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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)

									Page 1

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

									Page 2

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.

									Page 3

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.

									Page 4

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]

									Page 5

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

									Page 6

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

									Page 7

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 ALSO
     CCOR1D(3S), CCORM1D(3S), INTRO_FFT(3S), INTRO_SCSL(3S)

									Page 8

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