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#include "dgBCMatrix.h"
/* TODO
 *  - code for trans = 'T' in cscb_syrk
 *  - code for non-trivial cscb_trmm
 */

SEXP dgBCMatrix_validate(SEXP x)
{
    SEXP pp = GET_SLOT(x, Matrix_pSym),
    ip = GET_SLOT(x, Matrix_iSym),
    xp = GET_SLOT(x, Matrix_xSym),
    dp = getAttrib(xp, R_DimSymbol);
    int *pv = INTEGER(pp),
    *dim = INTEGER(dp),
    ncol = length(pp) - 1;
    int nnz = pv[ncol];

    if (!(isReal(xp) && isArray(xp)))
    return mkString(_("slot x should be a real array"));
    if (length(dp) != 3)
    return mkString(_("slot x should be a 3-dimensional array"));
    if (length(ip) != nnz)
    return mkString(_("length of slot i does not match last element of slot p"));
    if (dim[2] != nnz)
    return
        mkString(_("third dimension of slot x does not match number of nonzeros"));
    return ScalarLogical(1);
}

/** 
 * Perform one of the matrix operations 
 *  C := alpha*op(A)*B + beta*C
 * or
 *  C := alpha*B*op(A) + beta*C
 * where A is a compressed, sparse, blocked matrix and
 * B and C are dense matrices.
 * 
 * @param side LFT or RGT
 * @param transa TRN or NTR
 * @param m number of rows in C
 * @param n number of columns in C
 * @param k number of rows in B if side == LFT, otherwise
 *        number of columns in B.
 * @param alpha
 * @param A pointer to a dgBCMatrix object
 * @param B matrix to be multiplied
 * @param ldb leading dimension of b as declared in the calling
 *        routine
 * @param beta scalar multiplier of c
 * @param C product matrix to be modified
 * @param ldc leading dimension of c as declared in the calling
 *        routine
 */
void
cscb_mm(enum CBLAS_SIDE side, enum CBLAS_TRANSPOSE transa,
    int m, int n, int k, double alpha, SEXP A,
    const double B[], int ldb, double beta, double C[], int ldc)
{
    SEXP AxP = GET_SLOT(A, Matrix_xSym),
    ApP = GET_SLOT(A, Matrix_pSym);
    int *adims = INTEGER(getAttrib(AxP, R_DimSymbol)),
    *Ap = INTEGER(ApP),
    *Ai = INTEGER(GET_SLOT(A, Matrix_iSym)),
    ancb = length(ApP) - 1, /* number of column blocks */
    anrb;           /* number of row blocks */
    int absz = adims[0] * adims[1]; /* block size */
    int j;
    double *Ax = REAL(AxP);

    if (ldc < m) error(_("incompatible dims m=%d, ldc=%d"), m, ldc);
    if (side == LFT) {
    /* B is of size k by n */
    if (ldb < k)
        error(_("incompatible L dims k=%d, ldb=%d, n=%d, nr=%d, nc=%d"),
          k, ldb, n, adims[0], adims[1]);
    if (transa == TRN) {
        if (m % adims[1] || k % adims[0])
        error(_("incompatible LT dims m=%d, k = %d, nr=%d, nc=%d"),
              m, k, adims[0], adims[1]);
        if (ancb != m/adims[1])
        error(_("incompatible LT dims m=%d, ancb=%d, adims=[%d,%d,%d]"),
              m, ancb, adims[0], adims[1], adims[2]);
        anrb = k/adims[0];
    } else {
        if (m % adims[0] || k % adims[1])
        error(_("incompatible LN dims m=%d, k = %d, nr=%d, nc=%d"),
              m, k, adims[0], adims[1]);
        if (ancb != k/adims[1])
        error(_("incompatible LN dims k=%d, ancb=%d, adims=[%d,%d,%d]"),
              k, ancb, adims[0], adims[1], adims[2]);
        anrb = m/adims[0];
    }
    for (j = 0; j < ancb; j++) {
        int kk, j2 = Ap[j + 1];
        for (kk = Ap[j]; kk < j2; kk++) {
        int ii = Ai[kk];
        if (ii < 0 || ii >= anrb)
            error(_("improper row index ii=%d, anrb=%d"), ii, anrb);
        if (transa == TRN) {
            F77_CALL(dgemm)("T", "N", adims+1, &n, adims,
                    &alpha, Ax + kk * absz, adims,
                    B + ii * adims[0], &ldb,
                    &beta, C + j * adims[1], &ldc);
        } else {
            F77_CALL(dgemm)("N", "N", adims, &n, adims+1,
                    &alpha, Ax + kk * absz, adims,
                    B + j * adims[1], &ldb,
                    &beta, C + ii * adims[0], &ldc);
        }
        }
    }
    } else {
    /* B is of size m by k */
    error(_("Call to cscb_mm must have side == LFT"));
    }
}

