dsptri.c

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/* dsptri.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;
static doublereal c_b11 = -1.;
static doublereal c_b13 = 0.;

/* Subroutine */ int dsptri_(char *uplo, integer *n, doublereal *ap, integer *
        ipiv, doublereal *work, integer *info)
{
    /* System generated locals */
    integer i__1;
    doublereal d__1;

    /* Local variables */
    doublereal d__;
    integer j, k;
    doublereal t, ak;
    integer kc, kp, kx, kpc, npp;
    doublereal akp1;
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
            integer *);
    doublereal temp, akkp1;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
            doublereal *, integer *), dswap_(integer *, doublereal *, integer 
            *, doublereal *, integer *);
    integer kstep;
    extern /* Subroutine */ int dspmv_(char *, integer *, doublereal *, 
            doublereal *, doublereal *, integer *, doublereal *, doublereal *, 
             integer *);
    logical upper;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    integer kcnext;


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

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

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

/*  DSPTRI computes the inverse of a real symmetric indefinite matrix */
/*  A in packed storage using the factorization A = U*D*U**T or */
/*  A = L*D*L**T computed by DSPTRF. */

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

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the details of the factorization are stored */
/*          as an upper or lower triangular matrix. */
/*          = 'U':  Upper triangular, form is A = U*D*U**T; */
/*          = 'L':  Lower triangular, form is A = L*D*L**T. */

/*  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 block diagonal matrix D and the multipliers */
/*          used to obtain the factor U or L as computed by DSPTRF, */
/*          stored as a packed triangular matrix. */

/*          On exit, if INFO = 0, the (symmetric) inverse of the original */
/*          matrix, stored as a packed triangular matrix. The j-th column */
/*          of inv(A) is stored in the array AP as follows: */
/*          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; */
/*          if UPLO = 'L', */
/*             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n. */

/*  IPIV    (input) INTEGER array, dimension (N) */
/*          Details of the interchanges and the block structure of D */
/*          as determined by DSPTRF. */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (N) */

/*  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) = 0; the matrix is singular and its */
/*               inverse could not be computed. */

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

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

/*     Test the input parameters. */

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

/*     Quick return if possible */

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

/*     Check that the diagonal matrix D is nonsingular. */

    if (upper) {

/*        Upper triangular storage: examine D from bottom to top */

        kp = *n * (*n + 1) / 2;
        for (*info = *n; *info >= 1; --(*info)) {
            if (ipiv[*info] > 0 && ap[kp] == 0.) {
                return 0;
            }
            kp -= *info;
/* L10: */
        }
    } else {

/*        Lower triangular storage: examine D from top to bottom. */

        kp = 1;
        i__1 = *n;
        for (*info = 1; *info <= i__1; ++(*info)) {
            if (ipiv[*info] > 0 && ap[kp] == 0.) {
                return 0;
            }
            kp = kp + *n - *info + 1;
/* L20: */
        }
    }
    *info = 0;

    if (upper) {

/*        Compute inv(A) from the factorization A = U*D*U'. */

/*        K is the main loop index, increasing from 1 to N in steps of */
/*        1 or 2, depending on the size of the diagonal blocks. */

        k = 1;
        kc = 1;
L30:

/*        If K > N, exit from loop. */

        if (k > *n) {
            goto L50;
        }

        kcnext = kc + k;
        if (ipiv[k] > 0) {

/*           1 x 1 diagonal block */

/*           Invert the diagonal block. */

            ap[kc + k - 1] = 1. / ap[kc + k - 1];

/*           Compute column K of the inverse. */

            if (k > 1) {
                i__1 = k - 1;
                dcopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1);
                i__1 = k - 1;
                dspmv_(uplo, &i__1, &c_b11, &ap[1], &work[1], &c__1, &c_b13, &
                        ap[kc], &c__1);
                i__1 = k - 1;
                ap[kc + k - 1] -= ddot_(&i__1, &work[1], &c__1, &ap[kc], &
                        c__1);
            }
            kstep = 1;
        } else {

/*           2 x 2 diagonal block */

/*           Invert the diagonal block. */

            t = (d__1 = ap[kcnext + k - 1], abs(d__1));
            ak = ap[kc + k - 1] / t;
            akp1 = ap[kcnext + k] / t;
            akkp1 = ap[kcnext + k - 1] / t;
            d__ = t * (ak * akp1 - 1.);
            ap[kc + k - 1] = akp1 / d__;
            ap[kcnext + k] = ak / d__;
            ap[kcnext + k - 1] = -akkp1 / d__;

/*           Compute columns K and K+1 of the inverse. */

            if (k > 1) {
                i__1 = k - 1;
                dcopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1);
                i__1 = k - 1;
                dspmv_(uplo, &i__1, &c_b11, &ap[1], &work[1], &c__1, &c_b13, &
                        ap[kc], &c__1);
                i__1 = k - 1;
                ap[kc + k - 1] -= ddot_(&i__1, &work[1], &c__1, &ap[kc], &
                        c__1);
                i__1 = k - 1;
                ap[kcnext + k - 1] -= ddot_(&i__1, &ap[kc], &c__1, &ap[kcnext]
, &c__1);
                i__1 = k - 1;
                dcopy_(&i__1, &ap[kcnext], &c__1, &work[1], &c__1);
                i__1 = k - 1;
                dspmv_(uplo, &i__1, &c_b11, &ap[1], &work[1], &c__1, &c_b13, &
                        ap[kcnext], &c__1);
                i__1 = k - 1;
                ap[kcnext + k] -= ddot_(&i__1, &work[1], &c__1, &ap[kcnext], &
                        c__1);
            }
            kstep = 2;
            kcnext = kcnext + k + 1;
        }

