tpmqrt - Man Page

subroutine ctpmqrt (side, trans, m, n, k, l, nb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
CTPMQRT
subroutine dtpmqrt (side, trans, m, n, k, l, nb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
DTPMQRT
subroutine stpmqrt (side, trans, m, n, k, l, nb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
STPMQRT
subroutine ztpmqrt (side, trans, m, n, k, l, nb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
ZTPMQRT

CTPMQRT  

Purpose:

 CTPMQRT applies a complex orthogonal matrix Q obtained from a
 'triangular-pentagonal' complex block reflector H to a general
 complex matrix C, which consists of two blocks A and B.

Parameters

SIDE

          SIDE is CHARACTER*1
          = 'L': apply Q or Q**H from the Left;
          = 'R': apply Q or Q**H from the Right.

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'C':  Conjugate transpose, apply Q**H.

M

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

N

          N is INTEGER
          The number of columns of the matrix B. N >= 0.

K

          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.

L

          L is INTEGER
          The order of the trapezoidal part of V.
          K >= L >= 0.  See Further Details.

NB

          NB is INTEGER
          The block size used for the storage of T.  K >= NB >= 1.
          This must be the same value of NB used to generate T
          in CTPQRT.

V

          V is COMPLEX array, dimension (LDV,K)
          The i-th column must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          CTPQRT in B.  See Further Details.

LDV

          LDV is INTEGER
          The leading dimension of the array V.
          If SIDE = 'L', LDV >= max(1,M);
          if SIDE = 'R', LDV >= max(1,N).

T

          T is COMPLEX array, dimension (LDT,K)
          The upper triangular factors of the block reflectors
          as returned by CTPQRT, stored as a NB-by-K matrix.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= NB.

A

          A is COMPLEX array, dimension
          (LDA,N) if SIDE = 'L' or
          (LDA,K) if SIDE = 'R'
          On entry, the K-by-N or M-by-K matrix A.
          On exit, A is overwritten by the corresponding block of
          Q*C or Q**H*C or C*Q or C*Q**H.  See Further Details.

LDA

          LDA is INTEGER
          The leading dimension of the array A.
          If SIDE = 'L', LDC >= max(1,K);
          If SIDE = 'R', LDC >= max(1,M).

B

          B is COMPLEX array, dimension (LDB,N)
          On entry, the M-by-N matrix B.
          On exit, B is overwritten by the corresponding block of
          Q*C or Q**H*C or C*Q or C*Q**H.  See Further Details.

LDB

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

WORK

          WORK is COMPLEX array. The dimension of WORK is
           N*NB if SIDE = 'L', or  M*NB if SIDE = 'R'.

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 columns of the pentagonal matrix V contain the elementary reflectors
  H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
  trapezoidal block V2:

        V = [V1]
            [V2].

  The size of the trapezoidal block V2 is determined by the parameter L,
  where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L
  rows of a K-by-K upper triangular matrix.  If L=K, V2 is upper triangular;
  if L=0, there is no trapezoidal block, hence V = V1 is rectangular.

  If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is M-by-K.
                      [B]

  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is N-by-K.

  The complex orthogonal matrix Q is formed from V and T.

  If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.

  If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.

  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.

  If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.

Definition at line 214 of file ctpmqrt.f.

DTPMQRT  

Purpose:

 DTPMQRT applies a real orthogonal matrix Q obtained from a
 'triangular-pentagonal' real block reflector H to a general
 real matrix C, which consists of two blocks A and B.

Parameters

SIDE

          SIDE is CHARACTER*1
          = 'L': apply Q or Q**T from the Left;
          = 'R': apply Q or Q**T from the Right.

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'T':  Transpose, apply Q**T.

M

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

N

          N is INTEGER
          The number of columns of the matrix B. N >= 0.

K

          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.

L

          L is INTEGER
          The order of the trapezoidal part of V.
          K >= L >= 0.  See Further Details.

NB

          NB is INTEGER
          The block size used for the storage of T.  K >= NB >= 1.
          This must be the same value of NB used to generate T
          in CTPQRT.

