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---
:name: sorghr
:md5sum: 15d5df3b0bf735669e7d3581fa3c5dcb
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- ilo:
:type: integer
:intent: input
- ihi:
:type: integer
:intent: input
- a:
:type: real
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- tau:
:type: real
:intent: input
:dims:
- n-1
- work:
:type: real
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: ihi-ilo
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SORGHR generates a real orthogonal matrix Q which is defined as the\n\
* product of IHI-ILO elementary reflectors of order N, as returned by\n\
* SGEHRD:\n\
*\n\
* Q = H(ilo) H(ilo+1) . . . H(ihi-1).\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix Q. N >= 0.\n\
*\n\
* ILO (input) INTEGER\n\
* IHI (input) INTEGER\n\
* ILO and IHI must have the same values as in the previous call\n\
* of SGEHRD. Q is equal to the unit matrix except in the\n\
* submatrix Q(ilo+1:ihi,ilo+1:ihi).\n\
* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.\n\
*\n\
* A (input/output) REAL array, dimension (LDA,N)\n\
* On entry, the vectors which define the elementary reflectors,\n\
* as returned by SGEHRD.\n\
* On exit, the N-by-N orthogonal matrix Q.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* TAU (input) REAL array, dimension (N-1)\n\
* TAU(i) must contain the scalar factor of the elementary\n\
* reflector H(i), as returned by SGEHRD.\n\
*\n\
* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))\n\
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The dimension of the array WORK. LWORK >= IHI-ILO.\n\
* For optimum performance LWORK >= (IHI-ILO)*NB, where NB is\n\
* the optimal blocksize.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the optimal size of the WORK array, returns\n\
* this value as the first entry of the WORK array, and no error\n\
* message related to LWORK is issued by XERBLA.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
*\n\n\
* =====================================================================\n\
*\n"
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