CCORM1D(3S)CCORM1D(3S)NAME
CCORM1D, ZCORM1D, SCORM1D, DCORM1D - Compute multiple 1D correlations
SYNOPSIS
Single precision complex
Fortran:
CALL CCORM1D (x, incx, ldx, ix0, nx, nseq, h, inch, ih0, nh, y,
incy, ldy, iy0, ny)
C/C++:
#include <scsl_fft.h>
void ccorm1d (scsl_complex *x, int incx, int ldx, int ix0, int
nx, int nseq, scsl_complex *h, int inch, int ih0, int nh,
scsl_complex *y, int incy, int ldy, int iy0, int ny);
C++ STL:
#include <complex.h>
#include <scsl_fft.h>
void ccorm1d (complex<float> *x, int incx, int ldx, int ix0,
int nx, int nseq, complex<float> *h, int inch, int ih0, int nh,
complex<float> *y, int incy, int ldy, int iy0, int ny);
Double precision complex
Fortran:
CALL ZCORM1D (x, incx, ldx, ix0, nx, nseq, h, inch, ih0, nh, y,
incy, ldy, iy0, ny)
C/C++:
#include <scsl_fft.h>
void zcorm1d (scsl_zomplex *x, int incx, int ldx, int ix0, int
nx, int nseq, scsl_zomplex *h, int inch, int ih0, int nh,
scsl_zomplex *y, int incy, int ldy, int iy0, int ny);
C++ STL:
#include <complex.h>
#include <scsl_fft.h>
void zcorm1d (complex<double> *x, int incx, int ldx, int ix0,
int nx, int nseq, complex<double> *h, int inch, int ih0, int
nh, complex<double> *y, int incy, int ldy, int iy0, int ny);
Single precision
Fortran:
CALL SCORM1D (x, incx, ldx, ix0, nx, nseq, h, inch, ih0, nh, y,
incy, ldy, iy0, ny)
C/C++:
#include <scsl_fft.h>
void scorm1d (float *x, int incx, int ldx, int ix0, int nx, int
nseq, float *h, int inch, int ih0, int nh, float *y, int incy,
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CCORM1D(3S)CCORM1D(3S)
int ldy, int iy0, int ny);
Double precision
Fortran:
CALL DCORM1D (x, incx, ldx, ix0, nx, nseq, h, inch, ih0, nh, y,
incy, ldy, iy0, ny)
C/C++:
#include <scsl_fft.h>
void dcorm1d (double *x, int incx, int ldx, int ix0, int nx,
int nseq, double *h, int inch, int ih0, int nh, double *y, int
incy, int ldy, 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 each
column of the two-dimentionsal data array x, producing the output two-
dimensional array y.
Suppose h is a sequence of nh elements and X is a 2D matrix with nseq
columns, and nx elements in each column, as follows:
h = [ h(0), h(1), ..., h(nh - 1) ] ,
and
x(0, 0) x(0, 1) x(0, 2) ... x(0, nseq-1)
x(1, 0) x(1, 1) x(1, 2) ... x(1, nseq-1)
X = x(2, 0) x(2, 1) x(2, 2) ... x(2, nseq-1)
... ... ... ... ...
x(nx-1, 0) x(nx-1, 1) x(nx-1, 2) ... x(nx-1, nseq-1)
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CCORM1D(3S)CCORM1D(3S)
Then each column of the output matrix:
y(0, 0) y(0, 1) y(0, 2) ... y(0, nseq-1)
y(1, 0) y(1, 1) y(1, 2) ... y(1, nseq-1)
Y = y(2, 0) y(2, 1) y(2, 2) ... y(2, nseq-1)
... ... ... ... ...
y(ny-1, 0) y(ny-1, 1) y(ny-1, 2) ... y(ny-1, nseq-1)
is obtained by correlating h with the corresponding column of X, so that:
nh-1
y(i,j) = Sum {h(k)*x(i+k,j)}, 0<=i<nx, 0<=j<nseq
k=0
The matrix Y has values defined for 0 <= i < nx and 0 <= j < nseq. In
the *CORM1D routines, the number of terms in each output column is
specified by an argument, ny. If ny < nx, the columns of y are
truncated. If ny >= nx, the terms beyond y(nx-1,j) are set to 0.
Generally, the sequences Cx(:,j), h and y(:,j) represent signals sampled
at equal time intervals, and the indexes of the vectors denote the sample
times. If the signals begin at the same time, we may, without loss of
generality, set the initial time to 0, as in the formulas above.
The *CORM1D 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
columns of 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 dimensions (ldx, nseq). (input).
CCORM1D: Single precision complex array.
ZCORM1D: Double precision complex array.
SCORM1D: Single precision array.
DCORM1D: Double precision array.
Input sequences to be correlated with h.
