Ejemplo n.º 1
0
int
f2c_sspr2(char* uplo, integer* N,
          real* alpha, 
          real* X, integer* incX,
          real* Y, integer* incY,
          real* A)
{
    sspr2_(uplo, N, alpha,
           X, incX, Y, incY, A);
    return 0;
}
Ejemplo n.º 2
0
/* Subroutine */ int sspgst_(integer *itype, char *uplo, integer *n, real *ap, 
	 real *bp, integer *info)
{
    /* System generated locals */
    integer i__1, i__2;
    real r__1;

    /* Local variables */
    integer j, k, j1, k1, jj, kk;
    real ct, ajj;
    integer j1j1;
    real akk;
    integer k1k1;
    real bjj, bkk;
    extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
    extern /* Subroutine */ int sspr2_(char *, integer *, real *, real *, 
	    integer *, real *, integer *, real *);
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    logical upper;
    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 *), xerbla_(char 
	    *, integer *);


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  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*1 */
/*          = '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 */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    --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_ */
Ejemplo n.º 3
0
void
sspr2(char uplo, int n, float alpha, float *x, int incx, float *y, int incy, float *a )
{
   sspr2_( &uplo, &n, &alpha, x, &incx, y, &incy, a );
}
Ejemplo n.º 4
0
/* Subroutine */ int ssbt21_(char *uplo, integer *n, integer *ka, integer *ks, 
	 real *a, integer *lda, real *d__, real *e, real *u, integer *ldu, 
	real *work, real *result)
{
    /* System generated locals */
    integer a_dim1, a_offset, u_dim1, u_offset, i__1, i__2, i__3, i__4;
    real r__1, r__2;

    /* Local variables */
    integer j, jc, jr, lw, ika;
    real ulp, unfl;
    extern /* Subroutine */ int sspr_(char *, integer *, real *, real *, 
	    integer *, real *), sspr2_(char *, integer *, real *, 
	    real *, integer *, real *, integer *, real *);
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *);
    real anorm;
    char cuplo[1];
    logical lower;
    real wnorm;
    extern doublereal slamch_(char *), slange_(char *, integer *, 
	    integer *, real *, integer *, real *), slansb_(char *, 
	    char *, integer *, integer *, real *, integer *, real *), slansp_(char *, char *, integer *, real *, real *);


/*  -- LAPACK test routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  SSBT21  generally checks a decomposition of the form */

/*          A = U S U' */

/*  where ' means transpose, A is symmetric banded, U is */
/*  orthogonal, and S is diagonal (if KS=0) or symmetric */
/*  tridiagonal (if KS=1). */

/*  Specifically: */

/*          RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and* */
/*          RESULT(2) = | I - UU' | / ( n ulp ) */

/*  Arguments */
/*  ========= */

/*  UPLO    (input) CHARACTER */
/*          If UPLO='U', the upper triangle of A and V will be used and */
/*          the (strictly) lower triangle will not be referenced. */
/*          If UPLO='L', the lower triangle of A and V will be used and */
/*          the (strictly) upper triangle will not be referenced. */

/*  N       (input) INTEGER */
/*          The size of the matrix.  If it is zero, SSBT21 does nothing. */
/*          It must be at least zero. */

/*  KA      (input) INTEGER */
/*          The bandwidth of the matrix A.  It must be at least zero.  If */
/*          it is larger than N-1, then max( 0, N-1 ) will be used. */

/*  KS      (input) INTEGER */
/*          The bandwidth of the matrix S.  It may only be zero or one. */
/*          If zero, then S is diagonal, and E is not referenced.  If */
/*          one, then S is symmetric tri-diagonal. */

/*  A       (input) REAL array, dimension (LDA, N) */
/*          The original (unfactored) matrix.  It is assumed to be */
/*          symmetric, and only the upper (UPLO='U') or only the lower */
/*          (UPLO='L') will be referenced. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of A.  It must be at least 1 */
/*          and at least min( KA, N-1 ). */

/*  D       (input) REAL array, dimension (N) */
/*          The diagonal of the (symmetric tri-) diagonal matrix S. */

