00001 /* cla_gbrpvgrw.f -- translated by f2c (version 20061008). 00002 You must link the resulting object file with libf2c: 00003 on Microsoft Windows system, link with libf2c.lib; 00004 on Linux or Unix systems, link with .../path/to/libf2c.a -lm 00005 or, if you install libf2c.a in a standard place, with -lf2c -lm 00006 -- in that order, at the end of the command line, as in 00007 cc *.o -lf2c -lm 00008 Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., 00009 00010 http://www.netlib.org/f2c/libf2c.zip 00011 */ 00012 00013 #include "f2c.h" 00014 #include "blaswrap.h" 00015 00016 doublereal cla_gbrpvgrw__(integer *n, integer *kl, integer *ku, integer * 00017 ncols, complex *ab, integer *ldab, complex *afb, integer *ldafb) 00018 { 00019 /* System generated locals */ 00020 integer ab_dim1, ab_offset, afb_dim1, afb_offset, i__1, i__2, i__3, i__4; 00021 real ret_val, r__1, r__2, r__3; 00022 00023 /* Builtin functions */ 00024 double r_imag(complex *); 00025 00026 /* Local variables */ 00027 integer i__, j, kd; 00028 real amax, umax, rpvgrw; 00029 00030 00031 /* -- LAPACK routine (version 3.2.1) -- */ 00032 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00033 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00034 /* -- April 2009 -- */ 00035 00036 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00037 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00038 00039 /* .. */ 00040 /* .. Scalar Arguments .. */ 00041 /* .. */ 00042 /* .. Array Arguments .. */ 00043 /* .. */ 00044 00045 /* Purpose */ 00046 /* ======= */ 00047 00048 /* CLA_GBRPVGRW computes the reciprocal pivot growth factor */ 00049 /* norm(A)/norm(U). The "max absolute element" norm is used. If this is */ 00050 /* much less than 1, the stability of the LU factorization of the */ 00051 /* (equilibrated) matrix A could be poor. This also means that the */ 00052 /* solution X, estimated condition numbers, and error bounds could be */ 00053 /* unreliable. */ 00054 00055 /* Arguments */ 00056 /* ========= */ 00057 00058 /* N (input) INTEGER */ 00059 /* The number of linear equations, i.e., the order of the */ 00060 /* matrix A. N >= 0. */ 00061 00062 /* KL (input) INTEGER */ 00063 /* The number of subdiagonals within the band of A. KL >= 0. */ 00064 00065 /* KU (input) INTEGER */ 00066 /* The number of superdiagonals within the band of A. KU >= 0. */ 00067 00068 /* NCOLS (input) INTEGER */ 00069 /* The number of columns of the matrix A. NCOLS >= 0. */ 00070 00071 /* AB (input) COMPLEX array, dimension (LDAB,N) */ 00072 /* On entry, the matrix A in band storage, in rows 1 to KL+KU+1. */ 00073 /* The j-th column of A is stored in the j-th column of the */ 00074 /* array AB as follows: */ 00075 /* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) */ 00076 00077 /* LDAB (input) INTEGER */ 00078 /* The leading dimension of the array AB. LDAB >= KL+KU+1. */ 00079 00080 /* AFB (input) COMPLEX array, dimension (LDAFB,N) */ 00081 /* Details of the LU factorization of the band matrix A, as */ 00082 /* computed by CGBTRF. U is stored as an upper triangular */ 00083 /* band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, */ 00084 /* and the multipliers used during the factorization are stored */ 00085 /* in rows KL+KU+2 to 2*KL+KU+1. */ 00086 00087 /* LDAFB (input) INTEGER */ 00088 /* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. */ 00089 00090 /* ===================================================================== */ 00091 00092 /* .. Local Scalars .. */ 00093 /* .. */ 00094 /* .. Intrinsic Functions .. */ 00095 /* .. */ 00096 /* .. Statement Functions .. */ 00097 /* .. */ 00098 /* .. Statement Function Definitions .. */ 00099 /* .. */ 00100 /* .. Executable Statements .. */ 00101 00102 /* Parameter adjustments */ 00103 ab_dim1 = *ldab; 00104 ab_offset = 1 + ab_dim1; 00105 ab -= ab_offset; 00106 afb_dim1 = *ldafb; 00107 afb_offset = 1 + afb_dim1; 00108 afb -= afb_offset; 00109 00110 /* Function Body */ 00111 rpvgrw = 1.f; 00112 kd = *ku + 1; 00113 i__1 = *ncols; 00114 for (j = 1; j <= i__1; ++j) { 00115 amax = 0.f; 00116 umax = 0.f; 00117 /* Computing MAX */ 00118 i__2 = j - *ku; 00119 /* Computing MIN */ 00120 i__4 = j + *kl; 00121 i__3 = min(i__4,*n); 00122 for (i__ = max(i__2,1); i__ <= i__3; ++i__) { 00123 /* Computing MAX */ 00124 i__2 = kd + i__ - j + j * ab_dim1; 00125 r__3 = (r__1 = ab[i__2].r, dabs(r__1)) + (r__2 = r_imag(&ab[kd + 00126 i__ - j + j * ab_dim1]), dabs(r__2)); 00127 amax = dmax(r__3,amax); 00128 } 00129 /* Computing MAX */ 00130 i__3 = j - *ku; 00131 i__2 = j; 00132 for (i__ = max(i__3,1); i__ <= i__2; ++i__) { 00133 /* Computing MAX */ 00134 i__3 = kd + i__ - j + j * afb_dim1; 00135 r__3 = (r__1 = afb[i__3].r, dabs(r__1)) + (r__2 = r_imag(&afb[kd 00136 + i__ - j + j * afb_dim1]), dabs(r__2)); 00137 umax = dmax(r__3,umax); 00138 } 00139 if (umax != 0.f) { 00140 /* Computing MIN */ 00141 r__1 = amax / umax; 00142 rpvgrw = dmin(r__1,rpvgrw); 00143 } 00144 } 00145 ret_val = rpvgrw; 00146 return ret_val; 00147 } /* cla_gbrpvgrw__ */