+/* The third argument to F() is a "prototype". For most prototypes, the first
+ letter (before the _) represents the return type and each other letter
+ (after the _) is an argument type. The types are:
+
+ - "m": A matrix of unrestricted dimensions.
+
+ - "d": A scalar.
+
+ - "v": A row or column vector.
+
+ - "e": Primarily for the first argument, this is a matrix with
+ unrestricted dimensions treated elementwise. Each element in the matrix
+ is passed to the implementation function separately.
+
+ - "n": This gets passed the "const struct matrix_expr *" that represents
+ the expression. This allows the evaluation function to grab the source
+ location of arguments so that it can report accurate error locations.
+
+ The fourth argument is an optional constraints string. For this purpose the
+ first argument is named "a", the second "b", and so on. The following kinds
+ of constraints are supported. For matrix arguments, the constraints are
+ applied to each value in the matrix separately:
+
+ - "a(0,1)" or "a[0,1]": 0 < a < 1 or 0 <= a <= 1, respectively. Any
+ integer may substitute for 0 and 1. Half-open constraints (] and [) are
+ also supported.
+
+ - "ai": Restrict a to integer values.
+
+ - "a>0", "a<0", "a>=0", "a<=0", "a!=0".
+
+ - "a<b", "a>b", "a<=b", "a>=b", "b!=0".
+*/
+#define MATRIX_FUNCTIONS \
+ F(ABS, "ABS", m_e, NULL) \
+ F(ALL, "ALL", d_m, NULL) \
+ F(ANY, "ANY", d_m, NULL) \
+ F(ARSIN, "ARSIN", m_e, "a[-1,1]") \
+ F(ARTAN, "ARTAN", m_e, NULL) \
+ F(BLOCK, "BLOCK", m_any, NULL) \
+ F(CHOL, "CHOL", m_mn, NULL) \
+ F(CMIN, "CMIN", m_m, NULL) \
+ F(CMAX, "CMAX", m_m, NULL) \
+ F(COS, "COS", m_e, NULL) \
+ F(CSSQ, "CSSQ", m_m, NULL) \
+ F(CSUM, "CSUM", m_m, NULL) \
+ F(DESIGN, "DESIGN", m_mn, NULL) \
+ F(DET, "DET", d_m, NULL) \
+ F(DIAG, "DIAG", m_m, NULL) \
+ F(EVAL, "EVAL", m_mn, NULL) \
+ F(EXP, "EXP", m_e, NULL) \
+ F(GINV, "GINV", m_m, NULL) \
+ F(GRADE, "GRADE", m_m, NULL) \
+ F(GSCH, "GSCH", m_mn, NULL) \
+ F(IDENT, "IDENT", IDENT, "ai>=0 bi>=0") \
+ F(INV, "INV", m_m, NULL) \
+ F(KRONEKER, "KRONEKER", m_mm, NULL) \
+ F(LG10, "LG10", m_e, "a>0") \
+ F(LN, "LN", m_e, "a>0") \
