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a/_downloads/59790902f856f463297d6568e11254ee/plot_cgls.ipynb b/_downloads/59790902f856f463297d6568e11254ee/plot_cgls.ipynb index 127581f6..66e0c8f9 100644 --- a/_downloads/59790902f856f463297d6568e11254ee/plot_cgls.ipynb +++ b/_downloads/59790902f856f463297d6568e11254ee/plot_cgls.ipynb @@ -69,7 +69,7 @@ }, "outputs": [], "source": [ - "xinv, istop, niter, r1norm, r2norm, cost = pylops_mpi.cgls(BDiag, y, niter=15, tol=1e-10, show=True)\nxinv_array = xinv.asarray()\n\nif rank == 0:\n print(f\"CGLS Solution xinv={xinv_array}\")\n # Visualize\n plt.figure(figsize=(18, 5))\n plt.plot(cost, lw=2, label=\"CGLS\")\n plt.title(\"Cost Function\")\n plt.legend()\n plt.tight_layout()" + "# Set initial guess `x0` to zeroes\nx0 = pylops_mpi.DistributedArray(BDiag.shape[1], dtype=np.float128)\nx0[:] = 0\nxinv, istop, niter, r1norm, r2norm, cost = pylops_mpi.cgls(BDiag, y, x0=x0, niter=15, tol=1e-10, show=True)\nxinv_array = xinv.asarray()\n\nif rank == 0:\n print(f\"CGLS Solution xinv={xinv_array}\")\n # Visualize\n plt.figure(figsize=(18, 5))\n plt.plot(cost, lw=2, label=\"CGLS\")\n plt.title(\"Cost Function\")\n plt.legend()\n plt.tight_layout()" ] } ], diff --git a/_downloads/afacec718d3958430d53150fa3b27203/lsm.py b/_downloads/afacec718d3958430d53150fa3b27203/lsm.py index 8793358a..9db25795 100644 --- a/_downloads/afacec718d3958430d53150fa3b27203/lsm.py +++ b/_downloads/afacec718d3958430d53150fa3b27203/lsm.py @@ -164,7 +164,10 @@ # solver. # Inverse -minv_dist = pylops_mpi.cgls(VStack, d_dist, niter=100, show=True)[0] +# Initializing x0 to zeroes +x0 = pylops_mpi.DistributedArray(VStack.shape[1], partition=pylops_mpi.Partition.BROADCAST) +x0[:] = 0 +minv_dist = pylops_mpi.cgls(VStack, d_dist, x0=x0, niter=100, show=True)[0] minv = minv_dist.asarray().reshape((nx, nz)) d_inv_dist = VStack @ minv_dist d_inv = d_inv_dist.asarray().reshape(nstot, nr, nt) diff --git a/_downloads/d5dae76a02f3b395d667034f44fd5555/lsm.ipynb b/_downloads/d5dae76a02f3b395d667034f44fd5555/lsm.ipynb index ff60281b..c391aed5 100644 --- a/_downloads/d5dae76a02f3b395d667034f44fd5555/lsm.ipynb +++ b/_downloads/d5dae76a02f3b395d667034f44fd5555/lsm.ipynb @@ -80,7 +80,7 @@ }, "outputs": [], "source": [ - "# Inverse\nminv_dist = pylops_mpi.cgls(VStack, d_dist, niter=100, show=True)[0]\nminv = minv_dist.asarray().reshape((nx, nz))\nd_inv_dist = VStack @ minv_dist\nd_inv = d_inv_dist.asarray().reshape(nstot, nr, nt)" + "# Inverse\n# Initializing x0 to zeroes\nx0 = pylops_mpi.DistributedArray(VStack.shape[1], partition=pylops_mpi.Partition.BROADCAST)\nx0[:] = 0\nminv_dist = pylops_mpi.cgls(VStack, d_dist, x0=x0, niter=100, show=True)[0]\nminv = minv_dist.asarray().reshape((nx, nz))\nd_inv_dist = VStack @ minv_dist\nd_inv = d_inv_dist.asarray().reshape(nstot, nr, nt)" ] }, { diff --git a/_downloads/df45e4bd89b90a14841f9e115c4b2a59/plot_cgls.py b/_downloads/df45e4bd89b90a14841f9e115c4b2a59/plot_cgls.py index e30e4122..713faf71 100644 --- 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To obtain the # overall inversion of the entire MPIBlockDiag, you can utilize the ``asarray()`` # function of the DistributedArray as shown below. -xinv, istop, niter, r1norm, r2norm, cost = pylops_mpi.cgls(BDiag, y, niter=15, tol=1e-10, show=True) + +# Set initial guess `x0` to zeroes +x0 = pylops_mpi.DistributedArray(BDiag.shape[1], dtype=np.float128) +x0[:] = 0 +xinv, istop, niter, r1norm, r2norm, cost = pylops_mpi.cgls(BDiag, y, x0=x0, niter=15, tol=1e-10, show=True) xinv_array = xinv.asarray() if rank == 0: diff --git a/_images/sphx_glr_lsm_001.png b/_images/sphx_glr_lsm_001.png index 6bb92848..244919fa 100644 Binary files a/_images/sphx_glr_lsm_001.png and b/_images/sphx_glr_lsm_001.png differ diff --git a/_images/sphx_glr_lsm_002.png b/_images/sphx_glr_lsm_002.png index a8303697..1e399d28 100644 Binary files a/_images/sphx_glr_lsm_002.png and b/_images/sphx_glr_lsm_002.png differ diff --git a/_images/sphx_glr_lsm_003.png b/_images/sphx_glr_lsm_003.png index 5efe9308..5e2b40d4 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-1047,12 +1047,17 @@

