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href="#3_ComplexLUdecomposition"> <link title="QR decomposition" rel="Section" href="#3_QRdecomposition"> <link title="QR Decomposition with Column Pivoting" rel="Section" href="#3_QRDecompositionwithColumnPivoting"> <link title="Singular Value Decomposition" rel="Section" href="#3_SingularValueDecomposition"> <link title="LQ decomposition" rel="Section" href="#3_LQdecomposition"> <link title="P^T L Q decomposition" rel="Section" href="#3_PTLQdecomposition"> <link title="Cholesky decomposition" rel="Section" href="#3_Choleskydecomposition"> <link title="Tridiagonal Decomposition of Real Symmetric Matrices" rel="Section" href="#3_TridiagonalDecompositionofRealSymmetricMatrices"> <link title="Tridiagonal Decomposition of Hermitian Matrices" rel="Section" href="#3_TridiagonalDecompositionofHermitianMatrices"> <link title="Bidiagonalization" rel="Section" href="#3_Bidiagonalization"> <link title="Householder solver" rel="Section" href="#3_Householdersolver"> <link title="Tridiagonal Systems" rel="Section" href="#3_TridiagonalSystems"> <link title="Exponential" rel="Section" href="#3_Exponential"> <link title="Low-level functions " rel="Subsection" href="#4_Lowlevelfunctions"> <link title="Higher-level functions" rel="Subsection" href="#4_Higherlevelfunctions"> <title>ocamlgsl 0.6.0 : Gsl_linalg</title> </head> <body> <div class="navbar"><a href="Gsl_sort.html">Previous</a> <a href="index.html">Up</a> <a href="Gsl_eigen.html">Next</a> </div> <center><h1>Module <a href="type_Gsl_linalg.html">Gsl_linalg</a></h1></center> <br> <pre><span class="keyword">module</span> Gsl_linalg: <code class="code">sig</code> <a href="Gsl_linalg.html">..</a> <code class="code">end</code></pre>Simple linear algebra operations<br> <hr width="100%"> <br> <a name="3_Simplematrixmultiplication"></a> <h3>Simple matrix multiplication</h3><br> <pre><span class="keyword">val</span> <a name="VALmatmult"></a>matmult : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> ?transpa:bool -><br> b:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> ?transpb:bool -> <a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> unit</code></pre><div class="info"> <code class="code">matmult a ~transpa b ~transpb c</code> stores in matrix <code class="code">c</code> the product of matrices <code class="code">a</code> and <code class="code">b</code>. <code class="code">transpa</code> or <code class="code">transpb</code> allow transposition of either matrix, so it can compute a.b or Trans(a).b or a.Trans(b) or Trans(a).Trans(b) . <p> See also <a href="Gsl_blas.html#VALgemm"><code class="code">Gsl_blas.gemm</code></a>.<br> </div> <br> <a name="3_LUdecomposition"></a> <h3>LU decomposition</h3><br> <br> <a name="4_Lowlevelfunctions"></a> <h4>Low-level functions </h4><br> <pre><span class="keyword">val</span> <a name="VAL_LU_decomp"></a>_LU_decomp : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> int</code></pre><pre><span class="keyword">val</span> <a name="VAL_LU_solve"></a>_LU_solve : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LU_svx"></a>_LU_svx : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> <a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LU_refine"></a>_LU_refine : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> lu:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -><br> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> res:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LU_invert"></a>_LU_invert : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> <a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LU_det"></a>_LU_det : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> int -> float</code></pre><pre><span class="keyword">val</span> <a name="VAL_LU_lndet"></a>_LU_lndet : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> float</code></pre><pre><span class="keyword">val</span> <a name="VAL_LU_sgndet"></a>_LU_sgndet : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> int -> int</code></pre><br> <a name="4_Higherlevelfunctions"></a> <h4>Higher-level functions</h4><br> <br> With these, the arguments are protected (copied) and necessary intermediate datastructures are allocated;<br> <pre><span class="keyword">val</span> <a name="VALdecomp_LU"></a>decomp_LU : <code class="type">?protect:bool -><br> [< `A of float array * int * int<br> | `AA of float array array<br> | `M of <a href="Gsl_matrix.html#TYPEmatrix">Gsl_matrix.matrix</a><br> | `MF of <a href="Gsl_matrix_flat.html#TYPEmatrix">Gsl_matrix_flat.matrix</a> ] -><br> <a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> * <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> * int</code></pre><pre><span class="keyword">val</span> <a name="VALsolve_LU"></a>solve_LU : <code class="type">?protect:bool -><br> [< `A of float array * int * int<br> | `AA of float array array<br> | `M of <a href="Gsl_matrix.html#TYPEmatrix">Gsl_matrix.matrix</a><br> | `MF of <a href="Gsl_matrix_flat.html#TYPEmatrix">Gsl_matrix_flat.matrix</a> ] -><br> [< `A of float array<br> | `V of <a href="Gsl_vector.html#TYPEvector">Gsl_vector.vector</a><br> | `VF of <a href="Gsl_vector_flat.html#TYPEvector">Gsl_vector_flat.vector</a> ] -><br> float array</code></pre><pre><span class="keyword">val</span> <a name="VALdet_LU"></a>det_LU : <code class="type">?protect:bool -><br> [< `A of float array * int * int<br> | `AA of float array array<br> | `M of <a href="Gsl_matrix.html#TYPEmatrix">Gsl_matrix.matrix</a><br> | `MF of <a href="Gsl_matrix_flat.html#TYPEmatrix">Gsl_matrix_flat.matrix</a> ] -><br> float</code></pre><pre><span class="keyword">val</span> <a name="VALinvert_LU"></a>invert_LU : <code class="type">?protect:bool -><br> ?result:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> [< `A of float array * int * int<br> | `AA of float array array<br> | `M of <a