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Functions | |
FLA_Error | FLA_Svd_uv_unb_var1 (dim_t n_iter_max, FLA_Obj A, FLA_Obj s, FLA_Obj U, FLA_Obj V, dim_t k_accum, dim_t b_alg) |
FLA_Error | FLA_Svd_uv_unb_var2 (dim_t n_iter_max, FLA_Obj A, FLA_Obj s, FLA_Obj U, FLA_Obj V, dim_t k_accum, dim_t b_alg) |
FLA_Error FLA_Svd_uv_unb_var1 | ( | dim_t | n_iter_max, |
FLA_Obj | A, | ||
FLA_Obj | s, | ||
FLA_Obj | U, | ||
FLA_Obj | V, | ||
dim_t | k_accum, | ||
dim_t | b_alg | ||
) |
References FLA_Apply_diag_matrix(), FLA_Bidiag_UT(), FLA_Bidiag_UT_create_T(), FLA_Bidiag_UT_extract_real_diagonals(), FLA_Bidiag_UT_form_U(), FLA_Bidiag_UT_form_V(), FLA_Bidiag_UT_realify(), FLA_Bsvd_v_opt_var1(), FLA_Copy(), FLA_Copyr(), FLA_Gemm(), FLA_Inv_scal(), FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_datatype_proj_to_complex(), FLA_Obj_datatype_proj_to_real(), FLA_Obj_equals(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_QR_UT(), FLA_QR_UT_create_T(), FLA_QR_UT_form_Q(), FLA_Scal(), FLA_Setr(), FLA_Sort_svd(), FLA_Svd_compute_scaling(), and FLA_ZERO.
{ FLA_Error r_val = FLA_SUCCESS; FLA_Datatype dt; FLA_Datatype dt_real; FLA_Datatype dt_comp; FLA_Obj scale, T, S, rL, rR, d, e, G, H; dim_t m_A, n_A; dim_t min_m_n; dim_t n_GH; double crossover_ratio = 17.0 / 9.0; n_GH = k_accum; m_A = FLA_Obj_length( A ); n_A = FLA_Obj_width( A ); min_m_n = FLA_Obj_min_dim( A ); dt = FLA_Obj_datatype( A ); dt_real = FLA_Obj_datatype_proj_to_real( A ); dt_comp = FLA_Obj_datatype_proj_to_complex( A ); // Create matrices to hold block Householder transformations. FLA_Bidiag_UT_create_T( A, &T, &S ); // Create vectors to hold the realifying scalars. FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rL ); FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rR ); // Create vectors to hold the diagonal and sub-diagonal. FLA_Obj_create( dt_real, min_m_n, 1, 0, 0, &d ); FLA_Obj_create( dt_real, min_m_n-1, 1, 0, 0, &e ); // Create matrices to hold the left and right Givens scalars. FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &G ); FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &H ); // Create a real scaling factor. FLA_Obj_create( dt_real, 1, 1, 0, 0, &scale ); // Compute a scaling factor; If none is needed, sigma will be set to one. FLA_Svd_compute_scaling( A, scale ); // Scale the matrix if scale is non-unit. if ( !FLA_Obj_equals( scale, FLA_ONE ) ) FLA_Scal( scale, A ); if ( m_A < crossover_ratio * n_A ) { // Reduce the matrix to bidiagonal form. // Apply scalars to rotate elements on the superdiagonal to the real domain. // Extract the diagonal and superdiagonal from A. FLA_Bidiag_UT( A, T, S ); FLA_Bidiag_UT_realify( A, rL, rR ); FLA_Bidiag_UT_extract_real_diagonals( A, d, e ); // Form U and V. FLA_Bidiag_UT_form_U( A, T, U ); FLA_Bidiag_UT_form_V( A, S, V ); // Apply the realifying scalars in rL and rR to U and V, respectively. { FLA_Obj UL, UR; FLA_Obj VL, VR; FLA_Part_1x2( U, &UL, &UR, min_m_n, FLA_LEFT ); FLA_Part_1x2( V, &VL, &VR, min_m_n, FLA_LEFT ); FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, UL ); FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, VL ); } // Perform a singular value decomposition on the bidiagonal matrix. r_val = FLA_Bsvd_v_opt_var1( n_iter_max, d, e, G, H, U, V, b_alg ); } else // if ( crossover_ratio * n_A <= m_A ) { FLA_Obj TQ, R; FLA_Obj AT, AB; FLA_Obj UL, UR; // Perform a QR factorization on A and form Q in U. FLA_QR_UT_create_T( A, &TQ ); FLA_QR_UT( A, TQ ); FLA_QR_UT_form_Q( A, TQ, U ); FLA_Obj_free( &TQ ); // Set the lower triangle of R to zero and then copy the upper // triangle of A to R. FLA_Part_2x1( A, &AT, &AB, n_A, FLA_TOP ); FLA_Obj_create( dt, n_A, n_A, 0, 0, &R ); FLA_Setr( FLA_LOWER_TRIANGULAR, FLA_ZERO, R ); FLA_Copyr( FLA_UPPER_TRIANGULAR, AT, R ); // Reduce the matrix to bidiagonal form. // Apply scalars to rotate elements on the superdiagonal to the real domain. // Extract the diagonal and superdiagonal from A. FLA_Bidiag_UT( R, T, S ); FLA_Bidiag_UT_realify( R, rL, rR ); FLA_Bidiag_UT_extract_real_diagonals( R, d, e ); // Form V from right Householder vectors in upper triangle of R. FLA_Bidiag_UT_form_V( R, S, V ); // Form U in R. FLA_Bidiag_UT_form_U( R, T, R ); // Apply the realifying scalars in rL and rR to U and V, respectively. FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, R ); FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, V ); // Perform a singular value decomposition on the bidiagonal matrix. r_val = FLA_Bsvd_v_opt_var1( n_iter_max, d, e, G, H, R, V, b_alg ); // Multiply R into U, storing the result in A and then copying back // to U. FLA_Part_1x2( U, &UL, &UR, n_A, FLA_LEFT ); FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, UL, R, FLA_ZERO, A ); FLA_Copy( A, UL ); FLA_Obj_free( &R ); } // Copy the converged eigenvalues to the output vector. FLA_Copy( d, s ); // Sort the singular values and singular vectors in descending order. FLA_Sort_svd( FLA_BACKWARD, s, U, V ); // If the matrix was scaled, rescale the singular values. if ( !FLA_Obj_equals( scale, FLA_ONE ) ) FLA_Inv_scal( scale, s ); FLA_Obj_free( &scale ); FLA_Obj_free( &T ); FLA_Obj_free( &S ); FLA_Obj_free( &rL ); FLA_Obj_free( &rR ); FLA_Obj_free( &d ); FLA_Obj_free( &e ); FLA_Obj_free( &G ); FLA_Obj_free( &H ); return r_val; }
FLA_Error FLA_Svd_uv_unb_var2 | ( | dim_t | n_iter_max, |
FLA_Obj | A, | ||
FLA_Obj | s, | ||
FLA_Obj | U, | ||
FLA_Obj | V, | ||
dim_t | k_accum, | ||
dim_t | b_alg | ||
) |
References FLA_Apply_diag_matrix(), FLA_Bidiag_UT(), FLA_Bidiag_UT_create_T(), FLA_Bidiag_UT_extract_real_diagonals(), FLA_Bidiag_UT_form_U(), FLA_Bidiag_UT_form_V(), FLA_Bidiag_UT_realify(), FLA_Bsvd_v_opt_var2(), FLA_Copy(), FLA_Copyr(), FLA_Gemm(), FLA_Inv_scal(), FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_datatype_proj_to_complex(), FLA_Obj_datatype_proj_to_real(), FLA_Obj_equals(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_QR_UT(), FLA_QR_UT_create_T(), FLA_QR_UT_form_Q(), FLA_Scal(), FLA_Set_to_identity(), FLA_Setr(), FLA_Sort_svd(), FLA_Svd_compute_scaling(), and FLA_ZERO.