Source code for pylops_mpi.DistributedArray

     ----------
     distarrays : :obj:`list`
         List of :class:`pylops_mpi.DistributedArray` objects.
-
+    base_comm : :obj:`mpi4py.MPI.Comm`, optional
+        Base MPI Communicator.
+        Defaults to ``mpi4py.MPI.COMM_WORLD``.
     """
 
-    def __init__(self, distarrays: List):
+    def __init__(self, distarrays: List, base_comm: MPI.Comm = MPI.COMM_WORLD):
         self.distarrays = distarrays
         self.narrays = len(distarrays)
+        self.base_comm = base_comm
+        self.rank = base_comm.Get_rank()
+        self.size = base_comm.Get_size()
 
     def __getitem__(self, index):
         return self.distarrays[index]
@@ -1128,6 +1133,8 @@ 
Source code for pylops_mpi.DistributedArray
         return self
 
     def multiply(self, stacked_array):
+        """Stacked Distributed Multiplication of arrays
+        """
         if isinstance(stacked_array, StackedDistributedArray):
             self._check_stacked_size(stacked_array)
         ProductArray = self.copy()
@@ -1143,6 +1150,8 @@ 
Source code for pylops_mpi.DistributedArray
         return ProductArray
 
     def dot(self, stacked_array):
+        """Dot Product of Stacked Distributed Arrays
+        """
         self._check_stacked_size(stacked_array)
         dotprod = 0.
         for iarr in range(self.narrays):
diff --git a/_modules/pylops_mpi/optimization/basic.html b/_modules/pylops_mpi/optimization/basic.html
index 48d28fbb..d9dcc678 100644
--- a/_modules/pylops_mpi/optimization/basic.html
+++ b/_modules/pylops_mpi/optimization/basic.html
@@ -447,16 +447,21 @@ 
Source code for pylops_mpi.optimization.basic
from typing import Callable, Optional, Tuple, Union
 
 from pylops.utils import NDArray
-from pylops_mpi import MPILinearOperator, DistributedArray, StackedDistributedArray
+from pylops_mpi import (
+    MPILinearOperator,
+    DistributedArray,
+    StackedDistributedArray,
+    MPIStackedLinearOperator
+)
 from pylops_mpi.optimization.cls_basic import CG, CGLS
 
 
 

 [docs]
 def cg(
-        Op: MPILinearOperator,
-        y: Union[DistributedArray, StackedDistributedArray] ,
-        x0: Optional[DistributedArray] = None,
+        Op: Union[MPILinearOperator, MPIStackedLinearOperator],
+        y: Union[DistributedArray, StackedDistributedArray],
+        x0: Union[DistributedArray, StackedDistributedArray],
         niter: int = 10,
         tol: float = 1e-4,
         show: bool = False,
@@ -465,16 +470,16 @@ 
Source code for pylops_mpi.optimization.basic
) -> Tuple[Union[DistributedArray, StackedDistributedArray], int, NDArray]:
     r"""Conjugate gradient
 
-    Solve a square system of equations given an MPILinearOperator ``Op`` and
+    Solve a square system of equations given either an MPILinearOperator or an MPIStackedLinearOperator ``Op`` and
     distributed data ``y`` using conjugate gradient iterations.
 
     Parameters
     ----------
-    Op : :obj:`pylops_mpi.MPILinearOperator`
+    Op : :obj:`pylops_mpi.MPILinearOperator` or :obj:`pylops_mpi.MPIStackedLinearOperator`
         Operator to invert of size :math:`[N \times N]`
     y : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`
         DistributedArray of size (N,)
-    x0 : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`, optional
+    x0 : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`
         Initial guess
     niter : :obj:`int`, optional
         Number of iterations
@@ -517,9 +522,9 @@ 
Source code for pylops_mpi.optimization.basic

 [docs]
 def cgls(
-        Op: MPILinearOperator,
+        Op: Union[MPILinearOperator, MPIStackedLinearOperator],
         y: Union[DistributedArray, StackedDistributedArray],
-        x0: Optional[Union[DistributedArray, StackedDistributedArray]] = None,
+        x0: Union[DistributedArray, StackedDistributedArray],
         niter: int = 10,
         damp: float = 0.0,
         tol: float = 1e-4,
@@ -529,16 +534,16 @@ 
Source code for pylops_mpi.optimization.basic
) -> Tuple[DistributedArray, int, int, float, float, NDArray]:
     r"""Conjugate gradient least squares
 
-    Solve an overdetermined system of equations given a MPILinearOperator ``Op`` and
+    Solve an overdetermined system of equations given either an MPILinearOperator or an MPIStackedLinearOperator``Op`` and
     distributed data ``y`` using conjugate gradient iterations.
 
     Parameters
     ----------
-    Op : :obj:`pylops_mpi.MPILinearOperator`
+    Op : :obj:`pylops_mpi.MPILinearOperator` or :obj:`pylops_mpi.MPIStackedLinearOperator`
         MPI Linear Operator to invert of size :math:`[N \times M]`
     y : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`
         DistributedArray of size (N,)
-    x0 : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`, optional
+    x0 : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`
         Initial guess
     niter : :obj:`int`, optional
         Number of iterations
diff --git a/_modules/pylops_mpi/optimization/cls_basic.html b/_modules/pylops_mpi/optimization/cls_basic.html
index f91ef0e8..89aab475 100644
--- a/_modules/pylops_mpi/optimization/cls_basic.html
+++ b/_modules/pylops_mpi/optimization/cls_basic.html
@@ -459,12 +459,12 @@ 
Source code for pylops_mpi.optimization.cls_basic
class CG(Solver):
     r"""Conjugate gradient
 
-    Solve a square system of equations given an MPILinearOperator ``Op`` and
+    Solve a square system of equations given either an MPILinearOperator or an MPIStackedLinearOperator ``Op`` and
     distributed data ``y`` using conjugate gradient iterations.
 
