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Functions
FLA_Tridiag_UT_l_unb_var1.c File Reference

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Functions

FLA_Error FLA_Tridiag_UT_l_unb_var1 (FLA_Obj A, FLA_Obj T)
 
FLA_Error FLA_Tridiag_UT_l_step_unb_var1 (FLA_Obj A, FLA_Obj T)
 

Function Documentation

◆ FLA_Tridiag_UT_l_step_unb_var1()

FLA_Error FLA_Tridiag_UT_l_step_unb_var1 ( FLA_Obj  A,
FLA_Obj  T 
)
19 {
20  FLA_Obj ATL, ATR, A00, a01, A02,
21  ABL, ABR, a10t, alpha11, a12t,
22  A20, a21, A22;
23  FLA_Obj TTL, TTR, T00, t01, T02,
24  TBL, TBR, t10t, tau11, t12t,
25  T20, t21, T22;
26  FLA_Obj zT, z01,
27  zB, zeta11,
28  z21;
29  FLA_Obj z;
30 
31  FLA_Obj inv_tau11;
32  FLA_Obj minus_inv_tau11;
33  FLA_Obj first_elem;
34  FLA_Obj beta;
35 
36  FLA_Obj a21_t,
37  a21_b;
38 
39  FLA_Datatype datatype_A;
40  dim_t m_A;
41  dim_t b_alg;
42 
43 
44  b_alg = FLA_Obj_length( T );
45 
46  datatype_A = FLA_Obj_datatype( A );
47  m_A = FLA_Obj_length( A );
48 
49  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &inv_tau11 );
50  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_inv_tau11 );
51  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &first_elem );
52  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &beta );
53  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
54 
55  FLA_Part_2x2( A, &ATL, &ATR,
56  &ABL, &ABR, 0, 0, FLA_TL );
57  FLA_Part_2x2( T, &TTL, &TTR,
58  &TBL, &TBR, 0, 0, FLA_TL );
59  FLA_Part_2x1( z, &zT,
60  &zB, 0, FLA_TOP );
61 
62  while ( FLA_Obj_length( ATL ) < b_alg )
63  {
64  FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
65  /* ************* */ /* ************************** */
66  &a10t, /**/ &alpha11, &a12t,
67  ABL, /**/ ABR, &A20, /**/ &a21, &A22,
68  1, 1, FLA_BR );
69  FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &t01, &T02,
70  /* ************* */ /* ************************ */
71  &t10t, /**/ &tau11, &t12t,
72  TBL, /**/ TBR, &T20, /**/ &t21, &T22,
73  1, 1, FLA_BR );
74  FLA_Repart_2x1_to_3x1( zT, &z01,
75  /* ** */ /* ****** */
76  &zeta11,
77  zB, &z21, 1, FLA_BOTTOM );
78 
79  /*------------------------------------------------------------*/
80 
81  if ( FLA_Obj_length( A22 ) > 0 )
82  {
83  FLA_Part_2x1( a21, &a21_t,
84  &a21_b, 1, FLA_TOP );
85 
86  // [ u21, tau11, a21 ] = House( a21 );
87  FLA_Househ2_UT( FLA_LEFT,
88  a21_t,
89  a21_b, tau11 );
90 
91  // inv_tau11 = 1 / tau11;
92  // minus_inv_tau11 = -1 / tau11;
93  FLA_Set( FLA_ONE, inv_tau11 );
94  FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
95  FLA_Copy( inv_tau11, minus_inv_tau11 );
96  FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
97 
98  // Save first element of a21_t and set it to one so we can use a21 as
99  // u21 in subsequent computations. We will restore a21_t later on.
100  FLA_Copy( a21_t, first_elem );
101  FLA_Set( FLA_ONE, a21_t );
102 
103  // z21 = A22 * u21;
104  FLA_Hemv( FLA_LOWER_TRIANGULAR, FLA_ONE, A22, a21, FLA_ZERO, z21 );
105 
106  // beta = u21' * z21 / 2;
107  FLA_Dotc( FLA_CONJUGATE, a21, z21, beta );
108  FLA_Inv_scal( FLA_TWO, beta );
109 
110  // z21 = ( z21 - beta / tau * u21 ) / tau;
111  FLA_Scal( minus_inv_tau11, beta );
112  FLA_Axpy( beta, a21, z21 );
113  FLA_Scal( inv_tau11, z21 );
114 
115  // A22 = A22 - u21 * z21' - z21 * u21';
116  FLA_Her2( FLA_LOWER_TRIANGULAR, FLA_MINUS_ONE, a21, z21, A22 );
117 
118  // t01 = U20' * u21;
119  FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
120 
121  // Restore first element of a21.
122  FLA_Copy( first_elem, a21_t );
123  }
124 
125  /*------------------------------------------------------------*/
126 
127  FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
128  a10t, alpha11, /**/ a12t,
129  /* ************** */ /* ************************ */
130  &ABL, /**/ &ABR, A20, a21, /**/ A22,
131  FLA_TL );
132  FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, t01, /**/ T02,
