tpqrt2(3) Library Functions Manual tpqrt2(3)

tpqrt2 - tpqrt2: QR factor, level 2


subroutine ctpqrt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
CTPQRT2 computes a QR 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 dtpqrt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
DTPQRT2 computes a QR 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 stpqrt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
STPQRT2 computes a QR 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 ztpqrt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
ZTPQRT2 computes a QR 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.

CTPQRT2 computes a QR 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:

 CTPQRT2 computes a QR 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 upper trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.

A

          A is COMPLEX 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

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

B

          B is COMPLEX 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

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

T

          T is COMPLEX array, dimension (LDT,N)
          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,N)

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 (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 (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 triangular
  factor of the block reflector.

Definition at line 172 of file ctpqrt2.f.

DTPQRT2 computes a QR 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:

 DTPQRT2 computes a 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.

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 upper trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.

A

          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

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

B

          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

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

T

          T is DOUBLE PRECISION array, dimension (LDT,N)
          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,N)

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 (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 (M+N)-by-(M+N) block reflector H is then given by
               H = I - W * T * W**T
  where W^H is the conjugate transpose of W and T is the upper triangular
  factor of the block reflector.

Definition at line 172 of file dtpqrt2.f.

STPQRT2 computes a QR 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:

 STPQRT2 computes a 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.

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 upper trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.

A

          A is REAL 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

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

B

          B is REAL 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

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

T

          T is REAL array, dimension (LDT,N)
          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,N)

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 (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 (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 triangular
  factor of the block reflector.

Definition at line 172 of file stpqrt2.f.

ZTPQRT2 computes a QR 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:

 ZTPQRT2 computes a QR 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 upper trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.

A

          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

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

B

          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

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

T

          T is COMPLEX*16 array, dimension (LDT,N)
          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,N)

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 (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 (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 triangular
  factor of the block reflector.

Definition at line 172 of file ztpqrt2.f.

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