Slow FFT in ksh93 and awk. Post: 303023145

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Operating Systems OS X (Apple) Slow FFT in ksh93 and awk. Post 303023145 by wisecracker on Wednesday 12th of September 2018 12:11:57 PM

09-12-2018

Registered User

Hi all...

Well guys, it took a while because of the serious limitations of ARexx for a stock AMIGA A1200 but here is a working FFT for it. ARexx has no ARRAY facility but there is a workaround. ;o)
Boy oh boy, ARexx's arithmetic is so convoluted and floating point precision is not the best.
This was a challenge. I could have generated SIN, COS and SQRT in pure ARexx but decided to use an external ARexx math(s) library instead...
It would be just as easy to create SIN, COS and SQRT in ksh too eliminating awk entirely but awk just made it easier...
Just for the record the AMIGA shell/terminal has a large subset of xterm's escape codes.
An exercise in futility? Maybe but serious fun nevertheless...
This is through FS-UAE AMIGA emulation and my real A1200 setup for easy transfer from this Macbook Pro.
ARexx code:

Code:

/* Simple_FFT_DEMO.rexx */

/* This ARexx version needs this dependency: */
/* http://aminet.net/package/util/rexx/RexxMathLib */
CALL ADDLIB('rexxmathlib.library',0,-30,0)

NUMERIC DIGITS 14

SAY ""
SAY "An experimental method to do an FFT in ARexx using the standard test values."
SAY "It requires rexxmathlib.library for the SIN and COS."
SAY "$VER Simple_FFT_DEMO.rexx_(C)06-09-2018_B.Walker_issued_under_GPL2."
SAY ""

/* Create standard test _ARRAYS_ REAL and IMAGINARY. */
/* These MUST be powers of 2 and greater than 2 in size. */
/* Real values, '1.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0' */
/* Imag values, '0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0' */
/* Not really ARRAYS but good enough for this DEMO! */
DO N=0 TO 3 BY 1
	REAL_ARRAY.N=1.0
END
DO N=4 TO 7 BY 1
	REAL_ARRAY.N=0.0
END
DO N=0 TO 7 BY 1
	IMAG_ARRAY.N=0.0
END

/* Display them. */
SAY "Input, REAL: IMAG:"
DO N=0 TO 7 BY 1
	SAY "        "||REAL_ARRAY.N||"   "||IMAG_ARRAY.N
END

/* Only constant required, 14 decimal places. */
PI=3.14159265358979 
/* N should be 8 by default in this DEMO. */
/* SAY "Number of elements = "||N||"..." */
N=N-1

CALL FFT

SAY ""
DO N=0 TO 7 BY 1
	SAY "REAL: "||+OUT_REAL.N||",    IMAG: "||+OUT_IMAG.N
END

SAY ""
SAY "Final FFT values to 5 decimal places:"
STR=""
DO N=0 TO 7 BY 1
	CALL ABS_COMPLEX
	NUMERIC DIGITS 14
	IF +ABS <= 0.000000000001
	THEN
		ABS=0
	ENDIF
	NUMERIC DIGITS 6
	STR=STR||+ABS||" "
END
SAY STR
SAY ""
EXIT

/* Create the subroutines required. */
/* FFT subroutine. */
FFT:
DO K=0 TO N BY 1
	SUMREAL=0.0
	SUMIMAG=0.0
	DO T=0 TO N BY 1
		ANGLE=(2.0*PI*T*K)/(N+1)
		SUMREAL=SUMREAL+(REAL_ARRAY.T*COS(ANGLE))+(IMAG_ARRAY.T*SIN(ANGLE))
		SUMIMAG=SUMIMAG-(REAL_ARRAY.T*SIN(ANGLE))+(IMAG_ARRAY.T*COS(ANGLE))
	END
	OUT_REAL.K=SUMREAL
	OUT_IMAG.K=SUMIMAG
END
RETURN
/* FFT subroutine end. */

/* Absolute value of complex number subroutine. */
ABS_COMPLEX:
	ABS=SQRT( (OUT_REAL.N**2)+(OUT_IMAG.N**2) )
RETURN
/* Absolute value of complex number subroutine end. */

wisecracker

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sorcsd

sorcsd.f(3)							      LAPACK							       sorcsd.f(3)

NAME

       sorcsd.f -

SYNOPSIS

   Functions/Subroutines
       recursive subroutine sorcsd (JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA,
	   U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, WORK, LWORK, IWORK, INFO)
	   SORCSD

Function/Subroutine Documentation
   recursive subroutine sorcsd (characterJOBU1, characterJOBU2, characterJOBV1T, characterJOBV2T, characterTRANS, characterSIGNS, integerM,
       integerP, integerQ, real, dimension( ldx11, * )X11, integerLDX11, real, dimension( ldx12, * )X12, integerLDX12, real, dimension( ldx21, *
       )X21, integerLDX21, real, dimension( ldx22,			   * )X22, integerLDX22, real, dimension( * )THETA, real, dimension( ldu1,
       * )U1, integerLDU1, real, dimension( ldu2, * )U2, integerLDU2, real, dimension( ldv1t, * )V1T, integerLDV1T, real, dimension( ldv2t, *
       )V2T, integerLDV2T, real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerINFO)
       SORCSD

