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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;

}