133  t10t, tau11, /**/ t12t,
134  /* ************** */ /* ********************** */
135  &TBL, /**/ &TBR, T20, t21, /**/ T22,
136  FLA_TL );
137  FLA_Cont_with_3x1_to_2x1( &zT, z01,
138  zeta11,
139  /* ** */ /* ****** */
140  &zB, z21, FLA_TOP );
141  }
142 
143  FLA_Obj_free( &inv_tau11 );
144  FLA_Obj_free( &minus_inv_tau11 );
145  FLA_Obj_free( &first_elem );
146  FLA_Obj_free( &beta );
147  FLA_Obj_free( &z );
148 
149  return FLA_SUCCESS;
150 }
FLA_Error FLA_Copy(FLA_Obj A, FLA_Obj B)
Definition: FLA_Copy.c:15
FLA_Error FLA_Scal(FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Scal.c:15
FLA_Error FLA_Dotc(FLA_Conj conj, FLA_Obj x, FLA_Obj y, FLA_Obj rho)
Definition: FLA_Dotc.c:13
FLA_Error FLA_Axpy(FLA_Obj alpha, FLA_Obj A, FLA_Obj B)
Definition: FLA_Axpy.c:15
FLA_Error FLA_Inv_scal(FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Inv_scal.c:13
FLA_Error FLA_Inv_scalc(FLA_Conj conjalpha, FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Inv_scalc.c:13
FLA_Error FLA_Her2(FLA_Uplo uplo, FLA_Obj alpha, FLA_Obj x, FLA_Obj y, FLA_Obj A)
Definition: FLA_Her2.c:13
FLA_Error FLA_Hemv(FLA_Uplo uplo, FLA_Obj alpha, FLA_Obj A, FLA_Obj x, FLA_Obj beta, FLA_Obj y)
Definition: FLA_Hemv.c:13
FLA_Error FLA_Gemv(FLA_Trans transa, FLA_Obj alpha, FLA_Obj A, FLA_Obj x, FLA_Obj beta, FLA_Obj y)
Definition: FLA_Gemv.c:15
FLA_Obj FLA_TWO
Definition: FLA_Init.c:17
FLA_Obj FLA_MINUS_ONE
Definition: FLA_Init.c:22
FLA_Obj FLA_ZERO
Definition: FLA_Init.c:20
FLA_Obj FLA_ONE
Definition: FLA_Init.c:18
FLA_Error FLA_Cont_with_3x3_to_2x2(FLA_Obj *ATL, FLA_Obj *ATR, FLA_Obj A00, FLA_Obj A01, FLA_Obj A02, FLA_Obj A10, FLA_Obj A11, FLA_Obj A12, FLA_Obj *ABL, FLA_Obj *ABR, FLA_Obj A20, FLA_Obj A21, FLA_Obj A22, FLA_Quadrant quadrant)
Definition: FLA_View.c:304
FLA_Error FLA_Part_2x2(FLA_Obj A, FLA_Obj *A11, FLA_Obj *A12, FLA_Obj *A21, FLA_Obj *A22, dim_t mb, dim_t nb, FLA_Quadrant quadrant)
Definition: FLA_View.c:17
FLA_Error FLA_Cont_with_3x1_to_2x1(FLA_Obj *AT, FLA_Obj A0, FLA_Obj A1, FLA_Obj *AB, FLA_Obj A2, FLA_Side side)
Definition: FLA_View.c:428
FLA_Error FLA_Repart_2x1_to_3x1(FLA_Obj AT, FLA_Obj *A0, FLA_Obj *A1, FLA_Obj AB, FLA_Obj *A2, dim_t mb, FLA_Side side)
Definition: FLA_View.c:226
FLA_Error FLA_Obj_create(FLA_Datatype datatype, dim_t m, dim_t n, dim_t rs, dim_t cs, FLA_Obj *obj)
Definition: FLA_Obj.c:55
FLA_Error FLA_Part_2x1(FLA_Obj A, FLA_Obj *A1, FLA_Obj *A2, dim_t mb, FLA_Side side)
Definition: FLA_View.c:76
dim_t FLA_Obj_length(FLA_Obj obj)
Definition: FLA_Query.c:116
FLA_Error FLA_Repart_2x2_to_3x3(FLA_Obj ATL, FLA_Obj ATR, FLA_Obj *A00, FLA_Obj *A01, FLA_Obj *A02, FLA_Obj *A10, FLA_Obj *A11, FLA_Obj *A12, FLA_Obj ABL, FLA_Obj ABR, FLA_Obj *A20, FLA_Obj *A21, FLA_Obj *A22, dim_t mb, dim_t nb, FLA_Quadrant quadrant)
Definition: FLA_View.c:142
FLA_Error FLA_Obj_free(FLA_Obj *obj)
Definition: FLA_Obj.c:588
FLA_Datatype FLA_Obj_datatype(FLA_Obj obj)
Definition: FLA_Query.c:13
int FLA_Datatype
Definition: FLA_type_defs.h:49
unsigned long dim_t
Definition: FLA_type_defs.h:71
FLA_Error FLA_Set(FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Set.c:13
FLA_Error FLA_Househ2_UT(FLA_Side side, FLA_Obj chi_1, FLA_Obj x2, FLA_Obj tau)
Definition: FLA_Househ2_UT.c:16
Definition: FLA_type_defs.h:159

References FLA_Axpy(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Dotc(), FLA_Gemv(), FLA_Hemv(), FLA_Her2(), FLA_Househ2_UT(), FLA_Inv_scal(), FLA_Inv_scalc(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Scal(), FLA_Set(), FLA_TWO, and FLA_ZERO.

Referenced by FLA_Tridiag_UT_l_unb_var1().

◆ FLA_Tridiag_UT_l_unb_var1()

FLA_Error FLA_Tridiag_UT_l_unb_var1 ( FLA_Obj  A,
FLA_Obj  T 
)
14 {
15  return FLA_Tridiag_UT_l_step_unb_var1( A, T );
16 }
FLA_Error FLA_Tridiag_UT_l_step_unb_var1(FLA_Obj A, FLA_Obj T)
Definition: FLA_Tridiag_UT_l_unb_var1.c:18

References FLA_Tridiag_UT_l_step_unb_var1().

Referenced by FLA_Tridiag_UT_l().