NAME

SYNOPSIS

  SUBROUTINE DCNVCOR( CNVCOR, FOUR, NX, X, IFX, INCX, NY, NPRE, M, Y, 
 *      IFY, INC1Y, INC2Y, NZ, K, Z, IFZ, INC1Z, INC2Z, WORK, LWORK)
  CHARACTER * 1 CNVCOR, FOUR
  INTEGER NX, IFX, INCX, NY, NPRE, M, IFY, INC1Y, INC2Y, NZ, K, IFZ, INC1Z, INC2Z, LWORK
  DOUBLE PRECISION X(*), Y(*), Z(*), WORK(*)
 
  SUBROUTINE DCNVCOR_64( CNVCOR, FOUR, NX, X, IFX, INCX, NY, NPRE, M, 
 *      Y, IFY, INC1Y, INC2Y, NZ, K, Z, IFZ, INC1Z, INC2Z, WORK, LWORK)
  CHARACTER * 1 CNVCOR, FOUR
  INTEGER*8 NX, IFX, INCX, NY, NPRE, M, IFY, INC1Y, INC2Y, NZ, K, IFZ, INC1Z, INC2Z, LWORK
  DOUBLE PRECISION X(*), Y(*), Z(*), WORK(*)
 

F95 INTERFACE

  SUBROUTINE CNVCOR( CNVCOR, FOUR, [NX], X, IFX, [INCX], NY, NPRE, M, 
 *       Y, IFY, INC1Y, INC2Y, NZ, K, Z, IFZ, INC1Z, INC2Z, WORK, [LWORK])
  CHARACTER(LEN=1) :: CNVCOR, FOUR
  INTEGER :: NX, IFX, INCX, NY, NPRE, M, IFY, INC1Y, INC2Y, NZ, K, IFZ, INC1Z, INC2Z, LWORK
  REAL(8), DIMENSION(:) :: X, Y, Z, WORK
 
  SUBROUTINE CNVCOR_64( CNVCOR, FOUR, [NX], X, IFX, [INCX], NY, NPRE, 
 *       M, Y, IFY, INC1Y, INC2Y, NZ, K, Z, IFZ, INC1Z, INC2Z, WORK, 
 *       [LWORK])
  CHARACTER(LEN=1) :: CNVCOR, FOUR
  INTEGER(8) :: NX, IFX, INCX, NY, NPRE, M, IFY, INC1Y, INC2Y, NZ, K, IFZ, INC1Z, INC2Z, LWORK
  REAL(8), DIMENSION(:) :: X, Y, Z, WORK
 

C INTERFACE

void dcnvcor(char cnvcor, char four, int nx, double *x, int ifx, int incx, int ny, int npre, int m, double *y, int ify, int inc1y, int inc2y, int nz, int k, double *z, int ifz, int inc1z, int inc2z, double *work, int lwork);

void dcnvcor_64(char cnvcor, char four, long nx, double *x, long ifx, long incx, long ny, long npre, long m, double *y, long ify, long inc1y, long inc2y, long nz, long k, double *z, long ifz, long inc1z, long inc2z, double *work, long lwork);

PURPOSE

ARGUMENTS

* CNVCOR (input)

\'V' or 'v' if convolution is desired, 'R' or 'r' if correlation is desired.

* FOUR (input)

\'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 filter and data vectors consist entirely of integers or vectors where elements of either the filter vector or a given data vector differ significantly in magnitude from the 1-norm of the vector.

* NX (input)

Length of the filter vector. NX >= 0. DCNVCOR will return immediately if NX = 0.

* X (input)

Filter vector.

* IFX (input)

Index of the first element of X. NX >= IFX >= 1.

* INCX (input)

Stride between elements of the filter vector in X. INCX > 0.

* NY (input)

Length of the input vectors. NY >= 0. DCNVCOR will return immediately if NY = 0.

* NPRE (input)

The number of implicit zeros prepended to the Y vectors. NPRE >= 0.

* M (input)

Number of input vectors. M >= 0. DCNVCOR will return immediately if M = 0.

* Y (input)

Input vectors.

* IFY (input)

Index of the first element of Y. NY >= IFY >= 1.

* INC1Y (input)

Stride between elements of the input vectors in Y. INC1Y > 0.

* INC2Y (input)

Stride between the input vectors in Y. INC2Y > 0.

* NZ (input)

Length of the output vectors. NZ >= 0. DCNVCOR will return immediately if NZ = 0. See the Notes section below for information about how this argument interacts with NX and NY to control circular versus end-off shifting.

* K (input)

Number of Z vectors. K >= 0. If K = 0 then DCNVCOR will return immediately. If K < M then only the first K input vectors will be processed. If K > M then M input vectors will be processed.

* Z (output)

Result vectors.

* IFZ (input)

Index of the first element of Z. NZ >= IFZ >= 1.

* INC1Z (input)

Stride between elements of the output vectors in Z. INC1Z > 0.

* INC2Z (input)

Stride between the output vectors in Z. INC2Z > 0.

* WORK (input/output)

Scratch space. Before the first call to DCNVCOR with particular values of the integer arguments the first element of WORK must be set to zero. If WORK is written between calls to DCNVCOR or if DCNVCOR 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 element of WORK to zero. This can avoid certain initializations that store their results into WORK, and avoiding the initialization can make DCNVCOR run faster.

* LWORK (input)

Length of WORK. LWORK >= 4*MAX(NX,NY,NZ)+15. .SH 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 DCNVCOR to compute the product of 1 + 2x + 3x**2 and 4 + 5x + 6x**2: