#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int ctbcon_(char *norm, char *uplo, char *diag, integer *n, integer *kd, complex *ab, integer *ldab, real *rcond, complex *work, real *rwork, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University March 31, 1993 Purpose ======= CTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then 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. UPLO (input) CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. DIAG (input) CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. N (input) INTEGER The order of the matrix A. N >= 0. KD (input) INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0. AB (input) COMPLEX array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. RCOND (output) REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK (workspace) COMPLEX array, dimension (2*N) RWORK (workspace) REAL 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; real r__1, r__2; /* Builtin functions */ double r_imag(complex *); /* Local variables */ static integer kase, kase1; static real scale; extern logical lsame_(char *, char *); static real anorm; static logical upper; static real xnorm; extern /* Subroutine */ int clacon_(integer *, complex *, complex *, real *, integer *); static integer ix; extern integer icamax_(integer *, complex *, integer *); extern doublereal clantb_(char *, char *, char *, integer *, integer *, complex *, integer *, real *), slamch_( char *); extern /* Subroutine */ int clatbs_(char *, char *, char *, char *, integer *, integer *, complex *, integer *, complex *, real *, real *, integer *), xerbla_(char * , integer *); static real ainvnm; extern /* Subroutine */ int csrscl_(integer *, real *, complex *, integer *); static logical onenrm; static char normin[1]; static real smlnum; static logical nounit; ab_dim1 = *ldab; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; --work; --rwork; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O"); nounit = lsame_(diag, "N"); if (! onenrm && ! lsame_(norm, "I")) { *info = -1; } else if (! upper && ! lsame_(uplo, "L")) { *info = -2; } else if (! nounit && ! lsame_(diag, "U")) { *info = -3; } else if (*n < 0) { *info = -4; } else if (*kd < 0) { *info = -5; } else if (*ldab < *kd + 1) { *info = -7; } if (*info != 0) { i__1 = -(*info); xerbla_("CTBCON", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { *rcond = 1.f; return 0; } *rcond = 0.f; smlnum = slamch_("Safe minimum") * (real) max(*n,1); /* Compute the 1-norm of the triangular matrix A or A'. */ anorm = clantb_(norm, uplo, diag, n, kd, &ab[ab_offset], ldab, &rwork[1]); /* Continue only if ANORM > 0. */ if (anorm > 0.f) { /* Estimate the 1-norm of the inverse of A. */ ainvnm = 0.f; *(unsigned char *)normin = 'N'; if (onenrm) { kase1 = 1; } else { kase1 = 2; } kase = 0; L10: clacon_(n, &work[*n + 1], &work[1], &ainvnm, &kase); if (kase != 0) { if (kase == kase1) { /* Multiply by inv(A). */ clatbs_(uplo, "No transpose", diag, normin, n, kd, &ab[ ab_offset], ldab, &work[1], &scale, &rwork[1], info); } else { /* Multiply by inv(A'). */ clatbs_(uplo, "Conjugate transpose", diag, normin, n, kd, &ab[ ab_offset], ldab, &work[1], &scale, &rwork[1], info); } *(unsigned char *)normin = 'Y'; /* Multiply by 1/SCALE if doing so will not cause overflow. */ if (scale != 1.f) { ix = icamax_(n, &work[1], &c__1); i__1 = ix; xnorm = (r__1 = work[i__1].r, dabs(r__1)) + (r__2 = r_imag(& work[ix]), dabs(r__2)); if (scale < xnorm * smlnum || scale == 0.f) { goto L20; } csrscl_(n, &scale, &work[1], &c__1); } goto L10; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.f) { *rcond = 1.f / anorm / ainvnm; } } L20: return 0; /* End of CTBCON */ } /* ctbcon_ */