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other:python:misc_by_jyp [2023/04/28 14:59] jypeter [Data representation] Added link to old tutorial |
other:python:misc_by_jyp [2023/09/27 13:53] jypeter Added a section with a link to "100 numpy exercises" |
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array([3. , 4.5, 8. ])</code> | array([3. , 4.5, 8. ])</code> | ||
+ | ==== Exercise your brain with numpy ==== | ||
+ | |||
+ | Have a look at [[https://github.com/rougier/numpy-100/blob/master/100_Numpy_exercises.ipynb|100 numpy exercises]] | ||
===== matplotlib related stuff ===== | ===== matplotlib related stuff ===== | ||
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FIXME Add parts (pages 28 to 37) of this [[https://wiki.lsce.ipsl.fr/pmip3/doku.php/other:python:jyp_steps#part_2|old tutorial]] to this section | FIXME Add parts (pages 28 to 37) of this [[https://wiki.lsce.ipsl.fr/pmip3/doku.php/other:python:jyp_steps#part_2|old tutorial]] to this section | ||
+ | |||
+ | ==== Base notions ==== | ||
+ | |||
+ | * **Never forget** that all the bits and pieces of information we use are coded in [[https://en.wikipedia.org/wiki/Binary_number#Counting_in_binary|base 2]] (''0''s and ''1''s ...), grouped in bytes! | ||
+ | * Some things can be stored exactly (integers, characters, ...) | ||
+ | * In other cases (**//real// numbers** that we work with all the time, compressed images/videos/music) we only store **//good enough approximation//** | ||
+ | |||
+ | * 1 byte <=> 8 bits | ||
+ | * ''REAL*4'' <=> 4 bytes <=> 32 bits | ||
+ | * For easier written/displayed representation, 1 byte is usually split into 2 groups of 4 bits, and displayed using base 16 and [[https://en.wikipedia.org/wiki/Hexadecimal|hexadecimal representation]] (characters ''0'', ''1'', ..., ''A'', ''B'', ..., ''F'') | ||
+ | * ''0000'' <=> ''0'',\\ ''0010'' <=> ''1'', ...,\\ ''1111'' <=> ''F'' | ||
+ | * ''1101'' <=> ''D'' in hexadecimal <=> ''13'' in decimal (''**1** * 8 + **1** * 4 + **0** * 2 + **1** * 1'') | ||
+ | * ''11111101'' in //base 2// <=> ''1111 1101'' <=> ''FD'' in //hexadecimal// <=> ''253'' (''15 * 16 + 13'') in //decimal// | ||
+ | |||
+ | * Base conversion with Python | ||
+ | * <code>>>> hex(13) # Decimal to Hexadecimal conversion | ||
+ | '0xd' | ||
+ | >>> hex(253) | ||
+ | '0xfd' | ||
+ | >>> hex(256) | ||
+ | '0x100' | ||
+ | >>> int('0x100', 16) # Hexadecimal to Decimal conversion | ||
+ | 256 | ||
+ | >>> int('1111', 2) # Binary to Decimal conversion | ||
+ | 15 | ||
+ | >>> int('11111101', 2) # '11111101' <=> '1111 1101' <=> 'FD' <=> 15 * 16 + 13 = 253 | ||
+ | 253 | ||
+ | >>> 013 # DANGER! Python considers an integer to be in OCTAL base if it starts with a 0 | ||
+ | 11 | ||
+ | >>> int('13', 8) # 1*8 + 3 | ||
+ | 11</code> | ||
+ | |||
+ | * More technical topics | ||
+ | * [[https://en.wikipedia.org/wiki/Bit_numbering|Bit numbering]]: the art of ordering bits, everything about MSB (Most Significant Byte) and LSB (Least Significant Byte) | ||
+ | * [[https://en.wikipedia.org/wiki/Endianness|Endianness]]: the art of ordering bytes | ||
==== Numerical values ==== | ==== Numerical values ==== | ||
- | * Binary data representation of some numbers: | + | * Binary data representation of some numbers (only some common types are listed here): |
+ | * Languages and packages **references** used below: | ||
+ | * Python: [[https://numpy.org/doc/stable/reference/arrays.scalars.html#sized-aliases|NumPy Sized aliases]] | ||
+ | * NetCDF: [[https://docs.unidata.ucar.edu/nug/current/md_types.html|Data Types]], [[https://docs.unidata.ucar.edu/netcdf-fortran/current/f90-variables.html#f90-language-types-corresponding-to-netcdf-external-data-types|Fortran related Data Types]], [[https://docs.unidata.ucar.edu/nug/current/_c_d_l.html#cdl_data_types|CDL Data Types]] | ||