+ F(MAGIC, "MAGIC", m_d, "ai>=3") \
+ F(MAKE, "MAKE", m_ddd, "ai>=0 bi>=0") \
+ F(MDIAG, "MDIAG", m_v, NULL) \
+ F(MMAX, "MMAX", d_m, NULL) \
+ F(MMIN, "MMIN", d_m, NULL) \
+ F(MOD, "MOD", m_md, "b!=0") \
+ F(MSSQ, "MSSQ", d_m, NULL) \
+ F(MSUM, "MSUM", d_m, NULL) \
+ F(NCOL, "NCOL", d_m, NULL) \
+ F(NROW, "NROW", d_m, NULL) \
+ F(RANK, "RANK", d_m, NULL) \
+ F(RESHAPE, "RESHAPE", m_mddn, NULL) \
+ F(RMAX, "RMAX", m_m, NULL) \
+ F(RMIN, "RMIN", m_m, NULL) \
+ F(RND, "RND", m_e, NULL) \
+ F(RNKORDER, "RNKORDER", m_m, NULL) \
+ F(RSSQ, "RSSQ", m_m, NULL) \
+ F(RSUM, "RSUM", m_m, NULL) \
+ F(SIN, "SIN", m_e, NULL) \
+ F(SOLVE, "SOLVE", m_mmn, NULL) \
+ F(SQRT, "SQRT", m_e, "a>=0") \
+ F(SSCP, "SSCP", m_m, NULL) \
+ F(SVAL, "SVAL", m_m, NULL) \
+ F(SWEEP, "SWEEP", m_mdn, NULL) \
+ F(T, "T", m_m, NULL) \
+ F(TRACE, "TRACE", d_m, NULL) \
+ F(TRANSPOS, "TRANSPOS", m_m, NULL) \
+ F(TRUNC, "TRUNC", m_e, NULL) \
+ F(UNIFORM, "UNIFORM", m_ddn, "ai>=0 bi>=0") \
+ F(PDF_BETA, "PDF.BETA", m_edd, "a[0,1] b>0 c>0") \
+ F(CDF_BETA, "CDF.BETA", m_edd, "a[0,1] b>0 c>0") \
+ F(IDF_BETA, "IDF.BETA", m_edd, "a[0,1] b>0 c>0") \
+ F(RV_BETA, "RV.BETA", d_dd, "a>0 b>0") \
+ F(NCDF_BETA, "NCDF.BETA", m_eddd, "a>=0 b>0 c>0 d>0") \
+ F(NPDF_BETA, "NCDF.BETA", m_eddd, "a>=0 b>0 c>0 d>0") \
+ F(CDF_BVNOR, "CDF.BVNOR", m_eed, "c[-1,1]") \
+ F(PDF_BVNOR, "PDF.BVNOR", m_eed, "c[-1,1]") \
+ F(CDF_CAUCHY, "CDF.CAUCHY", m_edd, "c>0") \
+ F(IDF_CAUCHY, "IDF.CAUCHY", m_edd, "a(0,1) c>0") \
+ F(PDF_CAUCHY, "PDF.CAUCHY", m_edd, "c>0") \
+ F(RV_CAUCHY, "RV.CAUCHY", d_dd, "b>0") \
+ F(CDF_CHISQ, "CDF.CHISQ", m_ed, "a>=0 b>0") \
+ F(CHICDF, "CHICDF", m_ed, "a>=0 b>0") \
+ F(IDF_CHISQ, "IDF.CHISQ", m_ed, "a[0,1) b>0") \
+ F(PDF_CHISQ, "PDF.CHISQ", m_ed, "a>=0 b>0") \
+ F(RV_CHISQ, "RV.CHISQ", d_d, "a>0") \
+ F(SIG_CHISQ, "SIG.CHISQ", m_ed, "a>=0 b>0") \
+ F(CDF_EXP, "CDF.EXP", m_ed, "a>=0 b>=0") \
+ F(IDF_EXP, "IDF.EXP", m_ed, "a[0,1) b>0") \
+ F(PDF_EXP, "PDF.EXP", m_ed, "a>=0 b>0") \
+ F(RV_EXP, "RV.EXP", d_d, "a>0") \
+ F(PDF_XPOWER, "PDF.XPOWER", m_edd, "b>0 c>=0") \
+ F(RV_XPOWER, "RV.XPOWER", d_dd, "a>0 c>=0") \