     Parameters
     ----------
-    Op : :obj:`pylops_mpi.MPILinearOperator`
+    Op : :obj:`pylops_mpi.MPILinearOperator` or :obj:`pylops_mpi.MPIStackedLinearOperator`
         Operator to invert of size :math:`[N \times N]`
 
     Notes
@@ -490,6 +490,8 @@ 
Source code for pylops_mpi.optimization.cls_basic
print(head1)
 
     def _print_step(self, x: Union[DistributedArray, StackedDistributedArray]) -> None:
+        if isinstance(x, StackedDistributedArray):
+            x = x.distarrays[0]
         strx = f"{x[0]:1.2e}        " if np.iscomplexobj(x.local_array) else f"{x[0]:11.4e}        "
         msg = f"{self.iiter:6g}        " + strx + f"{self.cost[self.iiter]:11.4e}"
         print(msg)
@@ -497,7 +499,7 @@ 
Source code for pylops_mpi.optimization.cls_basic
def setup(
             self,
             y: Union[DistributedArray, StackedDistributedArray],
-            x0: Optional[Union[DistributedArray, StackedDistributedArray]] = None,
+            x0: Union[DistributedArray, StackedDistributedArray],
             niter: Optional[int] = None,
             tol: float = 1e-4,
             show: bool = False,
@@ -508,9 +510,8 @@ 
Source code for pylops_mpi.optimization.cls_basic
        ----------
         y : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`
             Data of size (N,)
-        x0 : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`, optional
-            Initial guess of size (N,). If ``None``, initialize
-            internally as zero vector (will always default to :obj:`pylops_mpi.DistributedArray`)
+        x0 : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`
+            Initial guess of size (N,).
         niter : :obj:`int`, optional
             Number of iterations (default to ``None`` in case a user wants to manually step over the solver)
         tol : :obj:`float`, optional
@@ -529,16 +530,8 @@ 
Source code for pylops_mpi.optimization.cls_basic
self.niter = niter
         self.tol = tol
 
-        if x0 is None:
-            self.r = self.y.copy()
-            x = DistributedArray(global_shape=self.Op.shape[1],
-                                 partition=self.r.partition,
-                                 local_shapes=self.r.local_shapes,
-                                 dtype=y.dtype)
-            x[:] = 0
-        else:
-            x = x0.copy()
-            self.r = self.y - self.Op.matvec(x)
+        x = x0.copy()
+        self.r = self.y - self.Op.matvec(x)
         self.rank = x.rank
         self.c = self.r.copy()
         self.kold = np.abs(self.r.dot(self.r.conj()))
@@ -549,7 +542,10 @@ 
Source code for pylops_mpi.optimization.cls_basic
self.iiter = 0
 
         if show and self.rank == 0:
-            self._print_setup(np.iscomplexobj(x.local_array))
+            if isinstance(x, StackedDistributedArray):
+                self._print_setup(np.iscomplexobj([x1.local_array for x1 in x.distarrays]))
+            else:
+                self._print_setup(np.iscomplexobj(x.local_array))
         return x
 
     def step(self, x: Union[DistributedArray, StackedDistributedArray],
@@ -652,21 +648,20 @@ 
Source code for pylops_mpi.optimization.cls_basic
def solve(
             self,
             y: Union[DistributedArray, StackedDistributedArray],
-            x0: Optional[Union[DistributedArray, StackedDistributedArray]] = None,
+            x0: Union[DistributedArray, StackedDistributedArray],
             niter: int = 10,
             tol: float = 1e-4,
             show: bool = False,
             itershow: Tuple[int, int, int] = (10, 10, 10),
-    ) -> Tuple[DistributedArray, int, NDArray]:
+    ) -> Tuple[Union[DistributedArray, StackedDistributedArray], int, NDArray]:
         r"""Run entire solver
 
         Parameters
         ----------
         y : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`
             Data of size (N,)
-        x0 : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`, optional
-            Initial guess of size (N,). If ``None``, initialize
-            internally as zero vector (will always default to :obj:`pylops_mpi.DistributedArray`)
+        x0 : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`
+            Initial guess of size (N,).
         niter : :obj:`int`, optional
             Number of iterations
         tol : :obj:`float`, optional
@@ -701,12 +696,12 @@ 
Source code for pylops_mpi.optimization.cls_basic
class CGLS(Solver):
     r"""Conjugate gradient least squares
 
-    Solve an overdetermined system of equations given a MPILinearOperator ``Op``
+    Solve an overdetermined system of equations given either an MPILinearOperator or an MPIStackedLinearOperator ``Op``
     and distributed data ``y`` using conjugate gradient iterations.
 
     Parameters
     ----------
-    Op : :obj:`pylops_mpi.MPILinearOperator`
+    Op : :obj:`pylops_mpi.MPILinearOperator` or :obj:`pylops_mpi.MPIStackedLinearOperator`
         Operator to invert of size :math:`[N \times M]`
 
     Notes
@@ -739,6 +734,8 @@ 
Source code for pylops_mpi.optimization.cls_basic
print(head1)
 
     def _print_step(self, x: Union[DistributedArray, StackedDistributedArray]) -> None:
+        if isinstance(x, StackedDistributedArray):
+            x = x.distarrays[0]
         strx = f"{x[0]:1.2e}   " if np.iscomplexobj(x.local_array) else f"{x[0]:11.4e}        "
         msg = (
             f"{self.iiter:6g}       "
@@ -749,21 +746,20 @@ 
Source code for pylops_mpi.optimization.cls_basic
def setup(self,
               y: Union[DistributedArray, StackedDistributedArray],
-              x0: Optional[DistributedArray] = None,
+              x0: Union[DistributedArray, StackedDistributedArray],
               niter: Optional[int] = None,
               damp: float = 0.0,
               tol: float = 1e-4,
               show: bool = False,
-              ) -> DistributedArray:
+              ) -> Union[DistributedArray, StackedDistributedArray]:
         r"""Setup solver
 