+ | * Fortran: Intel Fortran Compiler [[https://www.intel.com/content/www/us/en/docs/fortran-compiler/developer-guide-reference/2023-1/intrinsic-data-types.html|Intrinsic Data Types]] | ||
* [[https://en.wikipedia.org/wiki/Integer_(computer_science)|Integers]] | * [[https://en.wikipedia.org/wiki/Integer_(computer_science)|Integers]] | ||
* Range: | * Range: | ||
- | * 4-byte integers (''numpy.int32''): −2,147,483,648 to 2,147,483,647 | + | * 4-byte //signed// integers: ''−2,147,483,648'' to ''2,147,483,647'' |
- | * 8-byte integers (''numpy.int64''): −9,223,372,036,854,775,808 to 9,223,372,036,854,775,807 | + | * Python: ''numpy.int32'' |
+ | * NetCDF: ''int'', ''NC_INT'' or ''NC_LONG'', ''NF90_INT'' | ||
+ | * Fortran: ''INTEGER*4'' | ||
+ | * 8-byte //signed// integers: ''−9,223,372,036,854,775,808'' to ''9,223,372,036,854,775,807'' | ||
+ | * Python: ''numpy.int64'' | ||
+ | * NetCDF: ''int64'', ''NC_INT64'' | ||
+ | * Fortran: ''INTEGER*8'' | ||
* Tech note: signed integers use [[https://en.wikipedia.org/wiki/Two%27s_complement|two's complement]] for coding negative integers | * Tech note: signed integers use [[https://en.wikipedia.org/wiki/Two%27s_complement|two's complement]] for coding negative integers | ||
* [[https://en.wikipedia.org/wiki/IEEE_754|Floating point numbers]] (//IEEE 754// standard aka //IEEE Standard for Binary Floating-Point for Arithmetic//) | * [[https://en.wikipedia.org/wiki/IEEE_754|Floating point numbers]] (//IEEE 754// standard aka //IEEE Standard for Binary Floating-Point for Arithmetic//) | ||
* Range: | * Range: | ||
- | * 4-byte float (''numpy.float32''): ~8 significant digits * 10E±38 | + | * 4-byte float: ''~8 significant digits * 10E±38'' |
+ | * Python: ''numpy.float32'' | ||
+ | * NetCDF: ''float'', ''NC-FLOAT'', ''NF90_FLOAT'' | ||
+ | * Fortran:''REAL*4'' | ||
* See also [[https://en.wikipedia.org/wiki/Single-precision_floating-point_format|Single-precision floating-point format]] | * See also [[https://en.wikipedia.org/wiki/Single-precision_floating-point_format|Single-precision floating-point format]] | ||
- | * 8-byte float (''numpy.float64''): ~15 significant digits * 10E±308 | + | * 8-byte float: ''~15 significant digits * 10E±308'' |
- | * Special values: | + | * Python: ''numpy.float64'' |
- | * [[https://en.wikipedia.org/wiki/NaN|NaN]] (''numpy.nan''): //Not a Number// | + | * NetCDF: ''double'', ''NC_DOUBLE'', ''NF90_DOUBLE'' |
- | * Infinity (''-numpy.inf'' and ''numpy.inf'') | + | * Fortran: ''REAL*8'' |
- | * Note: it is cleaner to use masks (and [[https://numpy.org/doc/stable/reference/maskedarray.generic.html|Numpy masked arrays]]) than NaNs, when you have to deal with missing values ! | + | * **Special values**: |
- | * [[https://en.wikipedia.org/wiki/Bit_numbering|Bit numbering]] | + | * [[https://en.wikipedia.org/wiki/NaN|NaN]]: //Not a Number// |
- | * [[https://en.wikipedia.org/wiki/Endianness|Endianness]] | + | * Python: ''numpy.nan'' |
+ | * Infinity | ||
+ | * Python: ''-numpy.inf'' and ''numpy.inf'' | ||
+ | * Note: it is cleaner to use masks (and [[https://numpy.org/doc/stable/reference/maskedarray.generic.html|Numpy masked arrays]]) rather than ''NaN''s, when you have to deal with missing values ! | ||
+ | * <wrap hi>The RISKS of working with (the wrong) floats</wrap>: | ||
+ | * [[https://en.wikipedia.org/wiki/Round-off_error|Round-off error]] | ||
+ | * [[https://en.wikipedia.org/wiki/Catastrophic_cancellation|Catastrophic cancellation]] | ||
+ | * [[https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html|What Every Computer Scientist Should Know About Floating-Point Arithmetic]] | ||
* A rather technical example: we //play// with a numpy 4-byte integer scalar | * A rather technical example: we //play// with a numpy 4-byte integer scalar | ||
* <code>>>> one_int32 = np.int32(1) | * <code>>>> one_int32 = np.int32(1) |