Developer Reference for Intel® oneAPI Math Kernel Library for C
?tpqrt
Computes a blocked QR factorization of a real or complex “triangular-pentagonal” matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.
Syntax
lapack_int LAPACKE_stpqrt(int matrix_layout, lapack_int m, lapack_int n, lapack_int l,
lapack_int nb, float *a, lapack_int lda, float *b,
lapack_int ldb, float *t, lapack_int ldt);
lapack_int LAPACKE_dtpqrt(int matrix_layout, lapack_int m, lapack_int n, lapack_int l,
lapack_int nb, double *a, lapack_int lda, double *b,
lapack_int ldb, double *t, lapack_int ldt);
lapack_int LAPACKE_ctpqrt(int matrix_layout, lapack_int m, lapack_int n, lapack_int l,
lapack_int nb, lapack_complex_float *a, lapack_int lda,
lapack_complex_float *b, lapack_int ldb,
lapack_complex_float *t, lapack_int ldt);
lapack_int LAPACKE_ztpqrt(int matrix_layout, lapack_int m, lapack_int n, lapack_int l,
lapack_int nb, lapack_complex_double *a, lapack_int lda,
lapack_complex_double *b, lapack_int ldb,
lapack_complex_double *t, lapack_int ldt);Include Files
mkl.h
Description
The input matrix C is an ( n + m )-by- n matrix
where A is an n -by- n upper triangular matrix, and B is an m -by- n pentagonal matrix consisting of an ( m - l )-by- n rectangular matrix B1 on top of an l -by- n upper trapezoidal matrix B2 :
The upper trapezoidal matrix B2 consists of the first l rows of an n -by- n upper triangular matrix, where 0 ≤ l ≤ min( m , n ). If l =0, B is an m -by- n rectangular matrix. If m = l = n , B is upper triangular. The elementary reflectors H(i) are stored in the i th column below the diagonal in the ( n + m )-by- n input matrix C . The structure of vectors defining the elementary reflectors is illustrated by:
The elements of the unit matrix I are not stored. Thus, V contains all of the necessary information, and is returned in array b .
The columns of V represent the vectors which define the H(i) s.
The number of blocks is k = ceiling( n / nb ), where each block is of order nb except for the last block, which is of order ib = n - ( k -1)* nb . For each of the k blocks, an upper triangular block reflector factor is computed: T1 , T2 , …, Tk . The nb -by- nb ( ib -by- ib for the last block) Ti s are stored in the nb -by- n array t as
t = [T1T2 ... Tk] .
Input Parameters
- matrix_layout
-
Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).
- m
-
The total number of rows in the matrix B ( m ≥ 0).
- n
-
The number of columns of the matrix B, and the order of the triangular matrix A. The value of n must be at least zero.
- l
-
The number of rows of the upper trapezoidal part of B (min( m , n ) ≥ l ≥ 0).
nb
The block size to use in the blocked QR factorization ( n ≥ nb ≥ 1).
- a , b , work
-
REAL for stpqrt DOUBLE PRECISION for dtpqrt COMPLEX for ctpqrt COMPLEX*16 for ztpqrt .
Arrays: a size lda * n contains the n -by- n upper triangular matrix A .
b size max(1, ldb * n ) for column major layout and max(1, ldb * m ) for row major layout , the pentagonal m -by- n matrix B . The first ( m - l ) rows contain the rectangular B1 matrix, and the next l rows contain the upper trapezoidal B2 matrix.
work size ( nb , n ) is a workspace array.
lda
The leading dimension of a ; at least max(1, n ).
ldb
The leading dimension of b ; at least max(1, m ) for column major layout and at least max(1, n ) for row major layout .
ldt
The leading dimension of t ; at least nb for column major layout and at least max(1, n ) for row major layout .
Output Parameters
- a
-
The elements on and above the diagonal of the array contain the upper triangular matrix R .
- b
-
The pentagonal matrix V .
- t
-
REAL for stpqrt DOUBLE PRECISION for dtpqrt COMPLEX for ctpqrt COMPLEX*16 for ztpqrt .
Array, size ldt * n for column major layout and ldt * nb for row major layout .
The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks.
Return Values
This function returns a value info .
If info=0 , the execution is successful.
If info = -i , the i -th parameter had an illegal value.