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CCORM1D(3S)CCORM1D(3S)
incx Integer. (input)
Increment between two successive values of a sequence in x.
incx must not be 0.
ldx Integer. (input)
The number of rows in x as it was declared in the calling
program (the leading dimension of x). ldx >= MAX(nx *
incx,1).
ix0 Integer. (input)
Sample corresponding to the first element of each 1D sequence
of x.
nx Integer. (input)
Size of each sequence (the number of elements in each sequence
of x). nx >= 0.
nseq Integer. (input)
The number of sequences to which the correlation will be
applied. nseq >= 0. If nseq = 0, the routine returns.
h Array of dimension nh. (input).
CCORM1D: Single precision complex array.
ZCORM1D: Double precision complex array.
SCORM1D: Single precision array.
DCORM1D: 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)
Sample corresponding to the first element of h.
nh Integer. (input)
The number of elements in the sequence h. nh >= 0. If nh = 0,
the routine returns.
y Array of dimensions (ldy, nseq). (output)
CCORM1D: Single precision complex array.
ZCORM1D: Double precision complex array.
SCORM1D: Single precision array.
DCORM1D: Double precision array.
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 y as it was declared in the calling
program (the leading dimension of y). ldy >= MAX(ny * incy, 1).
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iy0 Integer. (input)
Index of the first element of each 1D sequence of y.
ny Integer. (input)
Number of elements in each sequence of y. ny >= 0. If ny = 0,
the routine returns.
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]
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:
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CCORM1D(3S)CCORM1D(3S)
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 5 4-sample sequences x
with a filter h containing 3 samples:
Fortran:
REAL X(0:3,0:4), H(0:2), Y(0:5,0:4)
DO J = 0, 4
X(0,J) = J + 1.0
DO I = 1, 3
X(I,J) = -1.0 - j
ENDDO
ENDDO
DO I = 0, 2
H(I) = 1.0/(I+1)
ENDDO
CALL SCORM1D(X, 1, 4, 0, 4, 5, H, 1, 0, 3, Y, 1, 6, 0, 6)
C/C++:
#include <scsl_fft.h>
float x[5][4], h[3], y[5][6];
int i, j;
for (j=0; j<5; j++) {
x[j][0] = j + 1.0f;
for (i=1; i<4; i++) {
x[j][i] = -1.0f - j;
}
}
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CCORM1D(3S)CCORM1D(3S)
for (i=0; i<3; i++) {
h[i] = 1.0f/(i+1);
}
scorm1d((float *) x, 1, 4, 0, 4, 5, h, 1, 0, 3,
(float *) y, 1, 6, 0, 6);
The output is
Y(:,0) Y(:,1) Y(:,2) Y(:,3) Y(:,4)
Y(0,:) 0.1667 0.3333 0.5000 0.6667 0.8333
Y(1,:) -1.8333-3.6667-5.5000 -7.3333 -9.1667
Y(2,:) -1.5000-3.0000-4.5000 -6.0000 -7.5000
Y(3,:) -1.0000-2.0000-3.0000 -4.0000 -5.0000
Y(4,:) 0.0000 0.0000 0.0000 0.0000 0.0000
Y(5,:) 0.0000 0.0000 0.0000 0.0000 0.0000
Changing the values for ix0, ih0 and iy0 produces the following shifts in
the output:
ix0 = +1 Y(:,0) Y(:,1) Y(:,2) Y(:,3) Y(:,4)
Y(0,:) 0.1667 0.3333 0.5000 0.6667 0.8333
Y(1,:) 0.1667 0.3333 0.5000 0.6667 0.8333
Y(2,:) -1.8333-3.6667-5.5000 -7.3333 -9.1667
Y(3,:) -1.5000-3.0000-4.5000 -6.0000 -7.5000
Y(4,:) -1.0000-2.0000-3.0000 -4.0000 -5.0000
Y(5,:) 0.0000 0.0000 0.0000 0.0000 0.0000
ih0 = +1 Y(:,0) Y(:,1) Y(:,2) Y(:,3) Y(:,4)
Y(0,:) -1.8333-3.6667-5.5000 -7.3333 -9.1667
Y(1,:) -1.5000-3.0000-4.5000 -6.0000 -7.5000
Y(2,:) -1.0000-2.0000-3.0000 -4.0000 -5.0000
Y(3,:) 0.0000 0.0000 0.0000 0.0000 0.0000
Y(4,:) 0.0000 0.0000 0.0000 0.0000 0.0000
Y(5,:) 0.0000 0.0000 0.0000 0.0000 0.0000
iy0 = -1 Y(:,0) Y(:,1) Y(:,2) Y(:,3) Y(:,4)
Y(0,:) 0.1667 0.3333 0.5000 0.6667 0.8333
Y(1,:) 0.1667 0.3333 0.5000 0.6667 0.8333
Y(2,:) -1.8333-3.6667-5.5000 -7.3333 -9.1667
Y(3,:) -1.5000-3.0000-4.5000 -6.0000 -7.5000
Y(4,:) -1.0000-2.0000-3.0000 -4.0000 -5.0000
Y(5,:) 0.0000 0.0000 0.0000 0.0000 0.0000
SEE ALSOCCOR1D(3S), INTRO_FFT(3S), INTRO_SCSL(3S)
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