#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int chetri_(char *uplo, integer *n, complex *a, integer *lda, integer *ipiv, complex *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 September 30, 1994 Purpose ======= CHETRI computes the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF. 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**H; = 'L': Lower triangular, form is A = L*D*L**H. N (input) INTEGER The order of the matrix A. N >= 0. A (input/output) COMPLEX 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 CHETRF. On exit, if INFO = 0, the (Hermitian) 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 CHETRF. WORK (workspace) COMPLEX 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 complex c_b2 = {0.f,0.f}; static integer c__1 = 1; /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; real r__1; complex q__1, q__2; /* Builtin functions */ double c_abs(complex *); void r_cnjg(complex *, complex *); /* Local variables */ static complex temp, akkp1; static real d__; static integer j, k; static real t; extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer *, complex *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int chemv_(char *, integer *, complex *, complex * , integer *, complex *, integer *, complex *, complex *, integer * ), ccopy_(integer *, complex *, integer *, complex *, integer *), cswap_(integer *, complex *, integer *, complex *, integer *); static integer kstep; static logical upper; static real ak; static integer kp; extern /* Subroutine */ int xerbla_(char *, integer *); static real akp1; #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] 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_("CHETRI", &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)) { i__1 = a_subscr(*info, *info); if (ipiv[*info] > 0 && (a[i__1].r == 0.f && a[i__1].i == 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)) { i__2 = a_subscr(*info, *info); if (ipiv[*info] > 0 && (a[i__2].r == 0.f && a[i__2].i == 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 L50; } if (ipiv[k] > 0) { /* 1 x 1 diagonal block Invert the diagonal block. */ i__1 = a_subscr(k, k); i__2 = a_subscr(k, k); r__1 = 1.f / a[i__2].r; a[i__1].r = r__1, a[i__1].i = 0.f; /* Compute column K of the inverse. */ if (k > 1) { i__1 = k - 1; ccopy_(&i__1, &a_ref(1, k), &c__1, &work[1], &c__1); i__1 = k - 1; q__1.r = -1.f, q__1.i = 0.f; chemv_(uplo, &i__1, &q__1, &a[a_offset], lda, &work[1], &c__1, &c_b2, &a_ref(1, k), &c__1); i__1 = a_subscr(k, k); i__2 = a_subscr(k, k); i__3 = k - 1; cdotc_(&q__2, &i__3, &work[1], &c__1, &a_ref(1, k), &c__1); r__1 = q__2.r; q__1.r = a[i__2].r - r__1, q__1.i = a[i__2].i; a[i__1].r = q__1.r, a[i__1].i = q__1.i; } kstep = 1; } else { /* 2 x 2 diagonal block Invert the diagonal block. */ t = c_abs(&a_ref(k, k + 1)); i__1 = a_subscr(k, k); ak = a[i__1].r / t; i__1 = a_subscr(k + 1, k + 1); akp1 = a[i__1].r / t; i__1 = a_subscr(k, k + 1); q__1.r = a[i__1].r / t, q__1.i = a[i__1].i / t; akkp1.r = q__1.r, akkp1.i = q__1.i; d__ = t * (ak * akp1 - 1.f); i__1 = a_subscr(k, k); r__1 = akp1 / d__; a[i__1].r = r__1, a[i__1].i = 0.f; i__1 = a_subscr(k + 1, k + 1); r__1 = ak / d__; a[i__1].r = r__1, a[i__1].i = 0.f; i__1 = a_subscr(k, k + 1); q__2.r = -akkp1.r, q__2.i = -akkp1.i; q__1.r = q__2.r / d__, q__1.i = q__2.i / d__; a[i__1].r = q__1.r, a[i__1].i = q__1.i; /* Compute columns K and K+1 of the inverse. */ if (k > 1) { i__1 = k - 1; ccopy_(&i__1, &a_ref(1, k), &c__1, &work[1], &c__1); i__1 = k - 1; q__1.r = -1.f, q__1.i = 0.f; chemv_(uplo, &i__1, &q__1, &a[a_offset], lda, &work[1], &c__1, &c_b2, &a_ref(1, k), &c__1); i__1 = a_subscr(k, k); i__2 = a_subscr(k, k); i__3 = k - 1; cdotc_(&q__2, &i__3, &work[1], &c__1, &a_ref(1, k), &c__1); r__1 = q__2.r; q__1.r = a[i__2].r - r__1, q__1.i = a[i__2].i; a[i__1].r = q__1.r, a[i__1].i = q__1.i; i__1 = a_subscr(k, k + 1); i__2 = a_subscr(k, k + 1); i__3 = k - 1; cdotc_(&q__2, &i__3, &a_ref(1, k), &c__1, &a_ref(1, k + 1), & c__1); q__1.r = a[i__2].r - q__2.r, q__1.i = a[i__2].i - q__2.i; a[i__1].r = q__1.r, a[i__1].i = q__1.i; i__1 = k - 1; ccopy_(&i__1, &a_ref(1, k + 1), &c__1, &work[1], &c__1); i__1 = k - 1; q__1.r = -1.f, q__1.i = 0.f; chemv_(uplo, &i__1, &q__1, &a[a_offset], lda, &work[1], &c__1, &c_b2, &a_ref(1, k + 1), &c__1); i__1 = a_subscr(k + 1, k + 1); i__2 = a_subscr(k + 1, k + 1); i__3 = k - 1; cdotc_(&q__2, &i__3, &work[1], &c__1, &a_ref(1, k + 1), &c__1) ; r__1 = q__2.r; q__1.r = a[i__2].r - r__1, q__1.i = a[i__2].i; a[i__1].r = q__1.r, a[i__1].i = q__1.i; } 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; cswap_(&i__1, &a_ref(1, k), &c__1, &a_ref(1, kp), &c__1); i__1 = k - 1; for (j = kp + 1; j <= i__1; ++j) { r_cnjg(&q__1, &a_ref(j, k)); temp.r = q__1.r, temp.i = q__1.i; i__2 = a_subscr(j, k); r_cnjg(&q__1, &a_ref(kp, j)); a[i__2].r = q__1.r, a[i__2].i = q__1.i; i__2 = a_subscr(kp, j); a[i__2].r = temp.r, a[i__2].i = temp.i; /* L40: */ } i__1 = a_subscr(kp, k); r_cnjg(&q__1, &a_ref(kp, k)); a[i__1].r = q__1.r, a[i__1].i = q__1.i; i__1 = a_subscr(k, k); temp.r = a[i__1].r, temp.i = a[i__1].i; i__1 = a_subscr(k, k); i__2 = a_subscr(kp, kp); a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i; i__1 = a_subscr(kp, kp); a[i__1].r = temp.r, a[i__1].i = temp.i; if (kstep == 2) { i__1 = a_subscr(k, k + 1); temp.r = a[i__1].r, temp.i = a[i__1].i; i__1 = a_subscr(k, k + 1); i__2 = a_subscr(kp, k + 1); a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i; i__1 = a_subscr(kp, k + 1); a[i__1].r = temp.r, a[i__1].i = temp.i; } } k += kstep; 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. */ k = *n; L60: /* If K < 1, exit from loop. */ if (k < 1) { goto L80; } if (ipiv[k] > 0) { /* 1 x 1 diagonal block Invert the diagonal block. */ i__1 = a_subscr(k, k); i__2 = a_subscr(k, k); r__1 = 1.f / a[i__2].r; a[i__1].r = r__1, a[i__1].i = 0.f; /* Compute column K of the inverse. */ if (k < *n) { i__1 = *n - k; ccopy_(&i__1, &a_ref(k + 1, k), &c__1, &work[1], &c__1); i__1 = *n - k; q__1.r = -1.f, q__1.i = 0.f; chemv_(uplo, &i__1, &q__1, &a_ref(k + 1, k + 1), lda, &work[1] , &c__1, &c_b2, &a_ref(k + 1, k), &c__1); i__1 = a_subscr(k, k); i__2 = a_subscr(k, k); i__3 = *n - k; cdotc_(&q__2, &i__3, &work[1], &c__1, &a_ref(k + 