#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dgbcon_(char *norm, integer *n, integer *kl, integer *ku, doublereal *ab, integer *ldab, integer *ipiv, doublereal *anorm, doublereal *rcond, doublereal *work, integer *iwork, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= DGBCON estimates the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGBTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Arguments ========= NORM (input) CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. 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. 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). ANORM (input) DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. RCOND (output) DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK (workspace) DOUBLE PRECISION array, dimension (3*N) IWORK (workspace) INTEGER array, dimension (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 integer c__1 = 1; /* System generated locals */ integer ab_dim1, ab_offset, i__1, i__2, i__3; doublereal d__1; /* Local variables */ static integer kase; extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *); static integer kase1, j; static doublereal t, scale; extern logical lsame_(char *, char *); extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, integer *); static logical lnoti; extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); static integer kd; extern doublereal dlamch_(char *); static integer lm, jp, ix; extern /* Subroutine */ int dlacon_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int dlatbs_(char *, char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *), xerbla_(char *, integer *); static doublereal ainvnm; static logical onenrm; static char normin[1]; static doublereal smlnum; #define ab_ref(a_1,a_2) ab[(a_2)*ab_dim1 + a_1] ab_dim1 = *ldab; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; --ipiv; --work; --iwork; /* Function Body */ *info = 0; onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O"); if (! onenrm && ! lsame_(norm, "I")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*kl < 0) { *info = -3; } else if (*ku < 0) { *info = -4; } else if (*ldab < (*kl << 1) + *ku + 1) { *info = -6; } else if (*anorm < 0.) { *info = -8; } if (*info != 0) { i__1 = -(*info); xerbla_("DGBCON", &i__1); return 0; } /* Quick return if possible */ *rcond = 0.; if (*n == 0) { *rcond = 1.; return 0; } else if (*anorm == 0.) { return 0; } smlnum = dlamch_("Safe minimum"); /* Estimate the norm of inv(A). */ ainvnm = 0.; *(unsigned char *)normin = 'N'; if (onenrm) { kase1 = 1; } else { kase1 = 2; } kd = *kl + *ku + 1; lnoti = *kl > 0; kase = 0; L10: dlacon_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase); if (kase != 0) { if (kase == kase1) { /* Multiply by inv(L). */ 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); jp = ipiv[j]; t = work[jp]; if (jp != j) { work[jp] = work[j]; work[j] = t; } d__1 = -t; daxpy_(&lm, &d__1, &ab_ref(kd + 1, j), &c__1, &work[j + 1] , &c__1); /* L20: */ } } /* Multiply by inv(U). */ i__1 = *kl + *ku; dlatbs_("Upper", "No transpose", "Non-unit", normin, n, &i__1, & ab[ab_offset], ldab, &work[1], &scale, &work[(*n << 1) + 1], info); } else { /* Multiply by inv(U'). */ i__1 = *kl + *ku; dlatbs_("Upper", "Transpose", "Non-unit", normin, n, &i__1, &ab[ ab_offset], ldab, &work[1], &scale, &work[(*n << 1) + 1], info); /* Multiply by inv(L'). */ if (lnoti) { for (j = *n - 1; j >= 1; --j) { /* Computing MIN */ i__1 = *kl, i__2 = *n - j; lm = min(i__1,i__2); work[j] -= ddot_(&lm, &ab_ref(kd + 1, j), &c__1, &work[j + 1], &c__1); jp = ipiv[j]; if (jp != j) { t = work[jp]; work[jp] = work[j]; work[j] = t; } /* L30: */ } } } /* Divide X by 1/SCALE if doing so will not cause overflow. */ *(unsigned char *)normin = 'Y'; if (scale != 1.) { ix = idamax_(n, &work[1], &c__1); if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.) { goto L40; } drscl_(n, &scale, &work[1], &c__1); } goto L10; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.) { *rcond = 1. / ainvnm / *anorm; } L40: return 0; /* End of DGBCON */ } /* dgbcon_ */ #undef ab_ref