DTPQRT computes a blocked QR factorization of a real "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.
M is INTEGER The number of rows of the matrix B. M >= 0.
N is INTEGER The number of columns of the matrix B, and the order of the triangular matrix A. N >= 0.
L is INTEGER The number of rows of the upper trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details.
NB is INTEGER The block size to be used in the blocked QR. N >= NB >= 1.
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 is INTEGER The leading dimension of the array A. LDA >= max(1,N).
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 is INTEGER The leading dimension of the array B. LDB >= max(1,M).
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 is INTEGER The leading dimension of the array T. LDT >= NB.
WORK is DOUBLE PRECISION array, dimension (NB*N)
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Univ. of California Berkeley
Univ. of Colorado Denver
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 pentagonal 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 rectangular 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 computed: 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].
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