text: /* dsbt21.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 doublereal c_b22 = 1.;
  static doublereal c_b23 = 0.;
  
  /* Subroutine */ int dsbt21_(char *uplo, integer *n, integer *ka, integer *ks, 
  	 doublereal *a, integer *lda, doublereal *d__, doublereal *e, 
  	doublereal *u, integer *ldu, doublereal *work, doublereal *result)
  {
      /* System generated locals */
      integer a_dim1, a_offset, u_dim1, u_offset, i__1, i__2, i__3, i__4;
      doublereal d__1, d__2;
  
      /* Local variables */
      integer j, jc, jr, lw, ika;
      doublereal ulp, unfl;
      extern /* Subroutine */ int dspr_(char *, integer *, doublereal *, 
  	    doublereal *, integer *, doublereal *), dspr2_(char *, 
  	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
  	    integer *, doublereal *), dgemm_(char *, char *, integer *
  , integer *, integer *, doublereal *, doublereal *, integer *, 
  	    doublereal *, integer *, doublereal *, doublereal *, integer *);
      extern logical lsame_(char *, char *);
      doublereal anorm;
      char cuplo[1];
      logical lower;
      doublereal wnorm;
      extern doublereal dlamch_(char *), dlange_(char *, integer *, 
  	    integer *, doublereal *, integer *, doublereal *), 
  	    dlansb_(char *, char *, integer *, integer *, doublereal *, 
  	    integer *, doublereal *), dlansp_(char *, char *, 
  	    integer *, doublereal *, doublereal *);
  
  
  /*  -- LAPACK test routine (version 3.1) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  DSBT21  generally checks a decomposition of the form */
  
  /*          A = U S U' */
  
  /*  where ' means transpose, A is symmetric banded, U is */
  /*  orthogonal, and S is diagonal (if KS=0) or symmetric */
  /*  tridiagonal (if KS=1). */
  
  /*  Specifically: */
  
  /*          RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and* */
  /*          RESULT(2) = | I - UU' | / ( n ulp ) */
  
  /*  Arguments */
  /*  ========= */
  
  /*  UPLO    (input) CHARACTER */
  /*          If UPLO='U', the upper triangle of A and V will be used and */
  /*          the (strictly) lower triangle will not be referenced. */
  /*          If UPLO='L', the lower triangle of A and V will be used and */
  /*          the (strictly) upper triangle will not be referenced. */
  
  /*  N       (input) INTEGER */
  /*          The size of the matrix.  If it is zero, DSBT21 does nothing. */
  /*          It must be at least zero. */
  
  /*  KA      (input) INTEGER */
  /*          The bandwidth of the matrix A.  It must be at least zero.  If */
  /*          it is larger than N-1, then max( 0, N-1 ) will be used. */
  
  /*  KS      (input) INTEGER */
  /*          The bandwidth of the matrix S.  It may only be zero or one. */
  /*          If zero, then S is diagonal, and E is not referenced.  If */
  /*          one, then S is symmetric tri-diagonal. */
  
  /*  A       (input) DOUBLE PRECISION array, dimension (LDA, N) */
  /*          The original (unfactored) matrix.  It is assumed to be */
  /*          symmetric, and only the upper (UPLO='U') or only the lower */
  /*          (UPLO='L') will be referenced. */
  
  /*  LDA     (input) INTEGER */
  /*          The leading dimension of A.  It must be at least 1 */
  /*          and at least min( KA, N-1 ). */
  
  /*  D       (input) DOUBLE PRECISION array, dimension (N) */
  /*          The diagonal of the (symmetric tri-) diagonal matrix S. */
  
  /*  E       (input) DOUBLE PRECISION array, dimension (N-1) */
  /*          The off-diagonal of the (symmetric tri-) diagonal matrix S. */
  /*          E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and */
  /*          (3,2) element, etc. */
  /*          Not referenced if KS=0. */
  
  /*  U       (input) DOUBLE PRECISION array, dimension (LDU, N) */
  /*          The orthogonal matrix in the decomposition, expressed as a */
  /*          dense matrix (i.e., not as a product of Householder */
  /*          transformations, Givens transformations, etc.) */
  
  /*  LDU     (input) INTEGER */
  /*          The leading dimension of U.  LDU must be at least N and */
  /*          at least 1. */
  
  /*  WORK    (workspace) DOUBLE PRECISION array, dimension (N**2+N) */
  
  /*  RESULT  (output) DOUBLE PRECISION array, dimension (2) */
  /*          The values computed by the two tests described above.  The */
  /*          values are currently limited to 1/ulp, to avoid overflow. */
  
