add cond function in linalg package

README.md

@@ -5,7 +5,7 @@ MeteoInfo: GIS and scientific computation environment for meteorological communi
 [![DOI](https://zenodo.org/badge/172686439.svg)](https://zenodo.org/badge/latestdoi/172686439)
 [![Project Map](https://sourcespy.com/shield.svg)](https://sourcespy.com/github/meteoinfometeoinfo/)
 
-**MeteoInfo** is an intergrated framework for GIS application (**MeteoInfoMap**), scientific computation and 
+**MeteoInfo** is an integrated framework for GIS application (**MeteoInfoMap**), scientific computation and 
 visualization environment (**MeteoInfoLab**), especially for meteorological community.
 
 **MeteoInfoMap** is a GIS application which enables the user to visualize and analyze
@@ -18,8 +18,6 @@ ability of multiple dimensional array calculation and 2D/3D plotting.
 
 ![MeteoInfoLab GUI](images/MeteoInfoLab.PNG)
 
-**MeteoInfoLib** is a Java library providing main functions of MeteoInfoMap and MeteoInfoLab.
-
 It requires that Java 8 or greater be installed on your computer. See the
 http://www.java.com website for a free download of Java if you do not have it
 already installed.

meteoinfo-lab/milconfig.xml

@@ -1,36 +1,36 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <MeteoInfo File="milconfig.xml" Type="configurefile">
-  <Path OpenPath="D:\Working\MIScript\Jython\mis\plot_types\patch">
+  <Path OpenPath="D:\Working\MIScript\Jython\mis\common_math\linalg">
-    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\satellite"/>
-    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\satellite\omi"/>
-    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\plot_types\wind"/>
-    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\plot_types\pie"/>
-    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\io\micaps"/>
     <RecentFolder Folder="D:\Working\MIScript\Jython\mis\map\topology"/>
-    <RecentFolder Folder="D:\Working\MIScript\Jython\mis"/>
-    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\array"/>
-    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\plot_types"/>
     <RecentFolder Folder="D:\Working\MIScript\Jython\mis\plot_types\plot"/>
     <RecentFolder Folder="D:\Working\MIScript\Jython\mis\io"/>
     <RecentFolder Folder="D:\Working\MIScript\Jython\mis\io\radar"/>
     <RecentFolder Folder="D:\Working\MIScript\Jython\mis\map"/>
     <RecentFolder Folder="D:\Working\MIScript\Jython\mis\map\projection"/>
     <RecentFolder Folder="D:\Working\MIScript\Jython\mis\plot_types\patch"/>
+    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\plot_types"/>
+    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\plot_types\3d"/>
+    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\plot_types\3d\jogl"/>
+    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\plot_types\3d\jogl\city"/>
+    <RecentFolder Folder="D:\Working\MIScript\Jython\mis"/>
+    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\common_math"/>
+    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\array"/>
+    <RecentFolder Folder="D:\Working\MIScript\Jython\mis\common_math\linalg"/>
   </Path>
   <File>
     <OpenedFiles>
       <OpenedFile File="D:\MyProgram\java\MeteoInfoDev\toolbox\meteoview3d\_reload.py"/>
       <OpenedFile File="D:\MyProgram\java\MeteoInfoDev\toolbox\meteoview3d\mainGUI.py"/>
-      <OpenedFile File="D:\Working\MIScript\Jython\mis\io\micaps\mdfs_dataframe_2.py"/>
+      <OpenedFile File="D:\Working\MIScript\Jython\mis\common_math\linalg\svd.py"/>
-      <OpenedFile File="D:\Working\MIScript\Jython\mis\plot_types\patch\wind_circle_2.py"/>
+      <OpenedFile File="D:\Working\MIScript\Jython\mis\common_math\linalg\cond.py"/>
-      <OpenedFile File="D:\Working\MIScript\Jython\mis\plot_types\patch\wind_circle_1.py"/>
+      <OpenedFile File="D:\Working\MIScript\Jython\mis\common_math\linalg\norm_1.py"/>
     </OpenedFiles>
     <RecentFiles>
       <RecentFile File="D:\MyProgram\java\MeteoInfoDev\toolbox\meteoview3d\_reload.py"/>
       <RecentFile File="D:\MyProgram\java\MeteoInfoDev\toolbox\meteoview3d\mainGUI.py"/>
-      <RecentFile File="D:\Working\MIScript\Jython\mis\io\micaps\mdfs_dataframe_2.py"/>
+      <RecentFile File="D:\Working\MIScript\Jython\mis\common_math\linalg\svd.py"/>
-      <RecentFile File="D:\Working\MIScript\Jython\mis\plot_types\patch\wind_circle_2.py"/>
+      <RecentFile File="D:\Working\MIScript\Jython\mis\common_math\linalg\cond.py"/>
-      <RecentFile File="D:\Working\MIScript\Jython\mis\plot_types\patch\wind_circle_1.py"/>
+      <RecentFile File="D:\Working\MIScript\Jython\mis\common_math\linalg\norm_1.py"/>
     </RecentFiles>
   </File>
   <Font>

