text: /* dsptrf.f -- translated by f2c (version 20061008).
     You must link the resulting object file with libf2c:
  	on Microsoft Windows system, link with libf2c.lib;
  	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
  	or, if you install libf2c.a in a standard place, with -lf2c -lm
  	-- in that order, at the end of the command line, as in
  		cc *.o -lf2c -lm
  	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
  
  		http://www.netlib.org/f2c/libf2c.zip
  */
  
  #include "f2c.h"
  #include "blaswrap.h"
  
  /* Table of constant values */
  
  static integer c__1 = 1;
  
  /* Subroutine */ int dsptrf_(char *uplo, integer *n, doublereal *ap, integer *
  	ipiv, integer *info)
  {
      /* System generated locals */
      integer i__1, i__2;
      doublereal d__1, d__2, d__3;
  
      /* Builtin functions */
      double sqrt(doublereal);
  
      /* Local variables */
      integer i__, j, k;
      doublereal t, r1, d11, d12, d21, d22;
      integer kc, kk, kp;
      doublereal wk;
      integer kx, knc, kpc, npp;
      doublereal wkm1, wkp1;
      integer imax, jmax;
      extern /* Subroutine */ int dspr_(char *, integer *, doublereal *, 
  	    doublereal *, integer *, doublereal *);
      doublereal alpha;
      extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
  	    integer *);
      extern logical lsame_(char *, char *);
      extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, 
  	    doublereal *, integer *);
      integer kstep;
      logical upper;
      doublereal absakk;
      extern integer idamax_(integer *, doublereal *, integer *);
      extern /* Subroutine */ int xerbla_(char *, integer *);
      doublereal colmax, rowmax;
  
  
  /*  -- LAPACK routine (version 3.2) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  DSPTRF computes the factorization of a real symmetric matrix A stored */
  /*  in packed format using the Bunch-Kaufman diagonal pivoting method: */
  
  /*     A = U*D*U**T  or  A = L*D*L**T */
  
  /*  where U (or L) is a product of permutation and unit upper (lower) */
  /*  triangular matrices, and D is symmetric and block diagonal with */
  /*  1-by-1 and 2-by-2 diagonal blocks. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  UPLO    (input) CHARACTER*1 */
  /*          = 'U':  Upper triangle of A is stored; */
  /*          = 'L':  Lower triangle of A is stored. */
  
  /*  N       (input) INTEGER */
  /*          The order of the matrix A.  N >= 0. */
  
  /*  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
  /*          On entry, the upper or lower triangle of the symmetric matrix */
  /*          A, packed columnwise in a linear array.  The j-th column of A */
  /*          is stored in the array AP as follows: */
  /*          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
  /*          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
  
  /*          On exit, the block diagonal matrix D and the multipliers used */
  /*          to obtain the factor U or L, stored as a packed triangular */
  /*          matrix overwriting A (see below for further details). */
  
  /*  IPIV    (output) INTEGER array, dimension (N) */
  /*          Details of the interchanges and the block structure of D. */
  /*          If IPIV(k) > 0, then rows and columns k and IPIV(k) were */
  /*          interchanged and D(k,k) is a 1-by-1 diagonal block. */
  /*          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */
  /*          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */
  /*          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) = */
  /*          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */
  /*          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */
  
  /*  INFO    (output) INTEGER */
  /*          = 0: successful exit */
  /*          < 0: if INFO = -i, the i-th argument had an illegal value */
  /*          > 0: if INFO = i, D(i,i) is exactly zero.  The factorization */
  /*               has been completed, but the block diagonal matrix D is */
  /*               exactly singular, and division by zero will occur if it */
  /*               is used to solve a system of equations. */
  
  /*  Further Details */
  /*  =============== */
  
  /*  5-96 - Based on modifications by J. Lewis, Boeing Computer Services */
  /*         Company */
  
  /*  If UPLO = 'U', then A = U*D*U', where */
  /*     U = P(n)*U(n)* ... *P(k)U(k)* ..., */
  /*  i.e., U is a product of terms P(k)*U(k), where k decreases from n to */
  /*  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */
  /*  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as */
  /*  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such */
  /*  that if the diagonal block D(k) is of order s (s = 1 or 2), then */
  
