    // Copyright (C) 2010  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_MATRiX_TRSM_Hh_
    #define DLIB_MATRiX_TRSM_Hh_
    #include "lapack/fortran_id.h"
    #include "cblas_constants.h"

    namespace dlib
    {
        namespace blas_bindings
        {
    #ifdef DLIB_USE_BLAS
    #ifdef DLIB_DEFINE_CBLAS_API
            extern "C"
            {
                void cblas_strsm(const CBLAS_ORDER Order, const CBLAS_SIDE Side,
                                 const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE TransA,
                                 const CBLAS_DIAG Diag, const CBLAS_INT_TYPE M, const CBLAS_INT_TYPE N,
                                 const float alpha, const float *A, const CBLAS_INT_TYPE lda,
                                 float *B, const CBLAS_INT_TYPE ldb);

                void cblas_dtrsm(const CBLAS_ORDER Order, const CBLAS_SIDE Side,
                                 const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE TransA,
                                 const CBLAS_DIAG Diag, const CBLAS_INT_TYPE M, const CBLAS_INT_TYPE N,
                                 const double alpha, const double *A, const CBLAS_INT_TYPE lda,
                                 double *B, const CBLAS_INT_TYPE ldb);
            }
    #endif // if DLIB_DEFINE_CBLAS_API
    #endif // if DLIB_USE_BLAS

        // ------------------------------------------------------------------------------------

    /*  Purpose */
    /*  ======= */

    /*  DTRSM  solves one of the matrix equations */

    /*     op( A )*X = alpha*B,   or   X*op( A ) = alpha*B, */

    /*  where alpha is a scalar, X and B are m by n matrices, A is a unit, or */
    /*  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of */

    /*     op( A ) = A   or   op( A ) = A'. */

    /*  The matrix X is overwritten on B. */

    /*  Arguments */
    /*  ========== */

    /*  SIDE   - CHARACTER*1. */
    /*           On entry, SIDE specifies whether op( A ) appears on the left */
    /*           or right of X as follows: */

    /*              SIDE = 'L' or 'l'   op( A )*X = alpha*B. */

    /*              SIDE = 'R' or 'r'   X*op( A ) = alpha*B. */

    /*           Unchanged on exit. */

    /*  UPLO   - CHARACTER*1. */
    /*           On entry, UPLO specifies whether the matrix A is an upper or */
    /*           lower triangular matrix as follows: */

    /*              UPLO = 'U' or 'u'   A is an upper triangular matrix. */

    /*              UPLO = 'L' or 'l'   A is a lower triangular matrix. */

    /*           Unchanged on exit. */

    /*  TRANSA - CHARACTER*1. */
    /*           On entry, TRANSA specifies the form of op( A ) to be used in */
    /*           the matrix multiplication as follows: */

    /*              TRANSA = 'N' or 'n'   op( A ) = A. */

    /*              TRANSA = 'T' or 't'   op( A ) = A'. */

    /*              TRANSA = 'C' or 'c'   op( A ) = A'. */

    /*           Unchanged on exit. */

    /*  DIAG   - CHARACTER*1. */
    /*           On entry, DIAG specifies whether or not A is unit triangular */
    /*           as follows: */

    /*              DIAG = 'U' or 'u'   A is assumed to be unit triangular. */

    /*              DIAG = 'N' or 'n'   A is not assumed to be unit */
    /*                                  triangular. */

    /*           Unchanged on exit. */

    /*  M      - INTEGER. */
    /*           On entry, M specifies the number of rows of B. M must be at */
    /*           least zero. */
    /*           Unchanged on exit. */

    /*  N      - INTEGER. */
    /*           On entry, N specifies the number of columns of B.  N must be */
    /*           at least zero. */
    /*           Unchanged on exit. */

    /*  ALPHA  - DOUBLE PRECISION. */
    /*           On entry,  ALPHA specifies the scalar  alpha. When  alpha is */
    /*           zero then  A is not referenced and  B need not be set before */
    /*           entry. */
    /*           Unchanged on exit. */

