#include "f2c.h" #include "blaswrap.h" /* Table of constant values */ static doublereal c_b7 = -1.; static integer c__1 = 1; static doublereal c_b23 = 1.; /* Subroutine */ int dgbtrs_(char *trans, integer *n, integer *kl, integer * ku, integer *nrhs, doublereal *ab, integer *ldab, integer *ipiv, doublereal *b, integer *ldb, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, b_dim1, b_offset, i__1, i__2, i__3; /* Local variables */ integer i__, j, l, kd, lm; extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *), dswap_(integer *, doublereal *, integer *, doublereal *, integer *), dtbsv_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *); logical lnoti; extern /* Subroutine */ int xerbla_(char *, integer *); logical notran; /* -- LAPACK routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DGBTRS solves a system of linear equations */ /* A * X = B or A' * X = B */ /* with a general band matrix A using the LU factorization computed */ /* by DGBTRF. */ /* Arguments */ /* ========= */ /* TRANS (input) CHARACTER*1 */ /* Specifies the form of the system of equations. */ /* = 'N': A * X = B (No transpose) */ /* = 'T': A'* X = B (Transpose) */ /* = 'C': A'* X = B (Conjugate transpose = Transpose) */ /* N (input) INTEGER */ /* The order of the matrix A. N >= 0. */ /* KL (input) INTEGER */ /* The number of subdiagonals within the band of A. KL >= 0. */ /* KU (input) INTEGER */ /* The number of superdiagonals within the band of A. KU >= 0. */ /* NRHS (input) INTEGER */ /* The number of right hand sides, i.e., the number of columns */ /* of the matrix B. NRHS >= 0. */ /* AB (input) DOUBLE PRECISION array, dimension (LDAB,N) */ /* Details of the LU factorization of the band matrix A, as */ /* computed by DGBTRF. U is stored as an upper triangular band */ /* matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */ /* the multipliers used during the factorization are stored in */ /* rows KL+KU+2 to 2*KL+KU+1. */ /* LDAB (input) INTEGER */ /* The leading dimension of the array AB. LDAB >= 2*KL+KU+1. */ /* IPIV (input) INTEGER array, dimension (N) */ /* The pivot indices; for 1 <= i <= N, row i of the matrix was */ /* interchanged with row IPIV(i). */ /* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */ /* On entry, the right hand side matrix B. */ /* On exit, the 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 */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; --ipiv; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; /* Function Body */ *info = 0; notran = lsame_(trans, "N"); if (! notran && ! lsame_(trans, "T") && ! lsame_( trans, "C")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*kl < 0) { *info = -3; } else if (*ku < 0) { *info = -4; } else if (*nrhs < 0) { *info = -5; } else if (*ldab < (*kl << 1) + *ku + 1) { *info = -7; } else if (*ldb < max(1,*n)) { *info = -10; } if (*info != 0) { i__1 = -(*info); xerbla_("DGBTRS", &i__1); return 0; } /* Quick return if possible */ if (*n == 0 || *nrhs == 0) { return 0; } kd = *ku + *kl + 1; lnoti = *kl > 0; if (notran) { /* Solve A*X = B. */ /* Solve L*X = B, overwriting B with X. */ /* L is represented as a product of permutations and unit lower */ /* triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1), */ /* where each transformation L(i) is a rank-one modification of */ /* the identity matrix. */ if (lnoti) { i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ i__2 = *kl, i__3 = *n - j; lm = min(i__2,i__3); l = ipiv[j]; if (l != j) { dswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb); } dger_(&lm, nrhs, &c_b7, &ab[kd + 1 + j * ab_dim1], &c__1, &b[ j + b_dim1], ldb, &b[j + 1 + b_dim1], ldb); /* L10: */ } } i__1 = *nrhs; for (i__ = 1; i__ <= i__1; ++i__) { /* Solve U*X = B, overwriting B with X. */ i__2 = *kl + *ku; dtbsv_("Upper", "No transpose", "Non-unit", n, &i__2, &ab[ ab_offset], ldab, &b[i__ * b_dim1 + 1], &c__1); /* L20: */ } } else { /* Solve A'*X = B. */ i__1 = *nrhs; for (i__ = 1; i__ <= i__1; ++i__) { /* Solve U'*X = B, overwriting B with X. */ i__2 = *kl + *ku; dtbsv_("Upper", "Transpose", "Non-unit", n, &i__2, &ab[ab_offset], ldab, &b[i__ * b_dim1 + 1], &c__1); /* L30: */ } /* Solve L'*X = B, overwriting B with X. */ if (lnoti) { for (j = *n - 1; j >= 1; --j) { /* Computing MIN */ i__1 = *kl, i__2 = *n - j; lm = min(i__1,i__2); dgemv_("Transpose", &lm, nrhs, &c_b7, &b[j + 1 + b_dim1], ldb, &ab[kd + 1 + j * ab_dim1], &c__1, &c_b23, &b[j + b_dim1], ldb); l = ipiv[j]; if (l != j) { dswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb); } /* L40: */ } } } return 0; /* End of DGBTRS */ } /* dgbtrs_ */