href="Gsl_matrix.html#TYPEmatrix">Gsl_matrix.matrix</a><br> | `MF of <a href="Gsl_matrix_flat.html#TYPEmatrix">Gsl_matrix_flat.matrix</a> ] -><br> <a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a></code></pre><br> <a name="3_ComplexLUdecomposition"></a> <h3>Complex LU decomposition</h3><br> <pre><span class="keyword">val</span> <a name="VALcomplex_LU_decomp"></a>complex_LU_decomp : <code class="type"><a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> int</code></pre><pre><span class="keyword">val</span> <a name="VALcomplex_LU_solve"></a>complex_LU_solve : <code class="type"><a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -><br> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> b:<a href="Gsl_vectmat.html#TYPEcvec">Gsl_vectmat.cvec</a> -> x:<a href="Gsl_vectmat.html#TYPEcvec">Gsl_vectmat.cvec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALcomplex_LU_svx"></a>complex_LU_svx : <code class="type"><a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> <a href="Gsl_vectmat.html#TYPEcvec">Gsl_vectmat.cvec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALcomplex_LU_refine"></a>complex_LU_refine : <code class="type">a:<a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -><br> lu:<a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -><br> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -><br> b:<a href="Gsl_vectmat.html#TYPEcvec">Gsl_vectmat.cvec</a> -> x:<a href="Gsl_vectmat.html#TYPEcvec">Gsl_vectmat.cvec</a> -> res:<a href="Gsl_vectmat.html#TYPEcvec">Gsl_vectmat.cvec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALcomplex_LU_invert"></a>complex_LU_invert : <code class="type"><a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> <a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALcomplex_LU_det"></a>complex_LU_det : <code class="type"><a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -> int -> <a href="Gsl_complex.html#TYPEcomplex">Gsl_complex.complex</a></code></pre><pre><span class="keyword">val</span> <a name="VALcomplex_LU_lndet"></a>complex_LU_lndet : <code class="type"><a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -> float</code></pre><pre><span class="keyword">val</span> <a name="VALcomplex_LU_sgndet"></a>complex_LU_sgndet : <code class="type"><a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -> int -> <a href="Gsl_complex.html#TYPEcomplex">Gsl_complex.complex</a></code></pre><br> <a name="3_QRdecomposition"></a> <h3>QR decomposition</h3><br> <pre><span class="keyword">val</span> <a name="VAL_QR_decomp"></a>_QR_decomp : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> <a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QR_solve"></a>_QR_solve : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> <a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QR_svx"></a>_QR_svx : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> <a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QR_lssolve"></a>_QR_lssolve : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> <a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -><br> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> res:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QR_QTvec"></a>_QR_QTvec : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> <a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> v:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QR_Qvec"></a>_QR_Qvec : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> <a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> v:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QR_Rsolve"></a>_QR_Rsolve : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QR_Rsvx"></a>_QR_Rsvx : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QR_unpack"></a>_QR_unpack : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> q:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> r:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QR_QRsolve"></a>_QR_QRsolve : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> r:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QR_update"></a>_QR_update : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> r:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> w:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> v:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_R_solve"></a>_R_solve : <code class="type">r:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><br> <a name="3_QRDecompositionwithColumnPivoting"></a> <h3>QR Decomposition with Column Pivoting</h3><br> <pre><span class="keyword">val</span> <a name="VAL_QRPT_decomp"></a>_QRPT_decomp : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> p:<a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> norm:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> int</code></pre><pre><span class="keyword">val</span> <a name="VAL_QRPT_decomp2"></a>_QRPT_decomp2 : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> q:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> r:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> p:<a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> norm:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> int</code></pre><pre><span class="keyword">val</span> <a name="VAL_QRPT_solve"></a>_QRPT_solve : <code class="type">qr:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -><br> p:<a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QRPT_svx"></a>_QRPT_svx : <code class="type">qr:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> p:<a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QRPT_QRsolve"></a>_QRPT_QRsolve : <code class="type">q:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> r:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> p:<a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QRPT_update"></a>_QRPT_update : <code