CCOR2D(3S)CCOR2D(3S)NAME
CCOR2D, ZCOR2D, SCOR2D, DCOR2D - Compute the two-dimensional (2D)
correlation of two two-dimensional (2D) arrays
SYNOPSIS
Single precision complex
Fortran:
CALL CCOR2D (x, incx, ldx, ilx0, nx1, i2x0, nx2, h, inch, ldh,
i1h0, nh1, i2h0, nh2, y, incy, ldy, i1y0, ny1, i2y0, ny2)
C/C++:
#include <scsl_fft.h>
void ccor2d (scsl_complex *x, int incx, int ldx, int i1x0, int
nx1, int i2x0, int nx2, scsl_complex *h, int inch, int ldh, int
i1h0, int nh1, int i2h0, int nx2, scsl_complex *y, int incy,
int ldy, int i1y0, int ny1 int i2y0, int ny2);
C++ STL:
#include <complex.h>
#include <scsl_fft.h>
void ccor2d (complex<float> *x, int incx, int ldx, int i1x0,
int nx1, int i2x0, int nx2, complex<float> *h, int inch, int
ldh, int i1h0, int nh1, int i2h0, int nx2, complex<float> *y,
int incy, int ldy, int i1y0, int ny1 int i2y0, int ny2);
Double precision complex
Fortran:
CALL ZCOR2D (x, incx, ldx, i1x0, nx1, i2x0, nx2, h, inch, ldh,
i1h0, nh1, i2h0, nh2, y, incy, ldy, i1y0, ny1, i2y0, ny2)
C/C++:
#include <scsl_fft.h>
void zcor2d (scsl_zomplex *x, int incx, int ldx, int i1x0, int
nx1, int i2x0, int nx2, scsl_zomplex *h, int inch, int ldh, int
i1h0, int nh1, int i2h0, int nx2, scsl_zomplex *y, int incy,
int ldy, int i1y0, int ny1 int i2y0, int ny2)
C++ STL:
#include <complex.h>
#include <scsl_fft.h>
void zcor2d (complex<double> *x, int incx, int ldx, int i1x0,
int nx1, int i2x0, int nx2, complex<double> *h, int inch, int
ldh, int i1h0, int nh1, int i2h0, int nx2, complex<double> *y,
int incy, int ldy, int i1y0, int ny1, int i2y0, int ny2);
Single precision
Fortran:
CALL SCOR2D (x, incx, ldx, ilx0, nx1, i2x0, nx2, h, inch, ldh,
i1h0, nh1, i2h0, nh2, y, incy, ldy, i1y0, ny1, i2y0, ny2)
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CCOR2D(3S)CCOR2D(3S)
C/C++:
#include <scsl_fft.h>
void scor2d (float *x, int incx, int ldx, int i1x0, int nx1,
int i2x0, int nx2, float *h, int inch, int ldh, int i1h0, int
nh1, int i2h0, int nx2, float *y, int incy, int ldy, int i1y0,
int ny1 int i2y0, int ny2);
Double precision
Fortran:
CALL DCOR2D (x, incx, ldx, i1x0, nx1, i2x0, nx2, h, inch, ldh,
i1h0, nh1, i2h0, nh2, y, incy, ldy, i1y0, ny1, i2y0, ny2)
C/C++:
#include <scsl_fft.h>
void dcor2d (double *x, int incx, int ldx, int i1x0, int nx1,
int i2x0, int nx2, double *h, int inch, int ldh, int i1h0, int
nh1, int i2h0, int nx2, double *y, int incy, int ldy, int i1y0,
int ny1 int i2y0, int ny2);
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 a 2D filter array h with a 2D
array x, producing the output 2D array y.