/*  E       (input) REAL array, dimension (N-1) */
/*          The off-diagonal of the (symmetric tri-) diagonal matrix S. */
/*          E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and */
/*          (3,2) element, etc. */
/*          Not referenced if KS=0. */

/*  U       (input) REAL array, dimension (LDU, N) */
/*          The orthogonal matrix in the decomposition, expressed as a */
/*          dense matrix (i.e., not as a product of Householder */
/*          transformations, Givens transformations, etc.) */

/*  LDU     (input) INTEGER */
/*          The leading dimension of U.  LDU must be at least N and */
/*          at least 1. */

/*  WORK    (workspace) REAL array, dimension (N**2+N) */

/*  RESULT  (output) REAL array, dimension (2) */
/*          The values computed by the two tests described above.  The */
/*          values are currently limited to 1/ulp, to avoid overflow. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Constants */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --d__;
    --e;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1;
    u -= u_offset;
    --work;
    --result;

    /* Function Body */
    result[1] = 0.f;
    result[2] = 0.f;
    if (*n <= 0) {
	return 0;
    }

/* Computing MAX */
/* Computing MIN */
    i__3 = *n - 1;
    i__1 = 0, i__2 = min(i__3,*ka);
    ika = max(i__1,i__2);
    lw = *n * (*n + 1) / 2;

    if (lsame_(uplo, "U")) {
	lower = FALSE_;
	*(unsigned char *)cuplo = 'U';
    } else {
	lower = TRUE_;
	*(unsigned char *)cuplo = 'L';
    }

    unfl = slamch_("Safe minimum");
    ulp = slamch_("Epsilon") * slamch_("Base");

/*     Some Error Checks */

/*     Do Test 1 */

/*     Norm of A: */

/* Computing MAX */
    r__1 = slansb_("1", cuplo, n, &ika, &a[a_offset], lda, &work[1]);
    anorm = dmax(r__1,unfl);

/*     Compute error matrix:    Error = A - U S U' */

/*     Copy A from SB to SP storage format. */

    j = 0;
    i__1 = *n;
    for (jc = 1; jc <= i__1; ++jc) {
	if (lower) {
/* Computing MIN */
	    i__3 = ika + 1, i__4 = *n + 1 - jc;
	    i__2 = min(i__3,i__4);
	    for (jr = 1; jr <= i__2; ++jr) {
		++j;
		work[j] = a[jr + jc * a_dim1];
/* L10: */
	    }
	    i__2 = *n + 1 - jc;
	    for (jr = ika + 2; jr <= i__2; ++jr) {
		++j;
		work[j] = 0.f;
/* L20: */
	    }
	} else {
	    i__2 = jc;
	    for (jr = ika + 2; jr <= i__2; ++jr) {
		++j;
		work[j] = 0.f;
/* L30: */
	    }
/* Computing MIN */
	    i__2 = ika, i__3 = jc - 1;
	    for (jr = min(i__2,i__3); jr >= 0; --jr) {
		++j;
		work[j] = a[ika + 1 - jr + jc * a_dim1];
/* L40: */
	    }
	}
/* L50: */
    }

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
	r__1 = -d__[j];
	sspr_(cuplo, n, &r__1, &u[j * u_dim1 + 1], &c__1, &work[1])
		;
/* L60: */
    }

    if (*n > 1 && *ks == 1) {
	i__1 = *n - 1;
	for (j = 1; j <= i__1; ++j) {
	    r__1 = -e[j];
	    sspr2_(cuplo, n, &r__1, &u[j * u_dim1 + 1], &c__1, &u[(j + 1) * 
		    u_dim1 + 1], &c__1, &work[1]);
/* L70: */
	}
    }
    wnorm = slansp_("1", cuplo, n, &work[1], &work[lw + 1]);

    if (anorm > wnorm) {
	result[1] = wnorm / anorm / (*n * ulp);
    } else {
	if (anorm < 1.f) {
/* Computing MIN */
	    r__1 = wnorm, r__2 = *n * anorm;
	    result[1] = dmin(r__1,r__2) / anorm / (*n * ulp);
	} else {
/* Computing MIN */
	    r__1 = wnorm / anorm, r__2 = (real) (*n);
	    result[1] = dmin(r__1,r__2) / (*n * ulp);
	}
    }