  /*             (   I    v    0   )   k-s */
  /*     U(k) =  (   0    I    0   )   s */
  /*             (   0    0    I   )   n-k */
  /*                k-s   s   n-k */
  
  /*  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). */
  /*  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), */
  /*  and A(k,k), and v overwrites A(1:k-2,k-1:k). */
  
  /*  If UPLO = 'L', then A = L*D*L', where */
  /*     L = P(1)*L(1)* ... *P(k)*L(k)* ..., */
  /*  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to */
  /*  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */
  /*  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as */
  /*  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such */
  /*  that if the diagonal block D(k) is of order s (s = 1 or 2), then */
  
  /*             (   I    0     0   )  k-1 */
  /*     L(k) =  (   0    I     0   )  s */
  /*             (   0    v     I   )  n-k-s+1 */
  /*                k-1   s  n-k-s+1 */
  
  /*  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). */
  /*  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), */
  /*  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). */
  
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Test the input parameters. */
  
      /* Parameter adjustments */
      --ipiv;
      --ap;
  
      /* Function Body */
      *info = 0;
      upper = lsame_(uplo, "U");
      if (! upper && ! lsame_(uplo, "L")) {
  	*info = -1;
      } else if (*n < 0) {
  	*info = -2;
      }
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("DSPTRF", &i__1);
  	return 0;
      }
  
  /*     Initialize ALPHA for use in choosing pivot block size. */
  
      alpha = (sqrt(17.) + 1.) / 8.;
  
      if (upper) {
  
  /*        Factorize A as U*D*U' using the upper triangle of A */
  
  /*        K is the main loop index, decreasing from N to 1 in steps of */
  /*        1 or 2 */
  
  	k = *n;
  	kc = (*n - 1) * *n / 2 + 1;
  L10:
  	knc = kc;
  
  /*        If K < 1, exit from loop */
  
  	if (k < 1) {
  	    goto L110;
  	}
  	kstep = 1;
  
  /*        Determine rows and columns to be interchanged and whether */
  /*        a 1-by-1 or 2-by-2 pivot block will be used */
  
  	absakk = (d__1 = ap[kc + k - 1], abs(d__1));
  
  /*        IMAX is the row-index of the largest off-diagonal element in */
  /*        column K, and COLMAX is its absolute value */
  
  	if (k > 1) {
  	    i__1 = k - 1;
  	    imax = idamax_(&i__1, &ap[kc], &c__1);
  	    colmax = (d__1 = ap[kc + imax - 1], abs(d__1));
  	} else {
  	    colmax = 0.;
  	}
  
  	if (max(absakk,colmax) == 0.) {
  
  /*           Column K is zero: set INFO and continue */
  
  	    if (*info == 0) {
  		*info = k;
  	    }
  	    kp = k;
  	} else {
  	    if (absakk >= alpha * colmax) {
  
  /*              no interchange, use 1-by-1 pivot block */
  
  		kp = k;
  	    } else {
  
  /*              JMAX is the column-index of the largest off-diagonal */
  /*              element in row IMAX, and ROWMAX is its absolute value */
  
  		rowmax = 0.;
  		jmax = imax;
  		kx = imax * (imax + 1) / 2 + imax;
  		i__1 = k;
  		for (j = imax + 1; j <= i__1; ++j) {
  		    if ((d__1 = ap[kx], abs(d__1)) > rowmax) {
  			rowmax = (d__1 = ap[kx], abs(d__1));
  			jmax = j;
  		    }
  		    kx += j;
  /* L20: */
  		}
  		kpc = (imax - 1) * imax / 2 + 1;
  		if (imax > 1) {
  		    i__1 = imax - 1;
  		    jmax = idamax_(&i__1, &ap[kpc], &c__1);
  /* Computing MAX */
  		    d__2 = rowmax, d__3 = (d__1 = ap[kpc + jmax - 1], abs(
  			    d__1));
  		    rowmax = max(d__2,d__3);
  		}
  
  		if (absakk >= alpha * colmax * (colmax / rowmax)) {
  
  /*                 no interchange, use 1-by-1 pivot block */
  
  		    kp = k;
  		} else if ((d__1 = ap[kpc + imax - 1], abs(d__1)) >= alpha * 
  			rowmax) {
  