Let the following be the filter and data matrices:
H = h 0 <= i < nh1, 0 <= j < nh2
i, j
X = x 0 <= i < nx1, 0 <= j < nx2
i, j
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CCOR2D(3S)CCOR2D(3S)
The correlation is defined as:
Y(i,j) = Sum Sum H(k,l) * x(i+k, j+l)
k l
The matrix Y has values defined for 0<=i < nx1 and 0 <=j < nx2. In the
*COR2D routines, the number of terms in the output array is specified by
the arguments ny1 and ny2. If ny1 < nx1 or ny2 < nx2, the output array y
is truncated. If ny1 >= nx1 or ny2 >= nx2, the terms beyond i = nx1-1
and j = nx2-1 are set to 0.
By choosing ny2 > nx1 - nh1 + 1 or ny2 > nx2 - nh2 + 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 of each dimension
with zeros, except that no zeros are actually stored and no
multiplications by zero are actually done.
Generally, the arrays x, h and y represent signals sampled at equal
intervals in two dimensions, and the indexes of the arrays denote the
samples. If all three signals are aligned, we may, without loss of
generality, set the initial samples to 0 in both dimensions, as in the
formulas above.
The *COR2D routines, however, permit more generality than this. The
signals may be shifted from each other using input parameters specifying
the initial samples in each dimension. This can be useful in several
situations. For example, if the input array has leading zero values that
one does not wish to store, i1x0 and i2x0 may be set to the sample
corresponding to the first non-zero element in the input array, and
previous samples are treated as 0.
Note that, instead of (0,0), the initial sample could just as easily have
been labeled (1,1) or (10,1) or (0,-78); the relevant point is that the
first elements of each of the x, h and y arrays are defined to be the
same sample as long as i1x0 = i1h0 = i1y0 and i2x0 = i2h0 = i2y0.
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 dimensions (ldx, nx2). (input).
CCOR2D: Single precision complex array.
ZCOR2D: Double precision complex array.
SCOR2D: Single precision array.
DCOR2D: Double precision array.
Input array containing the data to be correlated with h
incx Integer. (input)
Increment between two successive values of x. incx must not be
0.
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CCOR2D(3S)CCOR2D(3S)
ldx Integer. (input)
The number of rows in the x array, as it was declared in the
calling program (the leading dimension of x). ldx >= MAX (nx1
* incx, 1).
i1x0 Integer. (input)
Sample corresonding to the first element of each column of x.
nx1 Integer. (input)
The number of elements in each column of x. nx1 >= 0.
i2x0 Integer. (input).
Sample corresponding to the first element of each row of x.
nx2 Integer. (input).
Number of elements in each row of x. nx2 >= 0.
h Array of dimensions (ldh, nh2). (input).
CCOR2D: Single precision complex array.
ZCOR2D: Double precision complex array.
SCOR2D: Single precision array.
DCOR2D: Double precision array.
Input array containing the filter matrix to be correlated with
x.
inch Integer. (input)
Increment between two successive values of h. inch must not be
0.
ldh Integer. (input)
The number of rows in the h array, as it was declared in the
calling program (the leading dimension of h). ldh >= MAX(nh1 *
inch, 1).
i1h0 Integer. (input)
Sample corresponding to the first element of each column of h.
nh1 Integer. (input)
Number of elements in each column of h. nh1 >= 0.
i2h0 Integer. (input)
Sample corresponding to the first element of each row of h.
nh2 Integer. (input)
Number of elements in each row of h. nh2 >= 0.
y Array of dimensions (ldy, ny2). (input and output)
CCOR2D: Single precision complex array.
ZCOR2D: Double precision complex array.
SCOR2D: Single precision array.
DCOR2D: Double precision array.
Output of correlation.
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CCOR2D(3S)CCOR2D(3S)
incy Integer. (input)
Increment between two successive values of a sequence in y.
incy must not be 0.
ldy Integer. (input)
The number of rows in the y array, as it was declared in the
calling program (the leading dimension of y). ldy >= MAX( ny1 *
incy, 1).
i1y0 Integer. (input)
Sample corresponding to the first element of each column of y.
ny1 Integer. (input)
Number of elements in each column of y. ny1 >= 0.
i2y0 Integer. (input) Sample corresponding to the first element of
each row of y.
ny2 Integer. (input)
Number of elements in each row of y. ny2 >= 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)
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]
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CCOR2D(3S)CCOR2D(3S)
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>
CAUTIONS
The arrays x, h and y must be non-overlapping.
