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---
:name: dgerqf
:md5sum: 522daeb5235e5276cf26a8dc9440df57
:category: :subroutine
:arguments:
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: doublereal
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- tau:
:type: doublereal
:intent: output
:dims:
- MIN(m,n)
- work:
:type: doublereal
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: m
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DGERQF computes an RQ factorization of a real M-by-N matrix A:\n\
* A = R * Q.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the matrix A. M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrix A. N >= 0.\n\
*\n\
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)\n\
* On entry, the M-by-N matrix A.\n\
* On exit,\n\
* if m <= n, the upper triangle of the subarray\n\
* A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;\n\
* if m >= n, the elements on and above the (m-n)-th subdiagonal\n\
* contain the M-by-N upper trapezoidal matrix R;\n\
* the remaining elements, with the array TAU, represent the\n\
* orthogonal matrix Q as a product of min(m,n) elementary\n\
* reflectors (see Further Details).\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,M).\n\
*\n\
* TAU (output) DOUBLE PRECISION array, dimension (min(M,N))\n\
* The scalar factors of the elementary reflectors (see Further\n\
* Details).\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,M).\n\
* For optimum performance LWORK >= M*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\
* Further Details\n\
* ===============\n\
*\n\
* The matrix Q is represented as a product of elementary reflectors\n\
*\n\
* Q = H(1) H(2) . . . H(k), where k = min(m,n).\n\
*\n\
* Each H(i) has the form\n\
*\n\
* H(i) = I - tau * v * v'\n\
*\n\
* where tau is a real scalar, and v is a real vector with\n\
* v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in\n\
* A(m-k+i,1:n-k+i-1), and tau in TAU(i).\n\
*\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n LOGICAL LQUERY\n INTEGER I, IB, IINFO, IWS, K, KI, KK, LDWORK, LWKOPT,\n $ MU, NB, NBMIN, NU, NX\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL DGERQ2, DLARFB, DLARFT, XERBLA\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX, MIN\n\
* ..\n\
* .. External Functions ..\n INTEGER ILAENV\n EXTERNAL ILAENV\n\
* ..\n"
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