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---
:name: dgeql2
:md5sum: a28ed88137c6b697773895e45d0d13a1
: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: workspace
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DGEQL2( M, N, A, LDA, TAU, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DGEQL2 computes a QL factorization of a real m by n matrix A:\n\
* A = Q * L.\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, if m >= n, the lower triangle of the subarray\n\
* A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;\n\
* if m <= n, the elements on and below the (n-m)-th\n\
* superdiagonal contain the m by n lower trapezoidal matrix L;\n\
* the remaining elements, with the array TAU, represent the\n\
* orthogonal matrix Q as a product of elementary reflectors\n\
* (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) DOUBLE PRECISION array, dimension (N)\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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in\n\
* A(1:m-k+i-1,n-k+i), and tau in TAU(i).\n\
*\n\
* =====================================================================\n\
*\n"
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