meteoinfo-lab/pylib/mipylib/numeric/core/_ndarray.py

@@ -698,6 +698,16 @@ class NDArray(object):
             else:
                 ArrayMath.setImage(self._array, val)
 
+    def conj(self):
+        """
+        Return the complex conjugate, element-wise.
+
+        The complex conjugate of a complex number is obtained by changing the sign of its imaginary part.
+
+        :return: (*array*) Complex conjugate array.
+        """
+        return NDArray(ArrayMath.conj(self._array))
+
     def min(self, axis=None):
         """
         Get minimum value along an axis.
@@ -707,8 +717,13 @@ class NDArray(object):
 
         :returns: Minimum values.
         """
-        if isinstance(axis, (list, tuple)) and len(axis) == self.ndim:
+        if self.ndim == 1:
             axis = None
+        elif isinstance(axis, (list, tuple)):
+            if len(axis) == 1:
+                axis = axis[0]
+            elif len(axis) == self.ndim:
+                axis = None
 
         if axis is None:
             r = ArrayMath.min(self._array)
@@ -768,8 +783,13 @@ class NDArray(object):
 
         :returns: Maximum values.
         """
-        if isinstance(axis, (list, tuple)) and len(axis) == self.ndim:
+        if self.ndim == 1:
             axis = None
+        elif isinstance(axis, (list, tuple)):
+            if len(axis) == 1:
+                axis = axis[0]
+            elif len(axis) == self.ndim:
+                axis = None
 
         if axis is None:
             r = ArrayMath.max(self._array)
@@ -787,12 +807,27 @@ class NDArray(object):
 
         returns: (*array_like*) Sum result
         """
-        if isinstance(axis, (list, tuple)) and len(axis) == self.ndim:
+        if self.ndim == 1:
             axis = None
+        elif isinstance(axis, (list, tuple)):
+            if len(axis) == 1:
+                axis = axis[0]
+            elif len(axis) == self.ndim:
+                axis = None
 
         if axis is None:
             return ArrayMath.sum(self._array)
         else:
+            if isinstance(axis, (list, tuple)):
+                aa = []
+                for a in axis:
+                    if a < 0:
+                        a = self.ndim + a
+                    aa.append(a)
+                axis = aa
+            else:
+                if axis < 0:
+                    axis = self.ndim + axis
             r = ArrayMath.sum(self._array, axis)
             return NDArray(r)
 

meteoinfo-lab/pylib/mipylib/numeric/core/fromnumeric.py

@@ -138,15 +138,15 @@ def sum(x, axis=None):
         r = ArrayMath.sum(x.asarray())
         return r
     else:
-        r = ArrayMath.sum(x.asarray(), axis)
+        r = x.sum(axis)
-        if type(x) is NDArray:
+        if isinstance(x, DimArray):
-            return NDArray(r)
-        else:
             dims = []
             for i in range(0, x.ndim):
                 if i != axis:
                     dims.append(x.dims[i])
-            return DimArray(NDArray(r), dims, x.fill_value, x.proj)
+            return DimArray(r, dims, x.fill_value, x.proj)
+        else:
+            return r
 
 
 def prod(x, axis=None):

meteoinfo-lab/pylib/mipylib/numeric/core/numeric.py

@@ -37,7 +37,7 @@ newaxis = None
 
 __all__ = [
     'pi','e','inf','nan','acos','abs','all','allclose','any','arange','arange1',
-    'argmin','argmax','argsort','array','array_split','asanyarray','asarray','asgridarray',
+    'argmin','argmax','argsort','array','array_split','amax','amin','asanyarray','asarray','asgridarray',
     'asgriddata','arcsin','asin','asmiarray','asstationdata','atleast_1d','atleast_2d','arctan','atan',
     'arctan2','atan2','ave_month','average','histogram','broadcast_to','cdiff','ceil',
     'concatenate','conj','conjugate','corrcoef','cos','cosh','cylinder','degrees','delete','delnan','diag','diff',
@@ -1525,6 +1525,19 @@ def min(a, axis=None):
     if isinstance(a, (list, tuple)):
         a = array(a)
     return a.min(axis)
+
+def amin(a, axis=None):
+    """
+    Return the minimum of an array or minimum along an axis.
+
+    `amin` is an alias of `~numeric.min`.
+
+    See Also
+    --------
+    min : alias of this function
+    NDArray.min : equivalent method
+    """
+    return min(a, axis)
     