        kp = (i__1 = ipiv[k], abs(i__1));
        if (kp != k) {

/*           Interchange rows and columns K and KP in the leading */
/*           submatrix A(1:k+1,1:k+1) */

            kpc = (kp - 1) * kp / 2 + 1;
            i__1 = kp - 1;
            dswap_(&i__1, &ap[kc], &c__1, &ap[kpc], &c__1);
            kx = kpc + kp - 1;
            i__1 = k - 1;
            for (j = kp + 1; j <= i__1; ++j) {
                kx = kx + j - 1;
                temp = ap[kc + j - 1];
                ap[kc + j - 1] = ap[kx];
                ap[kx] = temp;
/* L40: */
            }
            temp = ap[kc + k - 1];
            ap[kc + k - 1] = ap[kpc + kp - 1];
            ap[kpc + kp - 1] = temp;
            if (kstep == 2) {
                temp = ap[kc + k + k - 1];
                ap[kc + k + k - 1] = ap[kc + k + kp - 1];
                ap[kc + k + kp - 1] = temp;
            }
        }

        k += kstep;
        kc = kcnext;
        goto L30;
L50:

        ;
    } else {

/*        Compute inv(A) from the factorization A = L*D*L'. */

/*        K is the main loop index, increasing from 1 to N in steps of */
/*        1 or 2, depending on the size of the diagonal blocks. */

        npp = *n * (*n + 1) / 2;
        k = *n;
        kc = npp;
L60:

/*        If K < 1, exit from loop. */

        if (k < 1) {
            goto L80;
        }

        kcnext = kc - (*n - k + 2);
        if (ipiv[k] > 0) {

/*           1 x 1 diagonal block */

/*           Invert the diagonal block. */

            ap[kc] = 1. / ap[kc];

/*           Compute column K of the inverse. */

            if (k < *n) {
                i__1 = *n - k;
                dcopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1);
                i__1 = *n - k;
                dspmv_(uplo, &i__1, &c_b11, &ap[kc + *n - k + 1], &work[1], &
                        c__1, &c_b13, &ap[kc + 1], &c__1);
                i__1 = *n - k;
                ap[kc] -= ddot_(&i__1, &work[1], &c__1, &ap[kc + 1], &c__1);
            }
            kstep = 1;
        } else {

/*           2 x 2 diagonal block */

/*           Invert the diagonal block. */

            t = (d__1 = ap[kcnext + 1], abs(d__1));
            ak = ap[kcnext] / t;
            akp1 = ap[kc] / t;
            akkp1 = ap[kcnext + 1] / t;
            d__ = t * (ak * akp1 - 1.);
            ap[kcnext] = akp1 / d__;
            ap[kc] = ak / d__;
            ap[kcnext + 1] = -akkp1 / d__;

/*           Compute columns K-1 and K of the inverse. */

            if (k < *n) {
                i__1 = *n - k;
                dcopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1);
                i__1 = *n - k;
                dspmv_(uplo, &i__1, &c_b11, &ap[kc + (*n - k + 1)], &work[1], 
                        &c__1, &c_b13, &ap[kc + 1], &c__1);
                i__1 = *n - k;
                ap[kc] -= ddot_(&i__1, &work[1], &c__1, &ap[kc + 1], &c__1);
                i__1 = *n - k;
                ap[kcnext + 1] -= ddot_(&i__1, &ap[kc + 1], &c__1, &ap[kcnext 
                        + 2], &c__1);
                i__1 = *n - k;
                dcopy_(&i__1, &ap[kcnext + 2], &c__1, &work[1], &c__1);
                i__1 = *n - k;
                dspmv_(uplo, &i__1, &c_b11, &ap[kc + (*n - k + 1)], &work[1], 
                        &c__1, &c_b13, &ap[kcnext + 2], &c__1);
                i__1 = *n - k;
                ap[kcnext] -= ddot_(&i__1, &work[1], &c__1, &ap[kcnext + 2], &
                        c__1);
            }
            kstep = 2;
            kcnext -= *n - k + 3;
        }

        kp = (i__1 = ipiv[k], abs(i__1));
        if (kp != k) {

/*           Interchange rows and columns K and KP in the trailing */
/*           submatrix A(k-1:n,k-1:n) */

            kpc = npp - (*n - kp + 1) * (*n - kp + 2) / 2 + 1;
            if (kp < *n) {
                i__1 = *n - kp;
                dswap_(&i__1, &ap[kc + kp - k + 1], &c__1, &ap[kpc + 1], &
                        c__1);
            }
            kx = kc + kp - k;
            i__1 = kp - 1;
            for (j = k + 1; j <= i__1; ++j) {
                kx = kx + *n - j + 1;
                temp = ap[kc + j - k];
                ap[kc + j - k] = ap[kx];
                ap[kx] = temp;
/* L70: */
            }
            temp = ap[kc];
            ap[kc] = ap[kpc];
            ap[kpc] = temp;
            if (kstep == 2) {
                temp = ap[kc - *n + k - 1];
                ap[kc - *n + k - 1] = ap[kc - *n + kp - 1];
                ap[kc - *n + kp - 1] = temp;
            }
        }

        k -= kstep;
        kc = kcnext;
        goto L60;
L80:
        ;
    }

    return 0;

/*     End of DSPTRI */

} /* dsptri_ */