    /*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m */
    /*           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'. */
    /*           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k */
    /*           upper triangular part of the array  A must contain the upper */
    /*           triangular matrix  and the strictly lower triangular part of */
    /*           A is not referenced. */
    /*           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k */
    /*           lower triangular part of the array  A must contain the lower */
    /*           triangular matrix  and the strictly upper triangular part of */
    /*           A is not referenced. */
    /*           Note that when  DIAG = 'U' or 'u',  the diagonal elements of */
    /*           A  are not referenced either,  but are assumed to be  unity. */
    /*           Unchanged on exit. */

    /*  LDA    - INTEGER. */
    /*           On entry, LDA specifies the first dimension of A as declared */
    /*           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then */
    /*           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r' */
    /*           then LDA must be at least max( 1, n ). */
    /*           Unchanged on exit. */

    /*  B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ). */
    /*           Before entry,  the leading  m by n part of the array  B must */
    /*           contain  the  right-hand  side  matrix  B,  and  on exit  is */
    /*           overwritten by the solution matrix  X. */

    /*  LDB    - INTEGER. */
    /*           On entry, LDB specifies the first dimension of B as declared */
    /*           in  the  calling  (sub)  program.   LDB  must  be  at  least */
    /*           max( 1, m ). */
    /*           Unchanged on exit. */

    /*  Level 3 Blas routine. */

    /*  -- Written on 8-February-1989. */
    /*     Jack Dongarra, Argonne National Laboratory. */
    /*     Iain Duff, AERE Harwell. */
    /*     Jeremy Du Croz, Numerical Algorithms Group Ltd. */
    /*     Sven Hammarling, Numerical Algorithms Group Ltd. */

            template <typename T>
            void local_trsm(
                const CBLAS_ORDER Order,
                CBLAS_SIDE Side,
                CBLAS_UPLO Uplo,
                const CBLAS_TRANSPOSE TransA,
                const CBLAS_DIAG Diag,
                long m,
                long n,
                T alpha,
                const T *a,
                long lda,
                T *b,
                long ldb
            )
            /*!
                This is a copy of the dtrsm routine from the netlib.org BLAS which was run though
                f2c and converted into this form for use when a BLAS library is not available.
            !*/
            {
                if (Order == CblasRowMajor)
                {
                    // since row major ordering looks like transposition to FORTRAN we need to flip a
                    // few things.
                    if (Side == CblasLeft)
                        Side = CblasRight;
                    else
                        Side = CblasLeft;

                    if (Uplo == CblasUpper)
                        Uplo = CblasLower;
                    else
                        Uplo = CblasUpper;

                    std::swap(m,n);
                }

                /* System generated locals */
                long a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;

                /* Local variables */
                long i__, j, k, info;
                T temp;
                bool lside;
                long nrowa;
                bool upper;
                bool nounit;

                /* Parameter adjustments */
                a_dim1 = lda;
                a_offset = 1 + a_dim1;
                a -= a_offset;
                b_dim1 = ldb;
                b_offset = 1 + b_dim1;
                b -= b_offset;

                /* Function Body */
                lside = (Side == CblasLeft);
                if (lside)
                {
                    nrowa = m;
                } else
                {
                    nrowa = n;
                }
                nounit = (Diag == CblasNonUnit);
                upper = (Uplo == CblasUpper);

                info = 0;
                if (! lside && ! (Side == CblasRight)) {
                    info = 1;
                } else if (! upper && !(Uplo == CblasLower) ) {
                    info = 2;
                } else if (!(TransA == CblasNoTrans) &&
                           !(TransA == CblasTrans) &&
                           !(TransA == CblasConjTrans))  {
                    info = 3;
                } else if (!(Diag == CblasUnit) &&
                           !(Diag == CblasNonUnit) ) {
                    info = 4;
                } else if (m < 0) {
                    info = 5;
                } else if (n < 0) {
                    info = 6;
                } else if (lda < std::max<long>(1,nrowa)) {
                    info = 9;
                } else if (ldb < std::max<long>(1,m)) {
                    info = 11;
                }
                DLIB_CASSERT( info == 0, "Invalid inputs given to local_trsm");