         Parameters
         ----------
         y : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`
             Data of size :math:`[N \times 1]`
-        x0 : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`, optional
-            Initial guess  of size (M,). If ``None``, Defaults to a zero vector
-            (will always default to :obj:`pylops_mpi.DistributedArray`)
+        x0 : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`
+            Initial guess  of size (M,).
         niter : :obj:`int`, optional
             Number of iterations (default to ``None`` in case a user wants to
             manually step over the solver)
@@ -785,19 +781,10 @@ 
Source code for pylops_mpi.optimization.cls_basic
self.tol = tol
         self.niter = niter
 
-        # initialize solver
-        if x0 is None:
-            self.s = y.copy()
-            r = self.Op.rmatvec(self.s)
-            x = DistributedArray(global_shape=self.Op.shape[1], dtype=y.dtype,
-                                 local_shapes=r.local_shapes,
-                                 partition=r.partition)
-            x[:] = 0
-        else:
-            x = x0.copy()
-            self.s = self.y - self.Op.matvec(x)
-            damped_x = damp * x
-            r = self.Op.rmatvec(self.s) - damped_x
+        x = x0.copy()
+        self.s = self.y - self.Op.matvec(x)
+        damped_x = x * damp
+        r = self.Op.rmatvec(self.s) - damped_x
         self.rank = x.rank
         self.c = r.copy()
         self.q = self.Op.matvec(self.c)
@@ -812,7 +799,10 @@ 
Source code for pylops_mpi.optimization.cls_basic
# print setup
         if show and self.rank == 0:
-            self._print_setup(np.iscomplexobj(x.local_array))
+            if isinstance(x, StackedDistributedArray):
+                self._print_setup(np.iscomplexobj([x1.local_array for x1 in x.distarrays]))
+            else:
+                self._print_setup(np.iscomplexobj(x.local_array))
         return x
 
     def step(self, x: Union[DistributedArray, StackedDistributedArray],
@@ -874,7 +864,7 @@ 
Source code for pylops_mpi.optimization.cls_basic
        Returns
         -------
-        x : :obj:`pylops_mpi.DistributedArray`
+        x : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray
             Estimated model of size (M, ).
 
         """
@@ -918,7 +908,7 @@ 
Source code for pylops_mpi.optimization.cls_basic
def solve(self,
               y: Union[DistributedArray, StackedDistributedArray],
-              x0: Optional[Union[DistributedArray, StackedDistributedArray]] = None,
+              x0: Union[DistributedArray, StackedDistributedArray],
               niter: int = 10,
               damp: float = 0.0,
               tol: float = 1e-4,
@@ -932,8 +922,7 @@ 
Source code for pylops_mpi.optimization.cls_basic
        y : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`
             Data of size (N, )
         x0 : :obj:`pylops_mpi.DistributedArray` or :obj:`pylops_mpi.StackedDistributedArray`
-            Initial guess  of size (M, ). If ``None``, initialize internally as zero vector
-            (will always default to :obj:`pylops_mpi.DistributedArray`)
+            Initial guess  of size (M, ).
         niter : :obj:`int`, optional
             Number of iterations (default to ``None`` in case a user wants to
             manually step over the solver)
diff --git a/_sources/gallery/plot_cgls.rst.txt b/_sources/gallery/plot_cgls.rst.txt
index bcff517a..816553fa 100644
--- a/_sources/gallery/plot_cgls.rst.txt
+++ b/_sources/gallery/plot_cgls.rst.txt
@@ -102,11 +102,15 @@ are then obtained in a :py:class:`pylops_mpi.DistributedArray`. To obtain the
 overall inversion of the entire MPIBlockDiag, you can utilize the ``asarray()``
 function of the DistributedArray as shown below.
 
-.. GENERATED FROM PYTHON SOURCE LINES 48-59
+.. GENERATED FROM PYTHON SOURCE LINES 48-63
 
 .. code-block:: Python
 
-    xinv, istop, niter, r1norm, r2norm, cost = pylops_mpi.cgls(BDiag, y, niter=15, tol=1e-10, show=True)
+
+    # Set initial guess `x0` to zeroes
+    x0 = pylops_mpi.DistributedArray(BDiag.shape[1], dtype=np.float128)
+    x0[:] = 0
+    xinv, istop, niter, r1norm, r2norm, cost = pylops_mpi.cgls(BDiag, y, x0=x0, niter=15, tol=1e-10, show=True)
     xinv_array = xinv.asarray()
 
     if rank == 0:
@@ -153,7 +157,7 @@ function of the DistributedArray as shown below.
         14        9.9946e-01         3.9693e-03     3.9693e-03
         15        1.0000e+00         2.0763e-10     2.0763e-10
 
-    Iterations = 15        Total time (s) = 0.02
+    Iterations = 15        Total time (s) = 0.03
     -----------------------------------------------------------------
 
     CGLS Solution xinv=[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
@@ -164,7 +168,7 @@ function of the DistributedArray as shown below.
 
 .. rst-class:: sphx-glr-timing
 
-   **Total running time of the script:** (0 minutes 0.217 seconds)
+   **Total running time of the script:** (0 minutes 0.213 seconds)
 
 
 .. _sphx_glr_download_gallery_plot_cgls.py:
diff --git a/_sources/gallery/plot_derivative.rst.txt b/_sources/gallery/plot_derivative.rst.txt
index 93ec6bd3..9e4cf996 100644
--- a/_sources/gallery/plot_derivative.rst.txt
+++ b/_sources/gallery/plot_derivative.rst.txt
@@ -262,7 +262,7 @@ dimensions and concatenates them.
 
