Thread: [pure-lang-svn] SF.net SVN: pure-lang:[475] pure/trunk/lib/primitives.pure
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From: <ag...@us...> - 2008-08-12 19:17:25
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Revision: 475
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=475&view=rev
Author: agraef
Date: 2008-08-12 19:17:34 +0000 (Tue, 12 Aug 2008)
Log Message:
-----------
Cosmetic changes.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-08-12 13:59:55 UTC (rev 474)
+++ pure/trunk/lib/primitives.pure 2008-08-12 19:17:34 UTC (rev 475)
@@ -21,8 +21,7 @@
/* Throw an exception. */
-extern void pure_throw(expr*); // IMPURE!
-throw x = pure_throw x;
+extern void pure_throw(expr*) = throw; // IMPURE!
/* Convenience function to ensure a condition p. Returns 1 (true) if p holds,
and throws the given exception e otherwise. */
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From: <ag...@us...> - 2008-08-14 13:56:38
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Revision: 497
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=497&view=rev
Author: agraef
Date: 2008-08-14 13:56:45 +0000 (Thu, 14 Aug 2008)
Log Message:
-----------
Fix typo.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-08-14 13:37:16 UTC (rev 496)
+++ pure/trunk/lib/primitives.pure 2008-08-14 13:56:45 UTC (rev 497)
@@ -105,7 +105,6 @@
uint x::int = if x>=0 then bigint x else x+0x100000000L;
ulong x::bigint = if x>=0 then x else x+0x10000000000000000L;
-
/* Absolute value and sign of a number. */
abs x::int | abs x::bigint | abs x::double
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From: <ag...@us...> - 2008-08-14 23:14:16
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Revision: 501
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=501&view=rev
Author: agraef
Date: 2008-08-14 23:14:26 +0000 (Thu, 14 Aug 2008)
Log Message:
-----------
Fix some minor glitches in the pow function.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-08-14 23:10:55 UTC (rev 500)
+++ pure/trunk/lib/primitives.pure 2008-08-14 23:14:26 UTC (rev 501)
@@ -332,8 +332,8 @@
extern expr* bigint_pow(void*, int), double pow(double, double) = c_pow;
pow x::int y::int = bigint_pow (bigint x) y if y>=0;
-pow x::bigint y::bigint = bigint_pow x (int y) if int y>=0;
-pow x::double y::double = c_pow x y if x>=0 || int y==y;
+pow x::bigint y::bigint = bigint_pow x (int y) if y>=0;
+pow x::double y::double = c_pow x y if x>=0 || frac y==0.0;
// mixed int/bigint
pow x::int y::bigint = bigint_pow (bigint x) (int y) if y>=0;
@@ -343,12 +343,12 @@
pow x::double y::int |
pow x::double y::bigint = c_pow x (double y);
pow x::int y::double |
-pow x::bigint y::double = c_pow (double x) y if x>=0 || int y==y;
+pow x::bigint y::double = c_pow (double x) y if x>=0 || frac y==0.0;
/* The ^ operator. Works like pow, but always promotes its operands to double
and returns a double result. */
-x::double^y::double = c_pow x y if x>=0 || int y==y;
+x::double^y::double = c_pow x y if x>=0 || frac y==0.0;
x::int^y::int |
x::bigint^y::bigint |
x::int^y::bigint |
@@ -356,7 +356,7 @@
x::double^y::int |
x::double^y::bigint = c_pow x (double y);
x::int^y::double |
-x::bigint^y::double = c_pow (double x) y if x>=0 || int y==y;
+x::bigint^y::double = c_pow (double x) y if x>=0 || frac y==0.0;
= double x^y otherwise;
/* Pointer arithmetic. We do this using bigints, so that the code is portable
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From: <ag...@us...> - 2008-08-21 22:46:57
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Revision: 560
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=560&view=rev
Author: agraef
Date: 2008-08-21 22:47:08 +0000 (Thu, 21 Aug 2008)
Log Message:
-----------
Add missing nan check to ^ operator.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-08-21 21:59:02 UTC (rev 559)
+++ pure/trunk/lib/primitives.pure 2008-08-21 22:47:08 UTC (rev 560)
@@ -359,7 +359,7 @@
/* The ^ operator. Works like pow, but always promotes its operands to double
and returns a double result. */
-x::double^y::double = c_pow x y if x>=0 || frac y==0.0;
+x::double^y::double = c_pow x y if x>=0 || frac y==0.0 || nanp x || nanp y;
x::int^y::int |
x::bigint^y::bigint |
x::int^y::bigint |
@@ -367,7 +367,7 @@
x::double^y::int |
x::double^y::bigint = c_pow x (double y);
x::int^y::double |
-x::bigint^y::double = c_pow (double x) y if x>=0 || frac y==0.0;
+x::bigint^y::double = c_pow (double x) y if x>=0 || frac y==0.0 || nanp y;
= double x^y otherwise;
/* Pointer arithmetic. We do this using bigints, so that the code is portable
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From: <ag...@us...> - 2008-08-28 11:27:37
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Revision: 652
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=652&view=rev
Author: agraef
Date: 2008-08-28 11:27:46 +0000 (Thu, 28 Aug 2008)
Log Message:
-----------
Remove assert convenience function, it's not really worth having trivial stuff like that in the prelude.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-08-28 11:25:58 UTC (rev 651)
+++ pure/trunk/lib/primitives.pure 2008-08-28 11:27:46 UTC (rev 652)
@@ -23,11 +23,6 @@
extern void pure_throw(expr*) = throw; // IMPURE!
