text: /* zbdt01.f -- translated by f2c (version 20061008).
     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"
  #include "blaswrap.h"
  
  /* Table of constant values */
  
  static integer c__1 = 1;
  static doublecomplex c_b7 = {-1.,-0.};
  static doublecomplex c_b10 = {1.,0.};
  
  /* Subroutine */ int zbdt01_(integer *m, integer *n, integer *kd, 
  	doublecomplex *a, integer *lda, doublecomplex *q, integer *ldq, 
  	doublereal *d__, doublereal *e, doublecomplex *pt, integer *ldpt, 
  	doublecomplex *work, doublereal *rwork, doublereal *resid)
  {
      /* System generated locals */
      integer a_dim1, a_offset, pt_dim1, pt_offset, q_dim1, q_offset, i__1, 
  	    i__2, i__3, i__4, i__5, i__6, i__7;
      doublereal d__1, d__2;
      doublecomplex z__1, z__2, z__3;
  
      /* Local variables */
      integer i__, j;
      doublereal eps, anorm;
      extern /* Subroutine */ int zgemv_(char *, integer *, integer *, 
  	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
  	    integer *, doublecomplex *, doublecomplex *, integer *), 
  	    zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, 
  	    integer *);
      extern doublereal dlamch_(char *), zlange_(char *, integer *, 
  	    integer *, doublecomplex *, integer *, doublereal *), 
  	    dzasum_(integer *, doublecomplex *, integer *);
  
  
  /*  -- LAPACK test routine (version 3.1) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  ZBDT01 reconstructs a general matrix A from its bidiagonal form */
  /*     A = Q * B * P' */
  /*  where Q (m by min(m,n)) and P' (min(m,n) by n) are unitary */
  /*  matrices and B is bidiagonal. */
  
  /*  The test ratio to test the reduction is */
  /*     RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS ) */
  /*  where PT = P' and EPS is the machine precision. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  M       (input) INTEGER */
  /*          The number of rows of the matrices A and Q. */
  
  /*  N       (input) INTEGER */
  /*          The number of columns of the matrices A and P'. */
  
  /*  KD      (input) INTEGER */
  /*          If KD = 0, B is diagonal and the array E is not referenced. */
  /*          If KD = 1, the reduction was performed by xGEBRD; B is upper */
  /*          bidiagonal if M >= N, and lower bidiagonal if M < N. */
  /*          If KD = -1, the reduction was performed by xGBBRD; B is */
  /*          always upper bidiagonal. */
  
  /*  A       (input) COMPLEX*16 array, dimension (LDA,N) */
  /*          The m by n matrix A. */
  
  /*  LDA     (input) INTEGER */
  /*          The leading dimension of the array A.  LDA >= max(1,M). */
  
  /*  Q       (input) COMPLEX*16 array, dimension (LDQ,N) */
  /*          The m by min(m,n) unitary matrix Q in the reduction */
  /*          A = Q * B * P'. */
  
  /*  LDQ     (input) INTEGER */
  /*          The leading dimension of the array Q.  LDQ >= max(1,M). */
  
  /*  D       (input) DOUBLE PRECISION array, dimension (min(M,N)) */
  /*          The diagonal elements of the bidiagonal matrix B. */
  
  /*  E       (input) DOUBLE PRECISION array, dimension (min(M,N)-1) */
  /*          The superdiagonal elements of the bidiagonal matrix B if */
  /*          m >= n, or the subdiagonal elements of B if m < n. */
  
  /*  PT      (input) COMPLEX*16 array, dimension (LDPT,N) */
  /*          The min(m,n) by n unitary matrix P' in the reduction */
  /*          A = Q * B * P'. */
  
  /*  LDPT    (input) INTEGER */
  /*          The leading dimension of the array PT. */
  /*          LDPT >= max(1,min(M,N)). */
  
  /*  WORK    (workspace) COMPLEX*16 array, dimension (M+N) */
  
  /*  RWORK   (workspace) DOUBLE PRECISION array, dimension (M) */
  
  /*  RESID   (output) DOUBLE PRECISION */
  /*          The test ratio:  norm(A - Q * B * P') / ( n * norm(A) * EPS ) */
  