/*     Do Test 2 */

/*     Compute  UU' - I */

    sgemm_("N", "C", n, n, n, &c_b22, &u[u_offset], ldu, &u[u_offset], ldu, &
	    c_b23, &work[1], n);

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
	work[(*n + 1) * (j - 1) + 1] += -1.f;
/* L80: */
    }

/* Computing MIN */
/* Computing 2nd power */
    i__1 = *n;
    r__1 = slange_("1", n, n, &work[1], n, &work[i__1 * i__1 + 1]),
	     r__2 = (real) (*n);
    result[2] = dmin(r__1,r__2) / (*n * ulp);

    return 0;

/*     End of SSBT21 */

} /* ssbt21_ */
Ejemplo n.º 5
0
/* Subroutine */ int ssptrd_(char *uplo, integer *n, real *ap, real *d, real *
	e, real *tau, integer *info)
{
/*  -- LAPACK routine (version 2.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       March 31, 1993   


    Purpose   
    =======   

    SSPTRD reduces a real symmetric matrix A stored in packed form to   
    symmetric tridiagonal form T by an orthogonal similarity   
    transformation: Q**T * A * Q = T.   

    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)*(2*n-j)/2) = A(i,j) for j<=i<=n. 
  
            On exit, if UPLO = 'U', the diagonal and first superdiagonal 
  
            of A are overwritten by the corresponding elements of the   
            tridiagonal matrix T, and the elements above the first   
            superdiagonal, with the array TAU, represent the orthogonal   
            matrix Q as a product of elementary reflectors; if UPLO   
            = 'L', the diagonal and first subdiagonal of A are over-   
            written by the corresponding elements of the tridiagonal   
            matrix T, and the elements below the first subdiagonal, with 
  
            the array TAU, represent the orthogonal matrix Q as a product 
  
            of elementary reflectors. See Further Details.   

    D       (output) REAL array, dimension (N)   
            The diagonal elements of the tridiagonal matrix T:   
            D(i) = A(i,i).   

    E       (output) REAL array, dimension (N-1)   
            The off-diagonal elements of the tridiagonal matrix T:   
            E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. 
  

    TAU     (output) REAL array, dimension (N-1)   
            The scalar factors of the elementary reflectors (see Further 
  
            Details).   

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

    Further Details   
    ===============   

    If UPLO = 'U', the matrix Q is represented as a product of elementary 
  
    reflectors   

       Q = H(n-1) . . . H(2) H(1).   

    Each H(i) has the form   

       H(i) = I - tau * v * v'   

    where tau is a real scalar, and v is a real vector with   
    v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,   
    overwriting A(1:i-1,i+1), and tau is stored in TAU(i).   

    If UPLO = 'L', the matrix Q is represented as a product of elementary 
  
    reflectors   

       Q = H(1) H(2) . . . H(n-1).   

    Each H(i) has the form   

       H(i) = I - tau * v * v'   

    where tau is a real scalar, and v is a real vector with   
    v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,   
    overwriting A(i+2:n,i), and tau is stored in TAU(i).   

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


       Test the input parameters   

    
   Parameter adjustments   
       Function Body */
    /* Table of constant values */
    static integer c__1 = 1;
    static real c_b8 = 0.f;
    static real c_b14 = -1.f;
    
    /* System generated locals */
    integer i__1, i__2;
    /* Local variables */
    static real taui;
    extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
    static integer i;
    extern /* Subroutine */ int sspr2_(char *, integer *, real *, real *, 
	    integer *, real *, integer *, real *);
    static real alpha;
    extern logical lsame_(char *, char *);
    static integer i1;
    static logical upper;
    extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *, 
	    real *, integer *), sspmv_(char *, integer *, real *, real *, 
	    real *, integer *, real *, real *, integer *);
    static integer ii;
    extern /* Subroutine */ int xerbla_(char *, integer *), slarfg_(
	    integer *, real *, real *, integer *, real *);
    static integer i1i1;