-/* Convenience function to ensure a condition p. Returns 1 (true) if p holds,
- and throws the given exception e otherwise. */
-
-assert p e = if p then 1 else throw e;
-
/* Syntactic equality. */
extern bool same(expr* x, expr* y);
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From: <ag...@us...> - 2008-08-30 19:51:01
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Revision: 667
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=667&view=rev
Author: agraef
Date: 2008-08-30 19:51:11 +0000 (Sat, 30 Aug 2008)
Log Message:
-----------
Cosmetic changes.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-08-30 19:37:11 UTC (rev 666)
+++ pure/trunk/lib/primitives.pure 2008-08-30 19:51:11 UTC (rev 667)
@@ -23,17 +23,6 @@
extern void pure_throw(expr*) = throw; // IMPURE!
-/* Sentries. These are expression "guards" which are applied to the target
- expression when it is garbage-collected. The sentry function places a
- sentry at an expression (and returns the modified expression), clear_sentry
- removes, get_sentry returns it. NOTE: In the current implementation
- sentries can only be placed at applications and pointer objects. The sentry
- itself can be any type of object (but usually it's a function). */
-
-extern expr* pure_sentry(expr*,expr*) = sentry; // IMPURE!
-extern expr* pure_clear_sentry(expr*) = clear_sentry; // IMPURE!
-extern expr* pure_get_sentry(expr*) = get_sentry;
-
/* Syntactic equality. */
extern bool same(expr* x, expr* y);
@@ -424,3 +413,14 @@
put_string x::pointer y::string = pointer_put_string x y;
put_pointer x::pointer y::string = pointer_put_pointer x y;
put_pointer x::pointer y::pointer = pointer_put_pointer x y;
+
+/* Sentries. These are expression "guards" which are applied to the target
+ expression when it is garbage-collected. The sentry function places a
+ sentry at an expression (and returns the modified expression), clear_sentry
+ removes, get_sentry returns it. NOTE: In the current implementation
+ sentries can only be placed at applications and pointer objects. The sentry
+ itself can be any type of object (but usually it's a function). */
+
+extern expr* pure_sentry(expr*,expr*) = sentry; // IMPURE!
+extern expr* pure_clear_sentry(expr*) = clear_sentry; // IMPURE!
+extern expr* pure_get_sentry(expr*) = get_sentry;
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From: <ag...@us...> - 2008-09-15 04:40:54
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Revision: 760
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=760&view=rev
Author: agraef
Date: 2008-09-15 04:41:02 +0000 (Mon, 15 Sep 2008)
Log Message:
-----------
Simplify definitions of infp and nanp.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-09-12 11:39:25 UTC (rev 759)
+++ pure/trunk/lib/primitives.pure 2008-09-15 04:41:02 UTC (rev 760)
@@ -69,8 +69,8 @@
/* Predicates to check for inf and nan values. */
-infp x = case x of x::double = x!==nan && x-x===nan; _ = 0 end;
-nanp x = case x of x::double = x===nan; _ = 0 end;
+infp x = case x of x::double = x==inf || x==-inf; _ = 0 end;
+nanp x = case x of x::double = not (x==x); _ = 0 end;
/* Compute a 32 bit hash code of a Pure expression. */
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From: <ag...@us...> - 2008-09-15 05:34:49
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Revision: 762
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=762&view=rev
Author: agraef
Date: 2008-09-15 05:34:59 +0000 (Mon, 15 Sep 2008)
Log Message:
-----------
Properly handle the case of IEEE 754 negative zeros.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-09-15 04:56:26 UTC (rev 761)
+++ pure/trunk/lib/primitives.pure 2008-09-15 05:34:59 UTC (rev 762)
@@ -125,10 +125,13 @@
// Fractional part of x.
