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

/* Subroutine */ int sspgst_(integer *itype, char *uplo, integer *n, real *ap,
	 real *bp, integer *info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       March 31, 1993   


    Purpose   
    =======   

    SSPGST reduces a real symmetric-definite generalized eigenproblem   
    to standard form, using packed storage.   

    If ITYPE = 1, the problem is A*x = lambda*B*x,   
    and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)   

    If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or   
    B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.   

    B must have been previously factorized as U**T*U or L*L**T by SPPTRF.   

    Arguments   
    =========   

    ITYPE   (input) INTEGER   
            = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);   
            = 2 or 3: compute U*A*U**T or L**T*A*L.   

    UPLO    (input) CHARACTER   
            = 'U':  Upper triangle of A is stored and B is factored as   
                    U**T*U;   
            = 'L':  Lower triangle of A is stored and B is factored as   
                    L*L**T.   

    N       (input) INTEGER   
            The order of the matrices A and B.  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, if INFO = 0, the transformed matrix, stored in the   
            same format as A.   

    BP      (input) REAL array, dimension (N*(N+1)/2)   
            The triangular factor from the Cholesky factorization of B,   
            stored in the same format as A, as returned by SPPTRF.   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   

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


       Test the input parameters.   

       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    static real c_b9 = -1.f;
    static real c_b11 = 1.f;
    
    /* System generated locals */
    integer i__1, i__2;
    real r__1;
    /* Local variables */
    extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
    extern /* Subroutine */ int sspr2_(char *, integer *, real *, real *, 
	    integer *, real *, integer *, real *);
    static integer j, k;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    static logical upper;
    static integer j1, k1;
    extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *, 
	    real *, integer *), sspmv_(char *, integer *, real *, real *, 
	    real *, integer *, real *, real *, integer *), stpmv_(
	    char *, char *, char *, integer *, real *, real *, integer *), stpsv_(char *, char *, char *, integer *,
	     real *, real *, integer *);
    static integer jj, kk;
    static real ct;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static real ajj;
    static integer j1j1;
    static real akk;
    static integer k1k1;
    static real bjj, bkk;


    --bp;
    --ap;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (*itype < 1 || *itype > 3) {
	*info = -1;
    } else if (! upper && ! lsame_(uplo, "L")) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SSPGST", &i__1);
	return 0;
    }

    if (*itype == 1) {
	if (upper) {

/*           Compute inv(U')*A*inv(U)   

             J1 and JJ are the indices of A(1,j) and A(j,j) */

	    jj = 0;
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
		j1 = jj + 1;
		jj += j;

/*              Compute the j-th column of the upper triangle of A */

		bjj = bp[jj];
		stpsv_(uplo, "Transpose", "Nonunit", &j, &bp[1], &ap[j1], &
			c__1);
		i__2 = j - 1;
		sspmv_(uplo, &i__2, &c_b9, &ap[1], &bp[j1], &c__1, &c_b11, &
			ap[j1], &c__1);
		i__2 = j - 1;
		r__1 = 1.f / bjj;
		sscal_(&i__2, &r__1, &ap[j1], &c__1);
		i__2 = j - 1;
		ap[jj] = (ap[jj] - sdot_(&i__2, &ap[j1], &c__1, &bp[j1], &
			c__1)) / bjj;
/* L10: */
	    }
	} else {

/*           Compute inv(L)*A*inv(L')   

             KK and K1K1 are the indices of A(k,k) and A(k+1,k+1) */

	    kk = 1;
	    i__1 = *n;
	    for (k = 1; k <= i__1; ++k) {
		k1k1 = kk + *n - k + 1;

/*              Update the lower triangle of A(k:n,k:n) */

		akk = ap[kk];
		bkk = bp[kk];
/* Computing 2nd power */
		r__1 = bkk;
		akk /= r__1 * r__1;
		ap[kk] = akk;
		if (k < *n) {
		    i__2 = *n - k;
		    r__1 = 1.f / bkk;
		    sscal_(&i__2, &r__1, &ap[kk + 1], &c__1);
		    ct = akk * -.5f;
		    i__2 = *n - k;
		    saxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
			    ;
		    i__2 = *n - k;
		    sspr2_(uplo, &i__2, &c_b9, &ap[kk + 1], &c__1, &bp[kk + 1]
			    , &c__1, &ap[k1k1]);
		    i__2 = *n - k;
		    saxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
			    ;
		    i__2 = *n - k;
		    stpsv_(uplo, "No transpose", "Non-unit", &i__2, &bp[k1k1],
			     &ap[kk + 1], &c__1);
		}
		kk = k1k1;
/* L20: */
	    }
	}
    } else {
	if (upper) {

/*           Compute U*A*U'   

             K1 and KK are the indices of A(1,k) and A(k,k) */

	    kk = 0;
	    i__1 = *n;
	    for (k = 1; k <= i__1; ++k) {
		k1 = kk + 1;
		kk += k;

/*              Update the upper triangle of A(1:k,1:k) */

		akk = ap[kk];
		bkk = bp[kk];
		i__2 = k - 1;
		stpmv_(uplo, "No transpose", "Non-unit", &i__2, &bp[1], &ap[
			k1], &c__1);
		ct = akk * .5f;
		i__2 = k - 1;
		saxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
		i__2 = k - 1;
		sspr2_(uplo, &i__2, &c_b11, &ap[k1], &c__1, &bp[k1], &c__1, &
			ap[1]);
		i__2 = k - 1;
		saxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
		i__2 = k - 1;
		sscal_(&i__2, &bkk, &ap[k1], &c__1);
/* Computing 2nd power */
		r__1 = bkk;
		ap[kk] = akk * (r__1 * r__1);
/* L30: */
	    }
	} else {

/*           Compute L'*A*L   

             JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1) */

	    jj = 1;
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
		j1j1 = jj + *n - j + 1;

/*              Compute the j-th column of the lower triangle of A */

		ajj = ap[jj];
		bjj = bp[jj];
		i__2 = *n - j;
		ap[jj] = ajj * bjj + sdot_(&i__2, &ap[jj + 1], &c__1, &bp[jj 
			+ 1], &c__1);
		i__2 = *n - j;
		sscal_(&i__2, &bjj, &ap[jj + 1], &c__1);
		i__2 = *n - j;
		sspmv_(uplo, &i__2, &c_b11, &ap[j1j1], &bp[jj + 1], &c__1, &
			c_b11, &ap[jj + 1], &c__1);
		i__2 = *n - j + 1;
		stpmv_(uplo, "Transpose", "Non-unit", &i__2, &bp[jj], &ap[jj],
			 &c__1);
		jj = j1j1;
/* L40: */
	    }
	}
    }
    return 0;

/*     End of SSPGST */

} /* sspgst_ */