  /*                 interchange rows and columns K and IMAX, use 1-by-1 */
  /*                 pivot block */
  
  		    kp = imax;
  		} else {
  
  /*                 interchange rows and columns K-1 and IMAX, use 2-by-2 */
  /*                 pivot block */
  
  		    kp = imax;
  		    kstep = 2;
  		}
  	    }
  
  	    kk = k - kstep + 1;
  	    if (kstep == 2) {
  		knc = knc - k + 1;
  	    }
  	    if (kp != kk) {
  
  /*              Interchange rows and columns KK and KP in the leading */
  /*              submatrix A(1:k,1:k) */
  
  		i__1 = kp - 1;
  		dswap_(&i__1, &ap[knc], &c__1, &ap[kpc], &c__1);
  		kx = kpc + kp - 1;
  		i__1 = kk - 1;
  		for (j = kp + 1; j <= i__1; ++j) {
  		    kx = kx + j - 1;
  		    t = ap[knc + j - 1];
  		    ap[knc + j - 1] = ap[kx];
  		    ap[kx] = t;
  /* L30: */
  		}
  		t = ap[knc + kk - 1];
  		ap[knc + kk - 1] = ap[kpc + kp - 1];
  		ap[kpc + kp - 1] = t;
  		if (kstep == 2) {
  		    t = ap[kc + k - 2];
  		    ap[kc + k - 2] = ap[kc + kp - 1];
  		    ap[kc + kp - 1] = t;
  		}
  	    }
  
  /*           Update the leading submatrix */
  
  	    if (kstep == 1) {
  
  /*              1-by-1 pivot block D(k): column k now holds */
  
  /*              W(k) = U(k)*D(k) */
  
  /*              where U(k) is the k-th column of U */
  
  /*              Perform a rank-1 update of A(1:k-1,1:k-1) as */
  
  /*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)' */
  
  		r1 = 1. / ap[kc + k - 1];
  		i__1 = k - 1;
  		d__1 = -r1;
  		dspr_(uplo, &i__1, &d__1, &ap[kc], &c__1, &ap[1]);
  
  /*              Store U(k) in column k */
  
  		i__1 = k - 1;
  		dscal_(&i__1, &r1, &ap[kc], &c__1);
  	    } else {
  
  /*              2-by-2 pivot block D(k): columns k and k-1 now hold */
  
  /*              ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) */
  
  /*              where U(k) and U(k-1) are the k-th and (k-1)-th columns */
  /*              of U */
  
  /*              Perform a rank-2 update of A(1:k-2,1:k-2) as */
  
  /*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )' */
  /*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )' */
  
  		if (k > 2) {
  
  		    d12 = ap[k - 1 + (k - 1) * k / 2];
  		    d22 = ap[k - 1 + (k - 2) * (k - 1) / 2] / d12;
  		    d11 = ap[k + (k - 1) * k / 2] / d12;
  		    t = 1. / (d11 * d22 - 1.);
  		    d12 = t / d12;
  
  		    for (j = k - 2; j >= 1; --j) {
  			wkm1 = d12 * (d11 * ap[j + (k - 2) * (k - 1) / 2] - 
  				ap[j + (k - 1) * k / 2]);
  			wk = d12 * (d22 * ap[j + (k - 1) * k / 2] - ap[j + (k 
  				- 2) * (k - 1) / 2]);
  			for (i__ = j; i__ >= 1; --i__) {
  			    ap[i__ + (j - 1) * j / 2] = ap[i__ + (j - 1) * j /
  				     2] - ap[i__ + (k - 1) * k / 2] * wk - ap[
  				    i__ + (k - 2) * (k - 1) / 2] * wkm1;
  /* L40: */
  			}
  			ap[j + (k - 1) * k / 2] = wk;
  			ap[j + (k - 2) * (k - 1) / 2] = wkm1;
  /* L50: */
  		    }
  
