/*  -- translated by f2c (version 20191129).

   You must link the resulting object file with libf2c:

  on Microsoft Windows system, link with libf2c.lib;

  on Linux or Unix systems, link with .../path/to/libf2c.a -lm

  or, if you install libf2c.a in a standard place, with -lf2c -lm

  -- in that order, at the end of the command line, as in

    cc *.o -lf2c -lm

  Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

    http://www.netlib.org/f2c/libf2c.zip

*/

#include "f2c.h"

/* Table of constant values */

static integer c__1 = 1;

static doublereal c_b24 = 1.;

static doublereal c_b26 = 0.;

static doublereal c_b29 = -1.;

/* -----------------------------------------------------------------------   

   \BeginDoc   

   \Name: dgetv0   

   \Description:   

    Generate a random initial residual vector for the Arnoldi process.   

    Force the residual vector to be in the range of the operator OP.   

   \Usage:   

    call dgetv0   

       ( IDO, BMAT, ITRY, INITV, N, J, V, LDV, RESID, RNORM,   

         IPNTR, WORKD, IERR )   

   \Arguments   

    IDO     Integer.  (INPUT/OUTPUT)   

            Reverse communication flag.  IDO must be zero on the first   

            call to dgetv0.   

            -------------------------------------------------------------   

            IDO =  0: first call to the reverse communication interface   

            IDO = -1: compute  Y = OP * X  where   

                      IPNTR(1) is the pointer into WORKD for X,   

                      IPNTR(2) is the pointer into WORKD for Y.   

                      This is for the initialization phase to force the   

                      starting vector into the range of OP.   

            IDO =  2: compute  Y = B * X  where   

                      IPNTR(1) is the pointer into WORKD for X,   

                      IPNTR(2) is the pointer into WORKD for Y.   

            IDO = 99: done   

            -------------------------------------------------------------   

    BMAT    Character*1.  (INPUT)   

            BMAT specifies the type of the matrix B in the (generalized)   

            eigenvalue problem A*x = lambda*B*x.   

            B = 'I' -> standard eigenvalue problem A*x = lambda*x   

            B = 'G' -> generalized eigenvalue problem A*x = lambda*B*x   

    ITRY    Integer.  (INPUT)   

            ITRY counts the number of times that dgetv0 is called.   

            It should be set to 1 on the initial call to dgetv0.   

    INITV   Logical variable.  (INPUT)   

            .TRUE.  => the initial residual vector is given in RESID.   

            .FALSE. => generate a random initial residual vector.   

    N       Integer.  (INPUT)   

            Dimension of the problem.   

    J       Integer.  (INPUT)   

            Index of the residual vector to be generated, with respect to   

            the Arnoldi process.  J > 1 in case of a "restart".   

    V       Double precision N by J array.  (INPUT)   

            The first J-1 columns of V contain the current Arnoldi basis   

            if this is a "restart".   

    LDV     Integer.  (INPUT)   

            Leading dimension of V exactly as declared in the calling   

            program.   

    RESID   Double precision array of length N.  (INPUT/OUTPUT)   

            Initial residual vector to be generated.  If RESID is   

            provided, force RESID into the range of the operator OP.   

    RNORM   Double precision scalar.  (OUTPUT)   

            B-norm of the generated residual.   

    IPNTR   Integer array of length 3.  (OUTPUT)   

    WORKD   Double precision work array of length 2*N.  (REVERSE COMMUNICATION).   

            On exit, WORK(1:N) = B*RESID to be used in SSAITR.   

    IERR    Integer.  (OUTPUT)   

            =  0: Normal exit.   

            = -1: Cannot generate a nontrivial restarted residual vector   

                  in the range of the operator OP.   

   \EndDoc   

   -----------------------------------------------------------------------   

   \BeginLib   

   \Local variables:   

       xxxxxx  real   

   \References:   

    1. D.C. Sorensen, "Implicit Application of Polynomial Filters in   

       a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992),   

       pp 357-385.   

