397 lines
11 KiB
C
397 lines
11 KiB
C
/* dsytri.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 "clapack.h"
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
static doublereal c_b11 = -1.;
|
|
static doublereal c_b13 = 0.;
|
|
|
|
/* Subroutine */ int dsytri_(char *uplo, integer *n, doublereal *a, integer *
|
|
lda, integer *ipiv, doublereal *work, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, i__1;
|
|
doublereal d__1;
|
|
|
|
/* Local variables */
|
|
doublereal d__;
|
|
integer k;
|
|
doublereal t, ak;
|
|
integer kp;
|
|
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;
|
|
logical upper;
|
|
extern /* Subroutine */ int dsymv_(char *, integer *, doublereal *,
|
|
doublereal *, integer *, doublereal *, integer *, doublereal *,
|
|
doublereal *, 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 */
|
|
/* ======= */
|
|
|
|
/* DSYTRI computes the inverse of a real symmetric indefinite matrix */
|
|
/* A using the factorization A = U*D*U**T or A = L*D*L**T computed by */
|
|
/* DSYTRF. */
|
|
|
|
/* 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. */
|
|
|
|
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
|
|
/* On entry, the block diagonal matrix D and the multipliers */
|
|
/* used to obtain the factor U or L as computed by DSYTRF. */
|
|
|
|
/* On exit, if INFO = 0, the (symmetric) inverse of the original */
|
|
/* matrix. If UPLO = 'U', the upper triangular part of the */
|
|
/* inverse is formed and the part of A below the diagonal is not */
|
|
/* referenced; if UPLO = 'L' the lower triangular part of the */
|
|
/* inverse is formed and the part of A above the diagonal is */
|
|
/* not referenced. */
|
|
|
|
/* LDA (input) INTEGER */
|
|
/* The leading dimension of the array A. LDA >= max(1,N). */
|
|
|
|
/* IPIV (input) INTEGER array, dimension (N) */
|
|
/* Details of the interchanges and the block structure of D */
|
|
/* as determined by DSYTRF. */
|
|
|
|
/* 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 */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1;
|
|
a -= a_offset;
|
|
--ipiv;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
upper = lsame_(uplo, "U");
|
|
if (! upper && ! lsame_(uplo, "L")) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*lda < max(1,*n)) {
|
|
*info = -4;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DSYTRI", &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 */
|
|
|
|
for (*info = *n; *info >= 1; --(*info)) {
|
|
if (ipiv[*info] > 0 && a[*info + *info * a_dim1] == 0.) {
|
|
return 0;
|
|
}
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
|
|
/* Lower triangular storage: examine D from top to bottom. */
|
|
|
|
i__1 = *n;
|
|
for (*info = 1; *info <= i__1; ++(*info)) {
|
|
if (ipiv[*info] > 0 && a[*info + *info * a_dim1] == 0.) {
|