class="type">q:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> r:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> p:<a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> u:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> v:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QRPT_Rsolve"></a>_QRPT_Rsolve : <code class="type">qr:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> p:<a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_QRPT_Rsvx"></a>_QRPT_Rsvx : <code class="type">qr:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> p:<a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><br> <a name="3_SingularValueDecomposition"></a> <h3>Singular Value Decomposition</h3><br> <pre><span class="keyword">val</span> <a name="VAL_SV_decomp"></a>_SV_decomp : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> v:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> s:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> work:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_SV_decomp_mod"></a>_SV_decomp_mod : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> x:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> v:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> s:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> work:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_SV_decomp_jacobi"></a>_SV_decomp_jacobi : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> v:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> s:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_SV_solve"></a>_SV_solve : <code class="type">u:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> v:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> s:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><br> <a name="3_LQdecomposition"></a> <h3>LQ decomposition</h3><br> <pre><span class="keyword">val</span> <a name="VAL_LQ_decomp"></a>_LQ_decomp : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LQ_solve_T"></a>_LQ_solve_T : <code class="type">lq:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LQ_svx_T"></a>_LQ_svx_T : <code class="type">lq:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LQ_lssolve_T"></a>_LQ_lssolve_T : <code class="type">lq:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -><br> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> res:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LQ_Lsolve_T"></a>_LQ_Lsolve_T : <code class="type">lq:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LQ_Lsvx_T"></a>_LQ_Lsvx_T : <code class="type">lq:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_L_solve_T"></a>_L_solve_T : <code class="type">l:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LQ_vecQ"></a>_LQ_vecQ : <code class="type">lq:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> v:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LQ_vecQT"></a>_LQ_vecQT : <code class="type">lq:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> v:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LQ_unpack"></a>_LQ_unpack : <code class="type">lq:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> q:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> l:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LQ_update"></a>_LQ_update : <code class="type">q:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> r:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> v:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> w:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_LQ_LQsolve"></a>_LQ_LQsolve : <code class="type">q:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> l:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><br> <a name="3_PTLQdecomposition"></a> <h3>P^T L Q decomposition</h3><br> <pre><span class="keyword">val</span> <a name="VAL_PTLQ_decomp"></a>_PTLQ_decomp : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> norm:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> int</code></pre><pre><span class="keyword">val</span> <a name="VAL_PTLQ_decomp2"></a>_PTLQ_decomp2 : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> q:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> r:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> norm:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> int</code></pre><pre><span class="keyword">val</span> <a name="VAL_PTLQ_solve_T"></a>_PTLQ_solve_T : <code class="type">qr:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -><br> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_PTLQ_svx_T"></a>_PTLQ_svx_T : <code class="type">lq:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_PTLQ_LQsolve_T"></a>_PTLQ_LQsolve_T : <code class="type">q:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> l:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_PTLQ_Lsolve_T"></a>_PTLQ_Lsolve_T : <code class="type">lq:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_PTLQ_Lsvx_T"></a>_PTLQ_Lsvx_T : <code class="type">lq:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_PTLQ_update"></a>_PTLQ_update : <code class="type">q:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> l:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> <a href="Gsl_permut.html#TYPEpermut">Gsl_permut.permut</a> -> v:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> w:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><br> <a name="3_Choleskydecomposition"></a> <h3>Cholesky decomposition</h3><br> <pre><span class="keyword">val</span> <a name="VALcho_decomp"></a>cho_decomp : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALcho_solve"></a>cho_solve : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALcho_svx"></a>cho_svx : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> <a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALcho_decomp_unit"></a>cho_decomp_unit : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> <a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><br> <a