Implemented methods asin, acos, atan

lib/math.js

@@ -929,7 +929,7 @@ function sin(x) {
         return Math.sin(x);
     }
 
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         return new Complex(
             0.5 * Math.sin(x.re) * (Math.exp(-x.im) + Math.exp( x.im)),
             0.5 * Math.cos(x.re) * (Math.exp( x.im) - Math.exp(-x.im))
@@ -975,6 +975,127 @@ sin.doc = {
     ]
 };
 
+/**
+ * Calculate the inverse sine of a value, asin(x)
+ * @param {Number | Complex | Unit} x
+ * @return {Number | Complex} res
+ */
+function asin(x) {
+    if (isNumber(x)) {
+        if (x >= -1 && x <= 1) {
+            return Math.asin(x);
+        }
+        else {
+            return asin(new Complex(x, 0));
+        }
+    }
+
+    if (x instanceof Complex) {
+        // asin(z) = -i*log(iz + sqrt(1-z^2))
+        var re = x.re;
+        var im = x.im;
+        var temp1 = new Complex(
+            im * im - re * re + 1.0,
+            -2.0 * re * im
+        );
+
+        var temp2 = sqrt(temp1);
+        var temp3 = new Complex(
+            temp2.re - im,
+            temp2.im + re
+        );
+
+        var temp4 = log(temp3);
+
+        return new Complex(temp4.im, -temp4.re);
+    }
+
+    // TODO: implement array support
+    // TODO: implement matrix support
+
+    throw newUnsupportedTypeError('asin', x);
+}
+
+math.asin = asin;
+
+/**
+ * Function documentation
+ */
+asin.doc = {
+    'name': 'asin',
+    'category': 'Trigonometry',
+    'syntax': [
+        'asin(x)'
+    ],
+    'description': 'Compute the inverse sine of a value in radians.',
+    'examples': [
+        'asin(0.5)',
+        'asin(sin(2.3))'
+    ],
+    'seealso': [
+        'sin',
+        'acos',
+        'asin'
+    ]
+};
+
+/**
+ * Calculate the inverse tangent of a value, atan(x)
+ * @param {Number | Complex | Unit} x
+ * @return {Number | Complex} res
+ */
+function atan(x) {
+    if (isNumber(x)) {
+        return Math.atan(x);
+    }
+
+    if (x instanceof Complex) {
+        // atan(z) = 1/2 * i * (ln(1-iz) - ln(1+iz))
+        var re = x.re;
+        var im = x.im;
+        var den = re * re + (1.0 - im) * (1.0 - im);
+
+        var temp1 = new Complex(
+            (1.0 - im * im - re * re) / den,
+            (-2.0 * re) / den
+        );
+        var temp2 = log(temp1);
+
+        return new Complex(
+            -0.5 * temp2.im,
+            0.5 * temp2.re
+        );
+    }
+
+    // TODO: implement array support
+    // TODO: implement matrix support
+
+    throw newUnsupportedTypeError('atan', x);
+}
+
+math.atan = atan;
+
+/**
+ * Function documentation
+ */
+atan.doc = {
+    'name': 'atan',
+    'category': 'Trigonometry',
+    'syntax': [
+        'atan(x)'
+    ],
+    'description': 'Compute the inverse tangent of a value in radians.',
+    'examples': [
+        'atan(0.5)',
+        'atan(tan(2.3))'
+    ],
+    'seealso': [
+        'tan',
+        'acos',
+        'asin'
+    ]
+};
+
 /**
  * Calculate the cosine of a value, cos(x)
  * @param {Number | Complex | Unit} x
@@ -985,7 +1106,7 @@ function cos(x) {
         return Math.cos(x);
     }
 
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         // cos(z) = (exp(iz) + exp(-iz)) / 2
         return new Complex(
             0.5 * Math.cos(x.re) * (Math.exp(-x.im) + Math.exp(x.im)),
@@ -1042,7 +1163,7 @@ function tan(x) {
         return Math.tan(x);
     }
 
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         var den = Math.exp(-4.0 * x.im) +
             2.0 * Math.exp(-2.0 * x.im) * Math.cos(2.0 * x.re) +
             1.0;
@@ -1091,6 +1212,70 @@ tan.doc = {
     ]
 };
 