V

          V is DOUBLE PRECISION array, dimension (LDV,K)
          The i-th column must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          CTPQRT in B.  See Further Details.

LDV

          LDV is INTEGER
          The leading dimension of the array V.
          If SIDE = 'L', LDV >= max(1,M);
          if SIDE = 'R', LDV >= max(1,N).

T

          T is DOUBLE PRECISION array, dimension (LDT,K)
          The upper triangular factors of the block reflectors
          as returned by CTPQRT, stored as a NB-by-K matrix.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= NB.

A

          A is DOUBLE PRECISION array, dimension
          (LDA,N) if SIDE = 'L' or
          (LDA,K) if SIDE = 'R'
          On entry, the K-by-N or M-by-K matrix A.
          On exit, A is overwritten by the corresponding block of
          Q*C or Q**T*C or C*Q or C*Q**T.  See Further Details.

LDA

          LDA is INTEGER
          The leading dimension of the array A.
          If SIDE = 'L', LDC >= max(1,K);
          If SIDE = 'R', LDC >= max(1,M).

B

          B is DOUBLE PRECISION array, dimension (LDB,N)
          On entry, the M-by-N matrix B.
          On exit, B is overwritten by the corresponding block of
          Q*C or Q**T*C or C*Q or C*Q**T.  See Further Details.

LDB

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

WORK

          WORK is DOUBLE PRECISION array. The dimension of WORK is
           N*NB if SIDE = 'L', or  M*NB if SIDE = 'R'.

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 columns of the pentagonal matrix V contain the elementary reflectors
  H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
  trapezoidal block V2:

        V = [V1]
            [V2].

  The size of the trapezoidal block V2 is determined by the parameter L,
  where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L
  rows of a K-by-K upper triangular matrix.  If L=K, V2 is upper triangular;
  if L=0, there is no trapezoidal block, hence V = V1 is rectangular.

  If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is M-by-K.
                      [B]

  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is N-by-K.

  The real orthogonal matrix Q is formed from V and T.

  If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.

  If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C.

  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.

  If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.

Definition at line 214 of file dtpmqrt.f.

STPMQRT  

Purpose:

 STPMQRT applies a real orthogonal matrix Q obtained from a
 'triangular-pentagonal' real block reflector H to a general
 real matrix C, which consists of two blocks A and B.

Parameters

SIDE

          SIDE is CHARACTER*1
          = 'L': apply Q or Q^T from the Left;
          = 'R': apply Q or Q^T from the Right.

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'T':  Transpose, apply Q^T.

M

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

N

          N is INTEGER
          The number of columns of the matrix B. N >= 0.

K

          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.

L

          L is INTEGER
          The order of the trapezoidal part of V.
          K >= L >= 0.  See Further Details.

NB

          NB is INTEGER
          The block size used for the storage of T.  K >= NB >= 1.
          This must be the same value of NB used to generate T
          in CTPQRT.

V

          V is REAL array, dimension (LDV,K)
          The i-th column must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          CTPQRT in B.  See Further Details.

LDV

          LDV is INTEGER
          The leading dimension of the array V.
          If SIDE = 'L', LDV >= max(1,M);
          if SIDE = 'R', LDV >= max(1,N).

T

          T is REAL array, dimension (LDT,K)
          The upper triangular factors of the block reflectors
          as returned by CTPQRT, stored as a NB-by-K matrix.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= NB.

A

          A is REAL array, dimension
          (LDA,N) if SIDE = 'L' or
          (LDA,K) if SIDE = 'R'
          On entry, the K-by-N or M-by-K matrix A.
          On exit, A is overwritten by the corresponding block of
          Q*C or Q^T*C or C*Q or C*Q^T.  See Further Details.

LDA

          LDA is INTEGER
          The leading dimension of the array A.
          If SIDE = 'L', LDC >= max(1,K);
          If SIDE = 'R', LDC >= max(1,M).