/** 
 * Perform one of the matrix operations 
 *  C := alpha*A*A' + beta*C,
 * or
 *  C := alpha*A'*A + beta*C,
 * where A is a compressed, sparse, blocked matrix and
 * C is a compressed, sparse, symmetric blocked matrix.
 * 
 * @param uplo UPP or LOW for upper or lower
 * @param trans TRN or NTR for transpose or no transpose
 * @param alpha scalar multiplier of outer product
 * @param A compressed sparse blocked matrix
 * @param beta scalar multiplier of c
 * @param C compressed sparse blocked symmetric matrix to be updated
 */
void
cscb_syrk(enum CBLAS_UPLO uplo, enum CBLAS_TRANSPOSE trans,
      double alpha, SEXP A,
      double beta, SEXP C)
{
    SEXP AxP = GET_SLOT(A, Matrix_xSym),
    ApP = GET_SLOT(A, Matrix_pSym),
    CxP = GET_SLOT(C, Matrix_xSym),
    CpP = GET_SLOT(C, Matrix_pSym);
    int *adims = INTEGER(getAttrib(AxP, R_DimSymbol)),
    *Ai = INTEGER(GET_SLOT(A, Matrix_iSym)),
    *Ap = INTEGER(ApP),
    *cdims = INTEGER(getAttrib(CxP, R_DimSymbol)),
    *Ci = INTEGER(GET_SLOT(C, Matrix_iSym)),
    *Cp = INTEGER(CpP),
    j, k;
    double *Ax = REAL(AxP), *Cx = REAL(CxP), one = 1.;
    int scalar = (adims[0] == 1 && adims[1] == 1),
    anc = length(ApP) - 1,
    asz = adims[0] * adims[1],
    csz = cdims[0] * cdims[1];


    if (cdims[0] != cdims[1]) error(_("blocks in C must be square"));
    if (trans == TRN) {
                /* FIXME: Write this part */
    error(_("Code for trans == TRN not yet written"));
    } else {
    if (adims[0] != cdims[0])
        error(_("Inconsistent dimensions: A[%d,%d,%d], C[%d,%d,%d]"),
          adims[0], adims[1], adims[2],
          cdims[0], cdims[1], cdims[2]);
                /* check the row indices */
    for (k = 0; k < adims[2]; k++) {
        int aik = Ai[k];
        if (aik < 0 || aik >= cdims[2])
        error(_("Row index %d = %d is out of range [0, %d]"),
              k, aik, cdims[2] - 1);
    }
                /* multiply C by beta */
    if (beta != 1.)
        for (j = 0; j < csz * cdims[2]; j++) Cx[j] *= beta;
                /* individual products */
    for (j = 0; j < anc; j++) {
        int k, kk, k2 = Ap[j+1];
        for (k = Ap[j]; k < k2; k++) {
        int ii = Ai[k];
        int K = check_csc_index(Cp, Ci, ii, ii, 0);

        if (scalar) Cx[K] += alpha * Ax[k] * Ax[k];
        else F77_CALL(dsyrk)((uplo == UPP) ? "U" : "L", "N",
                     cdims, adims + 1,
                     &alpha, Ax + k * asz, adims,
                     &one, Cx + K * csz, cdims);
        for (kk = k+1; kk < k2; kk++) {
            int jj = Ai[kk];
            K = (uplo == UPP) ? check_csc_index(Cp, Ci, ii, jj, 0) :
            check_csc_index(Cp, Ci, jj, ii, 0);

            if (scalar) Cx[K] += alpha * Ax[k] * Ax[kk];
            else F77_CALL(dgemm)("N", "T", cdims, cdims + 1,
                     adims + 1, &alpha,
                     Ax+((uplo==UPP)?k:kk)*asz, adims,
                     Ax+((uplo==UPP)?kk:k)*asz, adims,
                     &one, Cx + K * csz, cdims);
        }
        }
    }
    }
}

static void
copy_transpose(double dest[], const double src[], int n)
{
    int i, j;
    for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
        dest[i + j * n] = src[j + i * n];
    }
    }
}

/** 
 * Create the LD^{T/2}D^{1/2}L' decomposition of the positive definite
 * symmetric dgBCMatrix matrix A (upper triangle stored) in L and D^{1/2}.
 * D^{1/2} denotes the upper Cholesky factor of the positive definite positive
 * definite block diagonal matrix D.  The diagonal blocks are of size nci.
 * 
 * @param A pointer to a dgBCMatrix object containing the upper
 * triangle of a positive definite symmetric matrix.
 * @param Parent the parent array for A
 * @param L pointer to a dgBCMatrix object to hold L
 * @param D pointer to a 3D array to hold D
 * 
 * @return n the number of column blocks in A for success.  A value
 * less than n indicates the first column block whose diagonal was not
 * positive definite.
 */
int
cscb_ldl(SEXP A, const int Parent[], SEXP L, SEXP D)
{
    SEXP ApP = GET_SLOT(A, Matrix_pSym),
    AxP = GET_SLOT(A, Matrix_xSym);
    int *adims = INTEGER(getAttrib(AxP, R_DimSymbol)),
    diag, info, j, k, n = length(ApP) - 1;
    int *Ai = INTEGER(GET_SLOT(A, Matrix_iSym)),
    *Ap = INTEGER(ApP),
    *Li = INTEGER(GET_SLOT(L, Matrix_iSym)),
    *Lp = INTEGER(GET_SLOT(L, Matrix_pSym)), nci = adims[0];
    int ncisqr = nci * nci;
    double *Lx = REAL(GET_SLOT(L, Matrix_xSym)),
    *Ax = REAL(AxP), *Dx = REAL(D), minus1 = -1., one = 1.;
    
    if (adims[1] != nci || nci < 1)
    error(_("cscb_ldl: dim(A) is [%d, %d, %d]"), adims[0], adims[1], adims[2]);
    for (j = 0, diag = 1; j < n; j++) { /* check for trivial structure */
    if (Parent[j] >= 0) {diag = 0; break;}
    }
    if (diag) {
    Memcpy(Dx, Ax, ncisqr * n);
    for (j = 0; j < n; j++) { /* form D_i^{1/2} */
        F77_CALL(dpotrf)("U", &nci, Dx + j * ncisqr, &nci, &k);
        if (k) return j; /* return block number, not col no. */
    }
    return n;
    }
    if (nci == 1) {
    k = R_ldl_numeric(n, Ap, Ai, Ax, Lp, Parent, Li, Lx, Dx,
              (int *) NULL, (int *) NULL);
    if (k < n) return k;
    for (j = 0; j < n; j++) Dx[j] = sqrt(Dx[j]);
    return n;
    } else {           /* Copy of ldl_numeric from the LDL package
                * modified for blocked sparse matrices */ 
    int i, k, p, p2, len, top;
    int *Lnz = Calloc(n, int),
        *Pattern = Calloc(n, int),
        *Flag = Calloc(n, int);
    double *Y = Calloc(n * ncisqr, double), *Yi = Calloc(ncisqr, double);

    for (k = 0; k < n; k++) {
        /* compute nonzero Pattern of kth row of L, in topological order */
        AZERO(Y + k*ncisqr, ncisqr); /* Y[,,0:k] is now all zero */
        top = n;        /* stack for pattern is empty */
        Flag[k] = k;    /* mark node k as visited */
        Lnz[k] = 0;     /* count of nonzeros in column k of L */
        p2 = Ap[k+1];
        for (p = Ap[k]; p < p2; p++) {
        i = Ai[p];  /* get A[i,k] */
        if (i > k) error(_("cscb_ldl: A has nonzeros below diagonal"));
                /* copy A(i,k) into Y */ 
        Memcpy(Y + i * ncisqr, Ax + p * ncisqr, ncisqr); 
        /* follow path from i to root of etree,
         * stop at flagged node */
        for (len = 0; Flag[i] != k; i = Parent[i]) {
            Pattern[len++] = i; /* L[k,i] is nonzero */
            Flag[i] = k; /* mark i as visited */
        }
        while (len > 0) { /* push path on top of stack */
            Pattern[--top] = Pattern[--len];
        }
        }
        /* Pattern [top ... n-1] now contains nonzero pattern of L[,k] */
        /* compute numerical values in kth row of L
         * (a sparse triangular solve) */
        Memcpy(Dx + k * ncisqr, Y + k * ncisqr, ncisqr); /* get D[,,k] */
        AZERO(Y + k*ncisqr, ncisqr); /* clear Y[,,k] */
        for (; top < n; top++) {
        i = Pattern[top];
        Memcpy(Yi, Y + i*ncisqr, ncisqr); /* copy Y[,,i] */
        AZERO(Y + i*ncisqr, ncisqr); /* clear Y[,,i] */
        p2 = Lp[i] + Lnz[i];
        for (p = Lp[i]; p < p2; p++) {
            F77_CALL(dgemm)("N", "N", &nci, &nci, &nci, &minus1,
                    Lx + p*ncisqr, &nci, Yi, &nci,
                    &one, Y + Li[p]*ncisqr, &nci);
        }
        /* FIXME: Is this the correct order and transposition? */
        F77_CALL(dtrsm)("L", "U", "T", "N", &nci, &nci,
                &one, Dx + i*ncisqr, &nci, Yi, &nci);
        F77_CALL(dsyrk)("U", "T", &nci, &nci, &minus1, Yi, &nci,
                &one, Dx + k*ncisqr, &nci);
        F77_CALL(dtrsm)("L", "U", "N", "N", &nci, &nci,
                &one, Dx + i*ncisqr, &nci, Yi, &nci);
        Li[p] = k;  /* store L[k,i] in column form of L */
        /* Yi contains L[k,i]', not L[k,i] */
        copy_transpose(Lx + p * ncisqr, Yi, nci);
        Lnz[i]++;   /* increment count of nonzeros in col i */
        }
        F77_CALL(dpotrf)("U", &nci, Dx + k*ncisqr, &nci, &info);
        if (info) {
        Free(Y); Free(Yi); Free(Pattern); Free(Flag); Free(Lnz); 
        return k;  /* failure, D[,,k] not positive definite */
        }
    }
    Free(Y); Free(Yi); Free(Pattern); Free(Flag); Free(Lnz);
    return n;   /* success, diagonal of D is all nonzero */
    }
    return -1;          /* -Wall */
}

