy0,
ny)
C/C++:
#include <scsl_fft.h>
void ccor1d (scsl_complex *x, int incx, int ix0, int nx,
scsl_complex *h, int inch, int ih0, int nh, scsl_complex *y,
int incy, int iy0, int ny);
C++ STL:
#include <complex.h>
#include <scsl_fft.h>
void ccor1d (complex<float> *x, int incx, int ix0, int nx,
complex<float> *h, int inch, int ih0, int nh, complex<float>
*y, int incy, int iy0, int ny);
Double precision complex
Fortran:
CALL ZCOR1D (x, incx, ix0, nx, h, inch, ih0, nh, y, incy, iy0,
ny);
C/C++:
#include <scsl_fft.h>
void zcor1d (scsl_zomplex *x, int incx, int ix0, int nx,
scsl_zomplex *h, int inch, int ih0, int nh, scsl_zomplex *y,
int incy, int iy0, int ny);
C++ STL:
#include <complex.h>
#include <scsl_fft.h>
void zcor1d (complex<double> *x, int incx, int ix0, int nx,
complex<double> *h, int inch, int ih0, int nh, complex<double>
*y, int incy, int iy0, int ny);
Single precision
Fortran:
CALL SCOR1D (x, incx, ix0, nx, h, inch, ih0, nh, y, incy, iy0,
ny)
C/C++:
#include <scsl_fft.h>
void scor1d (float *x, int incx, int ix0, int nx, float *h, int
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CCOR1D(3S)CCOR1D(3S)
inch, int ih0, int nh, float *y, int incy, int iy0, int ny);
Double precision
Fortran:
CALL DCOR1D (x, incx, ix0, nx, h, inch, ih0, nh, y, incy, iy0,
ny)
C/C++:
#include <scsl_fft.h>
void dcor1d (double *x, int incx, int ix0, int nx, double *h,
int inch, int ih0, int nh, double *y, int incy, int iy0, int
ny);
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
The C and C++ prototypes shown above are appropriate for the 4-byte
integer version of SCSL. When using the 8-byte integer version, the
variables of type int become long long and the <scsl_fft_i8.h> header
file should be included.
DESCRIPTION
These routines compute the correlation of the filter sequence h with the
data sequence x, producing the output sequence y.
Suppose h and x are two sequences of numbers, having nh and nx elements,
respectively.
h = [h(0), h(1), ..., h(nh - 1) ] , and
x = [x(0), x(1), ..., x(nx - 1) ] .
The correlation y is the sequence having elements defined by:
y(0) = h(0) * x(0) + h(1) * x(1) + ... + h(nh-1) * x(nh-1)
y(1) = h(0) * x(1) + h(1) * x(2) + ... + h(nh-1) * x(nh)y(2) = h(0) * x(2) + h(1) * x(3) + ... + h(nh-1) * x(nh+1)
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CCOR1D(3S)CCOR1D(3S)
This example definition assumes nx >= nh. The precise definition of the
correlation is:
min(nh-1,nx-1-k)
Y(j) = Sum {H(k)*x(j+k)}, j = 0, ..., ny-1.
k=0
In the *COR1D routines, the number of terms in the output sequence is
specified by an argument, ny. If ny < nx, the output sequence is just
truncated. If ny > nx, zeros are appended to the output sequence.
By choosing ny > nx-nh + 1, the routine does what is sometimes called
"post-tapered" correlation. The effect is as though the data sequence,
x, were padded on the end with zeros, except that no zeros are actually
stored and no multiplications by zero are actually done.
Generally, the sequences x, h and y represent signals sampled at equal
time intervals, and the indexes of the vectors denote the sample times.
If all three signals begin at the same time, we may, without loss of
generality, set the initial time to 0, as in the formulas above.
The *COR1D routines, however, permit more generality than this. The
signals may be time shifted from each other using input parameters
specifiying the initial time sample for each signal. This can be useful
in several situations. For example, if the input array has several
leading zero values that one does not wish to store, ix0 may be set to
the time sample corresponding to the first non-zero element in the input
array, and earlier time samples are treated as 0.
Note that, instead of 0, the initial time could just as easily have been
labeled 1 or 10 or -78; the relevant point is that the first elements of
each of the x, h and y arrays are defined to be the same time sample as
long as ix0 = ih0 = iy0.
See the NOTES section of this man page for information about the
interpretation of the data types described in the following arguments.
These routines have the following arguments:
x Array of dimension nx. (input).
CCOR1D: Single precision complex array.
ZCOR1D: Double precision complex array.
SCOR1D: Single precision array.
DCOR1D: Double precision array.
Input sequences to be correlated with h.
incx Integer. (input)
Increment between two successive values of x. incx must not be
0.
