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- gave everyone the GPL header

    1: /* functions to support the random number genrator
    2:    Copyright (C) 1992-2000 Michigan State University
    3: 
    4:    The CAPA system is free software; you can redistribute it and/or
    5:    modify it under the terms of the GNU Library General Public License as
    6:    published by the Free Software Foundation; either version 2 of the
    7:    License, or (at your option) any later version.
    8: 
    9:    The CAPA system is distributed in the hope that it will be useful,
   10:    but WITHOUT ANY WARRANTY; without even the implied warranty of
   11:    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   12:    Library General Public License for more details.
   13: 
   14:    You should have received a copy of the GNU Library General Public
   15:    License along with the CAPA system; see the file COPYING.  If not,
   16:    write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
   17:    Boston, MA 02111-1307, USA.  */
   18: 
   19: #include <math.h>
   20: float sdot(long n,float *sx,long incx,float *sy,long incy)
   21: {
   22: static long i,ix,iy,m,mp1;
   23: static float sdot,stemp;
   24:     stemp = sdot = 0.0;
   25:     if(n <= 0) return sdot;
   26:     if(incx == 1 && incy == 1) goto S20;
   27:     ix = iy = 1;
   28:     if(incx < 0) ix = (-n+1)*incx+1;
   29:     if(incy < 0) iy = (-n+1)*incy+1;
   30:     for(i=1; i<=n; i++) {
   31:         stemp += (*(sx+ix-1)**(sy+iy-1));
   32:         ix += incx;
   33:         iy += incy;
   34:     }
   35:     sdot = stemp;
   36:     return sdot;
   37: S20:
   38:     m = n % 5L;
   39:     if(m == 0) goto S40;
   40:     for(i=0; i<m; i++) stemp += (*(sx+i)**(sy+i));
   41:     if(n < 5) goto S60;
   42: S40:
   43:     mp1 = m+1;
   44:     for(i=mp1; i<=n; i+=5) stemp += (*(sx+i-1)**(sy+i-1)+*(sx+i)**(sy+i)+*(sx+i
   45:       +1)**(sy+i+1)+*(sx+i+2)**(sy+i+2)+*(sx+i+3)**(sy+i+3));
   46: S60:
   47:     sdot = stemp;
   48:     return sdot;
   49: }
   50: void spofa(float *a,long lda,long n,long *info)
   51: /*
   52:      SPOFA FACTORS A REAL SYMMETRIC POSITIVE DEFINITE MATRIX.
   53:      SPOFA IS USUALLY CALLED BY SPOCO, BUT IT CAN BE CALLED
   54:      DIRECTLY WITH A SAVING IN TIME IF  RCOND  IS NOT NEEDED.
   55:      (TIME FOR SPOCO) = (1 + 18/N)*(TIME FOR SPOFA) .
   56:      ON ENTRY
   57:         A       REAL(LDA, N)
   58:                 THE SYMMETRIC MATRIX TO BE FACTORED.  ONLY THE
   59:                 DIAGONAL AND UPPER TRIANGLE ARE USED.
   60:         LDA     INTEGER
   61:                 THE LEADING DIMENSION OF THE ARRAY  A .
   62:         N       INTEGER
   63:                 THE ORDER OF THE MATRIX  A .
   64:      ON RETURN
   65:         A       AN UPPER TRIANGULAR MATRIX  R  SO THAT  A = TRANS(R)*R
   66:                 WHERE  TRANS(R)  IS THE TRANSPOSE.
   67:                 THE STRICT LOWER TRIANGLE IS UNALTERED.
   68:                 IF  INFO .NE. 0 , THE FACTORIZATION IS NOT COMPLETE.
   69:         INFO    INTEGER
   70:                 = 0  FOR NORMAL RETURN.
   71:                 = K  SIGNALS AN ERROR CONDITION.  THE LEADING MINOR
   72:                      OF ORDER  K  IS NOT POSITIVE DEFINITE.
   73:      LINPACK.  THIS VERSION DATED 08/14/78 .
   74:      CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
   75:      SUBROUTINES AND FUNCTIONS
   76:      BLAS SDOT
   77:      FORTRAN SQRT
   78:      INTERNAL VARIABLES
   79: */
   80: {
   81: extern float sdot(long n,float *sx,long incx,float *sy,long incy);
   82: static long j,jm1,k;
   83: static float t,s;
   84: /*
   85:      BEGIN BLOCK WITH ...EXITS TO 40
   86: */
   87:     for(j=1; j<=n; j++) {
   88:         *info = j;
   89:         s = 0.0;
   90:         jm1 = j-1;
   91:         if(jm1 < 1) goto S20;
   92:         for(k=0; k<jm1; k++) {
   93:             t = *(a+k+(j-1)*lda)-sdot(k,(a+k*lda),1L,(a+(j-1)*lda),1L);
   94:             t /=  *(a+k+k*lda);
   95:             *(a+k+(j-1)*lda) = t;
   96:             s += (t*t);
   97:         }
   98: S20:
   99:         s = *(a+j-1+(j-1)*lda)-s;
  100: /*
  101:      ......EXIT
  102: */
  103:         if(s <= 0.0) goto S40;
  104:         *(a+j-1+(j-1)*lda) = sqrt(s);
  105:     }
  106:     *info = 0;
  107: S40:
  108:     return;
  109: }