+/**
+ * Calculate the inverse cosine of a value, acos(x)
+ * @param {Number | Complex | Unit} x
+ * @return {Number | Complex} res
+ */
+function acos(x) {
+    if (isNumber(x)) {
+        if (x >= -1 && x <= 1) {
+            return Math.acos(x);
+        }
+        else {
+            return acos(new Complex(x, 0));
+        }
+    }
+
+    if (x instanceof Complex) {
+        // acos(z) = 0.5*pi + i*log(iz + sqrt(1-z^2))
+        var temp1 = new Complex(
+            x.im * x.im - x.re * x.re + 1.0,
+            -2.0 * x.re * x.im
+        );
+        var temp2 = sqrt(temp1);
+        var temp3 = new Complex(
+            temp2.re - x.im,
+            temp2.im + x.re
+        );
+        var temp4 = log(temp3);
+
+        // 0.5*pi = 1.5707963267948966192313216916398
+        return new Complex(
+            1.57079632679489661923 - temp4.im,
+            temp4.re
+        );
+    }
+
+    // TODO: implement array support
+    // TODO: implement matrix support
+
+    throw newUnsupportedTypeError('acos', x);
+}
+
+math.acos = acos;
+
+/**
+ * Function documentation
+ */
+acos.doc = {
+    'name': 'acos',
+    'category': 'Trigonometry',
+    'syntax': [
+        'acos(x)'
+    ],
+    'description': 'Compute the inverse cosine of a value in radians.',
+    'examples': [
+        'acos(0.5)',
+        'acos(cos(2.3))'
+    ],
+    'seealso': [
+        'cos',
+        'acos',
+        'asin'
+    ]
+};
+
 /**
  * Calculate the exponent of a value, exp(x)
  * @param {Number | Complex} x
@@ -1100,7 +1285,7 @@ function exp (x) {
     if (isNumber(x)) {
         return Math.exp(x);
     }
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         var r = Math.exp(x.re);
         return new Complex(
             r * Math.cos(x.im),
@@ -1154,7 +1339,7 @@ function sqrt (x) {
         }
     }
 
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         var r = Math.sqrt(x.re * x.re + x.im * x.im);
         if (x.im >= 0.0) {
             return new Complex(
@@ -1211,7 +1396,7 @@ function abs(x) {
         return Math.abs(x);
     }
 
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         return Math.sqrt(x.re * x.re + x.im * x.im);
     }
 
@@ -1256,7 +1441,7 @@ function log(x) {
         }
     }
 
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         return new Complex (
             Math.log(Math.sqrt(x.re * x.re + x.im * x.im)),
             Math.atan2(x.im, x.re)

src/function/arithmetic/abs.js

@@ -8,7 +8,7 @@ function abs(x) {
         return Math.abs(x);
     }
 
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         return Math.sqrt(x.re * x.re + x.im * x.im);
     }
 

src/function/arithmetic/exp.js

@@ -7,7 +7,7 @@ function exp (x) {
     if (isNumber(x)) {
         return Math.exp(x);
     }
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         var r = Math.exp(x.re);
         return new Complex(
             r * Math.cos(x.im),

src/function/arithmetic/log.js

@@ -14,7 +14,7 @@ function log(x) {
         }
     }
 
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         return new Complex (
             Math.log(Math.sqrt(x.re * x.re + x.im * x.im)),
             Math.atan2(x.im, x.re)

src/function/arithmetic/sqrt.js

@@ -13,7 +13,7 @@ function sqrt (x) {
         }
     }
 
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         var r = Math.sqrt(x.re * x.re + x.im * x.im);
         if (x.im >= 0.0) {
             return new Complex(

src/function/trigonometry/acos.js

@@ -0,0 +1,63 @@
+/**
+ * Calculate the inverse cosine of a value, acos(x)
+ * @param {Number | Complex | Unit} x
+ * @return {Number | Complex} res
+ */
+function acos(x) {
+    if (isNumber(x)) {
+        if (x >= -1 && x <= 1) {
+            return Math.acos(x);
+        }
+        else {
+            return acos(new Complex(x, 0));
+        }
+    }
+
+    if (x instanceof Complex) {
+        // acos(z) = 0.5*pi + i*log(iz + sqrt(1-z^2))
+        var temp1 = new Complex(
+            x.im * x.im - x.re * x.re + 1.0,
+            -2.0 * x.re * x.im
+        );
+        var temp2 = sqrt(temp1);
+        var temp3 = new Complex(
+            temp2.re - x.im,
+            temp2.im + x.re
+        );
+        var temp4 = log(temp3);
+
+        // 0.5*pi = 1.5707963267948966192313216916398
+        return new Complex(
+            1.57079632679489661923 - temp4.im,
+            temp4.re
+        );
+    }
+
+    // TODO: implement array support
+    // TODO: implement matrix support
+
+    throw newUnsupportedTypeError('acos', x);
+}
+
+math.acos = acos;
+
+/**
+ * Function documentation
+ */
+acos.doc = {
+    'name': 'acos',
+    'category': 'Trigonometry',
+    'syntax': [
+        'acos(x)'
+    ],
+    'description': 'Compute the inverse cosine of a value in radians.',
+    'examples': [
+        'acos(0.5)',
+        'acos(cos(2.3))'
+    ],
+    'seealso': [
+        'cos',
+        'acos',
+        'asin'
+    ]
+};