    2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly   

       Restarted Arnoldi Iteration", Rice University Technical Report   

       TR95-13, Department of Computational and Applied Mathematics.   

   \Routines called:   

       second  ARPACK utility routine for timing.   

       dvout   ARPACK utility routine for vector output.   

       dlarnv  LAPACK routine for generating a random vector.   

       dgemv   Level 2 BLAS routine for matrix vector multiplication.   

       dcopy   Level 1 BLAS that copies one vector to another.   

       ddot    Level 1 BLAS that computes the scalar product of two vectors.   

       dnrm2   Level 1 BLAS that computes the norm of a vector.   

   \Author   

       Danny Sorensen               Phuong Vu   

       Richard Lehoucq              CRPC / Rice University   

       Dept. of Computational &     Houston, Texas   

       Applied Mathematics   

       Rice University   

       Houston, Texas   

   \SCCS Information: @(#)   

   FILE: getv0.F   SID: 2.6   DATE OF SID: 8/27/96   RELEASE: 2   

   \EndLib   

   -----------------------------------------------------------------------   

   Subroutine */ int igraphdgetv0_(integer *ido, char *bmat, integer *itry, logical 

  *initv, integer *n, integer *j, doublereal *v, integer *ldv, 

  doublereal *resid, doublereal *rnorm, integer *ipntr, doublereal *

  workd, integer *ierr)

{

    /* Initialized data */

    IGRAPH_F77_SAVE logical inits = TRUE_;

    /* System generated locals */

    integer v_dim1, v_offset, i__1;

    /* Builtin functions */

    double sqrt(doublereal);

    /* Local variables */

    IGRAPH_F77_SAVE real t0, t1, t2, t3;

    integer jj, nbx = 0;

    extern doublereal igraphddot_(integer *, doublereal *, integer *, doublereal *, 

      integer *);

    IGRAPH_F77_SAVE integer iter;

    IGRAPH_F77_SAVE logical orth;

    integer nopx = 0;

    extern doublereal igraphdnrm2_(integer *, doublereal *, integer *);

    IGRAPH_F77_SAVE integer iseed[4];

    extern /* Subroutine */ int igraphdgemv_(char *, integer *, integer *, 

      doublereal *, doublereal *, integer *, doublereal *, integer *, 

      doublereal *, doublereal *, integer *);

    integer idist;

    extern /* Subroutine */ int igraphdcopy_(integer *, doublereal *, integer *, 

      doublereal *, integer *);

    IGRAPH_F77_SAVE logical first;

    real tmvbx = 0;

    extern /* Subroutine */ int igraphdvout_(integer *, integer *, doublereal *, 

      integer *, char *, ftnlen);

    integer mgetv0 = 0;

    real tgetv0 = 0;

    IGRAPH_F77_SAVE doublereal rnorm0;

    extern /* Subroutine */ int igraphsecond_(real *);

    integer logfil, ndigit;

    extern /* Subroutine */ int igraphdlarnv_(integer *, integer *, integer *, 

      doublereal *);

    IGRAPH_F77_SAVE integer msglvl;

    real tmvopx = 0;

/*     %----------------------------------------------------%   

       | Include files for debugging and timing information |   

       %----------------------------------------------------%   

       %------------------%   

       | Scalar Arguments |   

       %------------------%   

       %-----------------%   

       | Array Arguments |   

       %-----------------%   

       %------------%   

       | Parameters |   

       %------------%   

       %------------------------%   

       | Local Scalars & Arrays |   

       %------------------------%   

       %----------------------%   

       | External Subroutines |   

       %----------------------%   

       %--------------------%   

       | External Functions |   

       %--------------------%   

       %---------------------%   

       | Intrinsic Functions |   

       %---------------------%   

       %-----------------%   

       | Data Statements |   

       %-----------------%   

       Parameter adjustments */

    --workd;

