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---
:name: dorgbr
:md5sum: 77e112eb51464cf117c5be590352f159
:category: :subroutine
:arguments:
- vect:
:type: char
:intent: input
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- k:
:type: integer
:intent: input
- a:
:type: doublereal
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- tau:
:type: doublereal
:intent: input
:dims:
- MIN(m,k)
- work:
:type: doublereal
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: MIN(m,n)
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DORGBR generates one of the real orthogonal matrices Q or P**T\n\
* determined by DGEBRD when reducing a real matrix A to bidiagonal\n\
* form: A = Q * B * P**T. Q and P**T are defined as products of\n\
* elementary reflectors H(i) or G(i) respectively.\n\
*\n\
* If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q\n\
* is of order M:\n\
* if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n\n\
* columns of Q, where m >= n >= k;\n\
* if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an\n\
* M-by-M matrix.\n\
*\n\
* If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T\n\
* is of order N:\n\
* if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m\n\
* rows of P**T, where n >= m >= k;\n\
* if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as\n\
* an N-by-N matrix.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* VECT (input) CHARACTER*1\n\
* Specifies whether the matrix Q or the matrix P**T is\n\
* required, as defined in the transformation applied by DGEBRD:\n\
* = 'Q': generate Q;\n\
* = 'P': generate P**T.\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the matrix Q or P**T to be returned.\n\
* M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrix Q or P**T to be returned.\n\
* N >= 0.\n\
* If VECT = 'Q', M >= N >= min(M,K);\n\
* if VECT = 'P', N >= M >= min(N,K).\n\
*\n\
* K (input) INTEGER\n\
* If VECT = 'Q', the number of columns in the original M-by-K\n\
* matrix reduced by DGEBRD.\n\
* If VECT = 'P', the number of rows in the original K-by-N\n\
* matrix reduced by DGEBRD.\n\
* K >= 0.\n\
*\n\
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)\n\
* On entry, the vectors which define the elementary reflectors,\n\
* as returned by DGEBRD.\n\
* On exit, the M-by-N matrix Q or P**T.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,M).\n\
*\n\
* TAU (input) DOUBLE PRECISION array, dimension\n\
* (min(M,K)) if VECT = 'Q'\n\
* (min(N,K)) if VECT = 'P'\n\
* TAU(i) must contain the scalar factor of the elementary\n\
* reflector H(i) or G(i), which determines Q or P**T, as\n\
* returned by DGEBRD in its array argument TAUQ or TAUP.\n\
*\n\
* WORK (workspace/output) DOUBLE PRECISION 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 >= max(1,min(M,N)).\n\
* For optimum performance LWORK >= min(M,N)*NB, where NB\n\
* is 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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