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Constants */
  
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1;
      a -= a_offset;
      --d__;
      --e;
      u_dim1 = *ldu;
      u_offset = 1 + u_dim1;
      u -= u_offset;
      --work;
      --result;
  
      /* Function Body */
      result[1] = 0.;
      result[2] = 0.;
      if (*n <= 0) {
  	return 0;
      }
  
  /* Computing MAX */
  /* Computing MIN */
      i__3 = *n - 1;
      i__1 = 0, i__2 = min(i__3,*ka);
      ika = max(i__1,i__2);
      lw = *n * (*n + 1) / 2;
  
      if (lsame_(uplo, "U")) {
  	lower = FALSE_;
  	*(unsigned char *)cuplo = 'U';
      } else {
  	lower = TRUE_;
  	*(unsigned char *)cuplo = 'L';
      }
  
      unfl = dlamch_("Safe minimum");
      ulp = dlamch_("Epsilon") * dlamch_("Base");
  
  /*     Some Error Checks */
  
  /*     Do Test 1 */
  
  /*     Norm of A: */
  
  /* Computing MAX */
      d__1 = dlansb_("1", cuplo, n, &ika, &a[a_offset], lda, &work[1]);
      anorm = max(d__1,unfl);
  
  /*     Compute error matrix:    Error = A - U S U' */
  
  /*     Copy A from SB to SP storage format. */
  
      j = 0;
      i__1 = *n;
      for (jc = 1; jc <= i__1; ++jc) {
  	if (lower) {
  /* Computing MIN */
  	    i__3 = ika + 1, i__4 = *n + 1 - jc;
  	    i__2 = min(i__3,i__4);
  	    for (jr = 1; jr <= i__2; ++jr) {
  		++j;
  		work[j] = a[jr + jc * a_dim1];
  /* L10: */
  	    }
  	    i__2 = *n + 1 - jc;
  	    for (jr = ika + 2; jr <= i__2; ++jr) {
  		++j;
  		work[j] = 0.;
  /* L20: */
  	    }
  	} else {
  	    i__2 = jc;
  	    for (jr = ika + 2; jr <= i__2; ++jr) {
  		++j;
  		work[j] = 0.;
  /* L30: */
  	    }
  /* Computing MIN */
  	    i__2 = ika, i__3 = jc - 1;
  	    for (jr = min(i__2,i__3); jr >= 0; --jr) {
  		++j;
  		work[j] = a[ika + 1 - jr + jc * a_dim1];
  /* L40: */
  	    }
  	}
  /* L50: */
      }
  
      i__1 = *n;
      for (j = 1; j <= i__1; ++j) {
  	d__1 = -d__[j];
  	dspr_(cuplo, n, &d__1, &u[j * u_dim1 + 1], &c__1, &work[1])
  		;
  /* L60: */
      }
  
      if (*n > 1 && *ks == 1) {
  	i__1 = *n - 1;
  	for (j = 1; j <= i__1; ++j) {
  	    d__1 = -e[j];
  	    dspr2_(cuplo, n, &d__1, &u[j * u_dim1 + 1], &c__1, &u[(j + 1) * 
  		    u_dim1 + 1], &c__1, &work[1]);
  /* L70: */
  	}
      }
      wnorm = dlansp_("1", cuplo, n, &work[1], &work[lw + 1]);
  
      if (anorm > wnorm) {
  	result[1] = wnorm / anorm / (*n * ulp);
      } else {
  	if (anorm < 1.) {
  /* Computing MIN */
  	    d__1 = wnorm, d__2 = *n * anorm;
  	    result[1] = min(d__1,d__2) / anorm / (*n * ulp);
  	} else {
  /* Computing MIN */
  	    d__1 = wnorm / anorm, d__2 = (doublereal) (*n);
  	    result[1] = min(d__1,d__2) / (*n * ulp);
  	}
      }
  
  /*     Do Test 2 */
  
  /*     Compute  UU' - I */
  
      dgemm_("N", "C", n, n, n, &c_b22, &u[u_offset], ldu, &u[u_offset], ldu, &
  	    c_b23, &work[1], n);
  
      i__1 = *n;
      for (j = 1; j <= i__1; ++j) {
  	work[(*n + 1) * (j - 1) + 1] += -1.;
  /* L80: */
      }
  
  /* Computing MIN */
  /* Computing 2nd power */
      i__1 = *n;
      d__1 = dlange_("1", n, n, &work[1], n, &work[i__1 * i__1 + 1]),
  	     d__2 = (doublereal) (*n);
      result[2] = min(d__1,d__2) / (*n * ulp);
  
      return 0;
  
  /*     End of DSBT21 */
  
  } /* dsbt21_ */
  