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CCOR1D(3S)CCOR1D(3S)
ix0 Integer. (input)
Time sample corresponding to the first element of x.
nx Integer. (input)
The number of elements in the sequence x. nx >= 0.
h Array of dimension nh. (input).
CCOR1D: Single precision complex array.
ZCOR1D: Double precision complex array.
SCOR1D: Single precision array.
DCOR1D: Double precision array.
Input sequence to be correlated with x.
inch Integer. (input)
Increment between two successive values of h. inch must not be
0.
ih0 Integer. (input)
Time sample correspondings to the first element of h.
nh Integer. (input)
The number of elements in the sequence h. nh >= 0.
y Array of dimension ny. (output)
CCOR1D: Single precision complex array.
ZCOR1D: Double precision complex array.
SCOR1D: Single precision array.
DCOR1D: Double precision array.
Output of the correlation. On entry, the array y need not be
initialized. On exit, the result overwrites y.
incy Integer. (input)
Increment between two successive values of y. incy must not be
0.
iy0 Integer. (input)
Time sample corresponding to the first element of y.
ny Integer. (input)
Number of elements in each sequence of y. ny >= 0.
NOTES
The following data types are described in this documentation:
Term Used Data type
Fortran:
Array dimensioned 0..n-1 x(0:n-1)
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CCOR1D(3S)CCOR1D(3S)
Array of dimensions (m,n) x(m,n)
Array of dimensions (m,n,p) x(m,n,p)
Integer INTEGER (INTEGER*8 for -lscs_i8[_mp])
Single precision REAL
Double precision DOUBLE PRECISION
Single precision complex COMPLEX
Double precision complex DOUBLE COMPLEX
C/C++:
Array dimensioned 0..n-1 x[n]
Array of dimensions (m,n) x[m*n] or x[n][m]
Array of dimensions (m,n,p) x[m*n*p] or x[p][n][m]
Integer int (long long for -lscs_i8[_mp])
Single precision float
Double precision double
Single precision complex scsl_complex
Double precision complex scsl_zomplex
C++ STL:
Array dimensioned 0..n-1 x[n]
Array of dimensions (m,n) x[m*n] or x[n][m]
Array of dimensions (m,n,p) x[m*n*p] or x[p][n][m]
Integer int (long long for -lscs_i8[_mp])
Single precision float
Double precision double
Single precision complex complex<float>
Double precision complex complex<double>
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CCOR1D(3S)CCOR1D(3S)CAUTIONS
The arrays x, h and y must be non-overlapping.
EXAMPLES
The following example computes the correlation of a 4-sample sequence x
with a filter h containing 3 samples:
Fortran:
REAL X(0:3), H(0:2), Y(0:5)
X(0) = 1.0
DO I = 1, 3
X(I) = -1.0
ENDDO
DO I = 0, 2
H(I) = 1.0/(I+1)
ENDDO
CALL SCOR1D(X(0), 1, 0, 4, H(0), 1, 0, 3, Y(0), 1, 0, 6)
C/C++:
#include <scsl_fft.h>
float x[4], h[3], y[6];
int i;
x[0] = 1.0f
for (i=1; i<4; i++) {
x[i] = -1.0f;
}
for (i=0; i<3; i++) {
h[i] = 1.0f/(i+1);
}
scor1d(x, 1, 0, 4, h, 1, 0, 3, y, 1, 0, 6);
The output is
Y(0)Y(1)Y(2)Y(3)Y(4)Y(5)
0.1667 -1.8333-1.5000 -1.0000 0.0000 0.0000
Changing the values for ix0, ih0 and iy0 produces the following shifts in
the output:
ix0 = +1 0.1667 0.1667 -1.8333 -1.5000 -1.0000 0.0000
ix0 = +2 0.3333 0.1667 0.1667 -1.8333-1.5000-1.0000
ix0 = -1-1.8333-1.5000-1.0000 0.0000 0.0000 0.0000
ix0 = -2-1.5000-1.0000 0.0000 0.0000 0.0000 0.0000
ih0 = +1 -1.8333-1.5000-1.0000 0.0000 0.0000 0.0000
ih0 = +2 -1.5000-1.0000 0.0000 0.0000 0.0000 0.0000
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CCOR1D(3S)CCOR1D(3S)
ih0 = -1 0.1667 0.1667 -1.8333 -1.5000 -1.0000 0.0000
ih0 = -2 0.3333 0.1667 0.1667 -1.8333-1.5000-1.0000
iy0 = +1 -1.8333-1.5000-1.0000 0.0000 0.0000 0.0000
iy0 = +2 -1.5000-1.0000 0.0000 0.0000 0.0000 0.0000
iy0 = -1 0.1667 0.1667 -1.8333 -1.5000 -1.0000 0.0000
iy0 = -2 0.3333 0.1667 0.1667 -1.8333-1.5000-1.0000
SEE ALSOINTRO_FFT(3S), INTRO_SCSL(3S)
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