#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int cgtsv_(integer *n, integer *nrhs, complex *dl, complex * d__, complex *du, complex *b, integer *ldb, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= CGTSV solves the equation A*X = B, where A is an N-by-N tridiagonal matrix, by Gaussian elimination with partial pivoting. Note that the equation A'*X = B may be solved by interchanging the order of the arguments DU and DL. Arguments ========= N (input) INTEGER The order of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. DL (input/output) COMPLEX array, dimension (N-1) On entry, DL must contain the (n-1) subdiagonal elements of A. On exit, DL is overwritten by the (n-2) elements of the second superdiagonal of the upper triangular matrix U from the LU factorization of A, in DL(1), ..., DL(n-2). D (input/output) COMPLEX array, dimension (N) On entry, D must contain the diagonal elements of A. On exit, D is overwritten by the n diagonal elements of U. DU (input/output) COMPLEX array, dimension (N-1) On entry, DU must contain the (n-1) superdiagonal elements of A. On exit, DU is overwritten by the (n-1) elements of the first superdiagonal of U. B (input/output) COMPLEX array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = N. ===================================================================== Parameter adjustments */ /* System generated locals */ integer b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7; real r__1, r__2, r__3, r__4; complex q__1, q__2, q__3, q__4, q__5; /* Builtin functions */ double r_imag(complex *); void c_div(complex *, complex *, complex *); /* Local variables */ static integer j, k; static complex temp, mult; extern /* Subroutine */ int xerbla_(char *, integer *); --dl; --d__; --du; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; /* Function Body */ *info = 0; if (*n < 0) { *info = -1; } else if (*nrhs < 0) { *info = -2; } else if (*ldb < max(1,*n)) { *info = -7; } if (*info != 0) { i__1 = -(*info); xerbla_("CGTSV ", &i__1); return 0; } if (*n == 0) { return 0; } i__1 = *n - 1; for (k = 1; k <= i__1; ++k) { i__2 = k; if (dl[i__2].r == 0.f && dl[i__2].i == 0.f) { /* Subdiagonal is zero, no elimination is required. */ i__2 = k; if (d__[i__2].r == 0.f && d__[i__2].i == 0.f) { /* Diagonal is zero: set INFO = K and return; a unique solution can not be found. */ *info = k; return 0; } } else /* if(complicated condition) */ { i__2 = k; i__3 = k; if ((r__1 = d__[i__2].r, dabs(r__1)) + (r__2 = r_imag(&d__[k]), dabs(r__2)) >= (r__3 = dl[i__3].r, dabs(r__3)) + (r__4 = r_imag(&dl[k]), dabs(r__4))) { /* No row interchange required */ c_div(&q__1, &dl[k], &d__[k]); mult.r = q__1.r, mult.i = q__1.i; i__2 = k + 1; i__3 = k + 1; i__4 = k; q__2.r = mult.r * du[i__4].r - mult.i * du[i__4].i, q__2.i = mult.r * du[i__4].i + mult.i * du[i__4].r; q__1.r = d__[i__3].r - q__2.r, q__1.i = d__[i__3].i - q__2.i; d__[i__2].r = q__1.r, d__[i__2].i = q__1.i; i__2 = *nrhs; for (j = 1; j <= i__2; ++j) { i__3 = k + 1 + j * b_dim1; i__4 = k + 1 + j * b_dim1; i__5 = k + j * b_dim1; q__2.r = mult.r * b[i__5].r - mult.i * b[i__5].i, q__2.i = mult.r * b[i__5].i + mult.i * b[i__5].r; q__1.r = b[i__4].r - q__2.r, q__1.i = b[i__4].i - q__2.i; b[i__3].r = q__1.r, b[i__3].i = q__1.i; /* L10: */ } if (k < *n - 1) { i__2 = k; dl[i__2].r = 0.f, dl[i__2].i = 0.f; } } else { /* Interchange rows K and K+1 */ c_div(&q__1, &d__[k], &dl[k]); mult.r = q__1.r, mult.i = q__1.i; i__2 = k; i__3 = k; d__[i__2].r = dl[i__3].r, d__[i__2].i = dl[i__3].i; i__2 = k + 1; temp.r = d__[i__2].r, temp.i = d__[i__2].i; i__2 = k + 1; i__3 = k; q__2.r = mult.r * temp.r - mult.i * temp.i, q__2.i = mult.r * temp.i + mult.i * temp.r; q__1.r = du[i__3].r - q__2.r, q__1.i = du[i__3].i - q__2.i; d__[i__2].r = q__1.r, d__[i__2].i = q__1.i; if (k < *n - 1) { i__2 = k; i__3 = k + 1; dl[i__2].r = du[i__3].r, dl[i__2].i = du[i__3].i; i__2 = k + 1; q__2.r = -mult.r, q__2.i = -mult.i; i__3 = k; q__1.r = q__2.r * dl[i__3].r - q__2.i * dl[i__3].i, q__1.i = q__2.r * dl[i__3].i + q__2.i * dl[i__3] .r; du[i__2].r = q__1.r, du[i__2].i = q__1.i; } i__2 = k; du[i__2].r = temp.r, du[i__2].i = temp.i; i__2 = *nrhs; for (j = 1; j <= i__2; ++j) { i__3 = k + j * b_dim1; temp.r = b[i__3].r, temp.i = b[i__3].i; i__3 = k + j * b_dim1; i__4 = k + 1 + j * b_dim1; b[i__3].r = b[i__4].r, b[i__3].i = b[i__4].i; i__3 = k + 1 + j * b_dim1; i__4 = k + 1 + j * b_dim1; q__2.r = mult.r * b[i__4].r - mult.i * b[i__4].i, q__2.i = mult.r * b[i__4].i + mult.i * b[i__4].r; q__1.r = temp.r - q__2.r, q__1.i = temp.i - q__2.i; b[i__3].r = q__1.r, b[i__3].i = q__1.i; /* L20: */ } } } /* L30: */ } i__1 = *n; if (d__[i__1].r == 0.f && d__[i__1].i == 0.f) { *info = *n; return 0; } /* Back solve with the matrix U from the factorization. */ i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n + j * b_dim1; c_div(&q__1, &b[*n + j * b_dim1], &d__[*n]); b[i__2].r = q__1.r, b[i__2].i = q__1.i; if (*n > 1) { i__2 = *n - 1 + j * b_dim1; i__3 = *n - 1 + j * b_dim1; i__4 = *n - 1; i__5 = *n + j * b_dim1; q__3.r = du[i__4].r * b[i__5].r - du[i__4].i * b[i__5].i, q__3.i = du[i__4].r * b[i__5].i + du[i__4].i * b[i__5].r; q__2.r = b[i__3].r - q__3.r, q__2.i = b[i__3].i - q__3.i; c_div(&q__1, &q__2, &d__[*n - 1]); b[i__2].r = q__1.r, b[i__2].i = q__1.i; } for (k = *n - 2; k >= 1; --k) { i__2 = k + j * b_dim1; i__3 = k + j * b_dim1; i__4 = k; i__5 = k + 1 + j * b_dim1; q__4.r = du[i__4].r * b[i__5].r - du[i__4].i * b[i__5].i, q__4.i = du[i__4].r * b[i__5].i + du[i__4].i * b[i__5].r; q__3.r = b[i__3].r - q__4.r, q__3.i = b[i__3].i - q__4.i; i__6 = k; i__7 = k + 2 + j * b_dim1; q__5.r = dl[i__6].r * b[i__7].r - dl[i__6].i * b[i__7].i, q__5.i = dl[i__6].r * b[i__7].i + dl[i__6].i * b[i__7].r; q__2.r = q__3.r - q__5.r, q__2.i = q__3.i - q__5.i; c_div(&q__1, &q__2, &d__[k]); b[i__2].r = q__1.r, b[i__2].i = q__1.i; /* L40: */ } /* L50: */ } return 0; /* End of CGTSV */ } /* cgtsv_ */