tprfb(3)

NAME
tprfb - tprfb: applies Q (like larfb)

SYNOPSIS

  Functions
subroutine ctprfb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork)
CTPRFB applies a complex 'triangular-pentagonal' block reflector to a complex matrix, which is composed of two blocks.
subroutine dtprfb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork)
DTPRFB applies a real 'triangular-pentagonal' block reflector to a real matrix, which is composed of two blocks.
subroutine stprfb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork)
STPRFB applies a real 'triangular-pentagonal' block reflector to a real matrix, which is composed of two blocks.
subroutine ztprfb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork)
ZTPRFB applies a complex 'triangular-pentagonal' block reflector to a complex matrix, which is composed of two blocks.

Detailed Description

Function Documentation

  subroutine ctprfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldwork, * ) work, integer ldwork)

CTPRFB applies a complex 'triangular-pentagonal' block reflector to a complex matrix, which is composed of two blocks.

Purpose:

     CTPRFB applies a complex 'triangular-pentagonal' block reflector H or its
     conjugate transpose H**H to a complex matrix C, which is composed of two
     blocks A and B, either from the left or right.

Parameters
    SIDE

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

    TRANS

              TRANS is CHARACTER*1
              = 'N': apply H (No transpose)
              = 'C': apply H**H (Conjugate transpose)

    DIRECT

              DIRECT is CHARACTER*1
              Indicates how H is formed from a product of elementary
              reflectors
              = 'F': H = H(1) H(2) . . . H(k) (Forward)
              = 'B': H = H(k) . . . H(2) H(1) (Backward)

    STOREV

              STOREV is CHARACTER*1
              Indicates how the vectors which define the elementary
              reflectors are stored:
              = 'C': Columns
              = 'R': Rows

    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 order of the matrix T, i.e. the number of elementary
              reflectors whose product defines the block reflector.
              K >= 0.

    L

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

    V

              V is COMPLEX array, dimension
                                    (LDV,K) if STOREV = 'C'
                                    (LDV,M) if STOREV = 'R' and SIDE = 'L'
                                    (LDV,N) if STOREV = 'R' and SIDE = 'R'
              The pentagonal matrix V, which contains the elementary reflectors
              H(1), H(2), ..., H(K).  See Further Details.

    LDV

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

    T

              T is COMPLEX array, dimension (LDT,K)
              The triangular K-by-K matrix T in the representation of the
              block reflector.

    LDT

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

    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
              H*C or H**H*C or C*H or C*H**H.  See Further Details.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.
              If SIDE = 'L', LDA >= max(1,K);
              If SIDE = 'R', LDA >= 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
              H*C or H**H*C or C*H or C*H**H.  See Further Details.

    LDB

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

    WORK

              WORK is COMPLEX array, dimension
              (LDWORK,N) if SIDE = 'L',
              (LDWORK,K) if SIDE = 'R'.

    LDWORK

              LDWORK is INTEGER
              The leading dimension of the array WORK.
              If SIDE = 'L', LDWORK >= K;
              if SIDE = 'R', LDWORK >= M.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      The matrix C is a composite matrix formed from blocks A and B.
      The block B is of size M-by-N; if SIDE = 'R', A is of size M-by-K,
      and if SIDE = 'L', A is of size K-by-N.
      If SIDE = 'R' and DIRECT = 'F', C = [A B].
      If SIDE = 'L' and DIRECT = 'F', C = [A]
                                          [B].
      If SIDE = 'R' and DIRECT = 'B', C = [B A].
      If SIDE = 'L' and DIRECT = 'B', C = [B]
                                          [A].
      The pentagonal matrix V is composed of a rectangular block V1 and a
      trapezoidal block V2.  The size of the trapezoidal block is determined by
      the parameter L, where 0<=L<=K.  If L=K, the V2 block of V is triangular;
      if L=0, there is no trapezoidal block, thus V = V1 is rectangular.
      If DIRECT = 'F' and STOREV = 'C':  V = [V1]
                                             [V2]
         - V2 is upper trapezoidal (first L rows of K-by-K upper triangular)
      If DIRECT = 'F' and STOREV = 'R':  V = [V1 V2]
         - V2 is lower trapezoidal (first L columns of K-by-K lower triangular)
      If DIRECT = 'B' and STOREV = 'C':  V = [V2]
                                             [V1]
         - V2 is lower trapezoidal (last L rows of K-by-K lower triangular)
      If DIRECT = 'B' and STOREV = 'R':  V = [V2 V1]
         - V2 is upper trapezoidal (last L columns of K-by-K upper triangular)
      If STOREV = 'C' and SIDE = 'L', V is M-by-K with V2 L-by-K.
      If STOREV = 'C' and SIDE = 'R', V is N-by-K with V2 L-by-K.
      If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.
      If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.