 .. rst-class:: sphx-glr-timing
 
-   **Total running time of the script:** (0 minutes 1.453 seconds)
+   **Total running time of the script:** (0 minutes 1.394 seconds)
 
 
 .. _sphx_glr_download_gallery_plot_derivative.py:
diff --git a/_sources/gallery/plot_distributed_array.rst.txt b/_sources/gallery/plot_distributed_array.rst.txt
index 5ebc3c1d..bb9ed8c0 100644
--- a/_sources/gallery/plot_distributed_array.rst.txt
+++ b/_sources/gallery/plot_distributed_array.rst.txt
@@ -308,7 +308,7 @@ of the array and multiplies the corresponding elements together.
 
 .. rst-class:: sphx-glr-timing
 
-   **Total running time of the script:** (0 minutes 1.871 seconds)
+   **Total running time of the script:** (0 minutes 1.481 seconds)
 
 
 .. _sphx_glr_download_gallery_plot_distributed_array.py:
diff --git a/_sources/gallery/plot_mpilinop.rst.txt b/_sources/gallery/plot_mpilinop.rst.txt
index 0269792d..e97d3133 100644
--- a/_sources/gallery/plot_mpilinop.rst.txt
+++ b/_sources/gallery/plot_mpilinop.rst.txt
@@ -214,7 +214,7 @@ to ensure that the operators align appropriately with their corresponding
 
 .. rst-class:: sphx-glr-timing
 
-   **Total running time of the script:** (0 minutes 0.415 seconds)
+   **Total running time of the script:** (0 minutes 0.335 seconds)
 
 
 .. _sphx_glr_download_gallery_plot_mpilinop.py:
diff --git a/_sources/gallery/plot_stacked_array.rst.txt b/_sources/gallery/plot_stacked_array.rst.txt
index d06cfb0c..ccf84bf8 100644
--- a/_sources/gallery/plot_stacked_array.rst.txt
+++ b/_sources/gallery/plot_stacked_array.rst.txt
@@ -403,7 +403,7 @@ of distributed arrays
 
 .. rst-class:: sphx-glr-timing
 
-   **Total running time of the script:** (0 minutes 0.016 seconds)
+   **Total running time of the script:** (0 minutes 0.015 seconds)
 
 
 .. _sphx_glr_download_gallery_plot_stacked_array.py:
diff --git a/_sources/gallery/plot_stacking.rst.txt b/_sources/gallery/plot_stacking.rst.txt
index 84b80086..976c6b29 100644
--- a/_sources/gallery/plot_stacking.rst.txt
+++ b/_sources/gallery/plot_stacking.rst.txt
@@ -279,7 +279,7 @@ corresponding vector :math:`x`.
 
 .. rst-class:: sphx-glr-timing
 
-   **Total running time of the script:** (0 minutes 0.524 seconds)
+   **Total running time of the script:** (0 minutes 0.426 seconds)
 
 
 .. _sphx_glr_download_gallery_plot_stacking.py:
diff --git a/_sources/gallery/sg_execution_times.rst.txt b/_sources/gallery/sg_execution_times.rst.txt
index c13fd437..62eec68d 100644
--- a/_sources/gallery/sg_execution_times.rst.txt
+++ b/_sources/gallery/sg_execution_times.rst.txt
@@ -6,7 +6,7 @@
 
 Computation times
 =================
-**00:04.495** total execution time for 6 files **from gallery**:
+**00:03.864** total execution time for 6 files **from gallery**:
 
 .. container::
 
@@ -33,20 +33,20 @@ Computation times
      - Time
      - Mem (MB)
    * - :ref:`sphx_glr_gallery_plot_distributed_array.py` (``plot_distributed_array.py``)
-     - 00:01.871
+     - 00:01.481
      - 0.0
    * - :ref:`sphx_glr_gallery_plot_derivative.py` (``plot_derivative.py``)
-     - 00:01.453
+     - 00:01.394
      - 0.0
    * - :ref:`sphx_glr_gallery_plot_stacking.py` (``plot_stacking.py``)
-     - 00:00.524
+     - 00:00.426
      - 0.0
    * - :ref:`sphx_glr_gallery_plot_mpilinop.py` (``plot_mpilinop.py``)
-     - 00:00.415
+     - 00:00.335
      - 0.0
    * - :ref:`sphx_glr_gallery_plot_cgls.py` (``plot_cgls.py``)
-     - 00:00.217
+     - 00:00.213
      - 0.0
    * - :ref:`sphx_glr_gallery_plot_stacked_array.py` (``plot_stacked_array.py``)
-     - 00:00.016
+     - 00:00.015
      - 0.0
diff --git a/_sources/sg_execution_times.rst.txt b/_sources/sg_execution_times.rst.txt
index 7f09455b..80b4b88b 100644
--- a/_sources/sg_execution_times.rst.txt
+++ b/_sources/sg_execution_times.rst.txt
@@ -6,7 +6,7 @@
 
 Computation times
 =================
-**02:26.632** total execution time for 8 files **from all galleries**:
+**02:25.558** total execution time for 8 files **from all galleries**:
 
 .. container::
 