+ F(CDF_F, "CDF.F", m_edd, "a>=0 b>0 c>0") \
+ F(FCDF, "FCDF", m_edd, "a>=0 b>0 c>0") \
+ F(IDF_F, "IDF.F", m_edd, "a[0,1) b>0 c>0") \
+ F(PDF_F, "PDF.F", m_edd, "a>=0 b>0 c>0") \
+ F(RV_F, "RV.F", d_dd, "a>0 b>0") \
+ F(SIG_F, "SIG.F", m_edd, "a>=0 b>0 c>0") \
+ F(CDF_GAMMA, "CDF.GAMMA", m_edd, "a>=0 b>0 c>0") \
+ F(IDF_GAMMA, "IDF.GAMMA", m_edd, "a[0,1] b>0 c>0") \
+ F(PDF_GAMMA, "PDF.GAMMA", m_edd, "a>=0 b>0 c>0") \
+ F(RV_GAMMA, "RV.GAMMA", d_dd, "a>0 b>0") \
+ F(PDF_LANDAU, "PDF.LANDAU", m_e, NULL) \
+ F(RV_LANDAU, "RV.LANDAU", d_none, NULL) \
+ F(CDF_LAPLACE, "CDF.LAPLACE", m_edd, "c>0") \
+ F(IDF_LAPLACE, "IDF.LAPLACE", m_edd, "a(0,1) c>0") \
+ F(PDF_LAPLACE, "PDF.LAPLACE", m_edd, "c>0") \
+ F(RV_LAPLACE, "RV.LAPLACE", d_dd, "b>0") \
+ F(RV_LEVY, "RV.LEVY", d_dd, "b(0,2]") \
+ F(RV_LVSKEW, "RV.LVSKEW", d_ddd, "b(0,2] c[-1,1]") \
+ F(CDF_LOGISTIC, "CDF.LOGISTIC", m_edd, "c>0") \
+ F(IDF_LOGISTIC, "IDF.LOGISTIC", m_edd, "a(0,1) c>0") \
+ F(PDF_LOGISTIC, "PDF.LOGISTIC", m_edd, "c>0") \
+ F(RV_LOGISTIC, "RV.LOGISTIC", d_dd, "b>0") \
+ F(CDF_LNORMAL, "CDF.LNORMAL", m_edd, "a>=0 b>0 c>0") \
+ F(IDF_LNORMAL, "IDF.LNORMAL", m_edd, "a[0,1) b>0 c>0") \
+ F(PDF_LNORMAL, "PDF.LNORMAL", m_edd, "a>=0 b>0 c>0") \
+ F(RV_LNORMAL, "RV.LNORMAL", d_dd, "a>0 b>0") \
+ F(CDF_NORMAL, "CDF.NORMAL", m_edd, "c>0") \
+ F(IDF_NORMAL, "IDF.NORMAL", m_edd, "a(0,1) c>0") \
+ F(PDF_NORMAL, "PDF.NORMAL", m_edd, "c>0") \
+ F(RV_NORMAL, "RV.NORMAL", d_dd, "b>0") \
+ F(CDFNORM, "CDFNORM", m_e, NULL) \
+ F(PROBIT, "PROBIT", m_e, "a(0,1)") \
+ F(NORMAL, "NORMAL", m_e, "a>0") \
+ F(PDF_NTAIL, "PDF.NTAIL", m_edd, "b>0 c>0") \
+ F(RV_NTAIL, "RV.NTAIL", d_dd, "a>0 b>0") \
+ F(CDF_PARETO, "CDF.PARETO", m_edd, "a>=b b>0 c>0") \
+ F(IDF_PARETO, "IDF.PARETO", m_edd, "a[0,1) b>0 c>0") \
+ F(PDF_PARETO, "PDF.PARETO", m_edd, "a>=b b>0 c>0") \
+ F(RV_PARETO, "RV.PARETO", d_dd, "a>0 b>0") \
+ F(CDF_RAYLEIGH, "CDF.RAYLEIGH", m_ed, "b>0") \
+ F(IDF_RAYLEIGH, "IDF.RAYLEIGH", m_ed, "a[0,1] b>0") \
+ F(PDF_RAYLEIGH, "PDF.RAYLEIGH", m_ed, "b>0") \
+ F(RV_RAYLEIGH, "RV.RAYLEIGH", d_d, "a>0") \
+ F(PDF_RTAIL, "PDF.RTAIL", m_edd, NULL) \
