cgtsvx.c
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00001 /* cgtsvx.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 /* Table of constant values */
00017 
00018 static integer c__1 = 1;
00019 
00020 /* Subroutine */ int cgtsvx_(char *fact, char *trans, integer *n, integer *
00021         nrhs, complex *dl, complex *d__, complex *du, complex *dlf, complex *
00022         df, complex *duf, complex *du2, integer *ipiv, complex *b, integer *
00023         ldb, complex *x, integer *ldx, real *rcond, real *ferr, real *berr, 
00024         complex *work, real *rwork, integer *info)
00025 {
00026     /* System generated locals */
00027     integer b_dim1, b_offset, x_dim1, x_offset, i__1;
00028 
00029     /* Local variables */
00030     char norm[1];
00031     extern logical lsame_(char *, char *);
00032     real anorm;
00033     extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
00034             complex *, integer *);
00035     extern doublereal slamch_(char *), clangt_(char *, integer *, 
00036             complex *, complex *, complex *);
00037     logical nofact;
00038     extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
00039             *, integer *, complex *, integer *), cgtcon_(char *, 
00040             integer *, complex *, complex *, complex *, complex *, integer *, 
00041             real *, real *, complex *, integer *), xerbla_(char *, 
00042             integer *), cgtrfs_(char *, integer *, integer *, complex 
00043             *, complex *, complex *, complex *, complex *, complex *, complex 
00044             *, integer *, complex *, integer *, complex *, integer *, real *, 
00045             real *, complex *, real *, integer *), cgttrf_(integer *, 
00046             complex *, complex *, complex *, complex *, integer *, integer *);
00047     logical notran;
00048     extern /* Subroutine */ int cgttrs_(char *, integer *, integer *, complex 
00049             *, complex *, complex *, complex *, integer *, complex *, integer 
00050             *, integer *);
00051 
00052 
00053 /*  -- LAPACK routine (version 3.2) -- */
00054 /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
00055 /*     November 2006 */
00056 
00057 /*     .. Scalar Arguments .. */
00058 /*     .. */
00059 /*     .. Array Arguments .. */
00060 /*     .. */
00061 
00062 /*  Purpose */
00063 /*  ======= */
00064 
00065 /*  CGTSVX uses the LU factorization to compute the solution to a complex */
00066 /*  system of linear equations A * X = B, A**T * X = B, or A**H * X = B, */
00067 /*  where A is a tridiagonal matrix of order N and X and B are N-by-NRHS */
00068 /*  matrices. */
00069 
00070 /*  Error bounds on the solution and a condition estimate are also */
00071 /*  provided. */
00072 
00073 /*  Description */
00074 /*  =========== */
00075 
00076 /*  The following steps are performed: */
00077 
00078 /*  1. If FACT = 'N', the LU decomposition is used to factor the matrix A */
00079 /*     as A = L * U, where L is a product of permutation and unit lower */
00080 /*     bidiagonal matrices and U is upper triangular with nonzeros in */
00081 /*     only the main diagonal and first two superdiagonals. */
00082 
00083 /*  2. If some U(i,i)=0, so that U is exactly singular, then the routine */
00084 /*     returns with INFO = i. Otherwise, the factored form of A is used */
00085 /*     to estimate the condition number of the matrix A.  If the */
00086 /*     reciprocal of the condition number is less than machine precision, */
00087 /*     INFO = N+1 is returned as a warning, but the routine still goes on */
00088 /*     to solve for X and compute error bounds as described below. */
00089 
00090 /*  3. The system of equations is solved for X using the factored form */
00091 /*     of A. */
00092 
00093 /*  4. Iterative refinement is applied to improve the computed solution */
00094 /*     matrix and calculate error bounds and backward error estimates */
00095 /*     for it. */
00096 
00097 /*  Arguments */
00098 /*  ========= */
00099 
00100 /*  FACT    (input) CHARACTER*1 */
00101 /*          Specifies whether or not the factored form of A has been */
00102 /*          supplied on entry. */
00103 /*          = 'F':  DLF, DF, DUF, DU2, and IPIV contain the factored form */
00104 /*                  of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not */
00105 /*                  be modified. */
00106 /*          = 'N':  The matrix will be copied to DLF, DF, and DUF */
00107 /*                  and factored. */
00108 
00109 /*  TRANS   (input) CHARACTER*1 */
00110 /*          Specifies the form of the system of equations: */
00111 /*          = 'N':  A * X = B     (No transpose) */
00112 /*          = 'T':  A**T * X = B  (Transpose) */
00113 /*          = 'C':  A**H * X = B  (Conjugate transpose) */
00114 
00115 /*  N       (input) INTEGER */
00116 /*          The order of the matrix A.  N >= 0. */
00117 
00118 /*  NRHS    (input) INTEGER */