/** 
 * Perform one of the dgBCMatrix-matrix operations B := alpha*op(A)*B
 * or B := alpha*B*op(A)
 * 
 * @param side LFT or RGT for left or right
 * @param uplo UPP or LOW for upper or lower
 * @param transa TRN or NTR for transpose or no transpose
 * @param diag UNT or NUN for unit or non-unit
 * @param alpha scalar multiplier
 * @param A pointer to a triangular dgBCMatrix object
 * @param B contents of the matrix B
 * @param m number of rows in B
 * @param n number of columns in B
 * @param ldb leading dimension of B as declared in the calling function
 */
void
cscb_trmm(enum CBLAS_SIDE side, enum CBLAS_UPLO uplo,
      enum CBLAS_TRANSPOSE transa, enum CBLAS_DIAG diag,
      double alpha, SEXP A, double B[], int m, int n, int ldb)
{
    SEXP /* ApP = GET_SLOT(A, Matrix_pSym), */
    AxP = GET_SLOT(A, Matrix_xSym);
    int /* *Ai = INTEGER(GET_SLOT(A, Matrix_iSym)), */
/*  *Ap = INTEGER(ApP), */
    *xdims = INTEGER(getAttrib(AxP, R_DimSymbol)),
    i, j/* , nb = length(ApP) - 1 */;
    
    if (xdims[0] != xdims[1])
    error(_("Argument A to cscb_trmm is not triangular"));
    if (alpha != 1.0) {
    for (j = 0; j < n; j++) { /* scale by alpha */
        for (i = 0; i < m; i++)
        B[i + j * ldb] *= alpha;
    }
    }
    if (diag == UNT && xdims[2] < 1) return; /* A is the identity */
    error(_("Code for non-identity cases of cscb_trmm not yet written"));
}

/** 
 * Solve a triangular system of the form op(A)*X = alpha*B where A
 * is a dgBCMatrix triangular matrix and B is a dense matrix.
 * 
 * @param uplo UPP or LOW
 * @param transa TRN or NTR
 * @param diag UNT or NUN
 * @param alpha scalar multiplier
 * @param A pointer to a triangular dgBCMatrix object
 * @param m number of rows in B
 * @param n number of columns in B
 * @param B pointer to the contents of the matrix B
 * @param ldb leading dimension of B as declared in the calling function
 */
void
cscb_trsm(enum CBLAS_UPLO uplo, enum CBLAS_TRANSPOSE transa,
      enum CBLAS_DIAG diag, double alpha, SEXP A,
      int m, int n, double B[], int ldb)
{
    SEXP ApP = GET_SLOT(A, Matrix_pSym),
    AxP = GET_SLOT(A, Matrix_xSym);
    int *Ai = INTEGER(GET_SLOT(A, Matrix_iSym)),
    *Ap = INTEGER(ApP),
    *xdims = INTEGER(getAttrib(AxP, R_DimSymbol)),
    i, j, nb = length(ApP) - 1;
    double *Ax = REAL(GET_SLOT(A, Matrix_xSym)), minus1 = -1., one = 1.;
    