                /*     Quick return if possible. */

                if (m == 0 || n == 0) {
                    return;
                }

                /*     And when  alpha.eq.zero. */

                if (alpha == 0.) {
                    i__1 = n;
                    for (j = 1; j <= i__1; ++j) {
                        i__2 = m;
                        for (i__ = 1; i__ <= i__2; ++i__) {
                            b[i__ + j * b_dim1] = 0.;
                            /* L10: */
                        }
                        /* L20: */
                    }
                    return;
                }

                /*     Start the operations. */

                if (lside) {
                    if (TransA == CblasNoTrans) {

                        /*           Form  B := alpha*inv( A )*B. */

                        if (upper) {
                            i__1 = n;
                            for (j = 1; j <= i__1; ++j) {
                                if (alpha != 1.) {
                                    i__2 = m;
                                    for (i__ = 1; i__ <= i__2; ++i__) {
                                        b[i__ + j * b_dim1] = alpha * b[i__ + j * b_dim1]
                                            ;
                                        /* L30: */
                                    }
                                }
                                for (k = m; k >= 1; --k) {
                                    if (b[k + j * b_dim1] != 0.) {
                                        if (nounit) {
                                            b[k + j * b_dim1] /= a[k + k * a_dim1];
                                        }
                                        i__2 = k - 1;
                                        for (i__ = 1; i__ <= i__2; ++i__) {
                                            b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
                                                i__ + k * a_dim1];
                                            /* L40: */
                                        }
                                    }
                                    /* L50: */
                                }
                                /* L60: */
                            }
                        } else {
                            i__1 = n;
                            for (j = 1; j <= i__1; ++j) {
                                if (alpha != 1.) {
                                    i__2 = m;
                                    for (i__ = 1; i__ <= i__2; ++i__) {
                                        b[i__ + j * b_dim1] = alpha * b[i__ + j * b_dim1]
                                            ;
                                        /* L70: */
                                    }
                                }
                                i__2 = m;
                                for (k = 1; k <= i__2; ++k) {
                                    if (b[k + j * b_dim1] != 0.) {
                                        if (nounit) {
                                            b[k + j * b_dim1] /= a[k + k * a_dim1];
                                        }
                                        i__3 = m;
                                        for (i__ = k + 1; i__ <= i__3; ++i__) {
                                            b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
                                                i__ + k * a_dim1];
                                            /* L80: */
                                        }
                                    }
                                    /* L90: */
                                }
                                /* L100: */
                            }
                        }
                    } else {

                        /*           Form  B := alpha*inv( A' )*B. */

                        if (upper) {
                            i__1 = n;
                            for (j = 1; j <= i__1; ++j) {
                                i__2 = m;
                                for (i__ = 1; i__ <= i__2; ++i__) {
                                    temp = alpha * b[i__ + j * b_dim1];
                                    i__3 = i__ - 1;
                                    for (k = 1; k <= i__3; ++k) {
                                        temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
                                        /* L110: */
                                    }
                                    if (nounit) {
                                        temp /= a[i__ + i__ * a_dim1];
                                    }
                                    b[i__ + j * b_dim1] = temp;
                                    /* L120: */
                                }
                                /* L130: */
                            }
                        } else {
                            i__1 = n;
                            for (j = 1; j <= i__1; ++j) {
                                for (i__ = m; i__ >= 1; --i__) {
                                    temp = alpha * b[i__ + j * b_dim1];
                                    i__2 = m;
                                    for (k = i__ + 1; k <= i__2; ++k) {
                                        temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
                                        /* L140: */
                                    }
                                    if (nounit) {
                                        temp /= a[i__ + i__ * a_dim1];
                                    }
                                    b[i__ + j * b_dim1] = temp;
                                    /* L150: */
                                }
                                /* L160: */
                            }
                        }
                    }
                } else {
                    if (TransA == CblasNoTrans) {