B

          B is REAL array, dimension (LDB,N)
          On entry, the M-by-N matrix B.
          On exit, B is overwritten by the corresponding block of
          Q*C or Q^T*C or C*Q or C*Q^T.  See Further Details.

LDB

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

WORK

          WORK is REAL array. The dimension of WORK is
           N*NB if SIDE = 'L', or  M*NB if SIDE = 'R'.

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 columns of the pentagonal matrix V contain the elementary reflectors
  H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
  trapezoidal block V2:

        V = [V1]
            [V2].

  The size of the trapezoidal block V2 is determined by the parameter L,
  where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L
  rows of a K-by-K upper triangular matrix.  If L=K, V2 is upper triangular;
  if L=0, there is no trapezoidal block, hence V = V1 is rectangular.

  If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is M-by-K.
                      [B]

  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is N-by-K.

  The real orthogonal matrix Q is formed from V and T.

  If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.

  If TRANS='T' and SIDE='L', C is on exit replaced with Q^T * C.

  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.

  If TRANS='T' and SIDE='R', C is on exit replaced with C * Q^T.

Definition at line 214 of file stpmqrt.f.

ZTPMQRT  

Purpose:

 ZTPMQRT applies a complex orthogonal matrix Q obtained from a
 'triangular-pentagonal' complex block reflector H to a general
 complex matrix C, which consists of two blocks A and B.

Parameters

SIDE

          SIDE is CHARACTER*1
          = 'L': apply Q or Q**H from the Left;
          = 'R': apply Q or Q**H from the Right.

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'C':  Conjugate transpose, apply Q**H.

M

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

N

          N is INTEGER
          The number of columns of the matrix B. N >= 0.

K

          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.

L

          L is INTEGER
          The order of the trapezoidal part of V.
          K >= L >= 0.  See Further Details.

NB

          NB is INTEGER
          The block size used for the storage of T.  K >= NB >= 1.
          This must be the same value of NB used to generate T
          in CTPQRT.

V

          V is COMPLEX*16 array, dimension (LDV,K)
          The i-th column must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          CTPQRT in B.  See Further Details.

LDV

          LDV is INTEGER
          The leading dimension of the array V.
          If SIDE = 'L', LDV >= max(1,M);
          if SIDE = 'R', LDV >= max(1,N).

T

          T is COMPLEX*16 array, dimension (LDT,K)
          The upper triangular factors of the block reflectors
          as returned by CTPQRT, stored as a NB-by-K matrix.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= NB.

A

          A is COMPLEX*16 array, dimension
          (LDA,N) if SIDE = 'L' or
          (LDA,K) if SIDE = 'R'
          On entry, the K-by-N or M-by-K matrix A.
          On exit, A is overwritten by the corresponding block of
          Q*C or Q**H*C or C*Q or C*Q**H.  See Further Details.

LDA

          LDA is INTEGER
          The leading dimension of the array A.
          If SIDE = 'L', LDC >= max(1,K);
          If SIDE = 'R', LDC >= max(1,M).

B

          B is COMPLEX*16 array, dimension (LDB,N)
          On entry, the M-by-N matrix B.
          On exit, B is overwritten by the corresponding block of
          Q*C or Q**H*C or C*Q or C*Q**H.  See Further Details.

LDB

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

WORK

          WORK is COMPLEX*16 array. The dimension of WORK is
           N*NB if SIDE = 'L', or  M*NB if SIDE = 'R'.

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 columns of the pentagonal matrix V contain the elementary reflectors
  H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
  trapezoidal block V2:

        V = [V1]
            [V2].

  The size of the trapezoidal block V2 is determined by the parameter L,
  where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L
  rows of a K-by-K upper triangular matrix.  If L=K, V2 is upper triangular;
  if L=0, there is no trapezoidal block, hence V = V1 is rectangular.

  If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is M-by-K.
                      [B]

  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is N-by-K.

  The complex orthogonal matrix Q is formed from V and T.

  If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.

  If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.

  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.

  If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.

Definition at line 214 of file ztpmqrt.f.