  		}
  
  	    }
  	}
  
  /*        Store details of the interchanges in IPIV */
  
  	if (kstep == 1) {
  	    ipiv[k] = kp;
  	} else {
  	    ipiv[k] = -kp;
  	    ipiv[k - 1] = -kp;
  	}
  
  /*        Decrease K and return to the start of the main loop */
  
  	k -= kstep;
  	kc = knc - k;
  	goto L10;
  
      } else {
  
  /*        Factorize A as L*D*L' using the lower triangle of A */
  
  /*        K is the main loop index, increasing from 1 to N in steps of */
  /*        1 or 2 */
  
  	k = 1;
  	kc = 1;
  	npp = *n * (*n + 1) / 2;
  L60:
  	knc = kc;
  
  /*        If K > N, exit from loop */
  
  	if (k > *n) {
  	    goto L110;
  	}
  	kstep = 1;
  
  /*        Determine rows and columns to be interchanged and whether */
  /*        a 1-by-1 or 2-by-2 pivot block will be used */
  
  	absakk = (d__1 = ap[kc], abs(d__1));
  
  /*        IMAX is the row-index of the largest off-diagonal element in */
  /*        column K, and COLMAX is its absolute value */
  
  	if (k < *n) {
  	    i__1 = *n - k;
  	    imax = k + idamax_(&i__1, &ap[kc + 1], &c__1);
  	    colmax = (d__1 = ap[kc + imax - k], abs(d__1));
  	} else {
  	    colmax = 0.;
  	}
  
  	if (max(absakk,colmax) == 0.) {
  
  /*           Column K is zero: set INFO and continue */
  
  	    if (*info == 0) {
  		*info = k;
  	    }
  	    kp = k;
  	} else {
  	    if (absakk >= alpha * colmax) {
  
  /*              no interchange, use 1-by-1 pivot block */
  
  		kp = k;
  	    } else {
  
  /*              JMAX is the column-index of the largest off-diagonal */
  /*              element in row IMAX, and ROWMAX is its absolute value */
  
  		rowmax = 0.;
  		kx = kc + imax - k;
  		i__1 = imax - 1;
  		for (j = k; j <= i__1; ++j) {
  		    if ((d__1 = ap[kx], abs(d__1)) > rowmax) {
  			rowmax = (d__1 = ap[kx], abs(d__1));
  			jmax = j;
  		    }
  		    kx = kx + *n - j;
  /* L70: */
  		}
  		kpc = npp - (*n - imax + 1) * (*n - imax + 2) / 2 + 1;
  		if (imax < *n) {
  		    i__1 = *n - imax;
  		    jmax = imax + idamax_(&i__1, &ap[kpc + 1], &c__1);
  /* Computing MAX */
  		    d__2 = rowmax, d__3 = (d__1 = ap[kpc + jmax - imax], abs(
  			    d__1));
  		    rowmax = max(d__2,d__3);
  		}
  
  		if (absakk >= alpha * colmax * (colmax / rowmax)) {
  
  /*                 no interchange, use 1-by-1 pivot block */
  
  		    kp = k;
  		} else if ((d__1 = ap[kpc], abs(d__1)) >= alpha * rowmax) {
  
  /*                 interchange rows and columns K and IMAX, use 1-by-1 */
  /*                 pivot block */
  
  		    kp = imax;
  		} else {
  
  /*                 interchange rows and columns K+1 and IMAX, use 2-by-2 */
  /*                 pivot block */
  
  		    kp = imax;
  		    kstep = 2;
  		}
  	    }
  
  	    kk = k + kstep - 1;
  	    if (kstep == 2) {
  		knc = knc + *n - k + 1;
  	    }
  	    if (kp != kk) {
  
