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NAME
zcnvcor - compute the convolution or correlation of double
precision complex vectors
SUBROUTINE ZCNVCOR (CNVCOR, FOUR, NX, X, IFX, INCX, NY,
NPRE, M, Y, IFY, INC1Y, INC2Y, NZ, K, Z, IFZ,
INC1Z, INC2Z, WORK, LWORK)
CHARACTER CNVCOR, FOUR
INTEGER IFX, IFY, IFZ, INCX, INC1Y, INC2Y, INC1Z, INC2Z, K,
LWORK, NPRE, NX, NY, M, NZ
DOUBLE COMPLEX X(*), Y(*), Z(*)
DOUBLE COMPLEX WORK(*)
#include <sunperf.h>
void zcnvcor(char cnvcor, char four, int nx, doublecomplex
*x, int ifx, int incx, int ny, int npre, int m,
doublecomplex *y, int ify, int inc1y, int inc2y,
int nz, int k, doublecomplex *z, int ifz, int
inc1z, int inc2z, doublecomplex *work, int lwork);
PURPOSE
ZCNVCOR computes the convolution or correlation of double
precision complex vectors.
ARGUMENTS
CNVCOR (input) CHARACTER
'V' or 'v' if convolution is desired, 'R' or 'r'
or correlation is desired.
FOUR (input) CHARACTER
'T' or 't' if the Fourier transform method is to
be used, 'D' or 'd' if the computation should be
done directly from the definition. The Fourier
transform method is generally faster, but it may
introduce noticeable errors into certain results,
notably when both the real and imaginary parts of
the filter and data vectors consist entirely of
integers or vectors where elements of either the
filter vector or a given data vector differ signi-
ficantly in magnitude from the 1-norm of the vec-
tor.
NX (input) INTEGER
Length of the filter vector. NX >= 0. ZCNVCOR
will return immediately if NX = 0.
X (input) DOUBLE COMPLEX(*)
Filter vector.
IFX (input) DOUBLE COMPLEX(*)
Index of the first element of X. NX >= IFX >= 1.
INCX (input) INTEGER
Stride between elements of the filter vector in X.
INCX > 0.
NY (input) INTEGER
Length of the input vectors. NY >= 0. ZCNVCOR
will return immediately if NY = 0.
NPRE (input) INTEGER
The number of implicit zeros prepended to the Y
vectors. NPRE >= 0.
Y (input) DOUBLE COMPLEX(*)
Input vectors.
IFY (input) DOUBLE COMPLEX(*)
Index of the first element of Y. NY >= IFY >= 1.
INC1Y (input) INTEGER
Stride between elements of the input vectors in Y.
INC1Y > 0.
INC2Y (input) INTEGER
Stride between the input vectors in Y. INC2Y > 0.
NZ (input) INTEGER
Length of the output vectors. NZ >= 0. ZCNVCOR
will return immediately if NZ = 0. See the Notes
section below for information about how this argu-
ment interacts with NX and NY to control circular
versus end-off shifting.
K (input) INTEGER
Number of Z vectors. K >= 0. If K = 0 then
ZCNVCOR will return immediately. If K < M then
only the first K input vectors will be processed.
If K > M then all input vectors will be processed
and the last M-K output vectors will be set to
zero on exit.
Z (output) DOUBLE COMPLEX(*)
Result vectors.
IFZ (input) DOUBLE COMPLEX(*)
Index of the first element of Z. NZ >= IFZ >= 1.
INC1Z (input) INTEGER
Stride between elements of the output vectors in
Z. INC1Z > 0.
INC2Z (input) INTEGER
Stride between the output vectors in Z. INC2Z >
0.
WORK (input/scratch) DOUBLE COMPLEX(LWORK)
Scratch space. Before the first call to ZCNVCOR
with particular values of the integer arguments
the first element of WORK must be set to zero. If
WORK is written between calls to ZCNVCOR or if
ZCNVCOR is called with different values of the
integer arguments then the first element of WORK
must again be set to zero before each call. If
WORK has not been written and the same values of
the integer arguments are used then the first ele-
ment of WORK to zero. This can avoid certain ini-
tializations that store their results into WORK,
and avoiding the initialization can make ZCNVCOR
run faster.