|
return 0;
|
|
}
|
|
/* 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;
|
|
L30:
|
|
|
|
/* If K > N, exit from loop. */
|
|
|
|
if (k > *n) {
|
|
goto L40;
|
|
}
|
|
|
|
if (ipiv[k] > 0) {
|
|
|
|
/* 1 x 1 diagonal block */
|
|
|
|
/* Invert the diagonal block. */
|
|
|
|
a[k + k * a_dim1] = 1. / a[k + k * a_dim1];
|
|
|
|
/* Compute column K of the inverse. */
|
|
|
|
if (k > 1) {
|
|
i__1 = k - 1;
|
|
dcopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &work[1], &c__1);
|
|
i__1 = k - 1;
|
|
dsymv_(uplo, &i__1, &c_b11, &a[a_offset], lda, &work[1], &
|
|
c__1, &c_b13, &a[k * a_dim1 + 1], &c__1);
|
|
i__1 = k - 1;
|
|
a[k + k * a_dim1] -= ddot_(&i__1, &work[1], &c__1, &a[k *
|
|
a_dim1 + 1], &c__1);
|
|
}
|
|
kstep = 1;
|
|
} else {
|
|
|
|
/* 2 x 2 diagonal block */
|
|
|
|
/* Invert the diagonal block. */
|
|
|
|
t = (d__1 = a[k + (k + 1) * a_dim1], abs(d__1));
|
|
ak = a[k + k * a_dim1] / t;
|
|
akp1 = a[k + 1 + (k + 1) * a_dim1] / t;
|
|
akkp1 = a[k + (k + 1) * a_dim1] / t;
|
|
d__ = t * (ak * akp1 - 1.);
|
|
a[k + k * a_dim1] = akp1 / d__;
|
|
a[k + 1 + (k + 1) * a_dim1] = ak / d__;
|
|
a[k + (k + 1) * a_dim1] = -akkp1 / d__;
|
|
|
|
/* Compute columns K and K+1 of the inverse. */
|
|
|
|
if (k > 1) {
|
|
i__1 = k - 1;
|
|
dcopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &work[1], &c__1);
|
|
i__1 = k - 1;
|
|
dsymv_(uplo, &i__1, &c_b11, &a[a_offset], lda, &work[1], &
|
|
c__1, &c_b13, &a[k * a_dim1 + 1], &c__1);
|
|
i__1 = k - 1;
|
|
a[k + k * a_dim1] -= ddot_(&i__1, &work[1], &c__1, &a[k *
|
|
a_dim1 + 1], &c__1);
|
|
i__1 = k - 1;
|
|
a[k + (k + 1) * a_dim1] -= ddot_(&i__1, &a[k * a_dim1 + 1], &
|
|
c__1, &a[(k + 1) * a_dim1 + 1], &c__1);
|
|
i__1 = k - 1;
|
|
dcopy_(&i__1, &a[(k + 1) * a_dim1 + 1], &c__1, &work[1], &
|
|
c__1);
|
|
i__1 = k - 1;
|
|
dsymv_(uplo, &i__1, &c_b11, &a[a_offset], lda, &work[1], &
|
|
c__1, &c_b13, &a[(k + 1) * a_dim1 + 1], &c__1);
|
|
i__1 = k - 1;
|
|
a[k + 1 + (k + 1) * a_dim1] -= ddot_(&i__1, &work[1], &c__1, &
|
|
a[(k + 1) * a_dim1 + 1], &c__1);
|
|
}
|
|
kstep = 2;
|
|
}
|
|
|
|
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) */
|
|
|
|
i__1 = kp - 1;
|
|
dswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &
|
|
c__1);
|
|
i__1 = k - kp - 1;
|
|
dswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + (kp + 1) *
|
|
a_dim1], lda);
|
|
temp = a[k + k * a_dim1];
|
|
a[k + k * a_dim1] = a[kp + kp * a_dim1];
|
|
a[kp + kp * a_dim1] = temp;
|
|
if (kstep == 2) {
|
|
temp = a[k + (k + 1) * a_dim1];
|
|
a[k + (k + 1) * a_dim1] = a[kp + (k + 1) * a_dim1];
|
|
a[kp + (k + 1) * a_dim1] = temp;
|
|
}
|
|
}
|
|
|
|
k += kstep;
|
|
goto L30;
|
|
L40:
|
|
|
|
;
|
|
} 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. */
|
|
|
|
k = *n;
|
|
L50:
|
|
|
|
/* If K < 1, exit from loop. */