Definition at line 249 of file ctprfb.f.

  subroutine dtprfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldwork, * ) work, integer ldwork)

DTPRFB applies a real 'triangular-pentagonal' block reflector to a real matrix, which is composed of two blocks.

Purpose:

     DTPRFB applies a real 'triangular-pentagonal' block reflector H or its
     transpose H**T to a real matrix C, which is composed of two
     blocks A and B, either from the left or right.

Parameters
    SIDE

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

    TRANS

              TRANS is CHARACTER*1
              = 'N': apply H (No transpose)
              = 'T': apply H**T (Transpose)

    DIRECT

              DIRECT is CHARACTER*1
              Indicates how H is formed from a product of elementary
              reflectors
              = 'F': H = H(1) H(2) . . . H(k) (Forward)
              = 'B': H = H(k) . . . H(2) H(1) (Backward)

    STOREV

              STOREV is CHARACTER*1
              Indicates how the vectors which define the elementary
              reflectors are stored:
              = 'C': Columns
              = 'R': Rows

    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 order of the matrix T, i.e. the number of elementary
              reflectors whose product defines the block reflector.
              K >= 0.

    L

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

    V

              V is DOUBLE PRECISION array, dimension
                                    (LDV,K) if STOREV = 'C'
                                    (LDV,M) if STOREV = 'R' and SIDE = 'L'
                                    (LDV,N) if STOREV = 'R' and SIDE = 'R'
              The pentagonal matrix V, which contains the elementary reflectors
              H(1), H(2), ..., H(K).  See Further Details.

    LDV

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

    T

              T is DOUBLE PRECISION array, dimension (LDT,K)
              The triangular K-by-K matrix T in the representation of the
              block reflector.

    LDT

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

    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
              H*C or H**T*C or C*H or C*H**T.  See Further Details.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.
              If SIDE = 'L', LDA >= max(1,K);
              If SIDE = 'R', LDA >= 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
              H*C or H**T*C or C*H or C*H**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, dimension
              (LDWORK,N) if SIDE = 'L',
              (LDWORK,K) if SIDE = 'R'.

    LDWORK

              LDWORK is INTEGER
              The leading dimension of the array WORK.
              If SIDE = 'L', LDWORK >= K;
              if SIDE = 'R', LDWORK >= M.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      The matrix C is a composite matrix formed from blocks A and B.
      The block B is of size M-by-N; if SIDE = 'R', A is of size M-by-K,
      and if SIDE = 'L', A is of size K-by-N.
      If SIDE = 'R' and DIRECT = 'F', C = [A B].
      If SIDE = 'L' and DIRECT = 'F', C = [A]
                                          [B].
      If SIDE = 'R' and DIRECT = 'B', C = [B A].
      If SIDE = 'L' and DIRECT = 'B', C = [B]
                                          [A].
      The pentagonal matrix V is composed of a rectangular block V1 and a
      trapezoidal block V2.  The size of the trapezoidal block is determined by
      the parameter L, where 0<=L<=K.  If L=K, the V2 block of V is triangular;
      if L=0, there is no trapezoidal block, thus V = V1 is rectangular.
      If DIRECT = 'F' and STOREV = 'C':  V = [V1]
                                             [V2]
         - V2 is upper trapezoidal (first L rows of K-by-K upper triangular)
      If DIRECT = 'F' and STOREV = 'R':  V = [V1 V2]
         - V2 is lower trapezoidal (first L columns of K-by-K lower triangular)
      If DIRECT = 'B' and STOREV = 'C':  V = [V2]
                                             [V1]
         - V2 is lower trapezoidal (last L rows of K-by-K lower triangular)
      If DIRECT = 'B' and STOREV = 'R':  V = [V2 V1]
         - V2 is upper trapezoidal (last L columns of K-by-K upper triangular)
      If STOREV = 'C' and SIDE = 'L', V is M-by-K with V2 L-by-K.
      If STOREV = 'C' and SIDE = 'R', V is N-by-K with V2 L-by-K.
      If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.
      If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.

Definition at line 249 of file dtprfb.f.

  subroutine stprfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldwork, * ) work, integer ldwork)

STPRFB applies a real 'triangular-pentagonal' block reflector to a real matrix, which is composed of two blocks.

Purpose:

     STPRFB applies a real 'triangular-pentagonal' block reflector H or its
     transpose H**T to a real matrix C, which is composed of two
     blocks A and B, either from the left or right.

