ztpqrt2 - pentagonal" matrix, which is composed of a triangular block and a pen- tagonal block, using the compact WY representation for Q
SUBROUTINE ZTPQRT2(M, N, L, A, LDA, B, LDB, T, LDT, INFO) INTEGER INFO, LDA, LDB, LDT, N, M, L DOUBLE COMPLEX A(LDA,*), B(LDB,*), T(LDT,*) SUBROUTINE ZTPQRT2_64(M, N, L, A, LDA, B, LDB, T, LDT, INFO) INTEGER*8 INFO, LDA, LDB, LDT, N, M, L DOUBLE COMPLEX A(LDA,*), B(LDB,*), T(LDT,*) F95 INTERFACE SUBROUTINE TPQRT2(M, N, L, A, LDA, B, LDB, T, LDT, INFO) INTEGER :: M, N, L, LDA, LDB, LDT, INFO COMPLEX(8), DIMENSION(:,:) :: A, B, T SUBROUTINE TPQRT2_64(M, N, L, A, LDA, B, LDB, T, LDT, INFO) INTEGER(8) :: M, N, L, LDA, LDB, LDT, INFO COMPLEX(8), DIMENSION(:,:) :: A, B, T C INTERFACE #include <sunperf.h> void ztpqrt2 (int m, int n, int l, doublecomplex *a, int lda, double- complex *b, int ldb, doublecomplex *t, int ldt, int *info); void ztpqrt2_64 (long m, long n, long l, doublecomplex *a, long lda, doublecomplex *b, long ldb, doublecomplex *t, long ldt, long *info);
Oracle Solaris Studio Performance Library ztpqrt2(3P)
NAME
ztpqrt2 - compute a QR factorization of a real or complex "triangular-
pentagonal" matrix, which is composed of a triangular block and a pen-
tagonal block, using the compact WY representation for Q
SYNOPSIS
SUBROUTINE ZTPQRT2(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
INTEGER INFO, LDA, LDB, LDT, N, M, L
DOUBLE COMPLEX A(LDA,*), B(LDB,*), T(LDT,*)
SUBROUTINE ZTPQRT2_64(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
INTEGER*8 INFO, LDA, LDB, LDT, N, M, L
DOUBLE COMPLEX A(LDA,*), B(LDB,*), T(LDT,*)
F95 INTERFACE
SUBROUTINE TPQRT2(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
INTEGER :: M, N, L, LDA, LDB, LDT, INFO
COMPLEX(8), DIMENSION(:,:) :: A, B, T
SUBROUTINE TPQRT2_64(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
INTEGER(8) :: M, N, L, LDA, LDB, LDT, INFO
COMPLEX(8), DIMENSION(:,:) :: A, B, T
C INTERFACE
#include <sunperf.h>
void ztpqrt2 (int m, int n, int l, doublecomplex *a, int lda, double-
complex *b, int ldb, doublecomplex *t, int ldt, int *info);
void ztpqrt2_64 (long m, long n, long l, doublecomplex *a, long lda,
doublecomplex *b, long ldb, doublecomplex *t, long ldt, long
*info);
PURPOSE
ztpqrt2 computes a QR factorization of a complex "triangular-pentago-
nal" matrix C, which is composed of a triangular block A and pentagonal
block B, using the compact WY representation for Q.
ARGUMENTS
M (input)
M is INTEGER
The total 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.
A (input/output)
A is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDT,N)
The N-by-N upper triangular factor T of the block reflector.
See Further Details.
LDT (input)
LDT is INTEGER
The leading dimension of the array T.
LDT >= max(1,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
(M+N)-by-(M+N) block reflector H is then given by
H = I - W * T * W**H
where W**H is the conjugate transpose of W and T is the upper triangu-
lar factor of the block reflector.
7 Nov 2015 ztpqrt2(3P)