    if (xdims[0] != xdims[1])
    error(_("Argument A to cscb_trsm is not triangular"));
    if (ldb < m || ldb <= 0 || n <= 0)
    error(_("cscb_trsm: inconsistent dims m = %d, n = %d, ldb = %d"),
          m, n, ldb);
    if (m != (nb * xdims[0]))
    error(_("cscb_trsm: inconsistent dims m = %d, A[%d,%d,]x%d"),
          m, xdims[0], xdims[1], xdims[2]);
    if (alpha != 1.0) {
    for (j = 0; j < n; j++) { /* scale by alpha */
        for (i = 0; i < m; i++)
        B[i + j * ldb] *= alpha;
    }
    }
    if (diag == UNT) {
    if (xdims[2] < 1) return; /* A is the identity */
    if (xdims[0] == 1) {    /* scalar case */
        if (uplo == UPP) error(_("Code for upper triangle not yet written"));
        if (transa == TRN) {
        for (j = 0; j < n; j++)
            R_ldl_ltsolve(m, B + j * ldb, Ap, Ai, Ax);
        } else {
        for (j = 0; j < n; j++)
            R_ldl_lsolve(m, B + j * ldb, Ap, Ai, Ax);
        }
        return;
    } else {
        int p, p2, sza = xdims[0] * xdims[0];

        if (uplo == UPP) error(_("Code for upper triangle not yet written"));
        if (transa == TRN) {
        for (j = nb - 1; j >= 0; j--) {
            p2 = Ap[j+1];
            for (p = Ap[j]; p < p2; p++)
            F77_CALL(dgemm)("T", "N", xdims, &n, xdims,
                    &minus1, Ax + p * sza, xdims,
                    B + Ai[p] * xdims[0], &ldb,
                    &one, B + j * xdims[0], &ldb);
        }
        } else {
        for (j = 0; j < nb; j++) {
            p2 = Ap[j+1];
            for (p = Ap[j]; p < p2; p++)
            F77_CALL(dgemm)("N", "N", xdims, &n, xdims,
                    &minus1, Ax + p * sza, xdims,
                    B + j * xdims[0], &ldb,
                    &one, B + Ai[p] * xdims[0], &ldb);
        }
        }
    }
    } else {error(_("Code for non-unit cases of cscb_trsm not yet written"));}
}

/** 
 * Perform one of the operations B := alpha*op(A)*B or
 * B := alpha*B*op(A) where A and B are both dgBCMatrix.
 * 
 * @param side
 * @param uplo
 * @param transa
 * @param diag
 * @param alpha scalar multiplier
 * @param A pointer to a triangular dgBCMatrix object
 * @param B pointer to a general dgBCMatrix matrix
 */
void
cscb_trcbm(enum CBLAS_SIDE side, enum CBLAS_UPLO uplo,
       enum CBLAS_TRANSPOSE transa, enum CBLAS_DIAG diag,
       double alpha, SEXP A, SEXP B)
{
    SEXP
/*  ApP = GET_SLOT(A, Matrix_pSym), */
    AxP = GET_SLOT(A, Matrix_xSym),
/*  , BpP = GET_SLOT(B, Matrix_pSym) */
    BxP = GET_SLOT(B, Matrix_xSym);
    int
/*  *Ai = INTEGER(GET_SLOT(A, Matrix_iSym)), */
/*  *Ap = INTEGER(ApP), */
/*  *Bi = INTEGER(GET_SLOT(B, Matrix_iSym)), */
/*  *Bp = INTEGER(BpP), */
    *axdims = INTEGER(getAttrib(AxP, R_DimSymbol)),
    *bxdims = INTEGER(getAttrib(BxP, R_DimSymbol)) 
/*  , ncbA = length(ApP) - 1 */
/*  , ncbB = length(BpP) - 1 */
    ;
    int i, nbx = bxdims[0] * bxdims[1] * bxdims[2];

    if (axdims[0] != axdims[1])
    error(_("Argument A to cscb_trcbm is not triangular"));
    if (alpha != 1.0) {
    for (i = 0; i < nbx; i++) { /* scale by alpha */
        REAL(BxP)[i] *= alpha;
    }
    }
    if (diag == UNT && axdims[2] < 1) return; /* A is the identity */
    error(_("Code for non-trivial cscb_trcbm not yet written"));
}