 def max(a, axis=None):
     """
@@ -1540,6 +1553,19 @@ def max(a, axis=None):
     if isinstance(a, (list, tuple)):
         a = array(a)
     return a.max(axis)
+
+def amax(a, axis=None):
+    """
+    Return the maximum of an array or maximum along an axis.
+
+    `amax` is an alias of `~numeric.max`.
+
+    See Also
+    --------
+    max : alias of this function
+    NDArray.max : equivalent method
+    """
+    return max(a, axis)
         
 def argmin(a, axis=None):
     """

meteoinfo-lab/pylib/mipylib/numeric/linalg/linalg.py

@@ -12,7 +12,7 @@ from org.meteoinfo.math.stats import StatsUtil
 
 from .. import core as np
 
-__all__ = ['solve', 'cholesky', 'det', 'lu', 'qr', 'svd', 'eig', 'inv', 'lstsq', 'slogdet',
+__all__ = ['solve', 'cholesky', 'cond', 'det', 'lu', 'qr', 'svd', 'eig', 'inv', 'lstsq', 'slogdet',
            'solve_triangular', 'norm', 'pinv']
 
 
@@ -177,7 +177,7 @@ def qr(a):
     return q, r
 
 
-def svd(a, full_matrices=True):
+def svd(a, full_matrices=True, compute_uv=True):
     """
     Singular Value Decomposition.
     
@@ -193,9 +193,13 @@ def svd(a, full_matrices=True):
     full_matrices: bool, optional
         If True (default), u and vh have the shapes (..., M, M) and (..., N, N), respectively.
         Otherwise, the shapes are (..., M, K) and (..., K, N), respectively, where K = min(M, N).
+    compute_uv:bool, optional
+        Whether to compute u and vh in addition to s. True by default.
         
     Returns
     -------
+    When `compute_uv` is True, the result is a namedtuple with the following attribute names:
+
     U : ndarray
         Unitary matrix having left singular vectors as columns.
         Of shape ``(M,K)``.
@@ -208,10 +212,13 @@ def svd(a, full_matrices=True):
     """
     r = LinalgUtil.svd(a.asarray(), full_matrices)
     # r = LinalgUtil.svd_EJML(a.asarray())
-    U = np.NDArray(r[0])
     s = np.NDArray(r[1])
-    Vh = np.NDArray(r[2])
+    if compute_uv:
-    return U, s, Vh
+        U = np.NDArray(r[0])
+        Vh = np.NDArray(r[2])
+        return U, s, Vh
+    else:
+        return s
 
 
 def eig(a):
@@ -326,6 +333,34 @@ def slogdet(a):
     return r[0], r[1]
 