+ F(RV_RTAIL, "RV.RTAIL", d_dd, NULL) \
+ F(CDF_T, "CDF.T", m_ed, "b>0") \
+ F(TCDF, "TCDF", m_ed, "b>0") \
+ F(IDF_T, "IDF.T", m_ed, "a(0,1) b>0") \
+ F(PDF_T, "PDF.T", m_ed, "b>0") \
+ F(RV_T, "RV.T", d_d, "a>0") \
+ F(CDF_T1G, "CDF.T1G", m_edd, NULL) \
+ F(IDF_T1G, "IDF.T1G", m_edd, "a(0,1)") \
+ F(PDF_T1G, "PDF.T1G", m_edd, NULL) \
+ F(RV_T1G, "RV.T1G", d_dd, NULL) \
+ F(CDF_T2G, "CDF.T2G", m_edd, NULL) \
+ F(IDF_T2G, "IDF.T2G", m_edd, "a(0,1)") \
+ F(PDF_T2G, "PDF.T2G", m_edd, NULL) \
+ F(RV_T2G, "RV.T2G", d_dd, NULL) \
+ F(CDF_UNIFORM, "CDF.UNIFORM", m_edd, "a<=c b<=c") \
+ F(IDF_UNIFORM, "IDF.UNIFORM", m_edd, "a[0,1] b<=c") \
+ F(PDF_UNIFORM, "PDF.UNIFORM", m_edd, "a<=c b<=c") \
+ F(RV_UNIFORM, "RV.UNIFORM", d_dd, "a<=b") \
+ F(CDF_WEIBULL, "CDF.WEIBULL", m_edd, "a>=0 b>0 c>0") \
+ F(IDF_WEIBULL, "IDF.WEIBULL", m_edd, "a[0,1) b>0 c>0") \
+ F(PDF_WEIBULL, "PDF.WEIBULL", m_edd, "a>=0 b>0 c>0") \
+ F(RV_WEIBULL, "RV.WEIBULL", d_dd, "a>0 b>0") \
+ F(CDF_BERNOULLI, "CDF.BERNOULLI", m_ed, "ai[0,1] b[0,1]") \
+ F(PDF_BERNOULLI, "PDF.BERNOULLI", m_ed, "ai[0,1] b[0,1]") \
+ F(RV_BERNOULLI, "RV.BERNOULLI", d_d, "a[0,1]") \
+ F(CDF_BINOM, "CDF.BINOM", m_edd, "bi>0 c[0,1]") \
+ F(PDF_BINOM, "PDF.BINOM", m_edd, "ai>=0<=b bi>0 c[0,1]") \
+ F(RV_BINOM, "RV.BINOM", d_dd, "ai>0 b[0,1]") \
+ F(CDF_GEOM, "CDF.GEOM", m_ed, "ai>=1 b[0,1]") \
+ F(PDF_GEOM, "PDF.GEOM", m_ed, "ai>=1 b[0,1]") \
+ F(RV_GEOM, "RV.GEOM", d_d, "a[0,1]") \
+ F(CDF_HYPER, "CDF.HYPER", m_eddd, "ai>=0<=d bi>0 ci>0<=b di>0<=b") \
+ F(PDF_HYPER, "PDF.HYPER", m_eddd, "ai>=0<=d bi>0 ci>0<=b di>0<=b") \
+ F(RV_HYPER, "RV.HYPER", d_ddd, "ai>0 bi>0<=a ci>0<=a") \
+ F(PDF_LOG, "PDF.LOG", m_ed, "a>=1 b(0,1]") \
+ F(RV_LOG, "RV.LOG", d_d, "a(0,1]") \
+ F(CDF_NEGBIN, "CDF.NEGBIN", m_edd, "a>=1 bi c(0,1]") \
+ F(PDF_NEGBIN, "PDF.NEGBIN", m_edd, "a>=1 bi c(0,1]") \
+ F(RV_NEGBIN, "RV.NEGBIN", d_dd, "ai b(0,1]") \
+ F(CDF_POISSON, "CDF.POISSON", m_ed, "ai>=0 b>0") \
+ F(PDF_POISSON, "PDF.POISSON", m_ed, "ai>=0 b>0") \
+ F(RV_POISSON, "RV.POISSON", d_d, "a>0")
+
+struct matrix_function_properties
+ {
+ const char *name;
+ const char *constraints;
+ };