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opencv/3rdparty/lapack/dsytri.c

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#include "clapack.h"
/* Subroutine */ int dsytri_(char *uplo, integer *n, doublereal *a, integer *
lda, integer *ipiv, doublereal *work, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
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.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static doublereal c_b11 = -1.;
static doublereal c_b13 = 0.;
/* System generated locals */
integer a_dim1, a_offset, i__1;
doublereal d__1;
/* Local variables */
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
static doublereal temp, akkp1, d__;
static integer k;
static doublereal t;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), dswap_(integer *, doublereal *, integer
*, doublereal *, integer *);
static integer kstep;
static logical upper;
extern /* Subroutine */ int dsymv_(char *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *);
static doublereal ak;
static integer kp;
extern /* Subroutine */ int xerbla_(char *, integer *);
static doublereal akp1;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
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_ref(*info, *info) == 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_ref(*info, *info) == 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_ref(k, k) = 1. / a_ref(k, k);
/* Compute column K of the inverse. */
if (k > 1) {
i__1 = k - 1;
dcopy_(&i__1, &a_ref(1, k), &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_ref(1, k), &c__1);
i__1 = k - 1;
a_ref(k, k) = a_ref(k, k) - ddot_(&i__1, &work[1], &c__1, &
a_ref(1, k), &c__1);
}
kstep = 1;
} else {
/* 2 x 2 diagonal block
Invert the diagonal block. */
t = (d__1 = a_ref(k, k + 1), abs(d__1));
ak = a_ref(k, k) / t;
akp1 = a_ref(k + 1, k + 1) / t;
akkp1 = a_ref(k, k + 1) / t;
d__ = t * (ak * akp1 - 1.);
a_ref(k, k) = akp1 / d__;
a_ref(k + 1, k + 1) = ak / d__;
a_ref(k, k + 1) = -akkp1 / d__;
/* Compute columns K and K+1 of the inverse. */
if (k > 1) {
i__1 = k - 1;
dcopy_(&i__1, &a_ref(1, k), &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_ref(1, k), &c__1);
i__1 = k - 1;
a_ref(k, k) = a_ref(k, k) - ddot_(&i__1, &work[1], &c__1, &
a_ref(1, k), &c__1);
i__1 = k - 1;
a_ref(k, k + 1) = a_ref(k, k + 1) - ddot_(&i__1, &a_ref(1, k),
&c__1, &a_ref(1, k + 1), &c__1);
i__1 = k - 1;
dcopy_(&i__1, &a_ref(1, k + 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_ref(1, k + 1), &c__1);
i__1 = k - 1;
a_ref(k + 1, k + 1) = a_ref(k + 1, k + 1) - ddot_(&i__1, &
work[1], &c__1, &a_ref(1, k + 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_ref(1, k), &c__1, &a_ref(1, kp), &c__1);
i__1 = k - kp - 1;
dswap_(&i__1, &a_ref(kp + 1, k), &c__1, &a_ref(kp, kp + 1), lda);
temp = a_ref(k, k);
a_ref(k, k) = a_ref(kp, kp);
a_ref(kp, kp) = temp;
if (kstep == 2) {
temp = a_ref(k, k + 1);
a_ref(k, k + 1) = a_ref(kp, k + 1);
a_ref(kp, k + 1) = 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_ref(k, k) = 1. / a_ref(k, k);
/* Compute column K of the inverse. */
if (k < *n) {
i__1 = *n - k;
dcopy_(&i__1, &a_ref(k + 1, k), &c__1, &work[1], &c__1);
i__1 = *n - k;
dsymv_(uplo, &i__1, &c_b11, &a_ref(k + 1, k + 1), lda, &work[
1], &c__1, &c_b13, &a_ref(k + 1, k), &c__1)
;
i__1 = *n - k;
a_ref(k, k) = a_ref(k, k) - ddot_(&i__1, &work[1], &c__1, &
a_ref(k + 1, k), &c__1);
}
kstep = 1;
} else {
/* 2 x 2 diagonal block
Invert the diagonal block. */
t = (d__1 = a_ref(k, k - 1), abs(d__1));
ak = a_ref(k - 1, k - 1) / t;
akp1 = a_ref(k, k) / t;
akkp1 = a_ref(k, k - 1) / t;
d__ = t * (ak * akp1 - 1.);
a_ref(k - 1, k - 1) = akp1 / d__;
a_ref(k, k) = ak / d__;
a_ref(k, k - 1) = -akkp1 / d__;
/* Compute columns K-1 and K of the inverse. */
if (k < *n) {
i__1 = *n - k;
dcopy_(&i__1, &a_ref(k + 1, k), &c__1, &work[1], &c__1);
i__1 = *n - k;
dsymv_(uplo, &i__1, &c_b11, &a_ref(k + 1, k + 1), lda, &work[
1], &c__1, &c_b13, &a_ref(k + 1, k), &c__1)
;
i__1 = *n - k;
a_ref(k, k) = a_ref(k, k) - ddot_(&i__1, &work[1], &c__1, &
a_ref(k + 1, k), &c__1);
i__1 = *n - k;
a_ref(k, k - 1) = a_ref(k, k - 1) - ddot_(&i__1, &a_ref(k + 1,
k), &c__1, &a_ref(k + 1, k - 1), &c__1);
i__1 = *n - k;
dcopy_(&i__1, &a_ref(k + 1, k - 1), &c__1, &work[1], &c__1);
i__1 = *n - k;
dsymv_(uplo, &i__1, &c_b11, &a_ref(k + 1, k + 1), lda, &work[
1], &c__1, &c_b13, &a_ref(k + 1, k - 1), &c__1);
i__1 = *n - k;
a_ref(k - 1, k - 1) = a_ref(k - 1, k - 1) - ddot_(&i__1, &
work[1], &c__1, &a_ref(k + 1, k - 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 trailing
submatrix A(k-1:n,k-1:n) */
if (kp < *n) {
i__1 = *n - kp;
dswap_(&i__1, &a_ref(kp + 1, k), &c__1, &a_ref(kp + 1, kp), &
c__1);
}
i__1 = kp - k - 1;
dswap_(&i__1, &a_ref(k + 1, k), &c__1, &a_ref(kp, k + 1), lda);
temp = a_ref(k, k);
a_ref(k, k) = a_ref(kp, kp);
a_ref(kp, kp) = temp;
if (kstep == 2) {
temp = a_ref(k, k - 1);
a_ref(k, k - 1) = a_ref(kp, k - 1);
a_ref(kp, k - 1) = temp;
}
}
k -= kstep;
goto L50;
L60:
;
}
return 0;
/* End of DSYTRI */
} /* dsytri_ */
#undef a_ref
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