 
+def _multi_svd_norm(x, row_axis, col_axis, op):
+    """Compute a function of the singular values of the 2-D matrices in `x`.
+
+    This is a private utility function used by `numpy.linalg.norm()`.
+
+    Parameters
+    ----------
+    x : ndarray
+    row_axis, col_axis : int
+        The axes of `x` that hold the 2-D matrices.
+    op : callable
+        This should be either amin or `amax` or `sum`.
+
+    Returns
+    -------
+    result : float or ndarray
+        If `x` is 2-D, the return values is a float.
+        Otherwise, it is an array with ``x.ndim - 2`` dimensions.
+        The return values are either the minimum or maximum or sum of the
+        singular values of the matrices, depending on whether `op`
+        is `amin` or `amax` or `sum`.
+
+    """
+    y = np.moveaxis(x, (row_axis, col_axis), (-2, -1))
+    result = op(svd(y, compute_uv=False), axis=-1)
+    return result
+
+
 def norm(x, ord=None, axis=None, keepdims=False):
     """
     Matrix or vector norm.
@@ -407,50 +442,144 @@ def norm(x, ord=None, axis=None, keepdims=False):
         # None of the str-type keywords for ord ('fro', 'nuc')
         # are valid for vectors
         elif isinstance(ord, str):
-            raise ValueError("Invalid norm order '{ord}' for vectors".format(ord))
+            raise ValueError("Invalid norm order {} for vectors".format(ord))
         else:
             absx = np.abs(x)
             absx **= ord
             ret = absx.sum(axis=axis)
-            ret **= np.reciprocal(ord)
+            ret **= (1. / ord)
             return ret
-    # elif len(axis) == 2:
+    elif len(axis) == 2:
-    #     row_axis, col_axis = axis
+        row_axis, col_axis = axis
-    #     row_axis = np.normalize_axis_index(row_axis, nd)
+        row_axis = np.normalize_axis_index(row_axis, nd)
-    #     col_axis = np.normalize_axis_index(col_axis, nd)
+        col_axis = np.normalize_axis_index(col_axis, nd)
-    #     if row_axis == col_axis:
+        if row_axis == col_axis:
-    #         raise ValueError('Duplicate axes given.')
+            raise ValueError('Duplicate axes given.')
-    #     if ord == 2:
+        if ord == 2:
-    #         ret =  _multi_svd_norm(x, row_axis, col_axis, amax)
+            ret =  _multi_svd_norm(x, row_axis, col_axis, np.amax)
-    #     elif ord == -2:
+        elif ord == -2:
-    #         ret = _multi_svd_norm(x, row_axis, col_axis, amin)
+            ret = _multi_svd_norm(x, row_axis, col_axis, np.amin)
-    #     elif ord == 1:
+        elif ord == 1:
-    #         if col_axis > row_axis:
+            if col_axis > row_axis:
-    #             col_axis -= 1
+                col_axis -= 1
-    #         ret = add.reduce(np.abs(x), axis=row_axis).max(axis=col_axis)
+            ret = np.sum(np.abs(x), axis=row_axis).max(axis=col_axis)
-    #     elif ord == np.inf:
+        elif ord == np.inf:
-    #         if row_axis > col_axis:
+            if row_axis > col_axis:
-    #             row_axis -= 1
+                row_axis -= 1
-    #         ret = add.reduce(np.abs(x), axis=col_axis).max(axis=row_axis)
+            ret = np.sum(np.abs(x), axis=col_axis).max(axis=row_axis)
-    #     elif ord == -1:
+        elif ord == -1:
-    #         if col_axis > row_axis:
+            if col_axis > row_axis:
-    #             col_axis -= 1
+                col_axis -= 1
-    #         ret = add.reduce(np.abs(x), axis=row_axis).min(axis=col_axis)
+            ret = np.sum(np.abs(x), axis=row_axis).min(axis=col_axis)
-    #     elif ord == -np.inf:
+        elif ord == -np.inf:
-    #         if row_axis > col_axis:
+            if row_axis > col_axis:
-    #             row_axis -= 1
+                row_axis -= 1
-    #         ret = add.reduce(np.abs(x), axis=col_axis).min(axis=row_axis)
+            ret = np.sum(np.abs(x), axis=col_axis).min(axis=row_axis)
-    #     elif ord in [None, 'fro', 'f']:
+        elif ord in [None, 'fro', 'f']:
