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---
:name: dlarzt
:md5sum: 794da30b757b5da1ded2c6c9124f7150
: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: doublereal
:intent: input/output
:dims:
- ldv
- "lsame_(&storev,\"C\") ? k : lsame_(&storev,\"R\") ? n : 0"
- ldv:
:type: integer
:intent: input
- tau:
:type: doublereal
:intent: input
:dims:
- k
- t:
:type: doublereal
:intent: output
:dims:
- ldt
- k
- ldt:
:type: integer
:intent: input
:substitutions:
ldt: k
:fortran_help: " SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLARZT forms the triangular factor T of a real block reflector\n\
* H of order > n, which is defined as a product of k elementary\n\
* 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\
* Currently, only STOREV = 'R' and DIRECT = 'B' are supported.\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, not supported yet)\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 (not supported yet)\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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (K)\n\
* TAU(i) must contain the scalar factor of the elementary\n\
* reflector H(i).\n\
*\n\
* T (output) DOUBLE PRECISION 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\
* Based on contributions by\n\
* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA\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_____\n\
* ( v1 v2 v3 ) / \\\n\
* ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 )\n\
* V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 )\n\
* ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 )\n\
* ( v1 v2 v3 )\n\
* . . .\n\
* . . .\n\
* 1 . .\n\
* 1 .\n\
* 1\n\
*\n\
* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':\n\
*\n\
* ______V_____\n\
* 1 / \\\n\
* . 1 ( 1 . . . . v1 v1 v1 v1 v1 )\n\
* . . 1 ( . 1 . . . v2 v2 v2 v2 v2 )\n\
* . . . ( . . 1 . . v3 v3 v3 v3 v3 )\n\
* . . .\n\
* ( v1 v2 v3 )\n\
* ( v1 v2 v3 )\n\
* V = ( v1 v2 v3 )\n\
* ( v1 v2 v3 )\n\
* ( v1 v2 v3 )\n\
*\n\
* =====================================================================\n\
*\n"
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