#include "blaswrap.h" /* -- translated by f2c (version 19990503). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include "f2c.h" /* Subroutine */ int dgtsv_(integer *n, integer *nrhs, doublereal *dl, doublereal *d__, doublereal *du, doublereal *b, integer *ldb, integer *info) { /* System generated locals */ integer b_dim1, b_offset, i__1, i__2; doublereal d__1, d__2; /* Local variables */ static doublereal fact, temp; static integer i__, j; extern /* Subroutine */ int xerbla_(char *, integer *); #define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1] /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University October 31, 1999 Purpose ======= DGTSV 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) DOUBLE PRECISION array, dimension (N-1) On entry, DL must contain the (n-1) sub-diagonal elements of A. On exit, DL is overwritten by the (n-2) elements of the second super-diagonal of the upper triangular matrix U from the LU factorization of A, in DL(1), ..., DL(n-2). D (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N-1) On entry, DU must contain the (n-1) super-diagonal elements of A. On exit, DU is overwritten by the (n-1) elements of the first super-diagonal of U. B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the N by NRHS matrix of 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 */ --dl; --d__; --du; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; 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_("DGTSV ", &i__1); return 0; } if (*n == 0) { return 0; } if (*nrhs == 1) { i__1 = *n - 2; for (i__ = 1; i__ <= i__1; ++i__) { if ((d__1 = d__[i__], abs(d__1)) >= (d__2 = dl[i__], abs(d__2))) { /* No row interchange required */ if (d__[i__] != 0.) { fact = dl[i__] / d__[i__]; d__[i__ + 1] -= fact * du[i__]; b_ref(i__ + 1, 1) = b_ref(i__ + 1, 1) - fact * b_ref(i__, 1); } else { *info = i__; return 0; } dl[i__] = 0.; } else { /* Interchange rows I and I+1 */ fact = d__[i__] / dl[i__]; d__[i__] = dl[i__]; temp = d__[i__ + 1]; d__[i__ + 1] = du[i__] - fact * temp; dl[i__] = du[i__ + 1]; du[i__ + 1] = -fact * dl[i__]; du[i__] = temp; temp = b_ref(i__, 1); b_ref(i__, 1) = b_ref(i__ + 1, 1); b_ref(i__ + 1, 1) = temp - fact * b_ref(i__ + 1, 1); } /* L10: */ } if (*n > 1) { i__ = *n - 1; if ((d__1 = d__[i__], abs(d__1)) >= (d__2 = dl[i__], abs(d__2))) { if (d__[i__] != 0.) { fact = dl[i__] / d__[i__]; d__[i__ + 1] -= fact * du[i__]; b_ref(i__ + 1, 1) = b_ref(i__ + 1, 1) - fact * b_ref(i__, 1); } else { *info = i__; return 0; } } else { fact = d__[i__] / dl[i__]; d__[i__] = dl[i__]; temp = d__[i__ + 1]; d__[i__ + 1] = du[i__] - fact * temp; du[i__] = temp; temp = b_ref(i__, 1); b_ref(i__, 1) = b_ref(i__ + 1, 1); b_ref(i__ + 1, 1) = temp - fact * b_ref(i__ + 1, 1); } } if (d__[*n] == 0.) { *info = *n; return 0; } } else { i__1 = *n - 2; for (i__ = 1; i__ <= i__1; ++i__) { if ((d__1 = d__[i__], abs(d__1)) >= (d__2 = dl[i__], abs(d__2))) { /* No row interchange required */ if (d__[i__] != 0.) { fact = dl[i__] / d__[i__]; d__[i__ + 1] -= fact * du[i__]; i__2 = *nrhs; for (j = 1; j <= i__2; ++j) { b_ref(i__ + 1, j) = b_ref(i__ + 1, j) - fact * b_ref( i__, j); /* L20: */ } } else { *info = i__; return 0; } dl[i__] = 0.; } else { /* Interchange rows I and I+1 */ fact = d__[i__] / dl[i__]; d__[i__] = dl[i__]; temp = d__[i__ + 1]; d__[i__ + 1] = du[i__] - fact * temp; dl[i__] = du[i__ + 1]; du[i__ + 1] = -fact * dl[i__]; du[i__] = temp; i__2 = *nrhs; for (j = 1; j <= i__2; ++j) { temp = b_ref(i__, j); b_ref(i__, j) = b_ref(i__ + 1, j); b_ref(i__ + 1, j) = temp - fact * b_ref(i__ + 1, j); /* L30: */ } } /* L40: */ } if (*n > 1) { i__ = *n - 1; if ((d__1 = d__[i__], abs(d__1)) >= (d__2 = dl[i__], abs(d__2))) { if (d__[i__] != 0.) { fact = dl[i__] / d__[i__]; d__[i__ + 1] -= fact * du[i__]; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { b_ref(i__ + 1, j) = b_ref(i__ + 1, j) - fact * b_ref( i__, j); /* L50: */ } } else { *info = i__; return 0; } } else { fact = d__[i__] / dl[i__]; d__[i__] = dl[i__]; temp = d__[i__ + 1]; d__[i__ + 1] = du[i__] - fact * temp; du[i__] = temp; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { temp = b_ref(i__, j); b_ref(i__, j) = b_ref(i__ + 1, j); b_ref(i__ + 1, j) = temp - fact * b_ref(i__ + 1, j); /* L60: */ } } } if (d__[*n] == 0.) { *info = *n; return 0; } } /* Back solve with the matrix U from the factorization. */ if (*nrhs <= 2) { j = 1; L70: b_ref(*n, j) = b_ref(*n, j) / d__[*n]; if (*n > 1) { b_ref(*n - 1, j) = (b_ref(*n - 1, j) - du[*n - 1] * b_ref(*n, j)) / d__[*n - 1]; } for (i__ = *n - 2; i__ >= 1; --i__) { b_ref(i__, j) = (b_ref(i__, j) - du[i__] * b_ref(i__ + 1, j) - dl[ i__] * b_ref(i__ + 2, j)) / d__[i__]; /* L80: */ } if (j < *nrhs) { ++j; goto L70; } } else { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { b_ref(*n, j) = b_ref(*n, j) / d__[*n]; if (*n > 1) { b_ref(*n - 1, j) = (b_ref(*n - 1, j) - du[*n - 1] * b_ref(*n, j)) / d__[*n - 1]; } for (i__ = *n - 2; i__ >= 1; --i__) { b_ref(i__, j) = (b_ref(i__, j) - du[i__] * b_ref(i__ + 1, j) - dl[i__] * b_ref(i__ + 2, j)) / d__[i__]; /* L90: */ } /* L100: */ } } return 0; /* End of DGTSV */ } /* dgtsv_ */ #undef b_ref