-    #         ret = np.sqrt(add.reduce((x.conj() * x).real, axis=axis))
+            ret = np.sqrt(np.sum((x.conj() * x).real, axis=axis))
-    #     elif ord == 'nuc':
+        elif ord == 'nuc':
-    #         ret = _multi_svd_norm(x, row_axis, col_axis, sum)
+            ret = _multi_svd_norm(x, row_axis, col_axis, np.sum)
-    #     else:
+        else:
-    #         raise ValueError("Invalid norm order for matrices.")
+            raise ValueError("Invalid norm order for matrices.")
-    #     if keepdims:
+        if keepdims:
-    #         ret_shape = list(x.shape)
+            ret_shape = list(x.shape)
-    #         ret_shape[axis[0]] = 1
+            ret_shape[axis[0]] = 1
-    #         ret_shape[axis[1]] = 1
+            ret_shape[axis[1]] = 1
-    #         ret = ret.reshape(ret_shape)
+            ret = ret.reshape(ret_shape)
-    #     return ret
+        return ret
-    # else:
+    else:
-    #     raise ValueError("Improper number of dimensions to norm.")
+        raise ValueError("Improper number of dimensions to norm.")
+
+
+def cond(x, p=None):
+    """
+    Compute the condition number of a matrix.
+
+    This function is capable of returning the condition number using
+    one of seven different norms, depending on the value of `p` (see
+    Parameters below).
+
+    Parameters
+    ----------
+    x : (..., M, N) array_like
+        The matrix whose condition number is sought.
+    p : {None, 1, -1, 2, -2, inf, -inf, 'fro'}, optional
+        Order of the norm used in the condition number computation:
+
+        =====  ============================
+        p      norm for matrices
+        =====  ============================
+        None   2-norm, computed directly using the ``SVD``
+        'fro'  Frobenius norm
+        inf    max(sum(abs(x), axis=1))
+        -inf   min(sum(abs(x), axis=1))
+        1      max(sum(abs(x), axis=0))
+        -1     min(sum(abs(x), axis=0))
+        2      2-norm (largest sing. value)
+        -2     smallest singular value
+        =====  ============================
+
+        inf means the `numpy.inf` object, and the Frobenius norm is
+        the root-of-sum-of-squares norm.
+
+    Returns
+    -------
+    c : {float, inf}
+        The condition number of the matrix. May be infinite.
+
+    See Also
+    --------
+    numpy.linalg.norm
+
+    Notes
+    -----
+    The condition number of `x` is defined as the norm of `x` times the
+    norm of the inverse of `x` [1]_; the norm can be the usual L2-norm
+    (root-of-sum-of-squares) or one of a number of other matrix norms.
+
+    References
+    ----------
+    .. [1] G. Strang, *Linear Algebra and Its Applications*, Orlando, FL,
+           Academic Press, Inc., 1980, pg. 285.
+
+    Examples
+    --------
+    >>> from mipylib.numeric import linalg as LA
+    >>> a = np.array([[1, 0, -1], [0, 1, 0], [1, 0, 1]])
+    >>> a
+    array([[ 1,  0, -1],
+           [ 0,  1,  0],
+           [ 1,  0,  1]])
+    >>> LA.cond(a)
+    1.4142135623730951
+    >>> LA.cond(a, 'fro')
+    3.1622776601683795
+    >>> LA.cond(a, np.inf)
+    2.0
+    >>> LA.cond(a, -np.inf)
+    1.0
+    >>> LA.cond(a, 1)
+    2.0
+    >>> LA.cond(a, -1)
+    1.0
+    >>> LA.cond(a, 2)
+    1.4142135623730951
+    >>> LA.cond(a, -2)
+    0.70710678118654746 # may vary
+    >>> min(LA.svd(a, compute_uv=False))*min(LA.svd(LA.inv(a), compute_uv=False))
+    0.70710678118654746 # may vary
+    """
+    x = np.asarray(x)  # in case we have a matrix
+    if p is None or p == 2 or p == -2:
+        s = svd(x, compute_uv=False)
+        if p == -2:
+            r = s[..., -1] / s[..., 0]
+        else:
+            r = s[..., 0] / s[..., -1]
+    else:
+        # Call inv(x) ignoring errors. The result array will
+        # contain nans in the entries where inversion failed.
+        invx = inv(x)
+        r = norm(x, p, axis=(-2, -1)) * norm(invx, p, axis=(-2, -1))
+
+    return r

meteoinfo-lab/pylib/mipylib/plotlib/_axes3dgl.py

@@ -1501,16 +1501,19 @@ class Axes3DGL(Axes3D):
 
     def isosurface(self, *args, **kwargs):
         """
-        creates a three-dimensional isosurface plot
+        creates a three-dimensional isosurface plot.
 
         :param x: (*array_like*) Optional. X coordinate array.
         :param y: (*array_like*) Optional. Y coordinate array.
         :param z: (*array_like*) Optional. Z coordinate array.
-        :param data: (*array_like*) 3D data array.
+        :param data: (*array_like*) Volume data array.
-        :param cmap: (*string*) Color map string.
+        :param isovalue: (*float*) Specified isosurface value.
-        :param nthread: (*int*) Thread number. Default is 4.
+        :param cdata: (*array_like*) Optional. Volume color data array.
+        :param facecolor: (*color*) Optional. Color map string.
+        :param cmap: (*string*) Optional. Color map string.
+        :param nthread: (*int*) Optional. Thread number. Default is 4.
 
-        :returns: 3D Mesh graphic
+        :returns: 3D Mesh graphic.
         """
         if len(args) <= 3:
             x = args[0].dimvalue(2)

meteoinfo-math/pom.xml

@@ -53,6 +53,16 @@
             <artifactId>openblas-platform</artifactId>
             <version>0.3.10-1.5.4</version>
         </dependency>
+        <dependency>
+            <groupId>org.bytedeco</groupId>
+            <artifactId>mkl-platform</artifactId>
+            <version>2020.3-1.5.4</version>
+        </dependency>
+        <dependency>
+            <groupId>org.bytedeco</groupId>
+            <artifactId>mkl-platform-redist</artifactId>
+            <version>2020.3-1.5.4</version>
+        </dependency>
         <dependency>
             <groupId>org.junit.jupiter</groupId>
             <artifactId>junit-jupiter</artifactId>

meteoinfo-math/src/main/java/org/meteoinfo/math/blas/BLAS.java

@@ -53,8 +53,8 @@ public interface BLAS {
         Logger logger = Logger.getLogger("BLAS.class");
 
         try {
-            Class<?> clazz = Class.forName("smile.math.blas.mkl.MKL");
+            Class<?> clazz = Class.forName("org.meteoinfo.math.blas.mkl.MKL");
-            logger.info("smile-mkl module is available.");
+            logger.info("mkl module is available.");
             return (BLAS) clazz.getDeclaredConstructor().newInstance();
         } catch (Exception e) {
             logger.info(String.format("Failed to create MKL instance: %s", e));

meteoinfo-math/src/main/java/org/meteoinfo/math/blas/LAPACK.java

@@ -53,8 +53,8 @@ public interface LAPACK {
         Logger logger = Logger.getLogger("LAPACK.class");
 
         try {
-            Class<?> clazz = Class.forName("smile.math.blas.mkl.MKL");
+            Class<?> clazz = Class.forName("org.meteoinfo.math.blas.mkl.MKL");
-            logger.info("smile-mkl module is available.");
+            logger.info("mkl module is available.");
             return (LAPACK) clazz.getDeclaredConstructor().newInstance();
         } catch (Exception e) {
             logger.info(String.format("Failed to create MKL instance: %s", e));

meteoinfo-ndarray/src/main/java/org/meteoinfo/ndarray/math/ArrayMath.java

@@ -6729,7 +6729,50 @@ public class ArrayMath {
                     ranges.add(new Range(current[idx], current[idx], 1));
                 }
             }
-            s = sum(a, ranges);
+            s = sumRange(a, ranges);
+            r.setDouble(i, s);
+            indexr.incr();
+        }
+
+        return r;
+    }
+
+    /**
+     * Compute sum value of an array along axes (dimension)
+     *
+     * @param a Array a
+     * @param axes Axes
+     * @return Sum value array
+     * @throws InvalidRangeException
+     */
+    public static Array sum(Array a, List<Integer> axes) throws InvalidRangeException {
+        int[] dataShape = a.getShape();
+        int[] shape = new int[dataShape.length - axes.size()];
+        int idx = 0;
+        for (int i = 0; i < dataShape.length; i++) {
+            if (axes.contains(i)) {
+                continue;
+            }
+            shape[idx] = dataShape[i];
+            idx += 1;
+        }
+        Array r = Array.factory(a.getDataType(), shape);
+        double s;
+        Index indexr = r.getIndex();
+        int[] current;
+        for (int i = 0; i < r.getSize(); i++) {
+            current = indexr.getCurrentCounter();
+            List<Range> ranges = new ArrayList<>();
+            idx = 0;
+            for (int j = 0; j < dataShape.length; j++) {
+                if (axes.contains(j)) {
+                    ranges.add(new Range(0, dataShape[j] - 1, 1));
+                } else {
+                    ranges.add(new Range(current[idx], current[idx], 1));
+                    idx += 1;
+                }
+            }
+            s = sumRange(a, ranges);
             r.setDouble(i, s);
             indexr.incr();
         }
@@ -6745,7 +6788,7 @@ public class ArrayMath {
      * @return Sum value
      * @throws InvalidRangeException
      */
-    public static double sum(Array a, List<Range> ranges) throws InvalidRangeException {
+    public static double sumRange(Array a, List<Range> ranges) throws InvalidRangeException {
         double s = 0.0, v;
         int n = 0;
         IndexIterator ii = a.getRangeIterator(ranges);
@@ -6763,7 +6806,7 @@ public class ArrayMath {
     }
 
     /**
-     * Compute the sum arry from a list of arrays
+     * Compute the sum array from a list of arrays
      *
      * @param alist list of arrays
      * @return Sum array