diff --git a/doc/helpdb.jl b/doc/helpdb.jl index ceda29b405e36..0c273dfd5fd85 100644 --- a/doc/helpdb.jl +++ b/doc/helpdb.jl @@ -426,6 +426,13 @@ "), +(E"Types",E"Base",E"maxintfloat",E"maxintfloat(type) + + The largest integer losslessly representable by the given floating- + point type + +"), + (E"Types",E"Base",E"sizeof",E"sizeof(type) Size, in bytes, of the canonical binary representation of the given @@ -1356,9 +1363,9 @@ collection[key...] = value "), -(E"Mathematical Functions",E"Base",E"mod",E"mod() +(E"Mathematical Functions",E"Base",E"mod",E"mod(x, m) - Modulus after division + Modulus after division, returning in the range [0,m) "), @@ -1368,12 +1375,24 @@ collection[key...] = value "), +(E"Mathematical Functions",E"Base",E"mod1",E"mod1(x, m) + + Modulus after division, returning in the range (0,m] + +"), + (E"Mathematical Functions",E"Base",E"//",E"//() Rational division "), +(E"Mathematical Functions",E"Base",E"num",E"num(x) + + Numerator of the rational representation of \"x\" + +"), + (E"Mathematical Functions",E"Base",E"den",E"den(x) Denominator of the rational representation of \"x\" @@ -1964,6 +1983,12 @@ collection[key...] = value "), +(E"Mathematical Functions",E"Base",E"factor",E"factor(n) + + Compute the prime factorization of an integer \"n\" + +"), + (E"Mathematical Functions",E"Base",E"gcd",E"gcd(x, y) Greatest common divisor @@ -1976,12 +2001,31 @@ collection[key...] = value "), +(E"Mathematical Functions",E"Base",E"gcdx",E"gcdx(x, y) + + Greatest common divisor, also returning integer coefficients \"u\" + and \"v\" that solve \"ux+vy == gcd(x,y)\" + +"), + +(E"Mathematical Functions",E"Base",E"ispow2",E"ispow2(n) + + Test whether \"n\" is a power of two + +"), + (E"Mathematical Functions",E"Base",E"nextpow2",E"nextpow2(n) Next power of two not less than \"n\" "), +(E"Mathematical Functions",E"Base",E"prevpow2",E"prevpow2(n) + + Previous power of two not greater than \"n\" + +"), + (E"Mathematical Functions",E"Base",E"nextpow",E"nextpow(a, n) Next power of \"a\" not less than \"n\" @@ -2008,6 +2052,12 @@ collection[key...] = value "), +(E"Mathematical Functions",E"Base",E"invmod",E"invmod(x, m) + + Inverse of \"x\", modulo \"m\" + +"), + (E"Mathematical Functions",E"Base",E"powermod",E"powermod(x, p, m) Compute \"mod(x^p, m)\" @@ -2202,6 +2252,34 @@ airyaiprime(x) "), +(E"Data Formats",E"Base",E"isbool",E"isbool(x) + + Test whether number or array is boolean + +"), + +(E"Data Formats",E"Base",E"int",E"int(x) + + Convert a number or array to the default integer type on your + platform. Alternatively, \"x\" can be a string, which is parsed as + an integer. + +"), + +(E"Data Formats",E"Base",E"integer",E"integer(x) + + Convert a number or array to integer type. If \"x\" is already of + integer type it is unchanged, otherwise it converts it to the + default integer type on your platform. + +"), + +(E"Data Formats",E"Base",E"isinteger",E"isinteger(x) + + Test whether a number or array is of integer type + +"), + (E"Data Formats",E"Base",E"int8",E"int8(x) Convert a number or array to \"Int8\" data type @@ -2226,6 +2304,12 @@ airyaiprime(x) "), +(E"Data Formats",E"Base",E"int128",E"int128(x) + + Convert a number or array to \"Int128\" data type + +"), + (E"Data Formats",E"Base",E"uint8",E"uint8(x) Convert a number or array to \"Uint8\" data type @@ -2250,6 +2334,12 @@ airyaiprime(x) "), +(E"Data Formats",E"Base",E"uint128",E"uint128(x) + + Convert a number or array to \"Uint128\" data type + +"), + (E"Data Formats",E"Base",E"float32",E"float32(x) Convert