#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dtrcon_(char *norm, char *uplo, char *diag, integer *n, doublereal *a, integer *lda, 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 March 31, 1993 Purpose ======= DTRCON estimates the reciprocal of the condition number of a triangular 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. A (input) DOUBLE PRECISION array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). 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 a_dim1, a_offset, i__1; doublereal d__1; /* Local variables */ static integer kase, kase1; static doublereal scale; extern logical lsame_(char *, char *); extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, integer *); static doublereal anorm; static logical upper; static doublereal xnorm; extern doublereal dlamch_(char *); extern /* Subroutine */ int dlacon_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); static integer ix; extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *); extern doublereal dlantr_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *); static doublereal ainvnm; extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *); static logical onenrm; static char normin[1]; static doublereal smlnum; static logical nounit; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --work; --iwork; /* 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 (*lda < max(1,*n)) { *info = -6; } if (*info != 0) { i__1 = -(*info); xerbla_("DTRCON", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { *rcond = 1.; return 0; } *rcond = 0.; smlnum = dlamch_("Safe minimum") * (doublereal) max(1,*n); /* Compute the norm of the triangular matrix A. */ anorm = dlantr_(norm, uplo, diag, n, n, &a[a_offset], lda, &work[1]); /* Continue only if ANORM > 0. */ if (anorm > 0.) { /* Estimate the norm of the inverse of A. */ ainvnm = 0.; *(unsigned char *)normin = 'N'; if (onenrm) { kase1 = 1; } else { kase1 = 2; } kase = 0; L10: dlacon_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase); if (kase != 0) { if (kase == kase1) { /* Multiply by inv(A). */ dlatrs_(uplo, "No transpose", diag, normin, n, &a[a_offset], lda, &work[1], &scale, &work[(*n << 1) + 1], info); } else { /* Multiply by inv(A'). */ dlatrs_(uplo, "Transpose", diag, normin, n, &a[a_offset], lda, &work[1], &scale, &work[(*n << 1) + 1], info); } *(unsigned char *)normin = 'Y'; /* Multiply by 1/SCALE if doing so will not cause overflow. */ if (scale != 1.) { ix = idamax_(n, &work[1], &c__1); xnorm = (d__1 = work[ix], abs(d__1)); if (scale < xnorm * smlnum || scale == 0.) { goto L20; } drscl_(n, &scale, &work[1], &c__1); } goto L10; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.) { *rcond = 1. / anorm / ainvnm; } } L20: return 0; /* End of DTRCON */ } /* dtrcon_ */