text: /* ../netlib/cpstf2.f -- translated by f2c (version 20100827). 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 "FLA_f2c.h" /* Table of constant values */
  static complex c_b1 =
  {
      1.f,0.f
  }
  ;
  static integer c__1 = 1;
  /* > \brief \b CPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric or comple x Hermitian positive semi-definite matrix. */
  /* =========== DOCUMENTATION =========== */
  /* Online html documentation available at */
  /* http://www.netlib.org/lapack/explore-html/ */
  /* > \htmlonly */
  /* > Download CPSTF2 + dependencies */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cpstf2. f"> */
  /* > [TGZ]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cpstf2. f"> */
  /* > [ZIP]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cpstf2. f"> */
  /* > [TXT]</a> */
  /* > \endhtmlonly */
  /* Definition: */
  /* =========== */
  /* SUBROUTINE CPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO ) */
  /* .. Scalar Arguments .. */
  /* REAL TOL */
  /* INTEGER INFO, LDA, N, RANK */
  /* CHARACTER UPLO */
  /* .. */
  /* .. Array Arguments .. */
  /* COMPLEX A( LDA, * ) */
  /* REAL WORK( 2*N ) */
  /* INTEGER PIV( N ) */
  /* .. */
  /* > \par Purpose: */
  /* ============= */
  /* > */
  /* > \verbatim */
  /* > */
  /* > CPSTF2 computes the Cholesky factorization with complete */
  /* > pivoting of a complex Hermitian positive semidefinite matrix A. */
  /* > */
  /* > The factorization has the form */
  /* > P**T * A * P = U**H * U , if UPLO = 'U', */
  /* > P**T * A * P = L * L**H, if UPLO = 'L', */
  /* > where U is an upper triangular matrix and L is lower triangular, and */
  /* > P is stored as vector PIV. */
  /* > */
  /* > This algorithm does not attempt to check that A is positive */
  /* > semidefinite. This version of the algorithm calls level 2 BLAS. */
  /* > \endverbatim */
  /* Arguments: */
  /* ========== */
  /* > \param[in] UPLO */
  /* > \verbatim */
  /* > UPLO is CHARACTER*1 */
  /* > Specifies whether the upper or lower triangular part of the */
  /* > symmetric matrix A is stored. */
  /* > = 'U': Upper triangular */
  /* > = 'L': Lower triangular */
  /* > \endverbatim */
  /* > */
  /* > \param[in] N */
  /* > \verbatim */
  /* > N is INTEGER */
  /* > The order of the matrix A. N >= 0. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] A */
  /* > \verbatim */
  /* > A is COMPLEX array, dimension (LDA,N) */
  /* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */
  /* > n by n upper triangular part of A contains the upper */
  /* > triangular part of the matrix A, and the strictly lower */
  /* > triangular part of A is not referenced. If UPLO = 'L', the */
  /* > leading n by n lower triangular part of A contains the lower */
  /* > triangular part of the matrix A, and the strictly upper */
  /* > triangular part of A is not referenced. */
  /* > */
  /* > On exit, if INFO = 0, the factor U or L from the Cholesky */
  /* > factorization as above. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] PIV */
  /* > \verbatim */
  /* > PIV is INTEGER array, dimension (N) */
  /* > PIV is such that the nonzero entries are P( PIV(K), K ) = 1. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] RANK */
  /* > \verbatim */
  /* > RANK is INTEGER */
  /* > The rank of A given by the number of steps the algorithm */
  /* > completed. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] TOL */
  /* > \verbatim */
  /* > TOL is REAL */
  /* > User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) ) */
  /* > will be used. The algorithm terminates at the (K-1)st step */
  /* > if the pivot <= TOL. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LDA */
  /* > \verbatim */
  /* > LDA is INTEGER */
  /* > The leading dimension of the array A. LDA >= max(1,N). */
  /* > \endverbatim */
  /* > */
  /* > \param[out] WORK */
  /* > \verbatim */
  /* > WORK is REAL array, dimension (2*N) */
  /* > Work space. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] INFO */
  /* > \verbatim */
  /* > INFO is INTEGER */
  /* > < 0: If INFO = -K, the K-th argument had an illegal value, */
  /* > = 0: algorithm completed successfully, and */
  /* > > 0: the matrix A is either rank deficient with computed rank */
  /* > as returned in RANK, or is indefinite. See Section 7 of */