  /*              Interchange rows and columns KK and KP in the trailing */
  /*              submatrix A(k:n,k:n) */
  
  		if (kp < *n) {
  		    i__1 = *n - kp;
  		    dswap_(&i__1, &ap[knc + kp - kk + 1], &c__1, &ap[kpc + 1], 
  			     &c__1);
  		}
  		kx = knc + kp - kk;
  		i__1 = kp - 1;
  		for (j = kk + 1; j <= i__1; ++j) {
  		    kx = kx + *n - j + 1;
  		    t = ap[knc + j - kk];
  		    ap[knc + j - kk] = ap[kx];
  		    ap[kx] = t;
  /* L80: */
  		}
  		t = ap[knc];
  		ap[knc] = ap[kpc];
  		ap[kpc] = t;
  		if (kstep == 2) {
  		    t = ap[kc + 1];
  		    ap[kc + 1] = ap[kc + kp - k];
  		    ap[kc + kp - k] = t;
  		}
  	    }
  
  /*           Update the trailing submatrix */
  
  	    if (kstep == 1) {
  
  /*              1-by-1 pivot block D(k): column k now holds */
  
  /*              W(k) = L(k)*D(k) */
  
  /*              where L(k) is the k-th column of L */
  
  		if (k < *n) {
  
  /*                 Perform a rank-1 update of A(k+1:n,k+1:n) as */
  
  /*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)' */
  
  		    r1 = 1. / ap[kc];
  		    i__1 = *n - k;
  		    d__1 = -r1;
  		    dspr_(uplo, &i__1, &d__1, &ap[kc + 1], &c__1, &ap[kc + *n 
  			    - k + 1]);
  
  /*                 Store L(k) in column K */
  
  		    i__1 = *n - k;
  		    dscal_(&i__1, &r1, &ap[kc + 1], &c__1);
  		}
  	    } else {
  
  /*              2-by-2 pivot block D(k): columns K and K+1 now hold */
  
  /*              ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) */
  
  /*              where L(k) and L(k+1) are the k-th and (k+1)-th columns */
  /*              of L */
  
  		if (k < *n - 1) {
  
  /*                 Perform a rank-2 update of A(k+2:n,k+2:n) as */
  
  /*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )' */
  /*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )' */
  
  		    d21 = ap[k + 1 + (k - 1) * ((*n << 1) - k) / 2];
  		    d11 = ap[k + 1 + k * ((*n << 1) - k - 1) / 2] / d21;
  		    d22 = ap[k + (k - 1) * ((*n << 1) - k) / 2] / d21;
  		    t = 1. / (d11 * d22 - 1.);
  		    d21 = t / d21;
  
  		    i__1 = *n;
  		    for (j = k + 2; j <= i__1; ++j) {
  			wk = d21 * (d11 * ap[j + (k - 1) * ((*n << 1) - k) / 
  				2] - ap[j + k * ((*n << 1) - k - 1) / 2]);
  			wkp1 = d21 * (d22 * ap[j + k * ((*n << 1) - k - 1) / 
  				2] - ap[j + (k - 1) * ((*n << 1) - k) / 2]);
  
  			i__2 = *n;
  			for (i__ = j; i__ <= i__2; ++i__) {
  			    ap[i__ + (j - 1) * ((*n << 1) - j) / 2] = ap[i__ 
  				    + (j - 1) * ((*n << 1) - j) / 2] - ap[i__ 
  				    + (k - 1) * ((*n << 1) - k) / 2] * wk - 
  				    ap[i__ + k * ((*n << 1) - k - 1) / 2] * 
  				    wkp1;
  /* L90: */
  			}
  
  			ap[j + (k - 1) * ((*n << 1) - k) / 2] = wk;
  			ap[j + k * ((*n << 1) - k - 1) / 2] = wkp1;
  
  /* L100: */
  		    }
  		}
  	    }
  	}
  
  /*        Store details of the interchanges in IPIV */
  
  	if (kstep == 1) {
  	    ipiv[k] = kp;
  	} else {
  	    ipiv[k] = -kp;
  	    ipiv[k + 1] = -kp;
  	}
  
  /*        Increase K and return to the start of the main loop */
  
  	k += kstep;
  	kc = knc + *n - k + 2;
  	goto L60;
  
      }
  
  L110:
      return 0;
  
  /*     End of DSPTRF */
  
  } /* dsptrf_ */
  