/* Subroutine */ int ctrcon_(char *norm, char *uplo, char *diag, integer *n, complex *a, integer *lda, real *rcond, complex *work, real *rwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1; real r__1, r__2; /* Builtin functions */ double r_imag(complex *); /* Local variables */ integer ix, kase, kase1; real scale; extern logical lsame_(char *, char *); integer isave[3]; real anorm; logical upper; extern /* Subroutine */ int clacn2_(integer *, complex *, complex *, real *, integer *, integer *); real xnorm; extern integer icamax_(integer *, complex *, integer *); extern doublereal slamch_(char *); extern /* Subroutine */ int xerbla_(char *, integer *); extern doublereal clantr_(char *, char *, char *, integer *, integer *, complex *, integer *, real *); real ainvnm; extern /* Subroutine */ int clatrs_(char *, char *, char *, char *, integer *, complex *, integer *, complex *, real *, real *, integer *), csrscl_(integer *, real *, complex *, integer *); logical onenrm; char normin[1]; real smlnum; logical nounit; /* -- LAPACK routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH. */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CTRCON 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) COMPLEX 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) 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 */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Statement Functions .. */ /* .. */ /* .. Statement Function definitions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_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 (*lda < max(1,*n)) { *info = -6; } if (*info != 0) { i__1 = -(*info); xerbla_("CTRCON", &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(1,*n); /* Compute the norm of the triangular matrix A. */ anorm = clantr_(norm, uplo, diag, n, n, &a[a_offset], lda, &rwork[1]); /* Continue only if ANORM > 0. */ if (anorm > 0.f) { /* Estimate the norm of the inverse of A. */ ainvnm = 0.f; *(unsigned char *)normin = 'N'; if (onenrm) { kase1 = 1; } else { kase1 = 2; } kase = 0; L10: clacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave); if (kase != 0) { if (kase == kase1) { /* Multiply by inv(A). */ clatrs_(uplo, "No transpose", diag, normin, n, &a[a_offset], lda, &work[1], &scale, &rwork[1], info); } else { /* Multiply by inv(A'). */ clatrs_(uplo, "Conjugate transpose", diag, normin, n, &a[ a_offset], lda, &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 CTRCON */ } /* ctrcon_ */
/* Subroutine */ int cgesvx_(char *fact, char *trans, integer *n, integer * nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * ipiv, char *equed, real *r__, real *c__, complex *b, integer *ldb, complex *x, integer *ldx, real *rcond, real *ferr, real *berr, complex *work, real *rwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5; real r__1, r__2; complex q__1; /* Local variables */ integer i__, j; real amax; char norm[1]; extern logical lsame_(char *, char *); real rcmin, rcmax, anorm; logical equil; extern real clange_(char *, integer *, integer *, complex *, integer *, real *); extern /* Subroutine */ int claqge_(integer *, integer *, complex *, integer *, real *, real *, real *, real *, real *, char *) , cgecon_(char *, integer *, complex *, integer *, real *, real *, complex *, real *, integer *); real colcnd; extern real slamch_(char *); extern /* Subroutine */ int cgeequ_(integer *, integer *, complex *, integer *, real *, real *, real *, real *, real *, integer *); logical nofact; extern /* Subroutine */ int cgerfs_(char *, integer *, integer *, complex *, integer *, complex *, integer *, integer *, complex *, integer *, complex *, integer *, real *, real *, complex *, real *, integer *), cgetrf_(integer *, integer *, complex *, integer *, integer *, integer *), clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *); real bignum; extern real clantr_(char *, char *, char *, integer *, integer *, complex *, integer *, real *); integer infequ; logical colequ; extern /* Subroutine */ int cgetrs_(char *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, integer *); real rowcnd; logical notran; real smlnum; logical rowequ; real rpvgrw; /* -- LAPACK driver routine (version 3.4.1) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* April 2012 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; af_dim1 = *ldaf; af_offset = 1 + af_dim1; af -= af_offset; --ipiv; --r__; --c__; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; --ferr; --berr; --work; --rwork; /* Function Body */ *info = 0; nofact = lsame_(fact, "N"); equil = lsame_(fact, "E"); notran = lsame_(trans, "N"); if (nofact || equil) { *(unsigned char *)equed = 'N'; rowequ = FALSE_; colequ = FALSE_; } else { rowequ = lsame_(equed, "R") || lsame_(equed, "B"); colequ = lsame_(equed, "C") || lsame_(equed, "B"); smlnum = slamch_("Safe minimum"); bignum = 1.f / smlnum; } /* Test the input parameters. */ if (! nofact && ! equil && ! lsame_(fact, "F")) { *info = -1; } else if (! notran && ! lsame_(trans, "T") && ! lsame_(trans, "C")) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*nrhs < 0) { *info = -4; } else if (*lda < max(1,*n)) { *info = -6; } else if (*ldaf < max(1,*n)) { *info = -8; } else if (lsame_(fact, "F") && ! (rowequ || colequ || lsame_(equed, "N"))) { *info = -10; } else { if (rowequ) { rcmin = bignum; rcmax = 0.f; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ r__1 = rcmin; r__2 = r__[j]; // , expr subst rcmin = min(r__1,r__2); /* Computing MAX */ r__1 = rcmax; r__2 = r__[j]; // , expr subst rcmax = max(r__1,r__2); /* L10: */ } if (rcmin <= 0.f) { *info = -11; } else if (*n > 0) { rowcnd = max(rcmin,smlnum) / min(rcmax,bignum); } else { rowcnd = 1.f; } } if (colequ && *info == 0) { rcmin = bignum; rcmax = 0.f; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ r__1 = rcmin; r__2 = c__[j]; // , expr subst rcmin = min(r__1,r__2); /* Computing MAX */ r__1 = rcmax; r__2 = c__[j]; // , expr subst rcmax = max(r__1,r__2); /* L20: */ } if (rcmin <= 0.f) { *info = -12; } else if (*n > 0) { colcnd = max(rcmin,smlnum) / min(rcmax,bignum); } else { colcnd = 1.f; } } if (*info == 0) { if (*ldb < max(1,*n)) { *info = -14; } else if (*ldx < max(1,*n)) { *info = -16; } } } if (*info != 0) { i__1 = -(*info); xerbla_("CGESVX", &i__1); return 0; } if (equil) { /* Compute row and column scalings to equilibrate the matrix A. */ cgeequ_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, & amax, &infequ); if (infequ == 0) { /* Equilibrate the matrix. */ claqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, & colcnd, &amax, equed); rowequ = lsame_(equed, "R") || lsame_(equed, "B"); colequ = lsame_(equed, "C") || lsame_(equed, "B"); } } /* Scale the right hand side. */ if (notran) { if (rowequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; i__4 = i__; i__5 = i__ + j * b_dim1; q__1.r = r__[i__4] * b[i__5].r; q__1.i = r__[i__4] * b[ i__5].i; // , expr subst b[i__3].r = q__1.r; b[i__3].i = q__1.i; // , expr subst /* L30: */ } /* L40: */ } } } else if (colequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; i__4 = i__; i__5 = i__ + j * b_dim1; q__1.r = c__[i__4] * b[i__5].r; q__1.i = c__[i__4] * b[i__5] .i; // , expr subst b[i__3].r = q__1.r; b[i__3].i = q__1.i; // , expr subst /* L50: */ } /* L60: */ } } if (nofact || equil) { /* Compute the LU factorization of A. */ clacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf); cgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info); /* Return if INFO is non-zero. */ if (*info > 0) { /* Compute the reciprocal pivot growth factor of the */ /* leading rank-deficient INFO columns of A. */ rpvgrw = clantr_("M", "U", "N", info, info, &af[af_offset], ldaf, &rwork[1]); if (rpvgrw == 0.f) { rpvgrw = 1.f; } else { rpvgrw = clange_("M", n, info, &a[a_offset], lda, &rwork[1]) / rpvgrw; } rwork[1] = rpvgrw; *rcond = 0.f; return 0; } } /* Compute the norm of the matrix A and the */ /* reciprocal pivot growth factor RPVGRW. */ if (notran) { *(unsigned char *)norm = '1'; } else { *(unsigned char *)norm = 'I'; } anorm = clange_(norm, n, n, &a[a_offset], lda, &rwork[1]); rpvgrw = clantr_("M", "U", "N", n, n, &af[af_offset], ldaf, &rwork[1]); if (rpvgrw == 0.f) { rpvgrw = 1.f; } else { rpvgrw = clange_("M", n, n, &a[a_offset], lda, &rwork[1]) / rpvgrw; } /* Compute the reciprocal of the condition number of A. */ cgecon_(norm, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1], info); /* Compute the solution matrix X. */ clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); cgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx, info); /* Use iterative refinement to improve the computed solution and */ /* compute error bounds and backward error estimates for it. */ cgerfs_(trans, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1], &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[ 1], &rwork[1], info); /* Transform the solution matrix X to a solution of the original */ /* system. */ if (notran) { if (colequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * x_dim1; i__4 = i__; i__5 = i__ + j * x_dim1; q__1.r = c__[i__4] * x[i__5].r; q__1.i = c__[i__4] * x[ i__5].i; // , expr subst x[i__3].r = q__1.r; x[i__3].i = q__1.i; // , expr subst /* L70: */ } /* L80: */ } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ferr[j] /= colcnd; /* L90: */ } } } else if (rowequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * x_dim1; i__4 = i__; i__5 = i__ + j * x_dim1; q__1.r = r__[i__4] * x[i__5].r; q__1.i = r__[i__4] * x[i__5] .i; // , expr subst x[i__3].r = q__1.r; x[i__3].i = q__1.i; // , expr subst /* L100: */ } /* L110: */ } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ferr[j] /= rowcnd; /* L120: */ } } /* Set INFO = N+1 if the matrix is singular to working precision. */ if (*rcond < slamch_("Epsilon")) { *info = *n + 1; } rwork[1] = rpvgrw; return 0; /* End of CGESVX */ }