|
|
|
|
if (k < 1) {
|
|
goto L60;
|
|
}
|
|
|
|
if (ipiv[k] > 0) {
|
|
|
|
/* 1 x 1 diagonal block */
|
|
|
|
/* Invert the diagonal block. */
|
|
|
|
a[k + k * a_dim1] = 1. / a[k + k * a_dim1];
|
|
|
|
/* Compute column K of the inverse. */
|
|
|
|
if (k < *n) {
|
|
i__1 = *n - k;
|
|
dcopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &work[1], &c__1);
|
|
i__1 = *n - k;
|
|
dsymv_(uplo, &i__1, &c_b11, &a[k + 1 + (k + 1) * a_dim1], lda,
|
|
&work[1], &c__1, &c_b13, &a[k + 1 + k * a_dim1], &
|
|
c__1);
|
|
i__1 = *n - k;
|
|
a[k + k * a_dim1] -= ddot_(&i__1, &work[1], &c__1, &a[k + 1 +
|
|
k * a_dim1], &c__1);
|
|
}
|
|
kstep = 1;
|
|
} else {
|
|
|
|
/* 2 x 2 diagonal block */
|
|
|
|
/* Invert the diagonal block. */
|
|
|
|
t = (d__1 = a[k + (k - 1) * a_dim1], abs(d__1));
|
|
ak = a[k - 1 + (k - 1) * a_dim1] / t;
|
|
akp1 = a[k + k * a_dim1] / t;
|
|
akkp1 = a[k + (k - 1) * a_dim1] / t;
|
|
d__ = t * (ak * akp1 - 1.);
|
|
a[k - 1 + (k - 1) * a_dim1] = akp1 / d__;
|
|
a[k + k * a_dim1] = ak / d__;
|
|
a[k + (k - 1) * a_dim1] = -akkp1 / d__;
|
|
|
|
/* Compute columns K-1 and K of the inverse. */
|
|
|
|
if (k < *n) {
|
|
i__1 = *n - k;
|
|
dcopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &work[1], &c__1);
|
|
i__1 = *n - k;
|
|
dsymv_(uplo, &i__1, &c_b11, &a[k + 1 + (k + 1) * a_dim1], lda,
|
|
&work[1], &c__1, &c_b13, &a[k + 1 + k * a_dim1], &
|
|
c__1);
|
|
i__1 = *n - k;
|
|
a[k + k * a_dim1] -= ddot_(&i__1, &work[1], &c__1, &a[k + 1 +
|
|
k * a_dim1], &c__1);
|
|
i__1 = *n - k;
|
|
a[k + (k - 1) * a_dim1] -= ddot_(&i__1, &a[k + 1 + k * a_dim1]
|
|
, &c__1, &a[k + 1 + (k - 1) * a_dim1], &c__1);
|
|
i__1 = *n - k;
|
|
dcopy_(&i__1, &a[k + 1 + (k - 1) * a_dim1], &c__1, &work[1], &
|
|
c__1);
|
|
i__1 = *n - k;
|
|
dsymv_(uplo, &i__1, &c_b11, &a[k + 1 + (k + 1) * a_dim1], lda,
|
|
&work[1], &c__1, &c_b13, &a[k + 1 + (k - 1) * a_dim1]
|
|
, &c__1);
|
|
i__1 = *n - k;
|
|
a[k - 1 + (k - 1) * a_dim1] -= ddot_(&i__1, &work[1], &c__1, &
|
|
a[k + 1 + (k - 1) * a_dim1], &c__1);
|
|
}
|
|
kstep = 2;
|
|
}
|
|
|
|
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) */
|
|
|
|
if (kp < *n) {
|
|
i__1 = *n - kp;
|
|
dswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + 1 + kp *
|
|
a_dim1], &c__1);
|
|
}
|
|
i__1 = kp - k - 1;
|
|
dswap_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[kp + (k + 1) *
|
|
a_dim1], lda);
|
|
temp = a[k + k * a_dim1];
|
|
a[k + k * a_dim1] = a[kp + kp * a_dim1];
|
|
a[kp + kp * a_dim1] = temp;
|
|
if (kstep == 2) {
|
|
temp = a[k + (k - 1) * a_dim1];
|
|
a[k + (k - 1) * a_dim1] = a[kp + (k - 1) * a_dim1];
|
|
a[kp + (k - 1) * a_dim1] = temp;
|
|
}
|
|
}
|
|
|
|
k -= kstep;
|
|
goto L50;
|
|
L60:
|
|
;
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of DSYTRI */
|
|
|
|
} /* dsytri_ */
|