EXAMPLES
The following example computes the correlation of a 4x4-sample array x
with a filter h containing 3x3 samples:
Fortran:
REAL X(0:3,0:3), H(0:2,0:2), Y(0:5,0:5)
DO J = 0, 3
DO I = 0, 3
X(I,J) = -1.0
ENDDO
ENDDO
X(0,0) = 1.0
DO J = 0, 2
DO I = 0, 2
H(i,j) = 1.0/(i+j+1)
ENDDO
ENDDO
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CCOR2D(3S)CCOR2D(3S)
CALL SCOR2D(X, 1, 4, 0, 4, 0, 4,
& H, 1, 3, 0, 3, 0, 3,
& Y, 1, 6, 0, 6, 0, 6)
C/C++:
#include <scsl_fft.h>
float x[4][4], h[3][3], y[6][6];
int i, j;
for (j=0; j<4; j++) {
for (i=0; i<4; i++) {
x[j][i] = -1.0f;
}
}
x[0][0] = 1.0f;
for (j=0; j<3; j++) {
for (i=0; i<3; i++) {
h[i] = 1.0f/(i+j+1);
}
}
scor2d((float *) x, 1, 4, 0, 4, 0, 4,
(float *) h, 1, 3, 0, 3, 0, 3,
(float *) y, 1, 6, 0, 6, 0, 6);
The output is
Y(*,0) Y(*,1) Y(*,2) Y(*,3) Y(*,4) Y(*,5)
Y(0,*) -1.7000-3.7000-2.9167 -1.8333 0.0000 0.0000
Y(1,*) -3.7000-3.7000-2.9167 -1.8333 0.0000 0.0000
Y(2,*) -2.9167-2.9167-2.3333 -1.5000 0.0000 0.0000
Y(3,*) -1.8333-1.8333-1.5000 -1.0000 0.0000 0.0000
Y(4,*) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Y(5,*) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Changing i1x0 to 1 produces the following shift in the output:
Y(*,0) Y(*,1) Y(*,2) Y(*,3) Y(*,4) Y(*,5)
Y(0,*) -0.8667-1.8667-1.4167 -0.8333 0.0000 0.0000
Y(1,*) -1.7000-3.7000-2.9167 -1.8333 0.0000 0.0000
Y(2,*) -3.7000-3.7000-2.9167 -1.8333 0.0000 0.0000
Y(3,*) -2.9167-2.9167-2.3333 -1.5000 0.0000 0.0000
Y(4,*) -1.8333-1.8333-1.5000 -1.0000 0.0000 0.0000
Y(5,*) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
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CCOR2D(3S)CCOR2D(3S)
Changing i2h0 to -1 produces the following shift in the output:
Y(*,0) Y(*,1) Y(*,2) Y(*,3) Y(*,4) Y(*,5)
Y(0,*) -3.7000-2.9167-1.8333 0.0000 0.0000 0.0000
Y(1,*) -3.7000-2.9167-1.8333 0.0000 0.0000 0.0000
Y(2,*) -2.9167-2.3333-1.5000 0.0000 0.0000 0.0000
Y(3,*) -1.8333-1.5000-1.0000 0.0000 0.0000 0.0000
Y(4,*) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Y(5,*) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Changing i1y0 to +1 and i2y0 to -1 produces the following shift in the
output:
Y(*,0) Y(*,1) Y(*,2) Y(*,3) Y(*,4) Y(*,5)
Y(0,*) -1.8667-3.7000-3.7000 -2.9167 -1.8333 0.0000
Y(1,*) -1.4167-2.9167-2.9167 -2.3333 -1.5000 0.0000
Y(2,*) -0.8333-1.8333-1.8333 -1.5000 -1.0000 0.0000
Y(3,*) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Y(4,*) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Y(5,*) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
SEE ALSOCCOR1D(3S), CCORM1D(3S), INTRO_FFT(3S), INTRO_SCSL(3S)
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