name="3_TridiagonalDecompositionofRealSymmetricMatrices"></a> <h3>Tridiagonal Decomposition of Real Symmetric Matrices</h3><br> <pre><span class="keyword">val</span> <a name="VALsymmtd_decomp"></a>symmtd_decomp : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALsymmtd_unpack"></a>symmtd_unpack : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -><br> q:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> diag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> subdiag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALsymmtd_unpack_T"></a>symmtd_unpack_T : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> diag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> subdiag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><br> <a name="3_TridiagonalDecompositionofHermitianMatrices"></a> <h3>Tridiagonal Decomposition of Hermitian Matrices</h3><br> <pre><span class="keyword">val</span> <a name="VALhermtd_decomp"></a>hermtd_decomp : <code class="type">a:<a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -> tau:<a href="Gsl_vectmat.html#TYPEcvec">Gsl_vectmat.cvec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALhermtd_unpack"></a>hermtd_unpack : <code class="type">a:<a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -><br> tau:<a href="Gsl_vectmat.html#TYPEcvec">Gsl_vectmat.cvec</a> -><br> q:<a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -> diag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> subdiag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALhermtd_unpack_T"></a>hermtd_unpack_T : <code class="type">a:<a href="Gsl_vectmat.html#TYPEcmat">Gsl_vectmat.cmat</a> -> diag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> subdiag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><br> <a name="3_Bidiagonalization"></a> <h3>Bidiagonalization</h3><br> <pre><span class="keyword">val</span> <a name="VALbidiag_decomp"></a>bidiag_decomp : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> tau_u:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> tau_v:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALbidiag_unpack"></a>bidiag_unpack : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau_u:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -><br> u:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau_v:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -><br> v:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> diag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> superdiag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALbidiag_unpack2"></a>bidiag_unpack2 : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> tau_u:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> tau_v:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> v:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALbidiag_unpack_B"></a>bidiag_unpack_B : <code class="type">a:<a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -><br> diag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> superdiag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><br> <a name="3_Householdersolver"></a> <h3>Householder solver</h3><br> <pre><span class="keyword">val</span> <a name="VAL_HH_solve"></a>_HH_solve : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VAL_HH_svx"></a>_HH_svx : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> <a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALsolve_HH"></a>solve_HH : <code class="type">?protect:bool -><br> [< `A of float array * int * int<br> | `AA of float array array<br> | `M of <a href="Gsl_matrix.html#TYPEmatrix">Gsl_matrix.matrix</a><br> | `MF of <a href="Gsl_matrix_flat.html#TYPEmatrix">Gsl_matrix_flat.matrix</a> ] -><br> [< `A of float array<br> | `V of <a href="Gsl_vector.html#TYPEvector">Gsl_vector.vector</a><br> | `VF of <a href="Gsl_vector_flat.html#TYPEvector">Gsl_vector_flat.vector</a> ] -><br> float array</code></pre><br> <a name="3_TridiagonalSystems"></a> <h3>Tridiagonal Systems</h3><br> <pre><span class="keyword">val</span> <a name="VALsolve_symm_tridiag"></a>solve_symm_tridiag : <code class="type">diag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -><br> offdiag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALsolve_tridiag"></a>solve_tridiag : <code class="type">diag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -><br> abovediag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -><br> belowdiag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALsolve_symm_cyc_tridiag"></a>solve_symm_cyc_tridiag : <code class="type">diag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -><br> offdiag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALsolve_cyc_tridiag"></a>solve_cyc_tridiag : <code class="type">diag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -><br> abovediag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -><br> belowdiag:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> b:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> x:<a href="Gsl_vectmat.html#TYPEvec">Gsl_vectmat.vec</a> -> unit</code></pre><br> <a name="3_Exponential"></a> <h3>Exponential</h3><br> <pre><span class="keyword">val</span> <a name="VAL_exponential"></a>_exponential : <code class="type"><a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> <a href="Gsl_vectmat.html#TYPEmat">Gsl_vectmat.mat</a> -> <a href="Gsl_fun.html#TYPEmode">Gsl_fun.mode</a> -> unit</code></pre><pre><span class="keyword">val</span> <a name="VALexponential"></a>exponential : <code class="type">?mode:<a href="Gsl_fun.html#TYPEmode">Gsl_fun.mode</a> -><br> [< `A of float array * int * int<br> | `M of <a href="Gsl_matrix.html#TYPEmatrix">Gsl_matrix.matrix</a><br> | `MF of <a href="Gsl_matrix_flat.html#TYPEmatrix">Gsl_matrix_flat.matrix</a> ] -><br> [ `M of <a href="Gsl_matrix.html#TYPEmatrix">Gsl_matrix.matrix</a> ]</code></pre></body></html>
