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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine stplqt | ( | integer | M, |
| integer | N, | ||
| integer | L, | ||
| integer | MB, | ||
| real, dimension( lda, * ) | A, | ||
| integer | LDA, | ||
| real, dimension( ldb, * ) | B, | ||
| integer | LDB, | ||
| real, dimension( ldt, * ) | T, | ||
| integer | LDT, | ||
| real, dimension( * ) | WORK, | ||
| integer | INFO | ||
| ) |
STPLQT
Download STPLQT + dependencies [TGZ] [ZIP] [TXT]
STPLQT computes a blocked LQ 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.
| [in] | M | M is INTEGER
The number of rows of the matrix B, and the order of the
triangular matrix A.
M >= 0. |
| [in] | N | N is INTEGER
The number of columns of the matrix B.
N >= 0. |
| [in] | L | L is INTEGER
The number of rows of the lower trapezoidal part of B.
MIN(M,N) >= L >= 0. See Further Details. |
| [in] | MB | MB is INTEGER
The block size to be used in the blocked QR. M >= MB >= 1. |
| [in,out] | A | A is REAL array, dimension (LDA,M)
On entry, the lower triangular M-by-M matrix A.
On exit, the elements on and below the diagonal of the array
contain the lower triangular matrix L. |
| [in] | LDA | LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M). |
| [in,out] | B | B is REAL array, dimension (LDB,N)
On entry, the pentagonal M-by-N matrix B. The first N-L columns
are rectangular, and the last L columns are lower trapezoidal.
On exit, B contains the pentagonal matrix V. See Further Details. |
| [in] | LDB | LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,M). |
| [out] | T | T is REAL array, dimension (LDT,N)
The lower triangular block reflectors stored in compact form
as a sequence of upper triangular blocks. See Further Details. |
| [in] | LDT | LDT is INTEGER
The leading dimension of the array T. LDT >= MB. |
| [out] | WORK | WORK is REAL array, dimension (MB*M) |
| [out] | INFO | INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value |
The input matrix C is a M-by-(M+N) matrix
C = [ A ] [ B ]
where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
upper trapezoidal matrix B2:
[ B ] = [ B1 ] [ B2 ]
[ B1 ] <- M-by-(N-L) rectangular
[ B2 ] <- M-by-L lower trapezoidal.
The lower trapezoidal matrix B2 consists of the first L columns of a
M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
B is rectangular M-by-N; if M=L=N, B is lower triangular.
The matrix W stores the elementary reflectors H(i) in the i-th row
above the diagonal (of A) in the M-by-(M+N) input matrix C
[ C ] = [ A ] [ B ]
[ A ] <- lower triangular M-by-M
[ B ] <- M-by-N pentagonal
so that W can be represented as
[ W ] = [ I ] [ V ]
[ I ] <- identity, M-by-M
[ 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 ] [ V2 ]
[ V1 ] <- M-by-(N-L) rectangular
[ V2 ] <- M-by-L lower trapezoidal.
The rows of V represent the vectors which define the H(i)'s.
The number of blocks is B = ceiling(M/MB), where each
block is of order MB except for the last block, which is of order
IB = M - (M-1)*MB. For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
for the last block) T's are stored in the MB-by-N matrix T as
T = [T1 T2 ... TB].Download STPLQT + dependencies [TGZ] [ZIP] [TXT]
STPLQT computes a blocked LQ 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.
| [in] | M | M is INTEGER
The number of rows of the matrix B, and the order of the
triangular matrix A.
M >= 0. |
| [in] | N | N is INTEGER
The number of columns of the matrix B.
N >= 0. |
| [in] | L | L is INTEGER
The number of rows of the lower trapezoidal part of B.
MIN(M,N) >= L >= 0. See Further Details. |
| [in] | MB | MB is INTEGER
The block size to be used in the blocked QR. M >= MB >= 1. |
| [in,out] | A | A is REAL array, dimension (LDA,N)
On entry, the lower triangular N-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the lower triangular matrix L. |
| [in] | LDA | LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N). |
| [in,out] | B | B is REAL array, dimension (LDB,N)
On entry, the pentagonal M-by-N matrix B. The first N-L columns
are rectangular, and the last L columns are lower trapezoidal.
On exit, B contains the pentagonal matrix V. See Further Details. |
| [in] | LDB | LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,M). |
| [out] | T | T is REAL array, dimension (LDT,N)
The lower triangular block reflectors stored in compact form
as a sequence of upper triangular blocks. See Further Details. |
| [in] | LDT | LDT is INTEGER
The leading dimension of the array T. LDT >= MB. |
| [out] | WORK | WORK is REAL array, dimension (MB*M) |
| [out] | INFO | INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value |
The input matrix C is a M-by-(M+N) matrix
C = [ A ] [ B ]
where A is an lower triangular N-by-N matrix, and B is M-by-N pentagonal
matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
upper trapezoidal matrix B2:
[ B ] = [ B1 ] [ B2 ]
[ B1 ] <- M-by-(N-L) rectangular
[ B2 ] <- M-by-L upper trapezoidal.
The lower trapezoidal matrix B2 consists of the first L columns of a
N-by-N lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
B is rectangular M-by-N; if M=L=N, B is lower triangular.
The matrix W stores the elementary reflectors H(i) in the i-th row
above the diagonal (of A) in the M-by-(M+N) input matrix C
[ C ] = [ A ] [ B ]
[ A ] <- lower triangular N-by-N
[ B ] <- M-by-N pentagonal
so that W can be represented as
[ W ] = [ I ] [ V ]
[ 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 ] [ V2 ]
[ V1 ] <- M-by-(N-L) rectangular
[ V2 ] <- M-by-L lower trapezoidal.
The rows of V represent the vectors which define the H(i)'s.
The number of blocks is B = ceiling(M/MB), where each
block is of order MB except for the last block, which is of order
IB = M - (M-1)*MB. For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
for the last block) T's are stored in the MB-by-N matrix T as
T = [T1 T2 ... TB]. 
1.9.4