/* ssytri.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 real c_b11 = -1.f;
static real c_b13 = 0.f;
/* Subroutine */ int ssytri_(char *uplo, integer *n, real *a, integer *lda,
integer *ipiv, real *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1;
real r__1;
/* Local variables */
real d__;
integer k;
real t, ak;
integer kp;
real akp1, temp;
extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
real akkp1;
extern logical lsame_(char *, char *);
integer kstep;
logical upper;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *), sswap_(integer *, real *, integer *, real *, integer *
), ssymv_(char *, integer *, real *, real *, integer *, real *,
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 */
/* ======= */
/* SSYTRI 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 */
/* SSYTRF. */
/* 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) REAL 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 SSYTRF. */
/* 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 SSYTRF. */
/* WORK (workspace) REAL 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_("SSYTRI", &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.f) {
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.f) {
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.f / a[k + k * a_dim1];
/* Compute column K of the inverse. */
if (k > 1) {
i__1 = k - 1;
scopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &work[1], &c__1);
i__1 = k - 1;
ssymv_(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] -= sdot_(&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 = (r__1 = a[k + (k + 1) * a_dim1], dabs(r__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.f);
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;
scopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &work[1], &c__1);
i__1 = k - 1;
ssymv_(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] -= sdot_(&i__1, &work[1], &c__1, &a[k *
a_dim1 + 1], &c__1);
i__1 = k - 1;
a[k + (k + 1) * a_dim1] -= sdot_(&i__1, &a[k * a_dim1 + 1], &
c__1, &a[(k + 1) * a_dim1 + 1], &c__1);
i__1 = k - 1;
scopy_(&i__1, &a[(k + 1) * a_dim1 + 1], &c__1, &work[1], &
c__1);
i__1 = k - 1;
ssymv_(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] -= sdot_(&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;
sswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &
c__1);
i__1 = k - kp - 1;
sswap_(&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.f / a[k + k * a_dim1];
/* Compute column K of the inverse. */
if (k < *n) {
i__1 = *n - k;
scopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &work[1], &c__1);
i__1 = *n - k;
ssymv_(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] -= sdot_(&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 = (r__1 = a[k + (k - 1) * a_dim1], dabs(r__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.f);
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;
scopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &work[1], &c__1);
i__1 = *n - k;
ssymv_(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] -= sdot_(&i__1, &work[1], &c__1, &a[k + 1 +
k * a_dim1], &c__1);
i__1 = *n - k;
a[k + (k - 1) * a_dim1] -= sdot_(&i__1, &a[k + 1 + k * a_dim1]
, &c__1, &a[k + 1 + (k - 1) * a_dim1], &c__1);
i__1 = *n - k;
scopy_(&i__1, &a[k + 1 + (k - 1) * a_dim1], &c__1, &work[1], &
c__1);
i__1 = *n - k;
ssymv_(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] -= sdot_(&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;
sswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + 1 + kp *
a_dim1], &c__1);
}
i__1 = kp - k - 1;
sswap_(&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 SSYTRI */
} /* ssytri_ */