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Quick return if possible */
  
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1;
      a -= a_offset;
      q_dim1 = *ldq;
      q_offset = 1 + q_dim1;
      q -= q_offset;
      --d__;
      --e;
      pt_dim1 = *ldpt;
      pt_offset = 1 + pt_dim1;
      pt -= pt_offset;
      --work;
      --rwork;
  
      /* Function Body */
      if (*m <= 0 || *n <= 0) {
  	*resid = 0.;
  	return 0;
      }
  
  /*     Compute A - Q * B * P' one column at a time. */
  
      *resid = 0.;
      if (*kd != 0) {
  
  /*        B is bidiagonal. */
  
  	if (*kd != 0 && *m >= *n) {
  
  /*           B is upper bidiagonal and M >= N. */
  
  	    i__1 = *n;
  	    for (j = 1; j <= i__1; ++j) {
  		zcopy_(m, &a[j * a_dim1 + 1], &c__1, &work[1], &c__1);
  		i__2 = *n - 1;
  		for (i__ = 1; i__ <= i__2; ++i__) {
  		    i__3 = *m + i__;
  		    i__4 = i__;
  		    i__5 = i__ + j * pt_dim1;
  		    z__2.r = d__[i__4] * pt[i__5].r, z__2.i = d__[i__4] * pt[
  			    i__5].i;
  		    i__6 = i__;
  		    i__7 = i__ + 1 + j * pt_dim1;
  		    z__3.r = e[i__6] * pt[i__7].r, z__3.i = e[i__6] * pt[i__7]
  			    .i;
  		    z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  		    work[i__3].r = z__1.r, work[i__3].i = z__1.i;
  /* L10: */
  		}
  		i__2 = *m + *n;
  		i__3 = *n;
  		i__4 = *n + j * pt_dim1;
  		z__1.r = d__[i__3] * pt[i__4].r, z__1.i = d__[i__3] * pt[i__4]
  			.i;
  		work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  		zgemv_("No transpose", m, n, &c_b7, &q[q_offset], ldq, &work[*
  			m + 1], &c__1, &c_b10, &work[1], &c__1);
  /* Computing MAX */
  		d__1 = *resid, d__2 = dzasum_(m, &work[1], &c__1);
  		*resid = max(d__1,d__2);
  /* L20: */
  	    }
  	} else if (*kd < 0) {
  
  /*           B is upper bidiagonal and M < N. */
  
  	    i__1 = *n;
  	    for (j = 1; j <= i__1; ++j) {
  		zcopy_(m, &a[j * a_dim1 + 1], &c__1, &work[1], &c__1);
  		i__2 = *m - 1;
  		for (i__ = 1; i__ <= i__2; ++i__) {
  		    i__3 = *m + i__;
  		    i__4 = i__;
  		    i__5 = i__ + j * pt_dim1;
  		    z__2.r = d__[i__4] * pt[i__5].r, z__2.i = d__[i__4] * pt[
  			    i__5].i;
  		    i__6 = i__;
  		    i__7 = i__ + 1 + j * pt_dim1;
  		    z__3.r = e[i__6] * pt[i__7].r, z__3.i = e[i__6] * pt[i__7]
  			    .i;
  		    z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  		    work[i__3].r = z__1.r, work[i__3].i = z__1.i;
  /* L30: */
  		}
  		i__2 = *m + *m;
  		i__3 = *m;
  		i__4 = *m + j * pt_dim1;
  		z__1.r = d__[i__3] * pt[i__4].r, z__1.i = d__[i__3] * pt[i__4]
  			.i;
  		work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  		zgemv_("No transpose", m, m, &c_b7, &q[q_offset], ldq, &work[*
  			m + 1], &c__1, &c_b10, &work[1], &c__1);
  /* Computing MAX */
  		d__1 = *resid, d__2 = dzasum_(m, &work[1], &c__1);
  		*resid = max(d__1,d__2);
  /* L40: */
  	    }
  	} else {
  
