dtpqrt - tagonal" matrix C, which is composed of a triangular block A and pen- tagonal block B, using the compact WY representation for Q
SUBROUTINE DTPQRT(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO) INTEGER INFO, LDA, LDB, LDT, N, M, L, NB DOUBLE PRECISION A(LDA,*), B(LDB,*), T(LDT,*), WORK(*) SUBROUTINE DTPQRT_64(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO) INTEGER*8 INFO, LDA, LDB, LDT, N, M, L, NB DOUBLE PRECISION A(LDA,*), B(LDB,*), T(LDT,*), WORK(*) F95 INTERFACE SUBROUTINE TPQRT(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO) INTEGER :: M, N, L, NB, LDA, LDB, LDT, INFO REAL(8), DIMENSION(:,:) :: A, B, T REAL(8), DIMENSION(:) :: WORK SUBROUTINE TPQRT_64(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO) INTEGER(8) :: M, N, L, NB, LDA, LDB, LDT, INFO REAL(8), DIMENSION(:,:) :: A, B, T REAL(8), DIMENSION(:) :: WORK C INTERFACE #include <sunperf.h> void dtpqrt (int m, int n, int l, int nb, double *a, int lda, double *b, int ldb, double *t, int ldt, int *info); void dtpqrt_64 (long m, long n, long l, long nb, double *a, long lda, double *b, long ldb, double *t, long ldt, long *info);
Oracle Solaris Studio Performance Library dtpqrt(3P)
NAME
dtpqrt - compute a blocked QR factorization of a real "triangular-pen-
tagonal" matrix C, which is composed of a triangular block A and pen-
tagonal block B, using the compact WY representation for Q
SYNOPSIS
SUBROUTINE DTPQRT(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
DOUBLE PRECISION A(LDA,*), B(LDB,*), T(LDT,*), WORK(*)
SUBROUTINE DTPQRT_64(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
INTEGER*8 INFO, LDA, LDB, LDT, N, M, L, NB
DOUBLE PRECISION A(LDA,*), B(LDB,*), T(LDT,*), WORK(*)
F95 INTERFACE
SUBROUTINE TPQRT(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
INTEGER :: M, N, L, NB, LDA, LDB, LDT, INFO
REAL(8), DIMENSION(:,:) :: A, B, T
REAL(8), DIMENSION(:) :: WORK
SUBROUTINE TPQRT_64(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
INTEGER(8) :: M, N, L, NB, LDA, LDB, LDT, INFO
REAL(8), DIMENSION(:,:) :: A, B, T
REAL(8), DIMENSION(:) :: WORK
C INTERFACE
#include <sunperf.h>
void dtpqrt (int m, int n, int l, int nb, double *a, int lda, double
*b, int ldb, double *t, int ldt, int *info);
void dtpqrt_64 (long m, long n, long l, long nb, double *a, long lda,
double *b, long ldb, double *t, long ldt, long *info);
PURPOSE
dtpqrt computes a blocked QR factorization of a real "triangular-pen-
tagonal" matrix C, which is composed of a triangular block A and pen-
tagonal block B, using the compact WY representation for Q.
ARGUMENTS
M (input)
M is INTEGER
The number of rows of the matrix B.
M >= 0.
N (input)
N is INTEGER
The number of columns of the matrix B, and the order of the
triangular matrix A.
N >= 0.
L (input)
L is INTEGER
The number of rows of the upper trapezoidal part of B.
MIN(M,N) >= L >= 0. See Further Details.
NB (input)
NB is INTEGER
The block size to be used in the blocked QR.
N >= NB >= 1.
A (input/output)
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the upper triangular N-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the upper triangular matrix R.
LDA (input)
LDA is INTEGER
The leading dimension of the array A.
LDA >= max(1,N).
B (input/output)
B is DOUBLE PRECISION array, dimension (LDB,N)
On entry, the pentagonal M-by-N matrix B. The first M-L rows
are rectangular, and the last L rows are upper trapezoidal.
On exit, B contains the pentagonal matrix V. See Further
Details.
LDB (input)
LDB is INTEGER
The leading dimension of the array B.
LDB >= max(1,M).
T (output)
T is DOUBLE PRECISION array, dimension (LDT,N)
The upper triangular block reflectors stored in compact form
as a sequence of upper triangular blocks. See Further
Details.
LDT (input)
LDT is INTEGER
The leading dimension of the array T.
LDT >= NB.
WORK (output)
WORK is DOUBLE PRECISION array, dimension (NB*N)
INFO (output)
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
FURTHER DETAILS
The input matrix C is a (N+M)-by-N matrix
C = [ A ]
[ B ]
where A is an upper triangular N-by-N matrix, and B is M-by-N pentago-
nal matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a
L-by-N upper trapezoidal matrix B2:
B = [ B1 ] <- (M-L)-by-N rectangular
[ B2 ] <- L-by-N upper trapezoidal.
The upper trapezoidal matrix B2 consists of the first L rows of a N-by-
N upper triangular matrix, where 0 <= L <= MIN(M,N). If L=0, B is rec-
tangular M-by-N; if M=L=N, B is upper triangular.
The matrix W stores the elementary reflectors H(i) in the i-th column
below the diagonal (of A) in the (N+M)-by-N input matrix C
C = [ A ] <- upper triangular N-by-N
[ B ] <- M-by-N pentagonal
so that W can be represented as
W = [ I ] <- identity, N-by-N
[ V ] <- M-by-N, same form as B.
Thus, all of information needed for W is contained on exit in B, which
we call V above. Note that V has the same form as B; that is,
V = [ V1 ] <- (M-L)-by-N rectangular
[ V2 ] <- L-by-N upper trapezoidal.
The columns of V represent the vectors which define the H(i)'s.
The number of blocks is B = ceiling(N/NB), where each block is of order
NB except for the last block, which is of order IB = N - (B-1)*NB. For
each of the B blocks, a upper triangular block reflector factor is com-
puted: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB for the last block)
T's are stored in the NB-by-N matrix T as
T = [T1 T2 ... TB].
7 Nov 2015 dtpqrt(3P)