@@ -33,26 +33,26 @@ Computation times
      - Time
      - Mem (MB)
    * - :ref:`sphx_glr_tutorials_poststack.py` (``../../tutorials/poststack.py``)
-     - 02:18.828
+     - 02:18.540
      - 0.0
    * - :ref:`sphx_glr_tutorials_lsm.py` (``../../tutorials/lsm.py``)
-     - 00:03.308
+     - 00:03.154
      - 0.0
    * - :ref:`sphx_glr_gallery_plot_distributed_array.py` (``../../examples/plot_distributed_array.py``)
-     - 00:01.871
+     - 00:01.481
      - 0.0
    * - :ref:`sphx_glr_gallery_plot_derivative.py` (``../../examples/plot_derivative.py``)
-     - 00:01.453
+     - 00:01.394
      - 0.0
    * - :ref:`sphx_glr_gallery_plot_stacking.py` (``../../examples/plot_stacking.py``)
-     - 00:00.524
+     - 00:00.426
      - 0.0
    * - :ref:`sphx_glr_gallery_plot_mpilinop.py` (``../../examples/plot_mpilinop.py``)
-     - 00:00.415
+     - 00:00.335
      - 0.0
    * - :ref:`sphx_glr_gallery_plot_cgls.py` (``../../examples/plot_cgls.py``)
-     - 00:00.217
+     - 00:00.213
      - 0.0
    * - :ref:`sphx_glr_gallery_plot_stacked_array.py` (``../../examples/plot_stacked_array.py``)
-     - 00:00.016
+     - 00:00.015
      - 0.0
diff --git a/_sources/tutorials/lsm.rst.txt b/_sources/tutorials/lsm.rst.txt
index cad4ed21..965365db 100644
--- a/_sources/tutorials/lsm.rst.txt
+++ b/_sources/tutorials/lsm.rst.txt
@@ -246,13 +246,16 @@ product with the broadcasted reflectivity at every location on the subsurface.
 We calculate the inverse using the :py:func:`pylops_mpi.optimization.basic.cgls`
 solver.
 
-.. GENERATED FROM PYTHON SOURCE LINES 165-172
+.. GENERATED FROM PYTHON SOURCE LINES 165-175
 
 .. code-block:: Python
 
 
     # Inverse
-    minv_dist = pylops_mpi.cgls(VStack, d_dist, niter=100, show=True)[0]
+    # Initializing x0 to zeroes
+    x0 = pylops_mpi.DistributedArray(VStack.shape[1], partition=pylops_mpi.Partition.BROADCAST)
+    x0[:] = 0
+    minv_dist = pylops_mpi.cgls(VStack, d_dist, x0=x0, niter=100, show=True)[0]
     minv = minv_dist.asarray().reshape((nx, nz))
     d_inv_dist = VStack @ minv_dist
     d_inv = d_inv_dist.asarray().reshape(nstot, nr, nt)
@@ -301,14 +304,14 @@ solver.
         99       -1.2546e-02         2.8528e+00     2.8528e+00
        100       -1.2389e-02         2.8342e+00     2.8342e+00
 
-    Iterations = 100        Total time (s) = 1.16
+    Iterations = 100        Total time (s) = 1.19
     -----------------------------------------------------------------
 
 
 
 
 
-.. GENERATED FROM PYTHON SOURCE LINES 173-209
+.. GENERATED FROM PYTHON SOURCE LINES 176-212
 
 .. code-block:: Python
 
@@ -382,7 +385,7 @@ solver.
 
 .. rst-class:: sphx-glr-timing
 
-   **Total running time of the script:** (0 minutes 3.308 seconds)
+   **Total running time of the script:** (0 minutes 3.154 seconds)
 
 
 .. _sphx_glr_download_tutorials_lsm.py:
diff --git a/_sources/tutorials/poststack.rst.txt b/_sources/tutorials/poststack.rst.txt
index 829d2e83..ef24482a 100644
--- a/_sources/tutorials/poststack.rst.txt
+++ b/_sources/tutorials/poststack.rst.txt
@@ -284,7 +284,7 @@ normal equations, and :math:`\mathbf{d}^{Norm}` is the data of the normal equati
         99        6.1544e-01         6.5026e-01     6.5026e-01
        100        6.1561e-01         6.4212e-01     6.4212e-01
 
-    Iterations = 100        Total time (s) = 29.06
+    Iterations = 100        Total time (s) = 29.61
     -----------------------------------------------------------------
 
 
@@ -349,7 +349,7 @@ normal equations, and :math:`\mathbf{d}^{Norm}` is the data of the normal equati
         99         6.3033e-01         1.9903e+02
        100         6.3026e-01         1.9777e+02
 
-    Iterations = 100        Total time (s) = 44.87
+    Iterations = 100        Total time (s) = 44.84
     -------------------------------------------------------
 
 
@@ -481,7 +481,7 @@ Finally, we display the modeling and inversion results
 
 .. rst-class:: sphx-glr-timing
 
-   **Total running time of the script:** (2 minutes 18.828 seconds)
+   **Total running time of the script:** (2 minutes 18.540 seconds)
 
 
 .. _sphx_glr_download_tutorials_poststack.py:
diff --git a/_sources/tutorials/sg_execution_times.rst.txt b/_sources/tutorials/sg_execution_times.rst.txt
index 6b126c09..ea953856 100644
--- a/_sources/tutorials/sg_execution_times.rst.txt
+++ b/_sources/tutorials/sg_execution_times.rst.txt
@@ -6,7 +6,7 @@
 
 Computation times
 =================
-**02:22.137** total execution time for 2 files **from tutorials**:
+**02:21.695** total execution time for 2 files **from tutorials**:
 
 .. container::
 
@@ -33,8 +33,8 @@ Computation times
      - Time
      - Mem (MB)
    * - :ref:`sphx_glr_tutorials_poststack.py` (``poststack.py``)
-     - 02:18.828
+     - 02:18.540
      - 0.0
    * - :ref:`sphx_glr_tutorials_lsm.py` (``lsm.py``)
-     - 00:03.308
+     - 00:03.154
      - 0.0
diff --git a/api/generated/pylops_mpi.StackedDistributedArray.html b/api/generated/pylops_mpi.StackedDistributedArray.html
index 7ea2dbb4..51198e5e 100644
--- a/api/generated/pylops_mpi.StackedDistributedArray.html
+++ b/api/generated/pylops_mpi.StackedDistributedArray.html
@@ -492,7 +492,7 @@
 
pylops_mpi.StackedDistributedArray#

 