                        /*           Form  B := alpha*B*inv( A ). */

                        if (upper) {
                            i__1 = n;
                            for (j = 1; j <= i__1; ++j) {
                                if (alpha != 1.) {
                                    i__2 = m;
                                    for (i__ = 1; i__ <= i__2; ++i__) {
                                        b[i__ + j * b_dim1] = alpha * b[i__ + j * b_dim1]
                                            ;
                                        /* L170: */
                                    }
                                }
                                i__2 = j - 1;
                                for (k = 1; k <= i__2; ++k) {
                                    if (a[k + j * a_dim1] != 0.) {
                                        i__3 = m;
                                        for (i__ = 1; i__ <= i__3; ++i__) {
                                            b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
                                                i__ + k * b_dim1];
                                            /* L180: */
                                        }
                                    }
                                    /* L190: */
                                }
                                if (nounit) {
                                    temp = 1. / a[j + j * a_dim1];
                                    i__2 = m;
                                    for (i__ = 1; i__ <= i__2; ++i__) {
                                        b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
                                        /* L200: */
                                    }
                                }
                                /* L210: */
                            }
                        } else {
                            for (j = n; j >= 1; --j) {
                                if (alpha != 1.) {
                                    i__1 = m;
                                    for (i__ = 1; i__ <= i__1; ++i__) {
                                        b[i__ + j * b_dim1] = alpha * b[i__ + j * b_dim1]
                                            ;
                                        /* L220: */
                                    }
                                }
                                i__1 = n;
                                for (k = j + 1; k <= i__1; ++k) {
                                    if (a[k + j * a_dim1] != 0.) {
                                        i__2 = m;
                                        for (i__ = 1; i__ <= i__2; ++i__) {
                                            b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
                                                i__ + k * b_dim1];
                                            /* L230: */
                                        }
                                    }
                                    /* L240: */
                                }
                                if (nounit) {
                                    temp = 1. / a[j + j * a_dim1];
                                    i__1 = m;
                                    for (i__ = 1; i__ <= i__1; ++i__) {
                                        b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
                                        /* L250: */
                                    }
                                }
                                /* L260: */
                            }
                        }
                    } else {

                        /*           Form  B := alpha*B*inv( A' ). */

                        if (upper) {
                            for (k = n; k >= 1; --k) {
                                if (nounit) {
                                    temp = 1. / a[k + k * a_dim1];
                                    i__1 = m;
                                    for (i__ = 1; i__ <= i__1; ++i__) {
                                        b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
                                        /* L270: */
                                    }
                                }
                                i__1 = k - 1;
                                for (j = 1; j <= i__1; ++j) {
                                    if (a[j + k * a_dim1] != 0.) {
                                        temp = a[j + k * a_dim1];
                                        i__2 = m;
                                        for (i__ = 1; i__ <= i__2; ++i__) {
                                            b[i__ + j * b_dim1] -= temp * b[i__ + k *
                                                b_dim1];
                                            /* L280: */
                                        }
                                    }
                                    /* L290: */
                                }
                                if (alpha != 1.) {
                                    i__1 = m;
                                    for (i__ = 1; i__ <= i__1; ++i__) {
                                        b[i__ + k * b_dim1] = alpha * b[i__ + k * b_dim1]
                                            ;
                                        /* L300: */
                                    }
                                }
                                /* L310: */
                            }
                        } else {
                            i__1 = n;
                            for (k = 1; k <= i__1; ++k) {
                                if (nounit) {
                                    temp = 1. / a[k + k * a_dim1];
                                    i__2 = m;
                                    for (i__ = 1; i__ <= i__2; ++i__) {
                                        b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
                                        /* L320: */
                                    }
                                }
                                i__2 = n;
                                for (j = k + 1; j <= i__2; ++j) {
                                    if (a[j + k * a_dim1] != 0.) {
                                        temp = a[j + k * a_dim1];
                                        i__3 = m;
                                        for (i__ = 1; i__ <= i__3; ++i__) {
                                            b[i__ + j * b_dim1] -= temp * b[i__ + k *
                                                b_dim1];
                                            /* L330: */
                                        }
                                    }
                                    /* L340: */
                                }
                                if (alpha != 1.) {
                                    i__2 = m;
                                    for (i__ = 1; i__ <= i__2; ++i__) {
                                        b[i__ + k * b_dim1] = alpha * b[i__ + k * b_dim1]
                                            ;
                                        /* L350: */
                                    }
                                }
                                /* L360: */
                            }
                        }
                    }
                }
            }