/** 
 * Solve one of the systems op(A)*X = alpha*B or
 * X*op(A) = alpha*B where A dgBCMatrix triangular and B is dgBCMatrix.
 * 
 * @param side LFT or RGT for left or right
 * @param uplo UPP or LOW for upper or lower
 * @param transa TRN or NTR for transpose or no transpose
 * @param diag UNT or NON for unit or non-unit
 * @param alpha scalar multiplier
 * @param A pointer to a triangular dgBCMatrix object
 * @param Parent parent array for the column blocks of A
 * @param B pointer to a general dgBCMatrix matrix
 */
void
cscb_trcbsm(enum CBLAS_SIDE side, enum CBLAS_UPLO uplo,
        enum CBLAS_TRANSPOSE transa, enum CBLAS_DIAG diag,
        double alpha, SEXP A, const int Parent[], SEXP B)
{
    SEXP ApP = GET_SLOT(A, Matrix_pSym),
    AxP = GET_SLOT(A, Matrix_xSym),
    BpP = GET_SLOT(B, Matrix_pSym),
    BxP = GET_SLOT(B, Matrix_xSym);
    int *Ai = INTEGER(GET_SLOT(A, Matrix_iSym)),
    *Ap = INTEGER(ApP),
    *Bi = INTEGER(GET_SLOT(B, Matrix_iSym)),
    *Bp = INTEGER(BpP),
    *axdims = INTEGER(getAttrib(AxP, R_DimSymbol)),
    *bxdims = INTEGER(getAttrib(BxP, R_DimSymbol)),
/*  ncbA = length(ApP) - 1, */
    ncbB = length(BpP) - 1;
    int i, j, nbx = bxdims[0] * bxdims[1] * bxdims[2];
    double *Ax = REAL(AxP), *Bx = REAL(BxP);

    if (axdims[0] != axdims[1])
    error(_("Argument A to cscb_trcbm is not triangular"));
    if (alpha != 1.0) {
    for (i = 0; i < nbx; i++) { /* scale by alpha */
        REAL(BxP)[i] *= alpha;
    }
    }
    if (diag == UNT && axdims[2] < 1) return;   /* A is the identity */
    if (diag == UNT && axdims[0] == 1) { /* can use R_ldl code */
    if ((side != LFT) && transa == TRN) {   /* case required for lmer */
        int *BTp, nnz = bxdims[2], nrbB;
        int *tmp = expand_cmprPt(ncbB, Bp, Calloc(nnz, int));
        int *BTi = Calloc(nnz, int);
        double *BTx = Calloc(nnz, double), *rhs;

                /* transpose B */
        for (i = 0, nrbB = -1; i < nnz; i++)
        if (Bi[i] > nrbB) nrbB = Bi[i];
        nrbB++;     /* max 0-based index is 1 too small */
        BTp = Calloc(nrbB, int);
        triplet_to_col(ncbB, nrbB, nnz, tmp, Bi, Bx, BTp, BTi, BTx);
                /* sanity check */
        if (BTp[nrbB] != nnz) error(_("cscb_trcbsm: transpose operation failed"));
        Free(tmp);
                /* Solve one column at a time */
        rhs = Calloc(ncbB, double);
        AZERO(Bx, nnz); /* zero the result */
        for (i = 0; i < nrbB; i++) {
        R_ldl_lsolve(ncbB,
                 expand_csc_column(rhs, ncbB, i, BTp, BTi, BTx),
                 Ap, Ai, Ax);
        /* write non-zeros in sol'n into B */
        for (j = 0; j < ncbB; j++) {
            if (rhs[j]) Bx[check_csc_index(Bp, Bi, i, j, 0)] = rhs[j];
        }
        }
        Free(rhs); Free(BTp); Free(BTx); Free(BTi);
        return;
    }
    error(_("cscb_trcbsm: method not yet written"));
    }
    error(_("cscb_trcbsm: method not yet written"));
}