  /* > LAPACK Working Note #161 for further information. */
  /* > \endverbatim */
  /* Authors: */
  /* ======== */
  /* > \author Univ. of Tennessee */
  /* > \author Univ. of California Berkeley */
  /* > \author Univ. of Colorado Denver */
  /* > \author NAG Ltd. */
  /* > \date September 2012 */
  /* > \ingroup complexOTHERcomputational */
  /* ===================================================================== */
  /* Subroutine */
  int cpstf2_(char *uplo, integer *n, complex *a, integer *lda, integer *piv, integer *rank, real *tol, real *work, integer *info)
  {
      /* System generated locals */
      integer a_dim1, a_offset, i__1, i__2, i__3;
      real r__1;
      complex q__1, q__2;
      /* Builtin functions */
      void r_cnjg(complex *, complex *);
      double sqrt(doublereal);
      /* Local variables */
      integer i__, j;
      real ajj;
      integer pvt;
      extern logical lsame_(char *, char *);
      extern /* Subroutine */
      int cgemv_(char *, integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *);
      complex ctemp;
      extern /* Subroutine */
      int cswap_(integer *, complex *, integer *, complex *, integer *);
      integer itemp;
      real stemp;
      logical upper;
      real sstop;
      extern /* Subroutine */
      int clacgv_(integer *, complex *, integer *);
      extern real slamch_(char *);
      extern /* Subroutine */
      int csscal_(integer *, real *, complex *, integer *), xerbla_(char *, integer *);
      extern integer smaxloc_(real *, integer *);
      extern logical sisnan_(real *);
      /* -- LAPACK computational routine (version 3.4.2) -- */
      /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
      /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
      /* September 2012 */
      /* .. Scalar Arguments .. */
      /* .. */
      /* .. Array Arguments .. */
      /* .. */
      /* ===================================================================== */
      /* .. Parameters .. */
      /* .. */
      /* .. Local Scalars .. */
      /* .. */
      /* .. External Functions .. */
      /* .. */
      /* .. External Subroutines .. */
      /* .. */
      /* .. Intrinsic Functions .. */
      /* .. */
      /* .. Executable Statements .. */
      /* Test the input parameters */
      /* Parameter adjustments */
      --work;
      --piv;
      a_dim1 = *lda;
      a_offset = 1 + a_dim1;
      a -= a_offset;
      /* Function Body */
      *info = 0;
      upper = lsame_(uplo, "U");
      if (! upper && ! lsame_(uplo, "L"))
      {
          *info = -1;
      }
      else if (*n < 0)
      {
          *info = -2;
      }
      else if (*lda < max(1,*n))
      {
          *info = -4;
      }
      if (*info != 0)
      {
          i__1 = -(*info);
          xerbla_("CPSTF2", &i__1);
          return 0;
      }
      /* Quick return if possible */
      if (*n == 0)
      {
          return 0;
      }
      /* Initialize PIV */
      i__1 = *n;
      for (i__ = 1;
              i__ <= i__1;
              ++i__)
      {
          piv[i__] = i__;
          /* L100: */
      }
      /* Compute stopping value */
      i__1 = *n;
      for (i__ = 1;
              i__ <= i__1;
              ++i__)
      {
          i__2 = i__ + i__ * a_dim1;
          work[i__] = a[i__2].r;
          /* L110: */
      }
      pvt = smaxloc_(&work[1], n);
      i__1 = pvt + pvt * a_dim1;
      ajj = a[i__1].r;
      if (ajj == 0.f || sisnan_(&ajj))
      {
          *rank = 0;
          *info = 1;
          goto L200;
      }
      /* Compute stopping value if not supplied */
      if (*tol < 0.f)
      {
          sstop = *n * slamch_("Epsilon") * ajj;
      }
      else
      {
          sstop = *tol;
      }
      /* Set first half of WORK to zero, holds dot products */
      i__1 = *n;
      for (i__ = 1;
              i__ <= i__1;
              ++i__)
      {
          work[i__] = 0.f;
          /* L120: */
      }
      if (upper)
      {
          /* Compute the Cholesky factorization P**T * A * P = U**H * U */
          i__1 = *n;
          for (j = 1;
                  j <= i__1;
                  ++j)
          {
              /* Find pivot, test for exit, else swap rows and columns */
              /* Update dot products, compute possible pivots which are */