 

-class pylops_mpi.StackedDistributedArray(distarrays)[source]#

+class pylops_mpi.StackedDistributedArray(distarrays, base_comm=<mpi4py.MPI.Intracomm object>)[source]#
 
Stacked DistributedArrays

 
Stack DistributedArray objects and power them with basic mathematical operations.
 This class allows one to work with a series of distributed arrays to avoid having to create
@@ -502,13 +502,16 @@ 
pylops_mpi.StackedDistributedArray

 
distarrayslist
List of pylops_mpi.DistributedArray objects.

 

+
base_commmpi4py.MPI.Comm, optional
Base MPI Communicator.
+Defaults to mpi4py.MPI.COMM_WORLD.

+

 

 

 

 
Methods

 
-
+
@@ -524,13 +527,13 @@ 
pylops_mpi.StackedDistributedArray

-
+
-
+
diff --git a/api/generated/pylops_mpi.optimization.basic.cg.html b/api/generated/pylops_mpi.optimization.basic.cg.html
index 9f85c773..5c3e0707 100644
--- a/api/generated/pylops_mpi.optimization.basic.cg.html
+++ b/api/generated/pylops_mpi.optimization.basic.cg.html
@@ -494,18 +494,18 @@
 
pylops_mpi.optimization.basic.cg#

 

-pylops_mpi.optimization.basic.cg(Op, y, x0=None, niter=10, tol=0.0001, show=False, itershow=(10, 10, 10), callback=None)[source]#

+pylops_mpi.optimization.basic.cg(Op, y, x0, niter=10, tol=0.0001, show=False, itershow=(10, 10, 10), callback=None)[source]#
 
Conjugate gradient

-
Solve a square system of equations given an MPILinearOperator Op and
+
Solve a square system of equations given either an MPILinearOperator or an MPIStackedLinearOperator Op and
 distributed data y using conjugate gradient iterations.

 

 
Parameters:

 

-
Oppylops_mpi.MPILinearOperator
Operator to invert of size \([N \times N]\)

+
Oppylops_mpi.MPILinearOperator or pylops_mpi.MPIStackedLinearOperator
Operator to invert of size \([N \times N]\)

 

 
ypylops_mpi.DistributedArray or pylops_mpi.StackedDistributedArray
DistributedArray of size (N,)

 

-
x0pylops_mpi.DistributedArray or pylops_mpi.StackedDistributedArray, optional
Initial guess

+
x0pylops_mpi.DistributedArray or pylops_mpi.StackedDistributedArray
Initial guess

 

 
niterint, optional
Number of iterations

 

diff --git a/api/generated/pylops_mpi.optimization.basic.cgls.html b/api/generated/pylops_mpi.optimization.basic.cgls.html
index 428cd63a..81234c54 100644
--- a/api/generated/pylops_mpi.optimization.basic.cgls.html
+++ b/api/generated/pylops_mpi.optimization.basic.cgls.html
@@ -494,18 +494,18 @@
 
pylops_mpi.optimization.basic.cgls#

 

 

-pylops_mpi.optimization.basic.cgls(Op, y, x0=None, niter=10, damp=0.0, tol=0.0001, show=False, itershow=(10, 10, 10), callback=None)[source]#

+pylops_mpi.optimization.basic.cgls(Op, y, x0, niter=10, damp=0.0, tol=0.0001, show=False, itershow=(10, 10, 10), callback=None)[source]#
 
Conjugate gradient least squares

-
Solve an overdetermined system of equations given a MPILinearOperator Op and
+
Solve an overdetermined system of equations given either an MPILinearOperator or an MPIStackedLinearOperator``Op`` and
 distributed data y using conjugate gradient iterations.

 

 
Parameters:

 

-
Oppylops_mpi.MPILinearOperator
MPI Linear Operator to invert of size \([N \times M]\)

+
Oppylops_mpi.MPILinearOperator or pylops_mpi.MPIStackedLinearOperator
MPI Linear Operator to invert of size \([N \times M]\)

 

 
ypylops_mpi.DistributedArray or pylops_mpi.StackedDistributedArray
DistributedArray of size (N,)

 

-
x0pylops_mpi.DistributedArray or pylops_mpi.StackedDistributedArray, optional
Initial guess

+
x0pylops_mpi.DistributedArray or pylops_mpi.StackedDistributedArray
Initial guess

 

 
niterint, optional
Number of iterations

 

diff --git a/api/generated/pylops_mpi.optimization.cls_basic.CG.html b/api/generated/pylops_mpi.optimization.cls_basic.CG.html
index 6e93cd4c..7ee23963 100644
--- a/api/generated/pylops_mpi.optimization.cls_basic.CG.html
+++ b/api/generated/pylops_mpi.optimization.cls_basic.CG.html
@@ -496,12 +496,12 @@ 
pylops_mpi.optimization.cls_basic.CG
 class pylops_mpi.optimization.cls_basic.CG(Op, callbacks=None)[source]#
 
Conjugate gradient

-
Solve a square system of equations given an MPILinearOperator Op and
+
Solve a square system of equations given either an MPILinearOperator or an MPIStackedLinearOperator Op and
 distributed data y using conjugate gradient iterations.