       Purpose:

	    SORCSD computes the CS decomposition of an M-by-M partitioned
	    orthogonal matrix X:

					    [  I  0  0 |  0  0	0 ]
					    [  0  C  0 |  0 -S	0 ]
		[ X11 | X12 ]	[ U1 |	  ] [  0  0  0 |  0  0 -I ] [ V1 |    ]**T
	    X = [-----------] = [---------] [---------------------] [---------]   .
		[ X21 | X22 ]	[    | U2 ] [  0  0  0 |  I  0	0 ] [	 | V2 ]
					    [  0  S  0 |  0  C	0 ]
					    [  0  0  I |  0  0	0 ]

	    X11 is P-by-Q. The orthogonal matrices U1, U2, V1, and V2 are P-by-P,
	    (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are
	    R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in
	    which R = MIN(P,M-P,Q,M-Q).

       Parameters:
	   JOBU1

		     JOBU1 is CHARACTER
		     = 'Y':	 U1 is computed;
		     otherwise:  U1 is not computed.

	   JOBU2

		     JOBU2 is CHARACTER
		     = 'Y':	 U2 is computed;
		     otherwise:  U2 is not computed.

	   JOBV1T

		     JOBV1T is CHARACTER
		     = 'Y':	 V1T is computed;
		     otherwise:  V1T is not computed.

	   JOBV2T

		     JOBV2T is CHARACTER
		     = 'Y':	 V2T is computed;
		     otherwise:  V2T is not computed.

	   TRANS

		     TRANS is CHARACTER
		     = 'T':	 X, U1, U2, V1T, and V2T are stored in row-major
				 order;
		     otherwise:  X, U1, U2, V1T, and V2T are stored in column-
				 major order.

	   SIGNS

		     SIGNS is CHARACTER
		     = 'O':	 The lower-left block is made nonpositive (the
				 "other" convention);
		     otherwise:  The upper-right block is made nonpositive (the
				 "default" convention).

	   M

		     M is INTEGER
		     The number of rows and columns in X.

	   P

		     P is INTEGER
		     The number of rows in X11 and X12. 0 <= P <= M.

	   Q

		     Q is INTEGER
		     The number of columns in X11 and X21. 0 <= Q <= M.

	   X11

		     X11 is REAL array, dimension (LDX11,Q)
		     On entry, part of the orthogonal matrix whose CSD is desired.

	   LDX11

		     LDX11 is INTEGER
		     The leading dimension of X11. LDX11 >= MAX(1,P).

	   X12

		     X12 is REAL array, dimension (LDX12,M-Q)
		     On entry, part of the orthogonal matrix whose CSD is desired.

	   LDX12

		     LDX12 is INTEGER
		     The leading dimension of X12. LDX12 >= MAX(1,P).

	   X21

		     X21 is REAL array, dimension (LDX21,Q)
		     On entry, part of the orthogonal matrix whose CSD is desired.

	   LDX21

		     LDX21 is INTEGER
		     The leading dimension of X11. LDX21 >= MAX(1,M-P).

	   X22

		     X22 is REAL array, dimension (LDX22,M-Q)
		     On entry, part of the orthogonal matrix whose CSD is desired.

	   LDX22

		     LDX22 is INTEGER
		     The leading dimension of X11. LDX22 >= MAX(1,M-P).

	   THETA

		     THETA is REAL array, dimension (R), in which R =
		     MIN(P,M-P,Q,M-Q).
		     C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
		     S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).

	   U1

		     U1 is REAL array, dimension (P)
		     If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.

	   LDU1

		     LDU1 is INTEGER
		     The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
		     MAX(1,P).

	   U2

		     U2 is REAL array, dimension (M-P)
		     If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
		     matrix U2.

	   LDU2

		     LDU2 is INTEGER
		     The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
		     MAX(1,M-P).

	   V1T

		     V1T is REAL array, dimension (Q)
		     If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
		     matrix V1**T.

	   LDV1T

		     LDV1T is INTEGER
		     The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
		     MAX(1,Q).

	   V2T

		     V2T is REAL array, dimension (M-Q)
		     If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal
		     matrix V2**T.

	   LDV2T

		     LDV2T is INTEGER
		     The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
		     MAX(1,M-Q).

	   WORK

		     WORK is REAL array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
		     If INFO > 0 on exit, WORK(2:R) contains the values PHI(1),
		     ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
		     define the matrix in intermediate bidiagonal-block form
		     remaining after nonconvergence. INFO specifies the number
		     of nonzero PHI's.

	   LWORK

		     LWORK is INTEGER
		     The dimension of the array WORK.

		     If LWORK = -1, then a workspace query is assumed; the routine
		     only calculates the optimal size of the WORK array, returns
		     this value as the first entry of the work array, and no error
		     message related to LWORK is issued by XERBLA.

	   IWORK

		     IWORK is INTEGER array, dimension (M-MIN(P, M-P, Q, M-Q))

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit.
		     < 0:  if INFO = -i, the i-th argument had an illegal value.
		     > 0:  SBBCSD did not converge. See the description of WORK
			   above for details.

       References:
	   [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 297 of file sorcsd.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       sorcsd.f(3)