a number or array to \"Float32\" data type @@ -2262,21 +2352,30 @@ airyaiprime(x) "), -(E"Data Formats",E"Base",E"complex64",E"complex64(r, i) +(E"Data Formats",E"Base",E"float",E"float(x) - Convert to \"r+i*im\" represented as a \"Complex64\" data type + Convert a number, array, or string to a \"FloatingPoint\" data + type. For numeric data, the smallest suitable \"FloatingPoint\" + type is used. For strings, it converts to \"Float64\". "), -(E"Data Formats",E"Base",E"complex128",E"complex128(r, i) +(E"Data Formats",E"Base",E"float64_valued",E"float64_valued(x::Rational) - Convert to \"r+i*im\" represented as a \"Complex128\" data type + True if \"x\" can be losslessly represented as a \"Float64\" data + type "), -(E"Data Formats",E"Base",E"float64",E"float64(x) +(E"Data Formats",E"Base",E"complex64",E"complex64(r, i) - Convert a number or array to \"Float64\" data type + Convert to \"r+i*im\" represented as a \"Complex64\" data type + +"), + +(E"Data Formats",E"Base",E"complex128",E"complex128(r, i) + + Convert to \"r+i*im\" represented as a \"Complex128\" data type "), @@ -2363,12 +2462,32 @@ airyaiprime(x) "), +(E"Numbers",E"Base",E"isinf",E"isinf(f) + + Test whether a number is infinite + +"), + (E"Numbers",E"Base",E"isnan",E"isnan(f) Test whether a floating point number is not a number (NaN) "), +(E"Numbers",E"Base",E"inf",E"inf(f) + + Returns infinity in the same floating point type as \"f\" (or \"f\" + can by the type itself) + +"), + +(E"Numbers",E"Base",E"nan",E"nan(f) + + Returns NaN in the same floating point type as \"f\" (or \"f\" can + by the type itself) + +"), + (E"Numbers",E"Base",E"nextfloat",E"nextfloat(f) Get the next floating point number in lexicographic order @@ -2471,6 +2590,14 @@ airyaiprime(x) "), +(E"Numbers",E"Base",E"isprime",E"isprime(x::Integer) -> Bool + + Returns \"true\" if \"x\" is prime, and \"false\" otherwise. + + **Example**: \"isprime(3) -> true\" + +"), + (E"Random Numbers",E"Base",E"srand",E"srand([rng], seed) Seed the RNG with a \"seed\", which may be an unsigned integer or a @@ -3010,35 +3137,139 @@ airyaiprime(x) "), -(E"Linear Algebra",E"Base",E"lu",E"lu(A) -> LU +(E"Linear Algebra",E"Base",E"factors",E"factors(F) + + Return the factors of a factorization \"F\". For example, in the + case of an LU decomposition, factors(LU) -> L, U, P + +"), + +(E"Linear Algebra",E"Base",E"lu",E"lu(A) -> L, U, P + + Compute the LU factorization of \"A\", such that \"A[P,:] = L*U\". + +"), + +(E"Linear Algebra",E"Base",E"lufact",E"lufact(A) -> LUDense + + Compute the LU factorization of \"A\" and return a \"LUDense\" + object. \"factors(lufact(A))\" returns the triangular matrices + containing the factorization. The following functions are available + for \"LUDense\" objects: \"size\", \"factors\", \"\\\", \"inv\", + \"det\". + +"), + +(E"Linear Algebra",E"Base",E"lufact!",E"lufact!(A) -> LUDense + + \"lufact!\" is the same as \"lufact\" but saves space by + overwriting the input A, instead of creating a copy. + +"), + +(E"Linear Algebra",E"Base",E"chol",E"chol(A[, LU]) -> F + + Compute Cholesky factorization of a symmetric positive-definite + matrix \"A\" and return the matrix \"F\". If \"LU\" is \"L\" + (Lower), \"A = L*L'\". If \"LU\" is \"U\" (Upper), \"A = R'*R\". + +"), + +(E"Linear Algebra",E"Base",E"cholfact",E"cholfact(A[, LU]) -> CholeskyDense + + Compute the Cholesky factorization of a symmetric positive-definite + matrix \"A\" and return a \"CholeskyDense\" object. \"LU\" may be + 'L' for using the lower part