 

 
Parameters:

 

-
Oppylops_mpi.MPILinearOperator
Operator to invert of size \([N \times N]\)

+
Oppylops_mpi.MPILinearOperator or pylops_mpi.MPIStackedLinearOperator
Operator to invert of size \([N \times N]\)

 

 

 

@@ -524,10 +524,10 @@ 
pylops_mpi.optimization.cls_basic.CG

-
+
-
+
diff --git a/api/generated/pylops_mpi.optimization.cls_basic.CGLS.html b/api/generated/pylops_mpi.optimization.cls_basic.CGLS.html
index a0f7609c..d0cdbd69 100644
--- a/api/generated/pylops_mpi.optimization.cls_basic.CGLS.html
+++ b/api/generated/pylops_mpi.optimization.cls_basic.CGLS.html
@@ -496,12 +496,12 @@ 
pylops_mpi.optimization.cls_basic.CGLS
 class pylops_mpi.optimization.cls_basic.CGLS(Op, callbacks=None)[source]#
 
Conjugate gradient least squares

-
Solve an overdetermined system of equations given a MPILinearOperator Op
+
Solve an overdetermined system of equations given either an MPILinearOperator or an MPIStackedLinearOperator Op
 and distributed data y using conjugate gradient iterations.

 

 
Parameters:

 

-
Oppylops_mpi.MPILinearOperator
Operator to invert of size \([N \times M]\)

+
Oppylops_mpi.MPILinearOperator or pylops_mpi.MPIStackedLinearOperator
Operator to invert of size \([N \times M]\)

 

 

 

@@ -527,10 +527,10 @@ 
pylops_mpi.optimization.cls_basic.CGLS

-
+
-
+
diff --git a/api/index.html b/api/index.html
index a9334f86..435c287f 100644
--- a/api/index.html
+++ b/api/index.html
@@ -499,7 +499,7 @@ 
DistributedArray

-
+
@@ -581,10 +581,10 @@ 
Basic#<
 

 
__init__(distarrays)
__init__(distarrays[, base_comm])

 

 

 
add(stacked_array)
dot(stacked_array)
Dot Product of Stacked Distributed Arrays

 

 
iadd(stacked_array)

 
Stacked Distributed In-Place Addition of arrays

 

 
multiply(stacked_array)
Stacked Distributed Multiplication of arrays

 

 
norm([ord])

 
numpy.linalg.norm method on stacked Distributed arrays

 
run(x[, niter, show, itershow])

 
Run solver

 
setup(y[, x0, niter, tol, show])
setup(y, x0[, niter, tol, show])

 
Setup solver

 
solve(y[, x0, niter, tol, show, itershow])
solve(y, x0[, niter, tol, show, itershow])

 
Run entire solver

 

 
step(x[, show])
run(x[, niter, show, itershow])

 
Run solver

 
setup(y[, x0, niter, damp, tol, show])
setup(y, x0[, niter, damp, tol, show])

 
Setup solver

 
solve(y[, x0, niter, damp, tol, show, itershow])
solve(y, x0[, niter, damp, tol, show, itershow])

 
Run entire solver

 

 
step(x[, show])
DistributedArray(global_shape[, base_comm, ...])

 
Distributed Numpy Arrays

 
StackedDistributedArray(distarrays)
StackedDistributedArray(distarrays[, base_comm])

 
Stacked DistributedArrays

 

 

 
-
+
-
+
diff --git a/gallery/plot_cgls.html b/gallery/plot_cgls.html
index d2aec4b1..b48054fe 100644
--- a/gallery/plot_cgls.html
+++ b/gallery/plot_cgls.html
@@ -510,7 +510,10 @@
 are then obtained in a pylops_mpi.DistributedArray. To obtain the
 overall inversion of the entire MPIBlockDiag, you can utilize the asarray()
 function of the DistributedArray as shown below.

-
xinv, istop, niter, r1norm, r2norm, cost = pylops_mpi.cgls(BDiag, y, niter=15, tol=1e-10, show=True)
+
# Set initial guess `x0` to zeroes
+x0 = pylops_mpi.DistributedArray(BDiag.shape[1], dtype=np.float128)
+x0[:] = 0
+xinv, istop, niter, r1norm, r2norm, cost = pylops_mpi.cgls(BDiag, y, x0=x0, niter=15, tol=1e-10, show=True)
 xinv_array = xinv.asarray()
 
 if rank == 0:
@@ -546,13 +549,13 @@
     14        9.9946e-01         3.9693e-03     3.9693e-03
     15        1.0000e+00         2.0763e-10     2.0763e-10
 
-Iterations = 15        Total time (s) = 0.02
+Iterations = 15        Total time (s) = 0.03
 -----------------------------------------------------------------
 
 CGLS Solution xinv=[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
 

 

-
Total running time of the script: (0 minutes 0.217 seconds)

+
Total running time of the script: (0 minutes 0.213 seconds)

 

 

-Gradient, x, y - 1st direction, xadj, y - 2nd direction
Total running time of the script: (0 minutes 1.453 seconds)

+Gradient, x, y - 1st direction, xadj, y - 2nd direction
Total running time of the script: (0 minutes 1.394 seconds)

-Multiplication, Rank-0
Total running time of the script: (0 minutes 1.871 seconds)

+Multiplication, Rank-0
Total running time of the script: (0 minutes 1.481 seconds)

-Adjoint, $x$, $y$
Total running time of the script: (0 minutes 0.415 seconds)

+Adjoint, $x$, $y$
Total running time of the script: (0 minutes 0.335 seconds)

 
cg(Op, y[, x0, niter, tol, show, itershow, ...])
cg(Op, y, x0[, niter, tol, show, itershow, ...])

 
Conjugate gradient

 
cgls(Op, y[, x0, niter, damp, tol, show, ...])
cgls(Op, y, x0[, niter, damp, tol, show, ...])

 
Conjugate gradient least squares