frac x::int | frac x::bigint | frac x::double = x-trunc x;
-/* Absolute value and sign of a number. */
+/* Absolute value and sign of a number. Note that these don't distinguish
+ between IEEE 754 positive and negative zeros; abs always returns 0.0, sgn 0
+ for these. The real sign bit of a floating point zero can be obtained with
+ sgn (1/x). */
abs x::int | abs x::bigint | abs x::double
- = if x>=0 then x else -x;
+ = if x>0 then x else -x;
sgn x::int | sgn x::bigint | sgn x::double
= if x>0 then 1 else if x<0 then -1 else 0;
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From: <ag...@us...> - 2008-09-18 13:35:50
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Revision: 786
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=786&view=rev
Author: agraef
Date: 2008-09-18 20:35:54 +0000 (Thu, 18 Sep 2008)
Log Message:
-----------
Add some basic matrix operations (type checking predicates for vectors).
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-09-18 20:19:31 UTC (rev 785)
+++ pure/trunk/lib/primitives.pure 2008-09-18 20:35:54 UTC (rev 786)
@@ -46,6 +46,22 @@
cmatrixp x = case x of _::cmatrix = 1; _ = 0 end;
imatrixp x = case x of _::imatrix = 1; _ = 0 end;
+/* Pure represents row and column vectors as matrices with 1 row or column,
+ respectively. The following predicates allow you to check for these special
+ kinds of matrices. */
+
+vectorp x = matrixp x && (n==1 || m==1 when n::int,m::int = dim x end);
+rowvectorp x = matrixp x && dim x!0==1;
+colvectorp x = matrixp x && dim x!1==1;
+
+cvectorp x = cmatrixp x && (n==1 || m==1 when n::int,m::int = dim x end);
+rowcvectorp x = cmatrixp x && dim x!0==1;
+colcvectorp x = cmatrixp x && dim x!1==1;
+
+ivectorp x = imatrixp x && (n==1 || m==1 when n::int,m::int = dim x end);
+rowivectorp x = imatrixp x && dim x!0==1;
+colivectorp x = imatrixp x && dim x!1==1;
+
/* Predicates to check for function objects, global (unbound) variables,
function applications, proper lists, list nodes and tuples. */
@@ -409,7 +425,7 @@
x::imatrix!(i::int,j::int)
= matrix_elem x i j
if (i>=0 && i<n && j>=0 && j<m
- when n,m = dim x end);
+ when n::int,m::int = dim x end);
= throw out_of_bounds otherwise;
/* IEEE floating point infinities and NaNs. Place these after the definitions
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From: <ag...@us...> - 2008-09-20 07:56:36
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Revision: 800
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=800&view=rev
Author: agraef
Date: 2008-09-20 07:56:32 +0000 (Sat, 20 Sep 2008)
Log Message:
-----------
Implement array slicing operations.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-09-20 07:03:48 UTC (rev 799)
+++ pure/trunk/lib/primitives.pure 2008-09-20 07:56:32 UTC (rev 800)
@@ -430,6 +430,16 @@
when n::int,m::int = dim x end);
= throw out_of_bounds otherwise;
+/* Slices. */
+
+x::matrix!!(ns,ms) = colcatmap (mth (rowcatmap (nth x) ns)) ms with
+ nth x n = catch (cst {}) (row x n);
+ mth x m = catch (cst {}) (col x m);
+ end;
+x::matrix!!ns = colcatmap (nth x) ns with
+ nth x n = catch (cst {}) {x!n};
+ end;
+
/* Extract rows and columns from a matrix. */
private matrix_slice;
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From: <ag...@us...> - 2008-09-20 08:20:55
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Revision: 801
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=801&view=rev
Author: agraef
Date: 2008-09-20 08:20:26 +0000 (Sat, 20 Sep 2008)
Log Message:
-----------
Add submatrix operation.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-09-20 07:56:32 UTC (rev 800)
+++ pure/trunk/lib/primitives.pure 2008-09-20 08:20:26 UTC (rev 801)
@@ -457,6 +457,11 @@
cols x::matrix = map (col x) (0..m-1) when _,m::int = dim x end;
+/* Extract a submatrix of a given size at a given offset. */
+
+submat x::matrix (i::int,j::int) (n::int,m::int)
+ = matrix_slice x i j (i+n) (j+m);
+
/* Construct matrices from lists of rows and columns. These take either
scalars or submatrices as inputs; corresponding dimensions must match.