        // ------------------------------------------------------------------------------------

            inline void cblas_trsm(const CBLAS_ORDER Order, const CBLAS_SIDE Side,
                                   const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE TransA,
                                   const CBLAS_DIAG Diag, const int M, const int N,
                                   const float alpha, const float *A, const int lda,
                                   float *B, const int ldb)
            {
    #ifdef DLIB_USE_BLAS
                if (M > 4)
                {
                    cblas_strsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
                    return;
                }
    #endif
                local_trsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
            }

            inline void cblas_trsm(const CBLAS_ORDER Order, const CBLAS_SIDE Side,
                                   const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE TransA,
                                   const CBLAS_DIAG Diag, const int M, const int N,
                                   const double alpha, const double *A, const int lda,
                                   double *B, const int ldb)
            {
    #ifdef DLIB_USE_BLAS
                if (M > 4)
                {
                    cblas_dtrsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
                    return;
                }
    #endif
                local_trsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
            }

            inline void cblas_trsm(const CBLAS_ORDER Order, const CBLAS_SIDE Side,
                                   const CBLAS_UPLO Uplo, const CBLAS_TRANSPOSE TransA,
                                   const CBLAS_DIAG Diag, const int M, const int N,
                                   const long double alpha, const long double *A, const int lda,
                                   long double *B, const int ldb)
            {
                local_trsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
            }

        // ------------------------------------------------------------------------------------

            template <
                typename T,
                long NR1, long NR2,
                long NC1, long NC2,
                typename MM
                >
            inline void triangular_solver (
                const CBLAS_SIDE Side,
                const CBLAS_UPLO Uplo,
                const CBLAS_TRANSPOSE TransA,
                const CBLAS_DIAG Diag,
                const matrix<T,NR1,NC1,MM,row_major_layout>& A,
                const T alpha,
                matrix<T,NR2,NC2,MM,row_major_layout>& B
            )
            {
                cblas_trsm(CblasRowMajor, Side,  Uplo, TransA, Diag, B.nr(), B.nc(),
                           alpha, &A(0,0), A.nc(), &B(0,0), B.nc());
            }

        // ------------------------------------------------------------------------------------

            template <
                typename T,
                long NR1, long NR2,
                long NC1, long NC2,
                typename MM
                >
            inline void triangular_solver (
                const CBLAS_SIDE Side,
                const CBLAS_UPLO Uplo,
                const CBLAS_TRANSPOSE TransA,
                const CBLAS_DIAG Diag,
                const matrix<T,NR1,NC1,MM,column_major_layout>& A,
                const T alpha,
                matrix<T,NR2,NC2,MM,column_major_layout>& B
            )
            {
                cblas_trsm(CblasColMajor, Side,  Uplo, TransA, Diag, B.nr(), B.nc(),
                           alpha, &A(0,0), A.nr(), &B(0,0), B.nr());
            }

        // ------------------------------------------------------------------------------------

            template <
                typename T,
                long NR1, long NR2,
                long NC1, long NC2,
                typename MM
                >
            inline void triangular_solver (
                const CBLAS_SIDE Side,
                const CBLAS_UPLO Uplo,
                const CBLAS_TRANSPOSE TransA,
                const CBLAS_DIAG Diag,
                const matrix<T,NR1,NC1,MM,column_major_layout>& A,
                matrix<T,NR2,NC2,MM,column_major_layout>& B,
                long rows_of_B
            )
            {
                const T alpha = 1;
                cblas_trsm(CblasColMajor, Side,  Uplo, TransA, Diag, rows_of_B, B.nc(),
                           alpha, &A(0,0), A.nr(), &B(0,0), B.nr());
            }

        // ------------------------------------------------------------------------------------

            template <
                typename T,
                long NR1, long NR2,
                long NC1, long NC2,
                typename MM,
                typename layout
                >
            inline void triangular_solver (
                const CBLAS_SIDE Side,
                const CBLAS_UPLO Uplo,
                const CBLAS_TRANSPOSE TransA,
                const CBLAS_DIAG Diag,
                const matrix<T,NR1,NC1,MM,layout>& A,
                matrix<T,NR2,NC2,MM,layout>& B
            )
            {
                const T alpha = 1;
                triangular_solver(Side, Uplo, TransA, Diag, A, alpha, B);
            }

        // ------------------------------------------------------------------------------------

        }
    }

    #endif // DLIB_MATRiX_TRSM_Hh_