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Fix stale references to cola.linalg.inverse in docs (#68)
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A few places in the docs still references `cola.linalg.inverse`. This PR
catches (hopefully) all of them.
Also some doc nits regarding spacing and capitalization.
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@mfinzi
mfinzi authored Sep 19, 2023
2 parents 14d9093 + 32e580c commit e3db6b7
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40 changes: 20 additions & 20 deletions docs/notebooks/Linalg_operations_walkthrough.ipynb
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Expand Up @@ -30,13 +30,13 @@
"import cola\n",
"\n",
"N=2000\n",
"U = cola.lazify(torch.randn(N,5))\n",
"V = cola.lazify(torch.randn(N,5))\n",
"D = cola.diag(torch.linspace(1,100,N))\n",
"U = cola.lazify(torch.randn(N, 5))\n",
"V = cola.lazify(torch.randn(N, 5))\n",
"D = cola.diag(torch.linspace(1, 100, N))\n",
"\n",
"A = U@U.T + D # a PSD matrix\n",
"B = U@V.T + D # a generic square matrix\n",
"C = V.T@D # a generic rectangular matrix\n",
"A = U @ U.T + D # a PSD matrix\n",
"B = U @ V.T + D # a generic square matrix\n",
"C = V.T @ D # a generic rectangular matrix\n",
"\n",
"x = torch.ones(N) # test vector x"
]
Expand Down Expand Up @@ -130,7 +130,7 @@
"id": "6e3b54b3",
"metadata": {},
"source": [
"`cola.linalg.inverse(A)` represents the linear operator $A^{-1}$ that, when applied to a vector $b$, it solves the linear system $A x = b$ and then outputs $x$.\n",
"`cola.linalg.inv(A)` represents the linear operator $A^{-1}$ that, when applied to a vector $b$, it solves the linear system $A x = b$ and then outputs $x$.\n",
"It does not, however, compute the inverse densely $A^{-1}$ and then multiply it by the vector $b$, and is exactly equivalent to calling `cola.linalg.solve` as shown below.\n"
]
},
Expand All @@ -150,8 +150,8 @@
"outputs": [],
"source": [
"# these two are exactly equivalent in CoLA\n",
"y = cola.linalg.solve(A,x)\n",
"y = cola.linalg.inv(A)@x"
"y = cola.linalg.solve(A, x)\n",
"y = cola.linalg.inv(A) @ x"
]
},
{
Expand Down Expand Up @@ -261,7 +261,7 @@
" if method == 'iterative':\n",
" print(f\"Computed inverse in {Binv.info['iterations']} iters with error {Binv.info['errors'][-1]:.1e}\")\n",
"\n",
"print(\"Actual residual error:\", torch.linalg.norm(B@y-x)/torch.linalg.norm(x))"
"print(\"Actual residual error:\", torch.linalg.norm(B @ y - x) / torch.linalg.norm(x))"
]
},
{
Expand Down Expand Up @@ -301,7 +301,7 @@
"source": [
"### SelfAdjoint\n",
"\n",
"Whether CoLA uses the more efficient Lanczos process or more costly version using Arnoldi depends on whether or not the matrix is `SelfAdjoint` (which guarantees an orthogonal eigenbasis). `SelfAdjoint` is considered a superset of `PSD`."
"Whether CoLA uses the more efficient Lanczos process or more costly version using Arnoldi depends on whether or not the matrix is `SelfAdjoint` (which gauruntees an orthogonal eigenbasis). `SelfAdjoint` is considered a superset of `PSD`."
