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---
:name: sgeqp3
:md5sum: d403640a3535834978e177dfacbf62cd
:category: :subroutine
:arguments:
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: real
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- jpvt:
:type: integer
:intent: input/output
:dims:
- n
- tau:
:type: real
:intent: output
:dims:
- MIN(m,n)
- work:
:type: real
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: 3*n+1
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SGEQP3 computes a QR factorization with column pivoting of a\n\
* matrix A: A*P = Q*R using Level 3 BLAS.\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) REAL array, dimension (LDA,N)\n\
* On entry, the M-by-N matrix A.\n\
* On exit, the upper triangle of the array contains the\n\
* min(M,N)-by-N upper trapezoidal matrix R; the elements below\n\
* the diagonal, together with the array TAU, represent the\n\
* orthogonal matrix Q as a product of min(M,N) elementary\n\
* reflectors.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,M).\n\
*\n\
* JPVT (input/output) INTEGER array, dimension (N)\n\
* On entry, if JPVT(J).ne.0, the J-th column of A is permuted\n\
* to the front of A*P (a leading column); if JPVT(J)=0,\n\
* the J-th column of A is a free column.\n\
* On exit, if JPVT(J)=K, then the J-th column of A*P was the\n\
* the K-th column of A.\n\
*\n\
* TAU (output) REAL array, dimension (min(M,N))\n\
* The scalar factors of the elementary reflectors.\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 >= 3*N+1.\n\
* For optimal performance LWORK >= 2*N+( N+1 )*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\
* 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/complex scalar, and v is a real/complex vector\n\
* with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in\n\
* A(i+1:m,i), and tau in TAU(i).\n\
*\n\
* Based on contributions by\n\
* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain\n\
* X. Sun, Computer Science Dept., Duke University, USA\n\
*\n\
* =====================================================================\n\
*\n"
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