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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine clarft | ( | character | DIRECT, |
character | STOREV, | ||
integer | N, | ||
integer | K, | ||
complex, dimension( ldv, * ) | V, | ||
integer | LDV, | ||
complex, dimension( * ) | TAU, | ||
complex, dimension( ldt, * ) | T, | ||
integer | LDT | ||
) |
CLARFT forms the triangular factor T of a block reflector H = I - vtvH
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CLARFT forms the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * V**H If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and H = I - V**H * T * V
[in] | DIRECT | DIRECT is CHARACTER*1 Specifies the order in which the elementary reflectors are multiplied to form the block reflector: = 'F': H = H(1) H(2) . . . H(k) (Forward) = 'B': H = H(k) . . . H(2) H(1) (Backward) |
[in] | STOREV | STOREV is CHARACTER*1 Specifies how the vectors which define the elementary reflectors are stored (see also Further Details): = 'C': columnwise = 'R': rowwise |
[in] | N | N is INTEGER The order of the block reflector H. N >= 0. |
[in] | K | K is INTEGER The order of the triangular factor T (= the number of elementary reflectors). K >= 1. |
[in] | V | V is COMPLEX array, dimension (LDV,K) if STOREV = 'C' (LDV,N) if STOREV = 'R' The matrix V. See further details. |
[in] | LDV | LDV is INTEGER The leading dimension of the array V. If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. |
[in] | TAU | TAU is COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i). |
[out] | T | T is COMPLEX array, dimension (LDT,K) The k by k triangular factor T of the block reflector. If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is lower triangular. The rest of the array is not used. |
[in] | LDT | LDT is INTEGER The leading dimension of the array T. LDT >= K. |
The shape of the matrix V and the storage of the vectors which define the H(i) is best illustrated by the following example with n = 5 and k = 3. The elements equal to 1 are not stored. DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) ( v1 1 ) ( 1 v2 v2 v2 ) ( v1 v2 1 ) ( 1 v3 v3 ) ( v1 v2 v3 ) ( v1 v2 v3 ) DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': V = ( v1 v2 v3 ) V = ( v1 v1 1 ) ( v1 v2 v3 ) ( v2 v2 v2 1 ) ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) ( 1 v3 ) ( 1 )
Definition at line 165 of file clarft.f.