]
},
{
Expand Down Expand Up @@ -354,7 +354,7 @@
"for method in ['dense', 'iterative']:\n",
" S = cola.linalg.sqrt(A,tol=1e-4, max_iters=100, method=method)\n",
" print(f\"S with method={method} is of type {type(S)}\")\n",
" print(\"error in sqrt:\", torch.linalg.norm(S@(S@x)-A@x)/torch.linalg.norm(A@x))"
" print(\"error in sqrt:\", torch.linalg.norm(S @ (S @ x) - A @ x) / torch.linalg.norm(A @ x))"
]
},
{
Expand Down Expand Up @@ -390,8 +390,8 @@
"expA = cola.linalg.exp(-A)\n",
"logA = cola.linalg.log(A)\n",
"Apow10 = cola.linalg.pow(A,10)\n",
"resolvent = cola.linalg.apply_unary(lambda x: 1/(x-1), A)\n",
"[print(op[:2,:2].to_dense()) for op in [expA, logA, Apow10, resolvent]];"
"resolvent = cola.linalg.apply_unary(lambda x: 1 / (x - 1), A)\n",
"[print(op[:2, :2].to_dense()) for op in [expA, logA, Apow10, resolvent]];"
]
},
{
Expand Down Expand Up @@ -423,8 +423,8 @@
}
],
"source": [
"ops = [cola.linalg.sqrt(B), cola.linalg.exp(-B), cola.linalg.pow(B,10)]\n",
"[print(op[:2,:2].to_dense()) for op in ops];"
"ops = [cola.linalg.sqrt(B), cola.linalg.exp(-B), cola.linalg.pow(B, 10)]\n",
"[print(op[:2, :2].to_dense()) for op in ops];"
]
},
{
Expand Down Expand Up @@ -483,7 +483,7 @@
],
"source": [
"diag = cola.linalg.diag(A)\n",
"off_diag = cola.linalg.diag(A,k=1)\n",
"off_diag = cola.linalg.diag(A, k=1)\n",
"print(f\"diagonal: {diag}\")\n",
"print(f\"off-diagonal: {off_diag}\")"
]
Expand All @@ -493,7 +493,7 @@
"id": "d321cde0",
"metadata": {},
"source": [
"## log determinants\n",
"## Log Determinants\n",
"\n",
"In the dense case, we compute log determinants from the Cholesky or LU decompositions depending on whether the matrix is PSD or not, and this runs in time $O(n^3)$.\n",
"\n",
Expand Down Expand Up @@ -523,8 +523,8 @@
}
],
"source": [
"print(\"Tr(log(A))\",cola.linalg.logdet(A, method='iterative', vtol=1e-1,tol=1e-4, max_iters=30, key=42))\n",
"print(\"SLQ:\", cola.linalg.logdet(A, method='iterative', tol=1e-3,max_iters=10))\n",
"print(\"Tr(log(A))\",cola.linalg.logdet(A, method='iterative', vtol=1e-1, tol=1e-4, max_iters=30, key=42))\n",
"print(\"SLQ:\", cola.linalg.logdet(A, method='iterative', tol=1e-3, max_iters=10))\n",
"print(\"Dense:\", cola.linalg.logdet(A, method='dense'))"
]
},
Expand Down
42 changes: 21 additions & 21 deletions docs/notebooks/colabs/Linalg_operations_walkthrough.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -47,13 +47,13 @@
"import cola\n",
"\n",
"N=2000\n",
"U = cola.lazify(torch.randn(N,5))\n",
"V = cola.lazify(torch.randn(N,5))\n",
"D = cola.diag(torch.linspace(1,100,N))\n",
"U = cola.lazify(torch.randn(N, 5))\n",
"V = cola.lazify(torch.randn(N, 5))\n",
"D = cola.diag(torch.linspace(1, 100, N))\n",
"\n",
"A = U@U.T + D # a PSD matrix\n",
"B = U@V.T + D # a generic square matrix\n",
"C = V.T@D # a generic rectangular matrix\n",
"A = U @ U.T + D # a PSD matrix\n",
"B = U @ V.T + D # a generic square matrix\n",
"C = V.T @ D # a generic rectangular matrix\n",
"\n",
"x = torch.ones(N) # test vector x"
]
Expand Down Expand Up @@ -147,7 +147,7 @@
"id": "6e3b54b3",
"metadata": {},
"source": [
"`cola.linalg.inverse(A)` represents the linear operator $A^{-1}$ that, when applied to a vector $b$, it solves the linear system $A x = b$ and then outputs $x$.\n",
"`cola.linalg.inv(A)` represents the linear operator $A^{-1}$ that, when applied to a vector $b$, it solves the linear system $A x = b$ and then outputs $x$.\n",
"It does not, however, compute the inverse densely $A^{-1}$ and then multiply it by the vector $b$, and is exactly equivalent to calling `cola.linalg.solve` as shown below.\n"
]
},
Expand All @@ -167,8 +167,8 @@
"outputs": [],
"source": [
"# these two are exactly equivalent in CoLA\n",
"y = cola.linalg.solve(A,x)\n",
"y = cola.linalg.inv(A)@x"
"y = cola.linalg.solve(A, x)\n",
"y = cola.linalg.inv(A) @ x"
]
},
{
Expand Down Expand Up @@ -278,7 +278,7 @@
" if method == 'iterative':\n",
" print(f\"Computed inverse in {Binv.info['iterations']} iters with error {Binv.info['errors'][-1]:.1e}\")\n",
"\n",
"print(\"Actual residual error:\", torch.linalg.norm(B@y-x)/torch.linalg.norm(x))"
"print(\"Actual residual error:\", torch.linalg.norm(B @ y - x) / torch.linalg.norm(x))"
]
},
{
Expand Down Expand Up @@ -371,7 +371,7 @@
"for method in ['dense', 'iterative']:\n",
" S = cola.linalg.sqrt(A,tol=1e-4, max_iters=100, method=method)\n",
" print(f\"S with method={method} is of type {type(S)}\")\n",
" print(\"error in sqrt:\", torch.linalg.norm(S@(S@x)-A@x)/torch.linalg.norm(A@x))"
