#include "blaswrap.h"
#include "f2c.h"

/* Subroutine */ int ssptrf_(char *uplo, integer *n, real *ap, integer *ipiv, 
	integer *info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    SSPTRF 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) REAL 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).   

    =====================================================================   


       Test the input parameters.   

       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    
    /* System generated locals */
    integer i__1, i__2;
    real r__1, r__2, r__3;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static integer imax, jmax;
    extern /* Subroutine */ int sspr_(char *, integer *, real *, real *, 
	    integer *, real *);
    static integer i__, j, k;
    static real t, alpha;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    static integer kstep;
    static logical upper;
    extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *, 
	    integer *);
    static real r1, d11, d12, d21, d22;
    static integer kc, kk, kp;
    static real absakk, wk;
    static integer kx;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer isamax_(integer *, real *, integer *);
    static real colmax, rowmax;
    static integer knc, kpc, npp;
    static real wkm1, wkp1;


    --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_("SSPTRF", &i__1);
	return 0;
    }

/*     Initialize ALPHA for use in choosing pivot block size. */

    alpha = (sqrt(17.f) + 1.f) / 8.f;

    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 = (r__1 = ap[kc + k - 1], dabs(r__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 = isamax_(&i__1, &ap[kc], &c__1);
	    colmax = (r__1 = ap[kc + imax - 1], dabs(r__1));
	} else {
	    colmax = 0.f;
	}

	if (dmax(absakk,colmax) == 0.f) {

/*           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.f;
		jmax = imax;
		kx = imax * (imax + 1) / 2 + imax;
		i__1 = k;
		for (j = imax + 1; j <= i__1; ++j) {
		    if ((r__1 = ap[kx], dabs(r__1)) > rowmax) {
			rowmax = (r__1 = ap[kx], dabs(r__1));
			jmax = j;
		    }
		    kx += j;
/* L20: */
		}
		kpc = (imax - 1) * imax / 2 + 1;
		if (imax > 1) {
		    i__1 = imax - 1;
		    jmax = isamax_(&i__1, &ap[kpc], &c__1);
/* Computing MAX */
		    r__2 = rowmax, r__3 = (r__1 = ap[kpc + jmax - 1], dabs(
			    r__1));
		    rowmax = dmax(r__2,r__3);
		}

		if (absakk >= alpha * colmax * (colmax / rowmax)) {

/*                 no interchange, use 1-by-1 pivot block */

		    kp = k;
		} else if ((r__1 = ap[kpc + imax - 1], dabs(r__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;
		sswap_(&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.f / ap[kc + k - 1];
		i__1 = k - 1;
		r__1 = -r1;
		sspr_(uplo, &i__1, &r__1, &ap[kc], &c__1, &ap[1]);

/*              Store U(k) in column k */

		i__1 = k - 1;
		sscal_(&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.f / (d11 * d22 - 1.f);
		    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 = (r__1 = ap[kc], dabs(r__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 + isamax_(&i__1, &ap[kc + 1], &c__1);
	    colmax = (r__1 = ap[kc + imax - k], dabs(r__1));
	} else {
	    colmax = 0.f;
	}

	if (dmax(absakk,colmax) == 0.f) {

/*           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.f;
		kx = kc + imax - k;
		i__1 = imax - 1;
		for (j = k; j <= i__1; ++j) {
		    if ((r__1 = ap[kx], dabs(r__1)) > rowmax) {
			rowmax = (r__1 = ap[kx], dabs(r__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 + isamax_(&i__1, &ap[kpc + 1], &c__1);
/* Computing MAX */
		    r__2 = rowmax, r__3 = (r__1 = ap[kpc + jmax - imax], dabs(
			    r__1));
		    rowmax = dmax(r__2,r__3);
		}

		if (absakk >= alpha * colmax * (colmax / rowmax)) {

/*                 no interchange, use 1-by-1 pivot block */

		    kp = k;
		} else if ((r__1 = ap[kpc], dabs(r__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;
		    sswap_(&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.f / ap[kc];
		    i__1 = *n - k;
		    r__1 = -r1;
		    sspr_(uplo, &i__1, &r__1, &ap[kc + 1], &c__1, &ap[kc + *n 
			    - k + 1]);

/*                 Store L(k) in column K */

		    i__1 = *n - k;
		    sscal_(&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.f / (d11 * d22 - 1.f);
		    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 SSPTRF */

} /* ssptrf_ */