    --resid;

    v_dim1 = *ldv;

    v_offset = 1 + v_dim1;

    v -= v_offset;

    --ipntr;

    /* Function Body   

       %-----------------------%   

       | Executable Statements |   

       %-----------------------%   

       %-----------------------------------%   

       | Initialize the seed of the LAPACK |   

       | random number generator           |   

       %-----------------------------------% */

    if (inits) {

  iseed[0] = 1;

  iseed[1] = 3;

  iseed[2] = 5;

  iseed[3] = 7;

  inits = FALSE_;

    }

    if (*ido == 0) {

/*        %-------------------------------%   

          | Initialize timing statistics  |   

          | & message level for debugging |   

          %-------------------------------% */

  igraphsecond_(&t0);

  msglvl = mgetv0;

  *ierr = 0;

  iter = 0;

  first = FALSE_;

  orth = FALSE_;

/*        %-----------------------------------------------------%   

          | Possibly generate a random starting vector in RESID |   

          | Use a LAPACK random number generator used by the    |   

          | matrix generation routines.                         |   

          |    idist = 1: uniform (0,1)  distribution;          |   

          |    idist = 2: uniform (-1,1) distribution;          |   

          |    idist = 3: normal  (0,1)  distribution;          |   

          %-----------------------------------------------------% */

  if (! (*initv)) {

      idist = 2;

      igraphdlarnv_(&idist, iseed, n, &resid[1]);

  }

/*        %----------------------------------------------------------%   

          | Force the starting vector into the range of OP to handle |   

          | the generalized problem when B is possibly (singular).   |   

          %----------------------------------------------------------% */

  igraphsecond_(&t2);

  if (*(unsigned char *)bmat == 'G') {

      ++nopx;

      ipntr[1] = 1;

      ipntr[2] = *n + 1;

      igraphdcopy_(n, &resid[1], &c__1, &workd[1], &c__1);

      *ido = -1;

      goto L9000;

  }

    }

/*     %-----------------------------------------%   

       | Back from computing OP*(initial-vector) |   

       %-----------------------------------------% */

    if (first) {

  goto L20;

    }

/*     %-----------------------------------------------%   

       | Back from computing B*(orthogonalized-vector) |   

       %-----------------------------------------------% */

    if (orth) {

  goto L40;

    }

    if (*(unsigned char *)bmat == 'G') {

  igraphsecond_(&t3);

  tmvopx += t3 - t2;

    }

/*     %------------------------------------------------------%   

       | Starting vector is now in the range of OP; r = OP*r; |   

       | Compute B-norm of starting vector.                   |   

       %------------------------------------------------------% */

    igraphsecond_(&t2);

    first = TRUE_;

    if (*(unsigned char *)bmat == 'G') {

  ++nbx;

  igraphdcopy_(n, &workd[*n + 1], &c__1, &resid[1], &c__1);

  ipntr[1] = *n + 1;

  ipntr[2] = 1;

  *ido = 2;

  goto L9000;

    } else if (*(unsigned char *)bmat == 'I') {

  igraphdcopy_(n, &resid[1], &c__1, &workd[1], &c__1);

    }

L20:

    if (*(unsigned char *)bmat == 'G') {

  igraphsecond_(&t3);

  tmvbx += t3 - t2;

    }

    first = FALSE_;

    if (*(unsigned char *)bmat == 'G') {

  rnorm0 = igraphddot_(n, &resid[1], &c__1, &workd[1], &c__1);

  rnorm0 = sqrt((abs(rnorm0)));

    } else if (*(unsigned char *)bmat == 'I') {

  rnorm0 = igraphdnrm2_(n, &resid[1], &c__1);

    }

    *rnorm = rnorm0;

/*     %---------------------------------------------%   

       | Exit if this is the very first Arnoldi step |   

       %---------------------------------------------% */

    if (*j == 1) {

  goto L50;