/** 
 * Perform one of the matrix-matrix operations 
 *      C := alpha*op(A)*op(B) + beta*C
 * on compressed, sparse, blocked matrices.
 * 
 * @param transa TRN or NTR for transpose or no transpose of A
 * @param transb TRN or NTR for transpose or no transpose of B
 * @param alpha scalar multiplier
 * @param A pointer to a dgBCMatrix object
 * @param B pointer to a dgBCMatrix object
 * @param beta scalar multiplier
 * @param C pointer to a dgBCMatrix object
 */
void
cscb_cscbm(enum CBLAS_TRANSPOSE transa, enum CBLAS_TRANSPOSE transb,
       double alpha, SEXP A, SEXP B, double beta, SEXP C)
{
    SEXP ApP = GET_SLOT(A, Matrix_pSym),
    AxP = GET_SLOT(A, Matrix_xSym),
    BpP = GET_SLOT(B, Matrix_pSym),
    BxP = GET_SLOT(B, Matrix_xSym),
    CxP = GET_SLOT(C, Matrix_xSym);
    int *Ap = INTEGER(ApP),
    *Ai = INTEGER(GET_SLOT(A, Matrix_iSym)),
    *Bp = INTEGER(BpP),
    *Bi = INTEGER(GET_SLOT(B, Matrix_iSym)),
    *Cp = INTEGER(GET_SLOT(C, Matrix_pSym)),
    *Ci = INTEGER(GET_SLOT(C, Matrix_iSym)),
    *adims = INTEGER(getAttrib(AxP, R_DimSymbol)),
    *bdims = INTEGER(getAttrib(BxP, R_DimSymbol)),
    *cdims = INTEGER(getAttrib(CxP, R_DimSymbol)),
    nca = length(ApP) - 1,
    ncb = length(BpP) - 1;
    int ablk = adims[0] * adims[1],
    bblk = bdims[0] * bdims[1],
    cblk = cdims[0] * cdims[1];
    double *Ax = REAL(AxP),
    *Bx = REAL(BxP),
    *Cx = REAL(CxP),
    one = 1.0;

    if ((transa == NTR) && transb == TRN) { /* transposed crossproduct */
    int jj;

    if (adims[1] != bdims[1] ||
        adims[0] != cdims[0] ||
        bdims[0] != cdims[1])
        error(_("C[%d,%d,%d] := A[%d,%d,%d] %*% t(B[%d,%d,%d])"),
          cdims[0], cdims[1], cdims[2],
          adims[0], adims[1], adims[2],
          bdims[0], bdims[1], bdims[2]);
    if (nca != ncb)
        error(_("C := A(ncblocks = %d) %*% t(B(ncblocks = %d)"), nca, ncb);
    if (beta != 1.) {   /* scale C by beta */
        int ctot = cdims[0] * cdims[1] * cdims[2];
        for (jj = 0; jj < ctot; jj++) Cx[jj] *= beta;
    }
    for (jj = 0; jj < nca; jj++) {
        int ia, ib, a2 = Ap[jj + 1], b2 = Bp[jj + 1];
        for (ia = Ap[jj]; ia < a2; ia++) {
        for (ib = Bp[jj]; ib < b2; ib++) {  
        F77_CALL(dgemm)("N", "T", cdims, cdims + 1, adims + 1,
                &alpha, Ax + ia * ablk, adims,
                Bx + ib * bblk, bdims, &one,
                Cx + check_csc_index(Cp,Ci,Ai[ia],Bi[ib],0)*cblk,
                cdims);
        }
        }
    }
    return;
    }
    error(_("Code not yet written"));
}

/** 
 * Coerce a dgBCMatrix to a dgCMatrix
 * 
 * @param A pointer to a dgBCMatrix object to coerce
 * 
 * @return pointer to a dgCMatrix
 */
SEXP dgBCMatrix_to_dgCMatrix(SEXP A)
{
    SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dgCMatrix"))),
    ApP = GET_SLOT(A, Matrix_pSym),
    AiP = GET_SLOT(A, Matrix_iSym),
    AxP = GET_SLOT(A, Matrix_xSym);
    int *Ai = INTEGER(AiP), *Ap = INTEGER(ApP), *Bi, *Bp, *Dims,
    *adims = INTEGER(getAttrib(AxP, R_DimSymbol)),
    ii, j, ncb = length(ApP) - 1, nnz, nrb;
    int nc = adims[1], nr = adims[0];
    int sz = nc * nr;
    double *Ax = REAL(AxP), *Bx;

    SET_SLOT(val, Matrix_factorSym, allocVector(VECSXP, 0));
    SET_SLOT(val, Matrix_DimSym, allocVector(INTSXP, 2));
    Dims = INTEGER(GET_SLOT(val, Matrix_DimSym));
    Dims[1] = ncb * adims[1];
                /* find number of row blocks */
    for (j = 0, nrb = -1; j < adims[2]; j++) if (Ai[j] > nrb) nrb = Ai[j];
    Dims[0] = (nrb + 1) * adims[0]; /* +1 because of 0-based indices */
    nnz = length(AxP);

