tplqt2 - Man Page

tplqt2: QR factor, level 2

Synopsis

Functions

subroutine ctplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
CTPLQT2
subroutine dtplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
DTPLQT2 computes a LQ 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.
subroutine stplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
STPLQT2 computes a LQ 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.
subroutine ztplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
ZTPLQT2 computes a LQ 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.

Detailed Description

Function Documentation

subroutine ctplqt2 (integer m, integer n, integer l, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldt, * ) t, integer ldt, integer info)

CTPLQT2

Purpose:

 CTPLQT2 computes a LQ a factorization of a complex 'triangular-pentagonal'
 matrix C, which is composed of a triangular block A and pentagonal block B,
 using the compact WY representation for Q.
Parameters

M

          M is INTEGER
          The total number of rows of the matrix B.
          M >= 0.

N

          N is INTEGER
          The number of columns of the matrix B, and the order of
          the triangular matrix A.
          N >= 0.

L

          L is INTEGER
          The number of rows of the lower trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.

A

          A is COMPLEX 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.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

B

          B is COMPLEX 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.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,M).

T

          T is COMPLEX array, dimension (LDT,M)
          The N-by-N upper triangular factor T of the block reflector.
          See Further Details.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max(1,M)

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  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 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
  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 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,

               W = [ 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 (M+N)-by-(M+N) block reflector H is then given by

               H = I - W**T * T * W

  where W^H is the conjugate transpose of W and T is the upper triangular
  factor of the block reflector.

Definition at line 161 of file ctplqt2.f.

subroutine dtplqt2 (integer m, integer n, integer l, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldt, * ) t, integer ldt, integer info)

DTPLQT2 computes a LQ 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.  

Purpose:

 DTPLQT2 computes a LQ a 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.
Parameters

M

          M is INTEGER
          The total number of rows of the matrix B.
          M >= 0.

N

          N is INTEGER
          The number of columns of the matrix B, and the order of
          the triangular matrix A.
          N >= 0.

L

          L is INTEGER
          The number of rows of the lower trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.

A

          A is DOUBLE PRECISION 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.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

B

          B is DOUBLE PRECISION 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.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,M).

T

          T is DOUBLE PRECISION array, dimension (LDT,M)
          The N-by-N upper triangular factor T of the block reflector.
          See Further Details.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max(1,M)

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  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 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
  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 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,

               W = [ 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 (M+N)-by-(M+N) block reflector H is then given by

               H = I - W**T * T * W

  where W^H is the conjugate transpose of W and T is the upper triangular
  factor of the block reflector.

Definition at line 176 of file dtplqt2.f.

subroutine stplqt2 (integer m, integer n, integer l, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldt, * ) t, integer ldt, integer info)

STPLQT2 computes a LQ 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.  

Purpose:

 STPLQT2 computes a LQ a 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.
Parameters

M

          M is INTEGER
          The total number of rows of the matrix B.
          M >= 0.

N

          N is INTEGER
          The number of columns of the matrix B, and the order of
          the triangular matrix A.
          N >= 0.

L

          L is INTEGER
          The number of rows of the lower trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.

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.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

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.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,M).

T

          T is REAL array, dimension (LDT,M)
          The N-by-N upper triangular factor T of the block reflector.
          See Further Details.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max(1,M)

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  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 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
  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 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,

               W = [ 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 (M+N)-by-(M+N) block reflector H is then given by

               H = I - W**T * T * W

  where W^H is the conjugate transpose of W and T is the upper triangular
  factor of the block reflector.

Definition at line 176 of file stplqt2.f.

subroutine ztplqt2 (integer m, integer n, integer l, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldt, * ) t, integer ldt, integer info)

ZTPLQT2 computes a LQ 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.  

Purpose:

 ZTPLQT2 computes a LQ a factorization of a complex 'triangular-pentagonal'
 matrix C, which is composed of a triangular block A and pentagonal block B,
 using the compact WY representation for Q.
Parameters

M

          M is INTEGER
          The total number of rows of the matrix B.
          M >= 0.

N

          N is INTEGER
          The number of columns of the matrix B, and the order of
          the triangular matrix A.
          N >= 0.

L

          L is INTEGER
          The number of rows of the lower trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.

A

          A is COMPLEX*16 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.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

B

          B is COMPLEX*16 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.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,M).

T

          T is COMPLEX*16 array, dimension (LDT,M)
          The N-by-N upper triangular factor T of the block reflector.
          See Further Details.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max(1,M)

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  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 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
  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 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,

               W = [ 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 (M+N)-by-(M+N) block reflector H is then given by

               H = I - W**T * T * W

  where W^H is the conjugate transpose of W and T is the upper triangular
  factor of the block reflector.

Definition at line 176 of file ztplqt2.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK