Esempio n. 1
0
/* Subroutine */ int spptrf_(char *uplo, integer *n, real *ap, integer *info)
{
    /* System generated locals */
    integer i__1, i__2;
    real r__1;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    integer j, jc, jj;
    real ajj;
    extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
    extern /* Subroutine */ int sspr_(char *, integer *, real *, real *, 
	    integer *, real *);
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    logical upper;
    extern /* Subroutine */ int 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 */
/*  ======= */

/*  SPPTRF computes the Cholesky factorization of a real symmetric */
/*  positive definite matrix A stored in packed format. */

/*  The factorization has the form */
/*     A = U**T * U,  if UPLO = 'U', or */
/*     A = L  * L**T,  if UPLO = 'L', */
/*  where U is an upper triangular matrix and L is lower triangular. */

/*  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. */
/*          See below for further details. */

/*          On exit, if INFO = 0, the triangular factor U or L from the */
/*          Cholesky factorization A = U**T*U or A = L*L**T, in the same */
/*          storage format as A. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  if INFO = i, the leading minor of order i is not */
/*                positive definite, and the factorization could not be */
/*                completed. */

/*  Further Details */
/*  ======= ======= */

/*  The packed storage scheme is illustrated by the following example */
/*  when N = 4, UPLO = 'U': */

/*  Two-dimensional storage of the symmetric matrix A: */

/*     a11 a12 a13 a14 */
/*         a22 a23 a24 */
/*             a33 a34     (aij = aji) */
/*                 a44 */

/*  Packed storage of the upper triangle of A: */

/*  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    --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_("SPPTRF", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

    if (upper) {

/*        Compute the Cholesky factorization A = U'*U. */

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

/*           Compute elements 1:J-1 of column J. */

	    if (j > 1) {
		i__2 = j - 1;
		stpsv_("Upper", "Transpose", "Non-unit", &i__2, &ap[1], &ap[
			jc], &c__1);
	    }

/*           Compute U(J,J) and test for non-positive-definiteness. */

	    i__2 = j - 1;
	    ajj = ap[jj] - sdot_(&i__2, &ap[jc], &c__1, &ap[jc], &c__1);
	    if (ajj <= 0.f) {
		ap[jj] = ajj;
		goto L30;
	    }
	    ap[jj] = sqrt(ajj);
/* L10: */
	}
    } else {

/*        Compute the Cholesky factorization A = L*L'. */

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

/*           Compute L(J,J) and test for non-positive-definiteness. */

	    ajj = ap[jj];
	    if (ajj <= 0.f) {
		ap[jj] = ajj;
		goto L30;
	    }
	    ajj = sqrt(ajj);
	    ap[jj] = ajj;

/*           Compute elements J+1:N of column J and update the trailing */
/*           submatrix. */

	    if (j < *n) {
		i__2 = *n - j;
		r__1 = 1.f / ajj;
		sscal_(&i__2, &r__1, &ap[jj + 1], &c__1);
		i__2 = *n - j;
		sspr_("Lower", &i__2, &c_b16, &ap[jj + 1], &c__1, &ap[jj + *n 
			- j + 1]);
		jj = jj + *n - j + 1;
	    }
/* L20: */
	}
    }
    goto L40;

L30:
    *info = j;

L40:
    return 0;

/*     End of SPPTRF */

} /* spptrf_ */
Esempio n. 2
0
/* Subroutine */ int spptri_(char *uplo, integer *n, real *ap, 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   
    =======   

    SPPTRI computes the inverse of a real symmetric positive definite   
    matrix A using the Cholesky factorization A = U**T*U or A = L*L**T   
    computed by SPPTRF.   

    Arguments   
    =========   

    UPLO    (input) CHARACTER*1   
            = 'U':  Upper triangular factor is stored in AP;   
            = 'L':  Lower triangular factor is stored in AP.   

    N       (input) INTEGER   
            The order of the matrix A.  N >= 0.   

    AP      (input/output) REAL array, dimension (N*(N+1)/2)   
            On entry, the triangular factor U or L from the Cholesky   
            factorization A = U**T*U or A = L*L**T, packed columnwise as 
  
            a linear array.  The j-th column of U or L is stored in the   
            array AP as follows:   
            if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;   
            if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.   

            On exit, the upper or lower triangle of the (symmetric)   
            inverse of A, overwriting the input factor U or L.   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   
            > 0:  if INFO = i, the (i,i) element of the factor U or L is 
  
                  zero, and the inverse could not be computed.   

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


       Test the input parameters.   

