/* 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_ */