
NAMEzlarft.f SYNOPSISFunctions/Subroutinessubroutine zlarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) Function/Subroutine Documentationsubroutine zlarft (characterDIRECT, characterSTOREV, integerN, integerK, complex*16, dimension( ldv, * )V, integerLDV, complex*16, dimension( * )TAU, complex*16, dimension( ldt, * )T, integerLDT)ZLARFT forms the triangular factor T of a block reflector H = I  vtvH Purpose:ZLARFT 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 ith 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 ith row of the array V, and H = I  V**H * T * V DIRECT
Author:
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)STOREV STOREV is CHARACTER*1 Specifies how the vectors which define the elementary reflectors are stored (see also Further Details): = 'C': columnwise = 'R': rowwiseN N is INTEGER The order of the block reflector H. N >= 0.K K is INTEGER The order of the triangular factor T (= the number of elementary reflectors). K >= 1.V V is COMPLEX*16 array, dimension (LDV,K) if STOREV = 'C' (LDV,N) if STOREV = 'R' The matrix V. See further details.LDV LDV is INTEGER The leading dimension of the array V. If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.TAU TAU is COMPLEX*16 array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i).T T is COMPLEX*16 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.LDT LDT is INTEGER The leading dimension of the array T. LDT >= K. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Further Details:
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 ) AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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