    
   Parameter adjustments   
       Function Body */
    /* Table of constant values */
    static real c_b8 = 1.f;
    static integer c__1 = 1;
    
    /* System generated locals */
    integer i__1, i__2;
    /* Local variables */
    extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
    extern /* Subroutine */ int sspr_(char *, integer *, real *, real *, 
	    integer *, real *);
    static integer j;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    static logical upper;
    extern /* Subroutine */ int stpmv_(char *, char *, char *, integer *, 
	    real *, real *, integer *);
    static integer jc, jj;
    extern /* Subroutine */ int xerbla_(char *, integer *), stptri_(
	    char *, char *, integer *, real *, integer *);
    static real ajj;
    static integer jjn;



#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_("SPPTRI", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

/*     Invert the triangular Cholesky factor U or L. */

    stptri_(uplo, "Non-unit", n, &AP(1), info);
    if (*info > 0) {
	return 0;
    }

    if (upper) {

/*        Compute the product inv(U) * inv(U)'. */

	jj = 0;
	i__1 = *n;
	for (j = 1; j <= *n; ++j) {
	    jc = jj + 1;
	    jj += j;
	    if (j > 1) {
		i__2 = j - 1;
		sspr_("Upper", &i__2, &c_b8, &AP(jc), &c__1, &AP(1));
	    }
	    ajj = AP(jj);
	    sscal_(&j, &ajj, &AP(jc), &c__1);
/* L10: */
	}

    } else {

/*        Compute the product inv(L)' * inv(L). */

	jj = 1;
	i__1 = *n;
	for (j = 1; j <= *n; ++j) {
	    jjn = jj + *n - j + 1;
	    i__2 = *n - j + 1;
	    AP(jj) = sdot_(&i__2, &AP(jj), &c__1, &AP(jj), &c__1);
	    if (j < *n) {
		i__2 = *n - j;
		stpmv_("Lower", "Transpose", "Non-unit", &i__2, &AP(jjn), &AP(
			jj + 1), &c__1);
	    }
	    jj = jjn;
/* L20: */
	}
    }

    return 0;

/*     End of SPPTRI */

} /* spptri_ */
Esempio n. 3
0
/* Subroutine */
int spptri_(char *uplo, integer *n, real *ap, integer *info)
{
    /* System generated locals */
    integer i__1, i__2;
    /* Local variables */
    integer j, jc, jj;
    real ajj;
    integer jjn;
    extern real sdot_(integer *, real *, integer *, real *, integer *);
    extern /* Subroutine */
    int sspr_(char *, integer *, real *, real *, integer *, real *);
    extern logical lsame_(char *, char *);
    extern /* Subroutine */
    int sscal_(integer *, real *, real *, integer *);
    logical upper;
    extern /* Subroutine */
    int stpmv_(char *, char *, char *, integer *, real *, real *, integer *), xerbla_(char * , integer *), stptri_(char *, char *, integer *, real *, integer *);
    /* -- LAPACK computational routine (version 3.4.0) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* November 2011 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. Parameters .. */
    /* .. */
    /* .. Local Scalars .. */
    /* .. */
    /* .. External Functions .. */
    /* .. */
    /* .. External Subroutines .. */
    /* .. */
    /* .. Executable Statements .. */
    /* Test the input parameters. */
    /* Parameter adjustments */
    --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_("SPPTRI", &i__1);
        return 0;
    }
    /* Quick return if possible */
    if (*n == 0)
    {
        return 0;
    }
    /* Invert the triangular Cholesky factor U or L. */
    stptri_(uplo, "Non-unit", n, &ap[1], info);
    if (*info > 0)
    {
        return 0;
    }
    if (upper)
    {
        /* Compute the product inv(U) * inv(U)**T. */
        jj = 0;
        i__1 = *n;
        for (j = 1;
                j <= i__1;
                ++j)
        {
            jc = jj + 1;
            jj += j;
            if (j > 1)
            {
                i__2 = j - 1;
                sspr_("Upper", &i__2, &c_b8, &ap[jc], &c__1, &ap[1]);
            }
            ajj = ap[jj];
            sscal_(&j, &ajj, &ap[jc], &c__1);
            /* L10: */
        }
    }
    else
    {
        /* Compute the product inv(L)**T * inv(L). */
        jj = 1;
        i__1 = *n;
        for (j = 1;
                j <= i__1;
                ++j)
        {
            jjn = jj + *n - j + 1;
            i__2 = *n - j + 1;
            ap[jj] = sdot_(&i__2, &ap[jj], &c__1, &ap[jj], &c__1);
            if (j < *n)
            {
                i__2 = *n - j;
                stpmv_("Lower", "Transpose", "Non-unit", &i__2, &ap[jjn], &ap[ jj + 1], &c__1);
            }
            jj = jjn;
            /* L20: */
        }
    }
    return 0;
    /* End of SPPTRI */
}