or 'U' for the upper part. The default + is to use 'U'. \"factors(cholfact(A))\" returns the triangular + matrix containing the factorization. The following functions are + available for \"CholeskyDense\" objects: \"size\", \"factors\", + \"\\\", \"inv\", \"det\". A \"LAPACK.PosDefException\" error is + thrown in case the matrix is not positive definite. + +"), + +(E"Linear Algebra",E"Base",E"cholpfact",E"cholpfact(A[, LU]) -> CholeskyPivotedDense + + Compute the pivoted Cholesky factorization of a symmetric positive + semi-definite matrix \"A\" and return a \"CholeskyDensePivoted\" + object. \"LU\" may be 'L' for using the lower part or 'U' for the + upper part. The default is to use 'U'. \"factors(cholpfact(A))\" + returns the triangular matrix containing the factorization. The + following functions are available for \"CholeskyDensePivoted\" + objects: \"size\", \"factors\", \"\\\", \"inv\", \"det\". A + \"LAPACK.RankDeficientException\" error is thrown in case the + matrix is rank deficient. + +"), + +(E"Linear Algebra",E"Base",E"cholpfact!",E"cholpfact!(A[, LU]) -> CholeskyPivotedDense + + \"cholpfact!\" is the same as \"cholpfact\" but saves space by + overwriting the input A, instead of creating a copy. + +"), + +(E"Linear Algebra",E"Base",E"qr",E"qr(A) -> Q, R + + Compute the QR factorization of \"A\" such that \"A = Q*R\". Also + see \"qrd\". + +"), + +(E"Linear Algebra",E"Base",E"qrfact",E"qrfact(A) + + Compute the QR factorization of \"A\" and return a \"QRDense\" + object. \"factors(qrfact(A))\" returns \"Q\" and \"R\". The + following functions are available for \"QRDense\" objects: + \"size\", \"factors\", \"qmulQR\", \"qTmulQR\", \"\\\". + +"), + +(E"Linear Algebra",E"Base",E"qrfact!",E"qrfact!(A) + + \"qrfact!\" is the same as \"qrfact\" but saves space by + overwriting the input A, instead of creating a copy. + +"), + +(E"Linear Algebra",E"Base",E"qrp",E"qrp(A) -> Q, R, P - Compute LU factorization. LU is an \"LU factorization\" type that - can be used as an ordinary matrix. + Compute the QR factorization of \"A\" with pivoting, such that + \"A*I[:,P] = Q*R\", where \"I\" is the identity matrix. Also see + \"qrpfact\". "), -(E"Linear Algebra",E"Base",E"chol",E"chol(A) +(E"Linear Algebra",E"Base",E"qrpfact",E"qrpfact(A) -> QRPivotedDense - Compute Cholesky factorization + Compute the QR factorization of \"A\" with pivoting and return a + \"QRDensePivoted\" object. \"factors(qrpfact(A))\" returns \"Q\" + and \"R\". The following functions are available for + \"QRDensePivoted\" objects: \"size\", \"factors\", \"qmulQR\", + \"qTmulQR\", \"\\\". "), -(E"Linear Algebra",E"Base",E"qr",E"qr(A) +(E"Linear Algebra",E"Base",E"qrpfact!",E"qrpfact!(A) -> QRPivotedDense - Compute QR factorization + \"qrpfact!\" is the same as \"qrpfact\" but saves space by + overwriting the input A, instead of creating a copy. "), -(E"Linear Algebra",E"Base",E"qrp",E"qrp(A) +(E"Linear Algebra",E"Base",E"qmulQR",E"qmulQR(QR, A) - Compute QR factorization with pivoting + Perform Q*A efficiently, where Q is a an orthogonal matrix defined + as the product of k elementary reflectors from the QR + decomposition. "), -(E"Linear Algebra",E"Base",E"factors",E"factors(D) +(E"Linear Algebra",E"Base",E"qTmulQR",E"qTmulQR(QR, A) - Return the factors of a decomposition D. For an LU decomposition, - factors(LU) -> L, U, p + Perform Q'>>*< L, U, P + Return the factors of a factorization ``F``. For example, in the case of an LU decomposition, factors(LU) -> L, U, P .. function:: lu(A) -> L, U, P