Nachschlagewerk MQL5Matrizen und VektorenOpenBLASSingular Value DecompositionSingularValueDecompositionBisect

SingularValueDecompositionBisect

Singular Value Decomposition, bisection algorithm (lapack function GESVDX).

Computing for type matrix<double>

bool  matrix::SingularValueDecompositionBisect(
   ENUM_SVD_VECTORS    jobv,     // computation accuracy level
   ENUM_BLAS_RANGE     range,    // subset of computable singular values
   double              lower,    // lower limit of the subset
   double              upper,    // upper limit of the subset
   vector&             S,        // vector of computed singular values
   matrix&             U,        // matrix of computed left vectors U
   matrix&             VT        // transposed matrix of right vectors VT
   );

Computing for type matrix<float>

bool  matrix::SingularValueDecompositionBisect(
   ENUM_SVD_VECTORS    jobv,     // computation accuracy level
   ENUM_BLAS_RANGE     range,    // subset of computable singular values
   double              lower,    // lower limit of the subset
   double              upper,    // upper limit of the subset
   vectorf&            S,        // vector of computed singular values
   matrixf&            U,        // matrix of computed left vectors U
   matrixf&            VT        // ransposed matrix of right vectors VT
   );

Computing for type matrix<complex>

bool  matrix::SingularValueDecompositionBisect(
   ENUM_SVD_VECTORS    jobv,     // computation accuracy level
   ENUM_BLAS_RANGE     range,    // subset of computable singular values
   double              lower,    // lower limit of the subset
   double              upper,    // upper limit of the subset
   vector              S,        // vector of computed singular values
   matrixc             U,        // matrix of computed left vectors U
   matrixc             VT        // transposed matrix of right vectors VT
   );

Computing for type matrix<complexf>

bool  matrix::SingularValueDecompositionBisect(
   ENUM_SVD_VECTORS    jobv,               // computation accuracy level
   ENUM_BLAS_RANGE     range,              // subset of computable singular values
   double              lower,              // lower limit of the subset
   double              upper,              // upper limit of the subset
   vectorf&            singular_values,    // vector of computed singular values
   matrixcf&           u,                  // matrix of computed left vectors U
   matrixcf&           vt                  // transposed matrix of right vectors VT
   );

Parameters

jobv

[in] ENUM_SVD_VECTORS enumeration value which determines the method for computing left and singular eigenvectors.

range

[in] ENUM_BLAS_RANGE enumeration value that defines a subset of computable singular values and vectors.

lower

[in] The lower limit of singular values subset; specified depending on the value of the range parameter.

upper

[in] The upper limit of singular values subset; specified depending on the value of the range parameter.

[out] Vector of singular values.

[out] Matrix of left singular vectors.

[out] Matrix of right singular vectors.

Return Value

Return true if successful, otherwise false in case of an error.

Note

Computation depends on the values of the jobuv and range parameters.

When BLASRANGE_A is set, all singular values are computed, and the lower and upper parameters are ignored.

With the BLASRANGE_V value, only those singular values (and their vectors) that fall within the range of real values specified by the 'lower' and 'upper' parameters are computed.

With the BLASRANGE_I value, only those singular values (and their vectors) that fall within the range of integer indices specified by the 'lower' and 'upper' parameters are computed. For example, with lower=0 and upper=2, only the first three singular values are computed.

ENUM_SVD_VECTORS

An enumeration defining the way to compute left and right singular vectors.

ID	Description
SVDVECTORS_N	Only singular values are computed, without vectors.
SVDVECTORS_U	Left singular vectors are computed.
SVDVECTORS_V	Right singular vectors are computed.
SVDVECTORS_UV	Left and right singular vectors are computed.

ENUM_BLAS_RANGE

An enumeration defining a subset of computable singular values and vectors.

ID	Description
BLASRANGE_A	All singular or eigenvalues will be found.
BLASRANGE_V	All singular or eigenvalues in the half-open interval (VL,VU] will be found.
BLASRANGE_I	Singular or eigenvalues from IL to IU will be found