#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int sgbcon_(char *norm, integer *n, integer *kl, integer *ku, real *ab, integer *ldab, integer *ipiv, real *anorm, real *rcond, real *work, integer *iwork, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Modified to call SLACN2 in place of SLACON, 7 Feb 03, SJH. Purpose ======= SGBCON 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 SGBTRF. 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) REAL array, dimension (LDAB,N) Details of the LU factorization of the band matrix A, as computed by SGBTRF. 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) REAL 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) REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK (workspace) REAL 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; real r__1; /* Local variables */ static integer j; static real t; static integer kd, lm, jp, ix, kase; extern doublereal sdot_(integer *, real *, integer *, real *, integer *); static integer kase1; static real scale; extern logical lsame_(char *, char *); static integer isave[3]; static logical lnoti; extern /* Subroutine */ int srscl_(integer *, real *, real *, integer *), saxpy_(integer *, real *, real *, integer *, real *, integer *), slacn2_(integer *, real *, real *, integer *, real *, integer *, integer *); extern doublereal slamch_(char *); extern /* Subroutine */ int xerbla_(char *, integer *); extern integer isamax_(integer *, real *, integer *); static real ainvnm; extern /* Subroutine */ int slatbs_(char *, char *, char *, char *, integer *, integer *, real *, integer *, real *, real *, real *, integer *); static logical onenrm; static char normin[1]; static real smlnum; ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; 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.f) { *info = -8; } if (*info != 0) { i__1 = -(*info); xerbla_("SGBCON", &i__1); return 0; } /* Quick return if possible */ *rcond = 0.f; if (*n == 0) { *rcond = 1.f; return 0; } else if (*anorm == 0.f) { return 0; } smlnum = slamch_("Safe minimum"); /* Estimate the norm of inv(A). */ ainvnm = 0.f; *(unsigned char *)normin = 'N'; if (onenrm) { kase1 = 1; } else { kase1 = 2; } kd = *kl + *ku + 1; lnoti = *kl > 0; kase = 0; L10: slacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave); 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; } r__1 = -t; saxpy_(&lm, &r__1, &ab[kd + 1 + j * ab_dim1], &c__1, & work[j + 1], &c__1); /* L20: */ } } /* Multiply by inv(U). */ i__1 = *kl + *ku; slatbs_("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; slatbs_("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] -= sdot_(&lm, &ab[kd + 1 + j * ab_dim1], &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.f) { ix = isamax_(n, &work[1], &c__1); if (scale < (r__1 = work[ix], dabs(r__1)) * smlnum || scale == 0.f) { goto L40; } srscl_(n, &scale, &work[1], &c__1); } goto L10; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.f) { *rcond = 1.f / ainvnm / *anorm; } L40: return 0; /* End of SGBCON */ } /* sgbcon_ */