00119 /*          The number of right hand sides, i.e., the number of columns */
00120 /*          of the matrix B.  NRHS >= 0. */
00121 
00122 /*  DL      (input) COMPLEX array, dimension (N-1) */
00123 /*          The (n-1) subdiagonal elements of A. */
00124 
00125 /*  D       (input) COMPLEX array, dimension (N) */
00126 /*          The n diagonal elements of A. */
00127 
00128 /*  DU      (input) COMPLEX array, dimension (N-1) */
00129 /*          The (n-1) superdiagonal elements of A. */
00130 
00131 /*  DLF     (input or output) COMPLEX array, dimension (N-1) */
00132 /*          If FACT = 'F', then DLF is an input argument and on entry */
00133 /*          contains the (n-1) multipliers that define the matrix L from */
00134 /*          the LU factorization of A as computed by CGTTRF. */
00135 
00136 /*          If FACT = 'N', then DLF is an output argument and on exit */
00137 /*          contains the (n-1) multipliers that define the matrix L from */
00138 /*          the LU factorization of A. */
00139 
00140 /*  DF      (input or output) COMPLEX array, dimension (N) */
00141 /*          If FACT = 'F', then DF is an input argument and on entry */
00142 /*          contains the n diagonal elements of the upper triangular */
00143 /*          matrix U from the LU factorization of A. */
00144 
00145 /*          If FACT = 'N', then DF is an output argument and on exit */
00146 /*          contains the n diagonal elements of the upper triangular */
00147 /*          matrix U from the LU factorization of A. */
00148 
00149 /*  DUF     (input or output) COMPLEX array, dimension (N-1) */
00150 /*          If FACT = 'F', then DUF is an input argument and on entry */
00151 /*          contains the (n-1) elements of the first superdiagonal of U. */
00152 
00153 /*          If FACT = 'N', then DUF is an output argument and on exit */
00154 /*          contains the (n-1) elements of the first superdiagonal of U. */
00155 
00156 /*  DU2     (input or output) COMPLEX array, dimension (N-2) */
00157 /*          If FACT = 'F', then DU2 is an input argument and on entry */
00158 /*          contains the (n-2) elements of the second superdiagonal of */
00159 /*          U. */
00160 
00161 /*          If FACT = 'N', then DU2 is an output argument and on exit */
00162 /*          contains the (n-2) elements of the second superdiagonal of */
00163 /*          U. */
00164 
00165 /*  IPIV    (input or output) INTEGER array, dimension (N) */
00166 /*          If FACT = 'F', then IPIV is an input argument and on entry */
00167 /*          contains the pivot indices from the LU factorization of A as */
00168 /*          computed by CGTTRF. */
00169 
00170 /*          If FACT = 'N', then IPIV is an output argument and on exit */
00171 /*          contains the pivot indices from the LU factorization of A; */
00172 /*          row i of the matrix was interchanged with row IPIV(i). */
00173 /*          IPIV(i) will always be either i or i+1; IPIV(i) = i indicates */
00174 /*          a row interchange was not required. */
00175 
00176 /*  B       (input) COMPLEX array, dimension (LDB,NRHS) */
00177 /*          The N-by-NRHS right hand side matrix B. */
00178 
00179 /*  LDB     (input) INTEGER */
00180 /*          The leading dimension of the array B.  LDB >= max(1,N). */
00181 
00182 /*  X       (output) COMPLEX array, dimension (LDX,NRHS) */
00183 /*          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X. */
00184 
00185 /*  LDX     (input) INTEGER */
00186 /*          The leading dimension of the array X.  LDX >= max(1,N). */
00187 
00188 /*  RCOND   (output) REAL */
00189 /*          The estimate of the reciprocal condition number of the matrix */
00190 /*          A.  If RCOND is less than the machine precision (in */
00191 /*          particular, if RCOND = 0), the matrix is singular to working */
00192 /*          precision.  This condition is indicated by a return code of */
00193 /*          INFO > 0. */
00194 
00195 /*  FERR    (output) REAL array, dimension (NRHS) */
00196 /*          The estimated forward error bound for each solution vector */
00197 /*          X(j) (the j-th column of the solution matrix X). */
00198 /*          If XTRUE is the true solution corresponding to X(j), FERR(j) */
00199 /*          is an estimated upper bound for the magnitude of the largest */
00200 /*          element in (X(j) - XTRUE) divided by the magnitude of the */
00201 /*          largest element in X(j).  The estimate is as reliable as */
00202 /*          the estimate for RCOND, and is almost always a slight */
00203 /*          overestimate of the true error. */
00204 
00205 /*  BERR    (output) REAL array, dimension (NRHS) */
00206 /*          The componentwise relative backward error of each solution */
00207 /*          vector X(j) (i.e., the smallest relative change in */
00208 /*          any element of A or B that makes X(j) an exact solution). */
00209 
00210 /*  WORK    (workspace) COMPLEX array, dimension (2*N) */