    if (nc == 1) {      /* x slot is in the correct order */
    SET_SLOT(val, Matrix_pSym, duplicate(ApP));
    SET_SLOT(val, Matrix_iSym, allocVector(INTSXP, nnz));
    SET_SLOT(val, Matrix_xSym, allocVector(REALSXP, nnz));
    Memcpy(REAL(GET_SLOT(val, Matrix_xSym)), Ax, nnz);
    if (nr == 1) {
        Memcpy(INTEGER(GET_SLOT(val, Matrix_iSym)), Ai, nnz);
    } else {
        Bi = INTEGER(GET_SLOT(val, Matrix_iSym));
        Bp = INTEGER(GET_SLOT(val, Matrix_pSym));
        for (j = 0; j <= ncb; j++) Bp[j] *= nr;
        for (j = 0; j < adims[2]; j++) {
        for (ii = 0; ii < nr; ii++) {
            Bi[j * nr + ii] = Ai[j] * nr + ii;
        }
        }
    }
    } else {
    SET_SLOT(val, Matrix_pSym, allocVector(INTSXP, Dims[1] + 1));
    Bp = INTEGER(GET_SLOT(val, Matrix_pSym));
    SET_SLOT(val, Matrix_iSym, allocVector(INTSXP, nnz));
    Bi = INTEGER(GET_SLOT(val, Matrix_iSym));
    SET_SLOT(val, Matrix_xSym, allocVector(REALSXP, nnz));
    Bx = REAL(GET_SLOT(val, Matrix_xSym));

    Bp[0] = 0;
    for (j = 0; j < ncb; j++) { /* Column blocks of A */
        int i, i1 = Ap[j], i2 = Ap[j + 1], jj;
        int nzbc = (i2 - i1) * nr; /* No. of non-zeroes in B column */

        for (jj = 0; jj < nc; jj++) { /* column within blocks */
        int jb = nc * j + jj; /* Column number in B */

        Bp[jb] = i1 * sz + jj * nzbc;
        for (i = i1; i < i2; i++) { /* index in Ai and Ax */
            for (ii = 0; ii < adims[0]; ii++) { /* row within blocks */
            int ind = ii + (i - i1) * nr + Bp[jb];

            Bi[ind] = Ai[i] * sz + jj * nzbc + ii;
            Bx[ind] = Ax[i * sz + jj * nc + ii];
            }
        }
        }
    }
    }
    UNPROTECT(1);
    return val;
}

SEXP dgBCMatrix_to_dgTMatrix(SEXP A)
{
    SEXP val = PROTECT(NEW_OBJECT(MAKE_CLASS("dgTMatrix"))),
    ApP = GET_SLOT(A, Matrix_pSym),
    AxP = GET_SLOT(A, Matrix_xSym);
    int *Ai = INTEGER(GET_SLOT(A, Matrix_iSym)), *Ap = INTEGER(ApP),
    *bdims = INTEGER(GET_SLOT(val, Matrix_DimSym)),
    *adims = INTEGER(getAttrib(AxP, R_DimSymbol)),
    i, j, k, kk, ncb = length(ApP) - 1, nnz = length(AxP), nrb;
    int *Aj = expand_cmprPt(ncb, Ap, Calloc(nnz, int)), 
    *Bi = INTEGER(ALLOC_SLOT(val, Matrix_iSym, INTSXP, nnz)),
    *Bj = INTEGER(ALLOC_SLOT(val, Matrix_jSym, INTSXP, nnz)),
    nblk = adims[2], nc = adims[1], nr = adims[0];
    int sz = nc * nr;
    int *ai = Calloc(sz, int), *aj = Calloc(sz, int);
    double *Ax = REAL(AxP),
    *Bx = REAL(ALLOC_SLOT(val, Matrix_xSym, REALSXP, nnz));

    Memcpy(Bx, Ax, nnz); /* x slot stays as is but w/o dim attribute */

    bdims[1] = ncb * adims[1];
    /* find number of row blocks */
    for (j = 0, nrb = -1; j < adims[2]; j++) if (Ai[j] > nrb) nrb = Ai[j];
    bdims[0] = (nrb + 1) * adims[0]; /* +1 because of 0-based indices */

    for (j = 0; j < nc; j++) {  /* arrays of inner indices */
    for (i = 0; i < nr; i++) {
        int ind = j * nc + i;
        ai[ind] = i;
        aj[ind] = j;
    }
    }
    for (i = 0, k = 0; k < nblk; k++) {
    for (kk = 0; kk < sz; kk++) {
        Bi[k * sz + kk] = Ai[k] * nr + ai[kk];
        Bj[k * sz + kk] = Aj[k] * nc + aj[kk];
    }
    }

    Free(Aj); Free(ai); Free(aj);
    UNPROTECT(1);
    return val;
}