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---
:name: zlarft
:md5sum: e49ec2f4472e3bae691c01b3a570c0e5
:category: :subroutine
:arguments:
- direct:
:type: char
:intent: input
- storev:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- k:
:type: integer
:intent: input
- v:
:type: doublecomplex
:intent: input/output
:dims:
- ldv
- "lsame_(&storev,\"C\") ? k : lsame_(&storev,\"R\") ? n : 0"
- ldv:
:type: integer
:intent: input
- tau:
:type: doublecomplex
:intent: input
:dims:
- k
- t:
:type: doublecomplex
:intent: output
:dims:
- ldt
- k
- ldt:
:type: integer
:intent: input
:substitutions:
ldt: k
:fortran_help: " SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZLARFT forms the triangular factor T of a complex block reflector H\n\
* of order n, which is defined as a product of k elementary reflectors.\n\
*\n\
* If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;\n\
*\n\
* If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.\n\
*\n\
* If STOREV = 'C', the vector which defines the elementary reflector\n\
* H(i) is stored in the i-th column of the array V, and\n\
*\n\
* H = I - V * T * V'\n\
*\n\
* If STOREV = 'R', the vector which defines the elementary reflector\n\
* H(i) is stored in the i-th row of the array V, and\n\
*\n\
* H = I - V' * T * V\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* DIRECT (input) CHARACTER*1\n\
* Specifies the order in which the elementary reflectors are\n\
* multiplied to form the block reflector:\n\
* = 'F': H = H(1) H(2) . . . H(k) (Forward)\n\
* = 'B': H = H(k) . . . H(2) H(1) (Backward)\n\
*\n\
* STOREV (input) CHARACTER*1\n\
* Specifies how the vectors which define the elementary\n\
* reflectors are stored (see also Further Details):\n\
* = 'C': columnwise\n\
* = 'R': rowwise\n\
*\n\
* N (input) INTEGER\n\
* The order of the block reflector H. N >= 0.\n\
*\n\
* K (input) INTEGER\n\
* The order of the triangular factor T (= the number of\n\
* elementary reflectors). K >= 1.\n\
*\n\
* V (input/output) COMPLEX*16 array, dimension\n\
* (LDV,K) if STOREV = 'C'\n\
* (LDV,N) if STOREV = 'R'\n\
* The matrix V. See further details.\n\
*\n\
* LDV (input) INTEGER\n\
* The leading dimension of the array V.\n\
* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.\n\
*\n\
* TAU (input) COMPLEX*16 array, dimension (K)\n\
* TAU(i) must contain the scalar factor of the elementary\n\
* reflector H(i).\n\
*\n\
* T (output) COMPLEX*16 array, dimension (LDT,K)\n\
* The k by k triangular factor T of the block reflector.\n\
* If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is\n\
* lower triangular. The rest of the array is not used.\n\
*\n\
* LDT (input) INTEGER\n\
* The leading dimension of the array T. LDT >= K.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* The shape of the matrix V and the storage of the vectors which define\n\
* the H(i) is best illustrated by the following example with n = 5 and\n\
* k = 3. The elements equal to 1 are not stored; the corresponding\n\
* array elements are modified but restored on exit. The rest of the\n\
* array is not used.\n\
*\n\
* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':\n\
*\n\
* V = ( 1 ) V = ( 1 v1 v1 v1 v1 )\n\
* ( v1 1 ) ( 1 v2 v2 v2 )\n\
* ( v1 v2 1 ) ( 1 v3 v3 )\n\
* ( v1 v2 v3 )\n\
* ( v1 v2 v3 )\n\
*\n\
* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':\n\
*\n\
* V = ( v1 v2 v3 ) V = ( v1 v1 1 )\n\
* ( v1 v2 v3 ) ( v2 v2 v2 1 )\n\
* ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )\n\
* ( 1 v3 )\n\
* ( 1 )\n\
*\n\
* =====================================================================\n\
*\n"
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