#include "blaswrap.h"
/* 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"

/* 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 */
    static integer j, jc, jr, lw, ika;
    static 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 *);
    static doublereal anorm;
    static char cuplo[1];
    static logical lower;
    static 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   


    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.   

    =====================================================================   


       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_ */