#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int cgbtrs_(char *trans, integer *n, integer *kl, integer * ku, integer *nrhs, complex *ab, integer *ldab, integer *ipiv, complex *b, integer *ldb, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= CGBTRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general band matrix A using the LU factorization computed by CGBTRF. Arguments ========= TRANS (input) CHARACTER*1 Specifies the form of the system of equations. = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate 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) COMPLEX array, dimension (LDAB,N) Details of the LU factorization of the band matrix A, as computed by CGBTRF. 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) COMPLEX 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 ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static complex c_b1 = {1.f,0.f}; static integer c__1 = 1; /* System generated locals */ integer ab_dim1, ab_offset, b_dim1, b_offset, i__1, i__2, i__3; complex q__1; /* Local variables */ static integer i__, j, l, kd, lm; extern logical lsame_(char *, char *); extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *), cgeru_(integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, integer *), cswap_(integer *, complex *, integer *, complex *, integer *), ctbsv_(char *, char *, char *, integer *, integer *, complex *, integer *, complex *, integer *); static logical lnoti; extern /* Subroutine */ int clacgv_(integer *, complex *, integer *), xerbla_(char *, integer *); static logical notran; 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_("CGBTRS", &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) { cswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb); } q__1.r = -1.f, q__1.i = -0.f; cgeru_(&lm, nrhs, &q__1, &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; ctbsv_("Upper", "No transpose", "Non-unit", n, &i__2, &ab[ ab_offset], ldab, &b[i__ * b_dim1 + 1], &c__1); /* L20: */ } } else if (lsame_(trans, "T")) { /* Solve A**T * X = B. */ i__1 = *nrhs; for (i__ = 1; i__ <= i__1; ++i__) { /* Solve U**T * X = B, overwriting B with X. */ i__2 = *kl + *ku; ctbsv_("Upper", "Transpose", "Non-unit", n, &i__2, &ab[ab_offset], ldab, &b[i__ * b_dim1 + 1], &c__1); /* L30: */ } /* Solve L**T * 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); q__1.r = -1.f, q__1.i = -0.f; cgemv_("Transpose", &lm, nrhs, &q__1, &b[j + 1 + b_dim1], ldb, &ab[kd + 1 + j * ab_dim1], &c__1, &c_b1, &b[j + b_dim1], ldb); l = ipiv[j]; if (l != j) { cswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb); } /* L40: */ } } } else { /* Solve A**H * X = B. */ i__1 = *nrhs; for (i__ = 1; i__ <= i__1; ++i__) { /* Solve U**H * X = B, overwriting B with X. */ i__2 = *kl + *ku; ctbsv_("Upper", "Conjugate transpose", "Non-unit", n, &i__2, &ab[ ab_offset], ldab, &b[i__ * b_dim1 + 1], &c__1); /* L50: */ } /* Solve L**H * 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); clacgv_(nrhs, &b[j + b_dim1], ldb); q__1.r = -1.f, q__1.i = -0.f; cgemv_("Conjugate transpose", &lm, nrhs, &q__1, &b[j + 1 + b_dim1], ldb, &ab[kd + 1 + j * ab_dim1], &c__1, &c_b1, &b[j + b_dim1], ldb); clacgv_(nrhs, &b[j + b_dim1], ldb); l = ipiv[j]; if (l != j) { cswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb); } /* L60: */ } } } return 0; /* End of CGBTRS */ } /* cgbtrs_ */