              /* stored in the second half of WORK */
              i__2 = *n;
              for (i__ = j;
                      i__ <= i__2;
                      ++i__)
              {
                  if (j > 1)
                  {
                      r_cnjg(&q__2, &a[j - 1 + i__ * a_dim1]);
                      i__3 = j - 1 + i__ * a_dim1;
                      q__1.r = q__2.r * a[i__3].r - q__2.i * a[i__3].i;
                      q__1.i = q__2.r * a[i__3].i + q__2.i * a[i__3].r; // , expr subst
                      work[i__] += q__1.r;
                  }
                  i__3 = i__ + i__ * a_dim1;
                  work[*n + i__] = a[i__3].r - work[i__];
                  /* L130: */
              }
              if (j > 1)
              {
                  i__2 = *n - j + 1;
                  itemp = smaxloc_(&work[*n + j], &i__2);
                  pvt = itemp + j - 1;
                  ajj = work[*n + pvt];
                  if (ajj <= sstop || sisnan_(&ajj))
                  {
                      i__2 = j + j * a_dim1;
                      a[i__2].r = ajj;
                      a[i__2].i = 0.f; // , expr subst
                      goto L190;
                  }
              }
              if (j != pvt)
              {
                  /* Pivot OK, so can now swap pivot rows and columns */
                  i__2 = pvt + pvt * a_dim1;
                  i__3 = j + j * a_dim1;
                  a[i__2].r = a[i__3].r;
                  a[i__2].i = a[i__3].i; // , expr subst
                  i__2 = j - 1;
                  cswap_(&i__2, &a[j * a_dim1 + 1], &c__1, &a[pvt * a_dim1 + 1], &c__1);
                  if (pvt < *n)
                  {
                      i__2 = *n - pvt;
                      cswap_(&i__2, &a[j + (pvt + 1) * a_dim1], lda, &a[pvt + ( pvt + 1) * a_dim1], lda);
                  }
                  i__2 = pvt - 1;
                  for (i__ = j + 1;
                          i__ <= i__2;
                          ++i__)
                  {
                      r_cnjg(&q__1, &a[j + i__ * a_dim1]);
                      ctemp.r = q__1.r;
                      ctemp.i = q__1.i; // , expr subst
                      i__3 = j + i__ * a_dim1;
                      r_cnjg(&q__1, &a[i__ + pvt * a_dim1]);
                      a[i__3].r = q__1.r;
                      a[i__3].i = q__1.i; // , expr subst
                      i__3 = i__ + pvt * a_dim1;
                      a[i__3].r = ctemp.r;
                      a[i__3].i = ctemp.i; // , expr subst
                      /* L140: */
                  }
                  i__2 = j + pvt * a_dim1;
                  r_cnjg(&q__1, &a[j + pvt * a_dim1]);
                  a[i__2].r = q__1.r;
                  a[i__2].i = q__1.i; // , expr subst
                  /* Swap dot products and PIV */
                  stemp = work[j];
                  work[j] = work[pvt];
                  work[pvt] = stemp;
                  itemp = piv[pvt];
                  piv[pvt] = piv[j];
                  piv[j] = itemp;
              }
              ajj = sqrt(ajj);
              i__2 = j + j * a_dim1;
              a[i__2].r = ajj;
              a[i__2].i = 0.f; // , expr subst
              /* Compute elements J+1:N of row J */
              if (j < *n)
              {
                  i__2 = j - 1;
                  clacgv_(&i__2, &a[j * a_dim1 + 1], &c__1);
                  i__2 = j - 1;
                  i__3 = *n - j;
                  q__1.r = -1.f;
                  q__1.i = -0.f; // , expr subst
                  cgemv_("Trans", &i__2, &i__3, &q__1, &a[(j + 1) * a_dim1 + 1], lda, &a[j * a_dim1 + 1], &c__1, &c_b1, &a[j + (j + 1) * a_dim1], lda);
                  i__2 = j - 1;
                  clacgv_(&i__2, &a[j * a_dim1 + 1], &c__1);
                  i__2 = *n - j;
                  r__1 = 1.f / ajj;
                  csscal_(&i__2, &r__1, &a[j + (j + 1) * a_dim1], lda);
              }
              /* L150: */
          }
      }
      else
      {
          /* Compute the Cholesky factorization P**T * A * P = L * L**H */
          i__1 = *n;
          for (j = 1;
                  j <= i__1;
                  ++j)
          {
              /* Find pivot, test for exit, else swap rows and columns */
              /* Update dot products, compute possible pivots which are */
