#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int sgttrf_(integer *n, real *dl, real *d__, real *du, real * du2, integer *ipiv, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SGTTRF computes an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges. The factorization has the form A = L * U where L is a product of permutation and unit lower bidiagonal matrices and U is upper triangular with nonzeros in only the main diagonal and first two superdiagonals. Arguments ========= N (input) INTEGER The order of the matrix A. DL (input/output) REAL 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-1) multipliers that define the matrix L from the LU factorization of A. D (input/output) REAL array, dimension (N) On entry, D must contain the diagonal elements of A. On exit, D is overwritten by the n diagonal elements of the upper triangular matrix U from the LU factorization of A. DU (input/output) REAL 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. DU2 (output) REAL array, dimension (N-2) On exit, DU2 is overwritten by the (n-2) elements of the second super-diagonal of U. IPIV (output) INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value > 0: if INFO = k, U(k,k) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations. ===================================================================== Parameter adjustments */ /* System generated locals */ integer i__1; real r__1, r__2; /* Local variables */ static integer i__; static real fact, temp; extern /* Subroutine */ int xerbla_(char *, integer *); --ipiv; --du2; --du; --d__; --dl; /* Function Body */ *info = 0; if (*n < 0) { *info = -1; i__1 = -(*info); xerbla_("SGTTRF", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Initialize IPIV(i) = i and DU2(I) = 0 */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { ipiv[i__] = i__; /* L10: */ } i__1 = *n - 2; for (i__ = 1; i__ <= i__1; ++i__) { du2[i__] = 0.f; /* L20: */ } i__1 = *n - 2; for (i__ = 1; i__ <= i__1; ++i__) { if ((r__1 = d__[i__], dabs(r__1)) >= (r__2 = dl[i__], dabs(r__2))) { /* No row interchange required, eliminate DL(I) */ if (d__[i__] != 0.f) { fact = dl[i__] / d__[i__]; dl[i__] = fact; d__[i__ + 1] -= fact * du[i__]; } } else { /* Interchange rows I and I+1, eliminate DL(I) */ fact = d__[i__] / dl[i__]; d__[i__] = dl[i__]; dl[i__] = fact; temp = du[i__]; du[i__] = d__[i__ + 1]; d__[i__ + 1] = temp - fact * d__[i__ + 1]; du2[i__] = du[i__ + 1]; du[i__ + 1] = -fact * du[i__ + 1]; ipiv[i__] = i__ + 1; } /* L30: */ } if (*n > 1) { i__ = *n - 1; if ((r__1 = d__[i__], dabs(r__1)) >= (r__2 = dl[i__], dabs(r__2))) { if (d__[i__] != 0.f) { fact = dl[i__] / d__[i__]; dl[i__] = fact; d__[i__ + 1] -= fact * du[i__]; } } else { fact = d__[i__] / dl[i__]; d__[i__] = dl[i__]; dl[i__] = fact; temp = du[i__]; du[i__] = d__[i__ + 1]; d__[i__ + 1] = temp - fact * d__[i__ + 1]; ipiv[i__] = i__ + 1; } } /* Check for a zero on the diagonal of U. */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (d__[i__] == 0.f) { *info = i__; goto L50; } /* L40: */ } L50: return 0; /* End of SGTTRF */ } /* sgttrf_ */