src/function/trigonometry/asin.js

@@ -0,0 +1,63 @@
+/**
+ * Calculate the inverse sine of a value, asin(x)
+ * @param {Number | Complex | Unit} x
+ * @return {Number | Complex} res
+ */
+function asin(x) {
+    if (isNumber(x)) {
+        if (x >= -1 && x <= 1) {
+            return Math.asin(x);
+        }
+        else {
+            return asin(new Complex(x, 0));
+        }
+    }
+
+    if (x instanceof Complex) {
+        // asin(z) = -i*log(iz + sqrt(1-z^2))
+        var re = x.re;
+        var im = x.im;
+        var temp1 = new Complex(
+            im * im - re * re + 1.0,
+            -2.0 * re * im
+        );
+
+        var temp2 = sqrt(temp1);
+        var temp3 = new Complex(
+            temp2.re - im,
+            temp2.im + re
+        );
+
+        var temp4 = log(temp3);
+
+        return new Complex(temp4.im, -temp4.re);
+    }
+
+    // TODO: implement array support
+    // TODO: implement matrix support
+
+    throw newUnsupportedTypeError('asin', x);
+}
+
+math.asin = asin;
+
+/**
+ * Function documentation
+ */
+asin.doc = {
+    'name': 'asin',
+    'category': 'Trigonometry',
+    'syntax': [
+        'asin(x)'
+    ],
+    'description': 'Compute the inverse sine of a value in radians.',
+    'examples': [
+        'asin(0.5)',
+        'asin(sin(2.3))'
+    ],
+    'seealso': [
+        'sin',
+        'acos',
+        'asin'
+    ]
+};

src/function/trigonometry/atan.js

@@ -0,0 +1,56 @@
+/**
+ * Calculate the inverse tangent of a value, atan(x)
+ * @param {Number | Complex | Unit} x
+ * @return {Number | Complex} res
+ */
+function atan(x) {
+    if (isNumber(x)) {
+        return Math.atan(x);
+    }
+
+    if (x instanceof Complex) {
+        // atan(z) = 1/2 * i * (ln(1-iz) - ln(1+iz))
+        var re = x.re;
+        var im = x.im;
+        var den = re * re + (1.0 - im) * (1.0 - im);
+
+        var temp1 = new Complex(
+            (1.0 - im * im - re * re) / den,
+            (-2.0 * re) / den
+        );
+        var temp2 = log(temp1);
+
+        return new Complex(
+            -0.5 * temp2.im,
+            0.5 * temp2.re
+        );
+    }
+
+    // TODO: implement array support
+    // TODO: implement matrix support
+
+    throw newUnsupportedTypeError('atan', x);
+}
+
+math.atan = atan;
+
+/**
+ * Function documentation
+ */
+atan.doc = {
+    'name': 'atan',
+    'category': 'Trigonometry',
+    'syntax': [
+        'atan(x)'
+    ],
+    'description': 'Compute the inverse tangent of a value in radians.',
+    'examples': [
+        'atan(0.5)',
+        'atan(tan(2.3))'
+    ],
+    'seealso': [
+        'tan',
+        'acos',
+        'asin'
+    ]
+};

src/function/trigonometry/cos.js

@@ -8,7 +8,7 @@ function cos(x) {
         return Math.cos(x);
     }
 
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         // cos(z) = (exp(iz) + exp(-iz)) / 2
         return new Complex(
             0.5 * Math.cos(x.re) * (Math.exp(-x.im) + Math.exp(x.im)),

src/function/trigonometry/sin.js

@@ -8,7 +8,7 @@ function sin(x) {
         return Math.sin(x);
     }
 
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         return new Complex(
             0.5 * Math.sin(x.re) * (Math.exp(-x.im) + Math.exp( x.im)),
             0.5 * Math.cos(x.re) * (Math.exp( x.im) - Math.exp(-x.im))

src/function/trigonometry/tan.js

@@ -8,7 +8,7 @@ function tan(x) {
         return Math.tan(x);
     }
 
-    if (isComplex(x)) {
+    if (x instanceof Complex) {
         var den = Math.exp(-4.0 * x.im) +
             2.0 * Math.exp(-2.0 * x.im) * Math.cos(2.0 * x.re) +
             1.0;

test/test.html

@@ -3,7 +3,7 @@
 <head>
     <title>mathjs test</title>
 
-    <script src="../math.js" type="text/javascript"></script>
+    <script src="../lib/math.js" type="text/javascript"></script>
 </head>
 <body>
     <p>