/* 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 "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 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_ */