" print(\"error in sqrt:\", torch.linalg.norm(S @ (S @ x) - A @ x) / torch.linalg.norm(A @ x))"
]
},
{
Expand Down Expand Up @@ -407,8 +407,8 @@
"expA = cola.linalg.exp(-A)\n",
"logA = cola.linalg.log(A)\n",
"Apow10 = cola.linalg.pow(A,10)\n",
"resolvent = cola.linalg.apply_unary(lambda x: 1/(x-1), A)\n",
"[print(op[:2,:2].to_dense()) for op in [expA, logA, Apow10, resolvent]];"
"resolvent = cola.linalg.apply_unary(lambda x: 1 / (x - 1), A)\n",
"[print(op[:2, :2].to_dense()) for op in [expA, logA, Apow10, resolvent]];"
]
},
{
Expand Down Expand Up @@ -440,8 +440,8 @@
}
],
"source": [
"ops = [cola.linalg.sqrt(B), cola.linalg.exp(-B), cola.linalg.pow(B,10)]\n",
"[print(op[:2,:2].to_dense()) for op in ops];"
"ops = [cola.linalg.sqrt(B), cola.linalg.exp(-B), cola.linalg.pow(B, 10)]\n",
"[print(op[:2, :2].to_dense()) for op in ops];"
]
},
{
Expand Down Expand Up @@ -500,7 +500,7 @@
],
"source": [
"diag = cola.linalg.diag(A)\n",
"off_diag = cola.linalg.diag(A,k=1)\n",
"off_diag = cola.linalg.diag(A, k=1)\n",
"print(f\"diagonal: {diag}\")\n",
"print(f\"off-diagonal: {off_diag}\")"
]
Expand All @@ -510,7 +510,7 @@
"id": "d321cde0",
"metadata": {},
"source": [
"## log determinants\n",
"## Log Determinants\n",
"\n",
"In the dense case, we compute log determinants from the Cholesky or LU decompositions depending on whether the matrix is PSD or not, and this runs in time $O(n^3)$.\n",
"\n",
Expand Down Expand Up @@ -540,8 +540,8 @@
}
],
"source": [
"print(\"Tr(log(A))\",cola.linalg.logdet(A, method='iterative', vtol=1e-1,tol=1e-4, max_iters=30, key=42))\n",
"print(\"SLQ:\", cola.linalg.logdet(A, method='iterative', tol=1e-3,max_iters=10))\n",
"print(\"Tr(log(A))\",cola.linalg.logdet(A, method='iterative', vtol=1e-1, tol=1e-4, max_iters=30, key=42))\n",
"print(\"SLQ:\", cola.linalg.logdet(A, method='iterative', tol=1e-3, max_iters=10))\n",
"print(\"Dense:\", cola.linalg.logdet(A, method='dense'))"
]
},
Expand Down Expand Up @@ -685,9 +685,9 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.5"
"version": "3.10.12"
}
},
"nbformat": 4,
"nbformat_minor": 4
"nbformat_minor": 5
}
2 changes: 1 addition & 1 deletion docs/notebooks/colabs/worksheet.ipynb
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Expand Up @@ -246,7 +246,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Having a PSD `LinearOperator` opens up the possiblity in CoLA to dispatch our favorite algorithm: CG. As we all know, CG has a couple of hyperparameters like the tolerance (set it to $10^{-10}$) and the max number of iterations (set it to 10K). _Hint_: Pass `method`, `tol` and `max_iters` to the function that you used in the previous exercise. To see what is going on under the hood, take a look at the [source code](https://github.com/wilson-labs/cola/blob/main/cola/linalg/inverse.py#L67)."
"Having a PSD `LinearOperator` opens up the possiblity in CoLA to dispatch our favorite algorithm: CG. As we all know, CG has a couple of hyperparameters like the tolerance (set it to $10^{-10}$) and the max number of iterations (set it to 10K). _Hint_: Pass `method`, `tol` and `max_iters` to the function that you used in the previous exercise. To see what is going on under the hood, take a look at the [source code](https://github.com/wilson-labs/cola/blob/main/cola/linalg/inv.py#L80)."
]
},
{
Expand Down
2 changes: 1 addition & 1 deletion docs/notebooks/worksheet.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -229,7 +229,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Having a PSD `LinearOperator` opens up the possibility in CoLA to dispatch our favorite algorithm: CG. As we all know, CG has a couple of hyperparameters like the tolerance (set it to $10^{-10}$) and the max number of iterations (set it to 10K). _Hint_: Pass `method`, `tol` and `max_iters` to the function that you used in the previous exercise. To see what is going on under the hood, take a look at the [source code](https://github.com/wilson-labs/cola/blob/main/cola/linalg/inverse.py#L67)."
"Having a PSD `LinearOperator` opens up the possibility in CoLA to dispatch our favorite algorithm: CG. As we all know, CG has a couple of hyperparameters like the tolerance (set it to $10^{-10}$) and the max number of iterations (set it to 10K). _Hint_: Pass `method`, `tol` and `max_iters` to the function that you used in the previous exercise. To see what is going on under the hood, take a look at the [source code](https://github.com/wilson-labs/cola/blob/main/cola/linalg/inv.py#L80)."
]
},
{
Expand Down

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