1, k), &c__1) ; r__1 = q__2.r; q__1.r = a[i__2].r - r__1, q__1.i = a[i__2].i; a[i__1].r = q__1.r, a[i__1].i = q__1.i; } kstep = 1; } else { /* 2 x 2 diagonal block Invert the diagonal block. */ t = c_abs(&a_ref(k, k - 1)); i__1 = a_subscr(k - 1, k - 1); ak = a[i__1].r / t; i__1 = a_subscr(k, k); akp1 = a[i__1].r / t; i__1 = a_subscr(k, k - 1); q__1.r = a[i__1].r / t, q__1.i = a[i__1].i / t; akkp1.r = q__1.r, akkp1.i = q__1.i; d__ = t * (ak * akp1 - 1.f); i__1 = a_subscr(k - 1, k - 1); r__1 = akp1 / d__; a[i__1].r = r__1, a[i__1].i = 0.f; i__1 = a_subscr(k, k); r__1 = ak / d__; a[i__1].r = r__1, a[i__1].i = 0.f; i__1 = a_subscr(k, k - 1); q__2.r = -akkp1.r, q__2.i = -akkp1.i; q__1.r = q__2.r / d__, q__1.i = q__2.i / d__; a[i__1].r = q__1.r, a[i__1].i = q__1.i; /* Compute columns K-1 and K of the inverse. */ if (k < *n) { i__1 = *n - k; ccopy_(&i__1, &a_ref(k + 1, k), &c__1, &work[1], &c__1); i__1 = *n - k; q__1.r = -1.f, q__1.i = 0.f; chemv_(uplo, &i__1, &q__1, &a_ref(k + 1, k + 1), lda, &work[1] , &c__1, &c_b2, &a_ref(k + 1, k), &c__1); i__1 = a_subscr(k, k); i__2 = a_subscr(k, k); i__3 = *n - k; cdotc_(&q__2, &i__3, &work[1], &c__1, &a_ref(k + 1, k), &c__1) ; r__1 = q__2.r; q__1.r = a[i__2].r - r__1, q__1.i = a[i__2].i; a[i__1].r = q__1.r, a[i__1].i = q__1.i; i__1 = a_subscr(k, k - 1); i__2 = a_subscr(k, k - 1); i__3 = *n - k; cdotc_(&q__2, &i__3, &a_ref(k + 1, k), &c__1, &a_ref(k + 1, k - 1), &c__1); q__1.r = a[i__2].r - q__2.r, q__1.i = a[i__2].i - q__2.i; a[i__1].r = q__1.r, a[i__1].i = q__1.i; i__1 = *n - k; ccopy_(&i__1, &a_ref(k + 1, k - 1), &c__1, &work[1], &c__1); i__1 = *n - k; q__1.r = -1.f, q__1.i = 0.f; chemv_(uplo, &i__1, &q__1, &a_ref(k + 1, k + 1), lda, &work[1] , &c__1, &c_b2, &a_ref(k + 1, k - 1), &c__1); i__1 = a_subscr(k - 1, k - 1); i__2 = a_subscr(k - 1, k - 1); i__3 = *n - k; cdotc_(&q__2, &i__3, &work[1], &c__1, &a_ref(k + 1, k - 1), & c__1); r__1 = q__2.r; q__1.r = a[i__2].r - r__1, q__1.i = a[i__2].i; a[i__1].r = q__1.r, a[i__1].i = q__1.i; } 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; cswap_(&i__1, &a_ref(kp + 1, k), &c__1, &a_ref(kp + 1, kp), & c__1); } i__1 = kp - 1; for (j = k + 1; j <= i__1; ++j) { r_cnjg(&q__1, &a_ref(j, k)); temp.r = q__1.r, temp.i = q__1.i; i__2 = a_subscr(j, k); r_cnjg(&q__1, &a_ref(kp, j)); a[i__2].r = q__1.r, a[i__2].i = q__1.i; i__2 = a_subscr(kp, j); a[i__2].r = temp.r, a[i__2].i = temp.i; /* L70: */ } i__1 = a_subscr(kp, k); r_cnjg(&q__1, &a_ref(kp, k)); a[i__1].r = q__1.r, a[i__1].i = q__1.i; i__1 = a_subscr(k, k); temp.r = a[i__1].r, temp.i = a[i__1].i; i__1 = a_subscr(k, k); i__2 = a_subscr(kp, kp); a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i; i__1 = a_subscr(kp, kp); a[i__1].r = temp.r, a[i__1].i = temp.i; if (kstep == 2) { i__1 = a_subscr(k, k - 1); temp.r = a[i__1].r, temp.i = a[i__1].i; i__1 = a_subscr(k, k - 1); i__2 = a_subscr(kp, k - 1); a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i; i__1 = a_subscr(kp, k - 1); a[i__1].r = temp.r, a[i__1].i = temp.i; } } k -= kstep; goto L60; L80: ; } return 0; /* End of CHETRI */ } /* chetri_ */ #undef a_ref #undef a_subscr