# sgeqp3(3) [centos man page]

```sgeqp3.f(3)							      LAPACK							       sgeqp3.f(3)

NAME
sgeqp3.f -

SYNOPSIS
Functions/Subroutines
subroutine sgeqp3 (M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)
SGEQP3

Function/Subroutine Documentation
subroutine sgeqp3 (integerM, integerN, real, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, real, dimension( * )TAU, real,
dimension( * )WORK, integerLWORK, integerINFO)
SGEQP3

Purpose:

SGEQP3 computes a QR factorization with column pivoting of a
matrix A:  A*P = Q*R  using Level 3 BLAS.

Parameters:
M

M is INTEGER
The number of rows of the matrix A. M >= 0.

N

N is INTEGER
The number of columns of the matrix A.  N >= 0.

A

A is REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the upper triangle of the array contains the
min(M,N)-by-N upper trapezoidal matrix R; the elements below
the diagonal, together with the array TAU, represent the
orthogonal matrix Q as a product of min(M,N) elementary
reflectors.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).

JPVT

JPVT is INTEGER array, dimension (N)
On entry, if JPVT(J).ne.0, the J-th column of A is permuted
to the front of A*P (a leading column); if JPVT(J)=0,
the J-th column of A is a free column.
On exit, if JPVT(J)=K, then the J-th column of A*P was the
the K-th column of A.

TAU

TAU is REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors.

WORK

WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO=0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK. LWORK >= 3*N+1.
For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB
is the optimal blocksize.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
September 2012

Further Details:

The matrix Q is represented as a product of elementary reflectors

Q = H(1) H(2) . . . H(k), where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v**T

where tau is a real scalar, and v is a real/complex vector
with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
A(i+1:m,i), and tau in TAU(i).

Contributors:
G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA

Definition at line 152 of file sgeqp3.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       sgeqp3.f(3)```

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```sgeqp3.f(3)							      LAPACK							       sgeqp3.f(3)

NAME
sgeqp3.f -

SYNOPSIS
Functions/Subroutines
subroutine sgeqp3 (M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)
SGEQP3

Function/Subroutine Documentation
subroutine sgeqp3 (integerM, integerN, real, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, real, dimension( * )TAU, real,
dimension( * )WORK, integerLWORK, integerINFO)
SGEQP3

Purpose:

SGEQP3 computes a QR factorization with column pivoting of a
matrix A:  A*P = Q*R  using Level 3 BLAS.

Parameters:
M

M is INTEGER
The number of rows of the matrix A. M >= 0.

N

N is INTEGER
The number of columns of the matrix A.  N >= 0.

A

A is REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the upper triangle of the array contains the
min(M,N)-by-N upper trapezoidal matrix R; the elements below
the diagonal, together with the array TAU, represent the
orthogonal matrix Q as a product of min(M,N) elementary
reflectors.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).

JPVT

JPVT is INTEGER array, dimension (N)
On entry, if JPVT(J).ne.0, the J-th column of A is permuted
to the front of A*P (a leading column); if JPVT(J)=0,
the J-th column of A is a free column.
On exit, if JPVT(J)=K, then the J-th column of A*P was the
the K-th column of A.

TAU

TAU is REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors.

WORK

WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO=0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK. LWORK >= 3*N+1.
For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB
is the optimal blocksize.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
November 2011

Further Details:

The matrix Q is represented as a product of elementary reflectors

Q = H(1) H(2) . . . H(k), where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v**T

where tau is a real/complex scalar, and v is a real/complex vector
with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
A(i+1:m,i), and tau in TAU(i).

Contributors:
G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA

Definition at line 152 of file sgeqp3.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       sgeqp3.f(3)```
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