rowcat combines submatrices vertically, like {x;y}; colcat combines them
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From: <ag...@us...> - 2008-09-20 09:24:41
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Revision: 804
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=804&view=rev
Author: agraef
Date: 2008-09-20 09:24:14 +0000 (Sat, 20 Sep 2008)
Log Message:
-----------
Comment change.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-09-20 09:21:34 UTC (rev 803)
+++ pure/trunk/lib/primitives.pure 2008-09-20 09:24:14 UTC (rev 804)
@@ -470,8 +470,7 @@
extern expr* matrix_rows(expr *x) = rowcat;
extern expr* matrix_columns(expr *x) = colcat;
-/* Combinations of rowcat/colcat and map, to be used in matrix
- comprehensions. */
+/* Combinations of rowcat/colcat and map. */
rowcatmap f [] = {};
rowcatmap f xs@(_:_) = rowcat (map f xs);
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From: <ag...@us...> - 2008-09-22 00:23:33
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Revision: 822
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=822&view=rev
Author: agraef
Date: 2008-09-22 00:23:30 +0000 (Mon, 22 Sep 2008)
Log Message:
-----------
Optimize the case of contiguous slices.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-09-21 23:02:11 UTC (rev 821)
+++ pure/trunk/lib/primitives.pure 2008-09-22 00:23:30 UTC (rev 822)
@@ -435,7 +435,15 @@
/* Slices. */
-x::matrix!!(ns,ms) = colcatmap (mth (rowcatmap (nth x) ns)) ms with
+x::matrix!!(ns,ms) = case ns,ms of
+ // optimize the case of contiguous slices
+ ns@(n:_),ms@(m:_) = submat x (n,m) (#ns,#ms)
+ if cont ns && cont ms;
+ _ = colcatmap (mth (rowcatmap (nth x) ns)) ms;
+ end with
+ cont [n] = 1;
+ cont (n::int:ns@(m::int:_)) = cont ns if m==n+1;
+ cont _ = 0 otherwise;
nth x n = catch (cst {}) (row x n);
mth x m = catch (cst {}) (col x m);
end;
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From: <ag...@us...> - 2008-09-22 17:46:52
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Revision: 827
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=827&view=rev
Author: agraef
Date: 2008-09-22 17:46:47 +0000 (Mon, 22 Sep 2008)
Log Message:
-----------
Add operation to pack matrices obtained as slices from larger matrices.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-09-22 17:24:18 UTC (rev 826)
+++ pure/trunk/lib/primitives.pure 2008-09-22 17:46:47 UTC (rev 827)
@@ -489,6 +489,14 @@
colcatmap f [] = {};
colcatmap f xs@(_:_) = colcat (map f xs);
+/* 'Pack' a matrix. This creates a copy of the matrix which has the data in
+ contiguous storage. If possible, it also frees up extra memory if the
+ matrix was created as a slice from a bigger matrix. The 'packed' predicate
+ can be used to verify whether a matrix is already packed. */
+
+pack x::matrix = colcat [x,{}];
+packed x::matrix = stride x==dim x!1;
+
/* Transpose a matrix. */
private matrix_transpose;
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From: <ag...@us...> - 2008-09-22 21:14:19
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Revision: 830
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=830&view=rev
Author: agraef
Date: 2008-09-22 21:14:10 +0000 (Mon, 22 Sep 2008)
Log Message:
-----------
Add matrix reversal operations.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-09-22 20:53:37 UTC (rev 829)
+++ pure/trunk/lib/primitives.pure 2008-09-22 21:14:10 UTC (rev 830)
@@ -532,6 +532,13 @@
x::matrix' = matrix_transpose x;
+/* Reverse a matrix. rowrev reverses the rows, colrev the columns, reverse
+ both dimensions. */
+
+rowrev x::matrix = rowcat (reverse (rows x));
+colrev x::matrix = colcat (reverse (cols x));
