dousuguang · April 4, 2022 13:36 · Feb 17, 2020 · Jan 28, 2020 · Jan 16, 2020 · Nov 27, 2019
diff --git a/SparseCholesky.md b/SparseCholesky.md
@@ -2,7 +2,7 @@ Scipy does not currently provide a routine for cholesky decomposition of a spars
 
 The following function receives a sparse symmetric positive-definite matrix A and returns a spase lower triangular matrix L such that A = LL^T.
 
-~~~
+~~~python
 from scipy.sparse import linalg as splinalg
 import scipy.sparse as sparse
 import sys

diff --git a/SparseCholesky.md b/SparseCholesky.md
@@ -10,7 +10,7 @@ import sys
 def sparse_cholesky(A): # The input matrix A must be a sparse symmetric positive-definite.
   
   n = A.shape[0]
-  LU = splinalg.splu(A,diag_pivot_thresh=0)
+  LU = splinalg.splu(A,diag_pivot_thresh=0) # sparse LU decomposition
   
   if ( LU.perm_r == np.arange(n) ).all() and ( LU.U.diagonal() > 0 ).all(): # check the matrix A is positive definite.
     return LU.L.dot( sparse.diags(LU.U.diagonal()**0.5) )

diff --git a/SparseCholesky.md b/SparseCholesky.md
@@ -1,4 +1,4 @@
-Scipy does not currently provide a routine for cholesky decomposition of a sparse matrix, and one have to rely on another external package such as scikit.sparse for the purpose. Here I implement cholesky decomposition of a sparse matrix only using scipy functions.
+Scipy does not currently provide a routine for cholesky decomposition of a sparse matrix, and one have to rely on another external package such as scikit.sparse for the purpose. Here I implement cholesky decomposition of a sparse matrix only using scipy functions. Our implementation relies on sparse LU deconposition.
 
 The following function receives a sparse symmetric positive-definite matrix A and returns a spase lower triangular matrix L such that A = LL^T.
 

diff --git a/SparseCholesky.md b/SparseCholesky.md
@@ -1,6 +1,6 @@
 Scipy does not currently provide a routine for cholesky decomposition of a sparse matrix, and one have to rely on another external package such as scikit.sparse for the purpose. Here I implement cholesky decomposition of a sparse matrix only using scipy functions.
 
-The following function receives a sparse symmetric positive-definite matrix A and returns a spase lower triangular matrix L such that $A = LL^T$.
+The following function receives a sparse symmetric positive-definite matrix A and returns a spase lower triangular matrix L such that A = LL^T.
 
 ~~~
 from scipy.sparse import linalg as splinalg

diff --git a/SparseCholesky.md b/SparseCholesky.md
@@ -1,4 +1,4 @@
-Scipy does not currently provide a routine for cholesky decomposition of a sparse matrix, and one have to use another external package such as scikit.sparse. Here I implement cholesky decomposition of a sparse matrix only using scipy.
+Scipy does not currently provide a routine for cholesky decomposition of a sparse matrix, and one have to rely on another external package such as scikit.sparse for the purpose. Here I implement cholesky decomposition of a sparse matrix only using scipy functions.
 
 The following function receives a sparse symmetric positive-definite matrix A and returns a spase lower triangular matrix L such that $A = LL^T$.
 

diff --git a/SparseCholesky.md b/SparseCholesky.md
@@ -8,10 +8,11 @@ import scipy.sparse as sparse
 import sys
 
 def sparse_cholesky(A): # The input matrix A must be a sparse symmetric positive-definite.
+  
   n = A.shape[0]
   LU = splinalg.splu(A,diag_pivot_thresh=0)
   
-  if ( LU.perm_r == np.arange(n) ).all() and ( LU.U.diagonal() > 0 ).all():
+  if ( LU.perm_r == np.arange(n) ).all() and ( LU.U.diagonal() > 0 ).all(): # check the matrix A is positive definite.
     return LU.L.dot( sparse.diags(LU.U.diagonal()**0.5) )
   else:
     sys.exit('The matrix is not positive definite')

diff --git a/SparseCholesky.md b/SparseCholesky.md
@@ -1,6 +1,6 @@
 Scipy does not currently provide a routine for cholesky decomposition of a sparse matrix, and one have to use another external package such as scikit.sparse. Here I implement cholesky decomposition of a sparse matrix only using scipy.
 
-The following function receives a sparse symmetric positive-definite matrix A and returns a spase lower triangular matrix L such that $$A = LL^T$$.
+The following function receives a sparse symmetric positive-definite matrix A and returns a spase lower triangular matrix L such that $A = LL^T$.
 
 ~~~
 from scipy.sparse import linalg as splinalg

diff --git a/SparseCholesky.md b/SparseCholesky.md
@@ -0,0 +1,19 @@
+Scipy does not currently provide a routine for cholesky decomposition of a sparse matrix, and one have to use another external package such as scikit.sparse. Here I implement cholesky decomposition of a sparse matrix only using scipy.
+
+The following function receives a sparse symmetric positive-definite matrix A and returns a spase lower triangular matrix L such that $$A = LL^T$$.
+
+~~~
+from scipy.sparse import linalg as splinalg
+import scipy.sparse as sparse
+import sys
+
+def sparse_cholesky(A): # The input matrix A must be a sparse symmetric positive-definite.
+  n = A.shape[0]
+  LU = splinalg.splu(A,diag_pivot_thresh=0)
+  
+  if ( LU.perm_r == np.arange(n) ).all() and ( LU.U.diagonal() > 0 ).all():
+    return LU.L.dot( sparse.diags(LU.U.diagonal()**0.5) )
+  else:
+    sys.exit('The matrix is not positive definite')
+  
+~~~
No results found