  /*           B is lower bidiagonal. */
  
  	    i__1 = *n;
  	    for (j = 1; j <= i__1; ++j) {
  		zcopy_(m, &a[j * a_dim1 + 1], &c__1, &work[1], &c__1);
  		i__2 = *m + 1;
  		i__3 = j * pt_dim1 + 1;
  		z__1.r = d__[1] * pt[i__3].r, z__1.i = d__[1] * pt[i__3].i;
  		work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  		i__2 = *m;
  		for (i__ = 2; i__ <= i__2; ++i__) {
  		    i__3 = *m + i__;
  		    i__4 = i__ - 1;
  		    i__5 = i__ - 1 + j * pt_dim1;
  		    z__2.r = e[i__4] * pt[i__5].r, z__2.i = e[i__4] * pt[i__5]
  			    .i;
  		    i__6 = i__;
  		    i__7 = i__ + j * pt_dim1;
  		    z__3.r = d__[i__6] * pt[i__7].r, z__3.i = d__[i__6] * pt[
  			    i__7].i;
  		    z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  		    work[i__3].r = z__1.r, work[i__3].i = z__1.i;
  /* L50: */
  		}
  		zgemv_("No transpose", m, m, &c_b7, &q[q_offset], ldq, &work[*
  			m + 1], &c__1, &c_b10, &work[1], &c__1);
  /* Computing MAX */
  		d__1 = *resid, d__2 = dzasum_(m, &work[1], &c__1);
  		*resid = max(d__1,d__2);
  /* L60: */
  	    }
  	}
      } else {
  
  /*        B is diagonal. */
  
  	if (*m >= *n) {
  	    i__1 = *n;
  	    for (j = 1; j <= i__1; ++j) {
  		zcopy_(m, &a[j * a_dim1 + 1], &c__1, &work[1], &c__1);
  		i__2 = *n;
  		for (i__ = 1; i__ <= i__2; ++i__) {
  		    i__3 = *m + i__;
  		    i__4 = i__;
  		    i__5 = i__ + j * pt_dim1;
  		    z__1.r = d__[i__4] * pt[i__5].r, z__1.i = d__[i__4] * pt[
  			    i__5].i;
  		    work[i__3].r = z__1.r, work[i__3].i = z__1.i;
  /* L70: */
  		}
  		zgemv_("No transpose", m, n, &c_b7, &q[q_offset], ldq, &work[*
  			m + 1], &c__1, &c_b10, &work[1], &c__1);
  /* Computing MAX */
  		d__1 = *resid, d__2 = dzasum_(m, &work[1], &c__1);
  		*resid = max(d__1,d__2);
  /* L80: */
  	    }
  	} else {
  	    i__1 = *n;
  	    for (j = 1; j <= i__1; ++j) {
  		zcopy_(m, &a[j * a_dim1 + 1], &c__1, &work[1], &c__1);
  		i__2 = *m;
  		for (i__ = 1; i__ <= i__2; ++i__) {
  		    i__3 = *m + i__;
  		    i__4 = i__;
  		    i__5 = i__ + j * pt_dim1;
  		    z__1.r = d__[i__4] * pt[i__5].r, z__1.i = d__[i__4] * pt[
  			    i__5].i;
  		    work[i__3].r = z__1.r, work[i__3].i = z__1.i;
  /* L90: */
  		}
  		zgemv_("No transpose", m, m, &c_b7, &q[q_offset], ldq, &work[*
  			m + 1], &c__1, &c_b10, &work[1], &c__1);
  /* Computing MAX */
  		d__1 = *resid, d__2 = dzasum_(m, &work[1], &c__1);
  		*resid = max(d__1,d__2);
  /* L100: */
  	    }
  	}
      }
  
  /*     Compute norm(A - Q * B * P') / ( n * norm(A) * EPS ) */
  
      anorm = zlange_("1", m, n, &a[a_offset], lda, &rwork[1]);
      eps = dlamch_("Precision");
  
      if (anorm <= 0.) {
  	if (*resid != 0.) {
  	    *resid = 1. / eps;
  	}
      } else {
  	if (anorm >= *resid) {
  	    *resid = *resid / anorm / ((doublereal) (*n) * eps);
  	} else {
  	    if (anorm < 1.) {
  /* Computing MIN */
  		d__1 = *resid, d__2 = (doublereal) (*n) * anorm;
  		*resid = min(d__1,d__2) / anorm / ((doublereal) (*n) * eps);
  	    } else {
  /* Computing MIN */
  		d__1 = *resid / anorm, d__2 = (doublereal) (*n);
  		*resid = min(d__1,d__2) / ((doublereal) (*n) * eps);
  	    }
  	}
      }
  
      return 0;
  
  /*     End of ZBDT01 */
  
  } /* zbdt01_ */
  