#define TAU(I) tau[(I)-1]
#define E(I) e[(I)-1]
#define D(I) d[(I)-1]
#define AP(I) ap[(I)-1]


    *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_("SSPTRD", &i__1);
	return 0;
    }

/*     Quick return if possible */

    if (*n <= 0) {
	return 0;
    }

    if (upper) {

/*        Reduce the upper triangle of A.   
          I1 is the index in AP of A(1,I+1). */

	i1 = *n * (*n - 1) / 2 + 1;
	for (i = *n - 1; i >= 1; --i) {

/*           Generate elementary reflector H(i) = I - tau * v * v'
   
             to annihilate A(1:i-1,i+1) */

	    slarfg_(&i, &AP(i1 + i - 1), &AP(i1), &c__1, &taui);
	    E(i) = AP(i1 + i - 1);

	    if (taui != 0.f) {

/*              Apply H(i) from both sides to A(1:i,1:i) */

		AP(i1 + i - 1) = 1.f;

/*              Compute  y := tau * A * v  storing y in TAU(1:
i) */

		sspmv_(uplo, &i, &taui, &AP(1), &AP(i1), &c__1, &c_b8, &TAU(1)
			, &c__1);

/*              Compute  w := y - 1/2 * tau * (y'*v) * v */

		alpha = taui * -.5f * sdot_(&i, &TAU(1), &c__1, &AP(i1), &
			c__1);
		saxpy_(&i, &alpha, &AP(i1), &c__1, &TAU(1), &c__1);

/*              Apply the transformation as a rank-2 update: 
  
                   A := A - v * w' - w * v' */

		sspr2_(uplo, &i, &c_b14, &AP(i1), &c__1, &TAU(1), &c__1, &AP(
			1));

		AP(i1 + i - 1) = E(i);
	    }
	    D(i + 1) = AP(i1 + i);
	    TAU(i) = taui;
	    i1 -= i;
/* L10: */
	}
	D(1) = AP(1);
    } else {

/*        Reduce the lower triangle of A. II is the index in AP of   
          A(i,i) and I1I1 is the index of A(i+1,i+1). */

	ii = 1;
	i__1 = *n - 1;
	for (i = 1; i <= *n-1; ++i) {
	    i1i1 = ii + *n - i + 1;

/*           Generate elementary reflector H(i) = I - tau * v * v'
   
             to annihilate A(i+2:n,i) */

	    i__2 = *n - i;
	    slarfg_(&i__2, &AP(ii + 1), &AP(ii + 2), &c__1, &taui);
	    E(i) = AP(ii + 1);

	    if (taui != 0.f) {

/*              Apply H(i) from both sides to A(i+1:n,i+1:n) 
*/

		AP(ii + 1) = 1.f;

/*              Compute  y := tau * A * v  storing y in TAU(i:
n-1) */

		i__2 = *n - i;
		sspmv_(uplo, &i__2, &taui, &AP(i1i1), &AP(ii + 1), &c__1, &
			c_b8, &TAU(i), &c__1);

/*              Compute  w := y - 1/2 * tau * (y'*v) * v */

		i__2 = *n - i;
		alpha = taui * -.5f * sdot_(&i__2, &TAU(i), &c__1, &AP(ii + 1)
			, &c__1);
		i__2 = *n - i;
		saxpy_(&i__2, &alpha, &AP(ii + 1), &c__1, &TAU(i), &c__1);

/*              Apply the transformation as a rank-2 update: 
  
                   A := A - v * w' - w * v' */

		i__2 = *n - i;
		sspr2_(uplo, &i__2, &c_b14, &AP(ii + 1), &c__1, &TAU(i), &
			c__1, &AP(i1i1));

		AP(ii + 1) = E(i);
	    }
	    D(i) = AP(ii);
	    TAU(i) = taui;
	    ii = i1i1;
/* L20: */
	}
	D(*n) = AP(ii);
    }

    return 0;

/*     End of SSPTRD */

} /* ssptrd_ */