+reverse x::matrix = rowrev (colrev x);
+
/* Matrix conversions. */
private matrix_double matrix_complex matrix_int;
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From: <ag...@us...> - 2008-09-22 21:52:50
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Revision: 831
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=831&view=rev
Author: agraef
Date: 2008-09-22 21:36:31 +0000 (Mon, 22 Sep 2008)
Log Message:
-----------
Add matrix/list conversion operations.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-09-22 21:14:10 UTC (rev 830)
+++ pure/trunk/lib/primitives.pure 2008-09-22 21:36:31 UTC (rev 831)
@@ -469,6 +469,20 @@
cols x::matrix = map (col x) (0..m-1) when _,m::int = dim x end;
+/* Convert a matrix to a list and vice versa. */
+
+list x::matrix = [[x!(i,j) | j=0..m-1] | i=0..n-1]
+ when n::int,m::int = dim x end;
+matrix [] = {};
+matrix xs@(x:_) = rowcatmap colcat xs;
+
+/* Convenience functions to create vectors from lists. */
+
+rowvector xs@[] | rowvector xs@(_:_)
+ = colcat xs;
+colvector xs@[] | colvector xs@(_:_)
+ = rowcat xs;
+
/* Extract (sub-,super-) diagonals from a matrix. Sub- and super-diagonals for
k=0 return the main diagonal. Indices for sub- and super-diagonals can also
be negative, in which case the corresponding super- or sub-diagonal is
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From: <ag...@us...> - 2008-09-23 05:31:32
|
Revision: 832
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=832&view=rev
Author: agraef
Date: 2008-09-23 05:31:30 +0000 (Tue, 23 Sep 2008)
Log Message:
-----------
Overhaul of matrix/list conversion operations.
Modified Paths:
--------------
pure/trunk/lib/primitives.pure
Modified: pure/trunk/lib/primitives.pure
===================================================================
--- pure/trunk/lib/primitives.pure 2008-09-22 21:36:31 UTC (rev 831)
+++ pure/trunk/lib/primitives.pure 2008-09-23 05:31:30 UTC (rev 832)
@@ -433,7 +433,7 @@
when n::int,m::int = dim x end);
= throw out_of_bounds otherwise;
-/* Slices. */
+/* Matrix slices. */
x::matrix!!(ns,ms) = case ns,ms of
// optimize the case of contiguous slices
@@ -469,24 +469,26 @@
cols x::matrix = map (col x) (0..m-1) when _,m::int = dim x end;
-/* Convert a matrix to a list and vice versa. */
+/* Convert a matrix to a list and vice versa. If x is a row vector then list x
+ converts it to a list of its elements; otherwise the result is the list of
+ the rows of the matrix. You can also use list2 to convert a matrix to a
+ list of lists. Conversely, matrix xs converts a list of lists or matrices
+ to the corresponding matrix. Otherwise, the result is a row vector. */
-list x::matrix = [[x!(i,j) | j=0..m-1] | i=0..n-1]
+list x::matrix = [x!i|i=0..#x-1] if rowvectorp x;
+ = rows x otherwise;
+list2 x::matrix = [[x!(i,j)|j=0..m-1]|i=0..n-1]
when n::int,m::int = dim x end;
+
matrix [] = {};
-matrix xs@(x:_) = rowcatmap colcat xs;
+matrix xs@(x:_) = rowcatmap colcat xs if all listp xs;
+ = rowcat xs if any matrixp xs;
+ = colcat xs otherwise;
-/* Convenience functions to create vectors from lists. */
-
-rowvector xs@[] | rowvector xs@(_:_)
- = colcat xs;
-colvector xs@[] | colvector xs@(_:_)
- = rowcat xs;
-
/* Extract (sub-,super-) diagonals from a matrix. Sub- and super-diagonals for
k=0 return the main diagonal. Indices for sub- and super-diagonals can also
be negative, in which case the corresponding super- or sub-diagonal is
- returned instead. */
+ returned instead. In each case the result is a row vector. */
private matrix_diag matrix_subdiag matrix_supdiag;
extern expr* matrix_diag(expr* x) = diag;
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