{ FLA_Error r_val = FLA_SUCCESS; FLA_Datatype dt; FLA_Datatype dt_real; FLA_Datatype dt_comp; FLA_Obj scale, T, S, rL, rR, d, e, G, H, RG, RH, W; dim_t m_A, n_A; dim_t min_m_n; dim_t n_GH; double crossover_ratio = 17.0 / 9.0; n_GH = k_accum; m_A = FLA_Obj_length( A ); n_A = FLA_Obj_width( A ); min_m_n = FLA_Obj_min_dim( A ); dt = FLA_Obj_datatype( A ); dt_real = FLA_Obj_datatype_proj_to_real( A ); dt_comp = FLA_Obj_datatype_proj_to_complex( A ); // If the matrix is a scalar, then the SVD is easy. if ( min_m_n == 1 ) { FLA_Copy( A, s ); FLA_Set_to_identity( U ); FLA_Set_to_identity( V ); return FLA_SUCCESS; } // Create matrices to hold block Householder transformations. FLA_Bidiag_UT_create_T( A, &T, &S ); // Create vectors to hold the realifying scalars. FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rL ); FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rR ); // Create vectors to hold the diagonal and sub-diagonal. FLA_Obj_create( dt_real, min_m_n, 1, 0, 0, &d ); FLA_Obj_create( dt_real, min_m_n-1, 1, 0, 0, &e ); // Create matrices to hold the left and right Givens scalars. FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &G ); FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &H ); // Create matrices to hold the left and right Givens matrices. FLA_Obj_create( dt_real, min_m_n, min_m_n, 0, 0, &RG ); FLA_Obj_create( dt_real, min_m_n, min_m_n, 0, 0, &RH ); FLA_Obj_create( dt, m_A, n_A, 0, 0, &W ); // Create a real scaling factor. FLA_Obj_create( dt_real, 1, 1, 0, 0, &scale ); // Compute a scaling factor; If none is needed, sigma will be set to one. FLA_Svd_compute_scaling( A, scale ); // Scale the matrix if scale is non-unit. if ( !FLA_Obj_equals( scale, FLA_ONE ) ) FLA_Scal( scale, A ); if ( m_A >= n_A ) { if ( m_A < crossover_ratio * n_A ) { // Reduce the matrix to bidiagonal form. // Apply scalars to rotate elements on the sub-diagonal to the real domain. // Extract the diagonal and sub-diagonal from A. FLA_Bidiag_UT( A, T, S ); FLA_Bidiag_UT_realify( A, rL, rR ); FLA_Bidiag_UT_extract_real_diagonals( A, d, e ); // Form U and V. FLA_Bidiag_UT_form_U( A, T, U ); FLA_Bidiag_UT_form_V( A, S, V ); // Apply the realifying scalars in rL and rR to U and V, respectively. { FLA_Obj UL, UR; FLA_Obj VL, VR; FLA_Part_1x2( U, &UL, &UR, min_m_n, FLA_LEFT ); FLA_Part_1x2( V, &VL, &VR, min_m_n, FLA_LEFT ); FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, UL ); FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, VL ); } // Perform a singular value decomposition on the bidiagonal matrix. r_val = FLA_Bsvd_v_opt_var2( n_iter_max, d, e, G, H, RG, RH, W, U, V, b_alg ); } else // if ( crossover_ratio * n_A <= m_A ) { FLA_Obj TQ, R; FLA_Obj AT, AB; FLA_Obj UL, UR; // Perform a QR factorization on A and form Q in U. FLA_QR_UT_create_T( A, &TQ ); FLA_QR_UT( A, TQ ); FLA_QR_UT_form_Q( A, TQ, U ); FLA_Obj_free( &TQ ); // Set the lower triangle of R to zero and then copy the upper // triangle of A to R. FLA_Part_2x1( A, &AT, &AB, n_A, FLA_TOP ); FLA_Obj_create( dt, n_A, n_A, 0, 0, &R ); FLA_Setr( FLA_LOWER_TRIANGULAR, FLA_ZERO, R ); FLA_Copyr( FLA_UPPER_TRIANGULAR, AT, R ); // Reduce the matrix to bidiagonal form. // Apply scalars to rotate elements on the superdiagonal to the real domain. // Extract the diagonal and superdiagonal from A. FLA_Bidiag_UT( R, T, S ); FLA_Bidiag_UT_realify( R, rL, rR ); FLA_Bidiag_UT_extract_real_diagonals( R, d, e ); // Form V from right Householder vectors in upper triangle of R. FLA_Bidiag_UT_form_V( R, S, V ); // Form U in R. FLA_Bidiag_UT_form_U( R, T, R ); // Apply the realifying scalars in rL and rR to U and V, respectively. FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, R ); FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, V ); // Perform a singular value decomposition on the bidiagonal matrix. r_val = FLA_Bsvd_v_opt_var2( n_iter_max, d, e, G, H, RG, RH, W, R, V, b_alg ); // Multiply R into U, storing the result in A and then copying back // to U. FLA_Part_1x2( U, &UL, &UR, n_A, FLA_LEFT ); FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, UL, R, FLA_ZERO, A ); FLA_Copy( A, UL ); FLA_Obj_free( &R ); } } else // if ( m_A < n_A ) { FLA_Check_error_code( FLA_NOT_YET_IMPLEMENTED ); } // Copy the converged eigenvalues to the output vector. FLA_Copy( d, s ); // Sort the singular values and singular vectors in descending order. FLA_Sort_svd( FLA_BACKWARD, s, U, V ); // If the matrix was scaled, rescale the singular values. if ( !FLA_Obj_equals( scale, FLA_ONE ) ) FLA_Inv_scal( scale, s ); FLA_Obj_free( &scale ); FLA_Obj_free( &T ); FLA_Obj_free( &S ); FLA_Obj_free( &rL ); FLA_Obj_free( &rR ); FLA_Obj_free( &d ); FLA_Obj_free( &e ); FLA_Obj_free( &G ); FLA_Obj_free( &H ); FLA_Obj_free( &RG ); FLA_Obj_free( &RH ); FLA_Obj_free( &W ); return r_val; }