    }

/*     %----------------------------------------------------------------   

       | Otherwise need to B-orthogonalize the starting vector against |   

       | the current Arnoldi basis using Gram-Schmidt with iter. ref.  |   

       | This is the case where an invariant subspace is encountered   |   

       | in the middle of the Arnoldi factorization.                   |   

       |                                                               |   

       |       s = V^{T}*B*r;   r = r - V*s;                           |   

       |                                                               |   

       | Stopping criteria used for iter. ref. is discussed in         |   

       | Parlett's book, page 107 and in Gragg & Reichel TOMS paper.   |   

       %---------------------------------------------------------------% */

    orth = TRUE_;

L30:

    i__1 = *j - 1;

    igraphdgemv_("T", n, &i__1, &c_b24, &v[v_offset], ldv, &workd[1], &c__1, &c_b26,

       &workd[*n + 1], &c__1);

    i__1 = *j - 1;

    igraphdgemv_("N", n, &i__1, &c_b29, &v[v_offset], ldv, &workd[*n + 1], &c__1, &

      c_b24, &resid[1], &c__1);

/*     %----------------------------------------------------------%   

       | Compute the B-norm of the orthogonalized starting vector |   

       %----------------------------------------------------------% */

    igraphsecond_(&t2);

    if (*(unsigned char *)bmat == 'G') {

  ++nbx;

  igraphdcopy_(n, &resid[1], &c__1, &workd[*n + 1], &c__1);

  ipntr[1] = *n + 1;

  ipntr[2] = 1;

  *ido = 2;

  goto L9000;

    } else if (*(unsigned char *)bmat == 'I') {

  igraphdcopy_(n, &resid[1], &c__1, &workd[1], &c__1);

    }

L40:

    if (*(unsigned char *)bmat == 'G') {

  igraphsecond_(&t3);

  tmvbx += t3 - t2;

    }

    if (*(unsigned char *)bmat == 'G') {

  *rnorm = igraphddot_(n, &resid[1], &c__1, &workd[1], &c__1);

  *rnorm = sqrt((abs(*rnorm)));

    } else if (*(unsigned char *)bmat == 'I') {

  *rnorm = igraphdnrm2_(n, &resid[1], &c__1);

    }

/*     %--------------------------------------%   

       | Check for further orthogonalization. |   

       %--------------------------------------% */

    if (msglvl > 2) {

  igraphdvout_(&logfil, &c__1, &rnorm0, &ndigit, "_getv0: re-orthonalization"

    " ; rnorm0 is", (ftnlen)38);

  igraphdvout_(&logfil, &c__1, rnorm, &ndigit, "_getv0: re-orthonalization ;"

    " rnorm is", (ftnlen)37);

    }

    if (*rnorm > rnorm0 * .717f) {

  goto L50;

    }

    ++iter;

    if (iter <= 1) {

/*        %-----------------------------------%   

          | Perform iterative refinement step |   

          %-----------------------------------% */

  rnorm0 = *rnorm;

  goto L30;

    } else {

/*        %------------------------------------%   

          | Iterative refinement step "failed" |   

          %------------------------------------% */

  i__1 = *n;

  for (jj = 1; jj <= i__1; ++jj) {

      resid[jj] = 0.;

/* L45: */

  }

  *rnorm = 0.;

  *ierr = -1;

    }

L50:

    if (msglvl > 0) {

  igraphdvout_(&logfil, &c__1, rnorm, &ndigit, "_getv0: B-norm of initial / "

    "restarted starting vector", (ftnlen)53);

    }

    if (msglvl > 2) {

  igraphdvout_(&logfil, n, &resid[1], &ndigit, "_getv0: initial / restarted "

    "starting vector", (ftnlen)43);

    }

    *ido = 99;

    igraphsecond_(&t1);

    tgetv0 += t1 - t0;

L9000:

    return 0;

/*     %---------------%   

       | End of dgetv0 |   

       %---------------% */

} /* igraphdgetv0_ */