00211 
00212 /*  RWORK   (workspace) REAL array, dimension (N) */
00213 
00214 /*  INFO    (output) INTEGER */
00215 /*          = 0:  successful exit */
00216 /*          < 0:  if INFO = -i, the i-th argument had an illegal value */
00217 /*          > 0:  if INFO = i, and i is */
00218 /*                <= N:  U(i,i) is exactly zero.  The factorization */
00219 /*                       has not been completed unless i = N, but the */
00220 /*                       factor U is exactly singular, so the solution */
00221 /*                       and error bounds could not be computed. */
00222 /*                       RCOND = 0 is returned. */
00223 /*                = N+1: U is nonsingular, but RCOND is less than machine */
00224 /*                       precision, meaning that the matrix is singular */
00225 /*                       to working precision.  Nevertheless, the */
00226 /*                       solution and error bounds are computed because */
00227 /*                       there are a number of situations where the */
00228 /*                       computed solution can be more accurate than the */
00229 /*                       value of RCOND would suggest. */
00230 
00231 /*  ===================================================================== */
00232 
00233 /*     .. Parameters .. */
00234 /*     .. */
00235 /*     .. Local Scalars .. */
00236 /*     .. */
00237 /*     .. External Functions .. */
00238 /*     .. */
00239 /*     .. External Subroutines .. */
00240 /*     .. */
00241 /*     .. Intrinsic Functions .. */
00242 /*     .. */
00243 /*     .. Executable Statements .. */
00244 
00245     /* Parameter adjustments */
00246     --dl;
00247     --d__;
00248     --du;
00249     --dlf;
00250     --df;
00251     --duf;
00252     --du2;
00253     --ipiv;
00254     b_dim1 = *ldb;
00255     b_offset = 1 + b_dim1;
00256     b -= b_offset;
00257     x_dim1 = *ldx;
00258     x_offset = 1 + x_dim1;
00259     x -= x_offset;
00260     --ferr;
00261     --berr;
00262     --work;
00263     --rwork;
00264 
00265     /* Function Body */
00266     *info = 0;
00267     nofact = lsame_(fact, "N");
00268     notran = lsame_(trans, "N");
00269     if (! nofact && ! lsame_(fact, "F")) {
00270         *info = -1;
00271     } else if (! notran && ! lsame_(trans, "T") && ! 
00272             lsame_(trans, "C")) {
00273         *info = -2;
00274     } else if (*n < 0) {
00275         *info = -3;
00276     } else if (*nrhs < 0) {
00277         *info = -4;
00278     } else if (*ldb < max(1,*n)) {
00279         *info = -14;
00280     } else if (*ldx < max(1,*n)) {
00281         *info = -16;
00282     }
00283     if (*info != 0) {
00284         i__1 = -(*info);
00285         xerbla_("CGTSVX", &i__1);
00286         return 0;
00287     }
00288 
00289     if (nofact) {
00290 
00291 /*        Compute the LU factorization of A. */
00292 
00293         ccopy_(n, &d__[1], &c__1, &df[1], &c__1);
00294         if (*n > 1) {
00295             i__1 = *n - 1;
00296             ccopy_(&i__1, &dl[1], &c__1, &dlf[1], &c__1);
00297             i__1 = *n - 1;
00298             ccopy_(&i__1, &du[1], &c__1, &duf[1], &c__1);
00299         }
00300         cgttrf_(n, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], info);
00301 
00302 /*        Return if INFO is non-zero. */
00303 
00304         if (*info > 0) {
00305             *rcond = 0.f;
00306             return 0;
00307         }
00308     }
00309 
00310 /*     Compute the norm of the matrix A. */
00311 
00312     if (notran) {
00313         *(unsigned char *)norm = '1';
00314     } else {
00315         *(unsigned char *)norm = 'I';
00316     }
00317     anorm = clangt_(norm, n, &dl[1], &d__[1], &du[1]);
00318 
00319 /*     Compute the reciprocal of the condition number of A. */
00320 
00321     cgtcon_(norm, n, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], &anorm, 
00322             rcond, &work[1], info);
00323 
00324 /*     Compute the solution vectors X. */
00325 
00326     clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
00327     cgttrs_(trans, n, nrhs, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], &x[
00328             x_offset], ldx, info);
00329 
00330 /*     Use iterative refinement to improve the computed solutions and */
00331 /*     compute error bounds and backward error estimates for them. */
00332 
00333     cgtrfs_(trans, n, nrhs, &dl[1], &d__[1], &du[1], &dlf[1], &df[1], &duf[1], 
00334              &du2[1], &ipiv[1], &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1]
00335 , &berr[1], &work[1], &rwork[1], info);
00336 
00337 /*     Set INFO = N+1 if the matrix is singular to working precision. */
00338 
00339     if (*rcond < slamch_("Epsilon")) {
00340         *info = *n + 1;
00341     }
00342 
00343     return 0;
00344 
00345 /*     End of CGTSVX */
00346 
00347 } /* cgtsvx_ */


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autogenerated on Sat Jun 8 2019 18:55:28