LWORK (input) INTEGER
Length of WORK. LWORK >= 2*MAX(NX,NY,NZ)+8.
NOTES
If any vector overlaps a writable vector, either because of
argument aliasing or ill-chosen values of the various INC
arguments, the results are undefined and may vary from one
run to the next.
The most common form of the computation, and the case that
executes fastest, is applying a filter vector X to a series
of vectors stored in the columns of Y with the result placed
into the columns of Z. In that case, INCX = 1, INC1Y = 1,
INC2Y >= NY, INC1Z = 1, INC2Z >= NZ. Another common form is
applying a filter vector X to a series of vectors stored in
the rows of Y and store the result in the row of Z, in which
case INCX = 1, INC1Y >= NY, INC2Y = 1, INC1Z >= NZ, and
INC2Z = 1.
A common use of convolution is to compute the products of
polynomials. The following code uses SCNVCOR to compute the
product of 1 + 2x + 3x**2 and 4 + 5x + 6x**2:
PROGRAM TEST
IMPLICIT NONE C
INTEGER LWORK, NX, NY, NZ
PARAMETER (NX = 3)
PARAMETER (NY = NX)
PARAMETER (NZ = 2*NY-1)
PARAMETER (LWORK = 4*NZ+32) C
REAL X(NX), Y(NY), Z(NZ), WORK(LWORK) C
DATA X / 1, 2, 3 /, Y / 4, 5, 6 /, WORK / LWORK*0 / C
PRINT 1000, 'X'
PRINT 1010, X
PRINT 1000, 'Y'
PRINT 1010, Y
CALL SCNVCOR ('V', 'T', NX, X, 1, 1,
$ NY, 0, 1, Y, 1, 1, 1,
$ NZ, 1, Z, 1, 1, 1, WORK, LWORK)
PRINT 1020, 'Z'
PRINT 1010, Z C
1000 FORMAT (1X, 'Input vector ', A1)
1010 FORMAT (1X, 300F5.0)
1020 FORMAT (1X, 'Output vector ', A1) C
END
The program above produces the following output:
Input vector X
1. 2. 3.
Input vector Y
4. 5. 6.
Output vector Z
4. 13. 28. 27. 18.
Making the output vector longer than the input vectors, as
in the example above, implicitly adds zeros to the end of
the input. No zeros are actually required in any of the
vectors, and none are used in the example, but the padding
provided by the implied zeros has the effect of an end-off
shift rather than an end-around shift of the input vectors.
The following code will compute the product between the vec-
tor [ 1, 2, 3 ] and the circulant matrix defined by the
initial column vector [ 4, 5, 6 ]:
PROGRAM TEST
IMPLICIT NONE C
INTEGER LWORK, NX, NY, NZ
PARAMETER (NX = 3)
PARAMETER (NY = NX)
PARAMETER (NZ = NY)
PARAMETER (LWORK = 4*NZ+32) C
REAL X(NX), Y(NY), Z(NZ), WORK(LWORK) C
DATA X / 1, 2, 3 /, Y / 4, 5, 6 /, WORK / LWORK*0 / C
PRINT 1000, 'X'
PRINT 1010, X
PRINT 1000, 'Y'
PRINT 1010, Y
CALL SCNVCOR ('V', 'T', NX, X, 1, 1,
$ NY, 0, 1, Y, 1, 1, 1,
$ NZ, 1, Z, 1, 1, 1, WORK, LWORK)
PRINT 1020, 'Z'
PRINT 1010, Z C
1000 FORMAT (1X, 'Input vector ', A1)
1010 FORMAT (1X, 300F5.0)
1020 FORMAT (1X, 'Output vector ', A1) C
END
The program above produces the following output:
Input vector X
1. 2. 3.
Input vector Y
4. 5. 6.
Output vector Z
31. 31. 28.
The difference between this example and the previous example
is that the length of the output vector is the same as the
length of the input vectors, so there are no implied zeros
on the end. With no implied zeros to shift into, the effect
of an end-off shift from the previous example does not occur
and the end-around shift results in a circulant matrix pro-
duct.
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