              /* stored in the second half of WORK */
              i__2 = *n;
              for (i__ = j;
                      i__ <= i__2;
                      ++i__)
              {
                  if (j > 1)
                  {
                      r_cnjg(&q__2, &a[i__ + (j - 1) * a_dim1]);
                      i__3 = i__ + (j - 1) * a_dim1;
                      q__1.r = q__2.r * a[i__3].r - q__2.i * a[i__3].i;
                      q__1.i = q__2.r * a[i__3].i + q__2.i * a[i__3].r; // , expr subst
                      work[i__] += q__1.r;
                  }
                  i__3 = i__ + i__ * a_dim1;
                  work[*n + i__] = a[i__3].r - work[i__];
                  /* L160: */
              }
              if (j > 1)
              {
                  i__2 = *n - j + 1;
                  itemp = smaxloc_(&work[*n + j], &i__2);
                  pvt = itemp + j - 1;
                  ajj = work[*n + pvt];
                  if (ajj <= sstop || sisnan_(&ajj))
                  {
                      i__2 = j + j * a_dim1;
                      a[i__2].r = ajj;
                      a[i__2].i = 0.f; // , expr subst
                      goto L190;
                  }
              }
              if (j != pvt)
              {
                  /* Pivot OK, so can now swap pivot rows and columns */
                  i__2 = pvt + pvt * a_dim1;
                  i__3 = j + j * a_dim1;
                  a[i__2].r = a[i__3].r;
                  a[i__2].i = a[i__3].i; // , expr subst
                  i__2 = j - 1;
                  cswap_(&i__2, &a[j + a_dim1], lda, &a[pvt + a_dim1], lda);
                  if (pvt < *n)
                  {
                      i__2 = *n - pvt;
                      cswap_(&i__2, &a[pvt + 1 + j * a_dim1], &c__1, &a[pvt + 1 + pvt * a_dim1], &c__1);
                  }
                  i__2 = pvt - 1;
                  for (i__ = j + 1;
                          i__ <= i__2;
                          ++i__)
                  {
                      r_cnjg(&q__1, &a[i__ + j * a_dim1]);
                      ctemp.r = q__1.r;
                      ctemp.i = q__1.i; // , expr subst
                      i__3 = i__ + j * a_dim1;
                      r_cnjg(&q__1, &a[pvt + i__ * a_dim1]);
                      a[i__3].r = q__1.r;
                      a[i__3].i = q__1.i; // , expr subst
                      i__3 = pvt + i__ * a_dim1;
                      a[i__3].r = ctemp.r;
                      a[i__3].i = ctemp.i; // , expr subst
                      /* L170: */
                  }
                  i__2 = pvt + j * a_dim1;
                  r_cnjg(&q__1, &a[pvt + j * a_dim1]);
                  a[i__2].r = q__1.r;
                  a[i__2].i = q__1.i; // , expr subst
                  /* Swap dot products and PIV */
                  stemp = work[j];
                  work[j] = work[pvt];
                  work[pvt] = stemp;
                  itemp = piv[pvt];
                  piv[pvt] = piv[j];
                  piv[j] = itemp;
              }
              ajj = sqrt(ajj);
              i__2 = j + j * a_dim1;
              a[i__2].r = ajj;
              a[i__2].i = 0.f; // , expr subst
              /* Compute elements J+1:N of column J */
              if (j < *n)
              {
                  i__2 = j - 1;
                  clacgv_(&i__2, &a[j + a_dim1], lda);
                  i__2 = *n - j;
                  i__3 = j - 1;
                  q__1.r = -1.f;
                  q__1.i = -0.f; // , expr subst
                  cgemv_("No Trans", &i__2, &i__3, &q__1, &a[j + 1 + a_dim1], lda, &a[j + a_dim1], lda, &c_b1, &a[j + 1 + j * a_dim1], &c__1);
                  i__2 = j - 1;
                  clacgv_(&i__2, &a[j + a_dim1], lda);
                  i__2 = *n - j;
                  r__1 = 1.f / ajj;
                  csscal_(&i__2, &r__1, &a[j + 1 + j * a_dim1], &c__1);
              }
              /* L180: */
          }
      }
      /* Ran to completion, A has full rank */
      *rank = *n;
      goto L200;
  L190: /* Rank is number of steps completed. Set INFO = 1 to signal */
      /* that the factorization cannot be used to solve a system. */
      *rank = j - 1;
      *info = 1;
  L200:
      return 0;
      /* End of CPSTF2 */
  }
  /* cpstf2_ */
  