Parameters
    SIDE

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

    TRANS

              TRANS is CHARACTER*1
              = 'N': apply H (No transpose)
              = 'T': apply H**T (Transpose)

    DIRECT

              DIRECT is CHARACTER*1
              Indicates how H is formed from a product of elementary
              reflectors
              = 'F': H = H(1) H(2) . . . H(k) (Forward)
              = 'B': H = H(k) . . . H(2) H(1) (Backward)

    STOREV

              STOREV is CHARACTER*1
              Indicates how the vectors which define the elementary
              reflectors are stored:
              = 'C': Columns
              = 'R': Rows

    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 order of the matrix T, i.e. the number of elementary
              reflectors whose product defines the block reflector.
              K >= 0.

    L

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

    V

              V is REAL array, dimension
                                    (LDV,K) if STOREV = 'C'
                                    (LDV,M) if STOREV = 'R' and SIDE = 'L'
                                    (LDV,N) if STOREV = 'R' and SIDE = 'R'
              The pentagonal matrix V, which contains the elementary reflectors
              H(1), H(2), ..., H(K).  See Further Details.

    LDV

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

    T

              T is REAL array, dimension (LDT,K)
              The triangular K-by-K matrix T in the representation of the
              block reflector.

    LDT

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

    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
              H*C or H**T*C or C*H or C*H**T.  See Further Details.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.
              If SIDE = 'L', LDA >= max(1,K);
              If SIDE = 'R', LDA >= 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
              H*C or H**T*C or C*H or C*H**T.  See Further Details.

    LDB

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

    WORK

              WORK is REAL array, dimension
              (LDWORK,N) if SIDE = 'L',
              (LDWORK,K) if SIDE = 'R'.

    LDWORK

              LDWORK is INTEGER
              The leading dimension of the array WORK.
              If SIDE = 'L', LDWORK >= K;
              if SIDE = 'R', LDWORK >= M.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      The matrix C is a composite matrix formed from blocks A and B.
      The block B is of size M-by-N; if SIDE = 'R', A is of size M-by-K,
      and if SIDE = 'L', A is of size K-by-N.
      If SIDE = 'R' and DIRECT = 'F', C = [A B].
      If SIDE = 'L' and DIRECT = 'F', C = [A]
                                          [B].
      If SIDE = 'R' and DIRECT = 'B', C = [B A].
      If SIDE = 'L' and DIRECT = 'B', C = [B]
                                          [A].
      The pentagonal matrix V is composed of a rectangular block V1 and a
      trapezoidal block V2.  The size of the trapezoidal block is determined by
      the parameter L, where 0<=L<=K.  If L=K, the V2 block of V is triangular;
      if L=0, there is no trapezoidal block, thus V = V1 is rectangular.
      If DIRECT = 'F' and STOREV = 'C':  V = [V1]
                                             [V2]
         - V2 is upper trapezoidal (first L rows of K-by-K upper triangular)
      If DIRECT = 'F' and STOREV = 'R':  V = [V1 V2]
         - V2 is lower trapezoidal (first L columns of K-by-K lower triangular)
      If DIRECT = 'B' and STOREV = 'C':  V = [V2]
                                             [V1]
         - V2 is lower trapezoidal (last L rows of K-by-K lower triangular)
      If DIRECT = 'B' and STOREV = 'R':  V = [V2 V1]
         - V2 is upper trapezoidal (last L columns of K-by-K upper triangular)
      If STOREV = 'C' and SIDE = 'L', V is M-by-K with V2 L-by-K.
      If STOREV = 'C' and SIDE = 'R', V is N-by-K with V2 L-by-K.
      If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.
      If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.

Definition at line 249 of file stprfb.f.

  subroutine ztprfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldwork, * ) work, integer ldwork)

ZTPRFB applies a complex 'triangular-pentagonal' block reflector to a complex matrix, which is composed of two blocks.

Purpose:

     ZTPRFB applies a complex 'triangular-pentagonal' block reflector H or its
     conjugate transpose H**H to a complex matrix C, which is composed of two
     blocks A and B, either from the left or right.

Parameters
    SIDE

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

    TRANS

              TRANS is CHARACTER*1
              = 'N': apply H (No transpose)
              = 'C': apply H**H (Conjugate transpose)

    DIRECT

              DIRECT is CHARACTER*1
              Indicates how H is formed from a product of elementary
              reflectors
              = 'F': H = H(1) H(2) . . . H(k) (Forward)
              = 'B': H = H(k) . . . H(2) H(1) (Backward)

    STOREV

              STOREV is CHARACTER*1
              Indicates how the vectors which define the elementary
              reflectors are stored:
              = 'C': Columns
              = 'R': Rows

    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 order of the matrix T, i.e. the number of elementary
              reflectors whose product defines the block reflector.
              K >= 0.

    L

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

    V

              V is COMPLEX*16 array, dimension
                                    (LDV,K) if STOREV = 'C'
                                    (LDV,M) if STOREV = 'R' and SIDE = 'L'
                                    (LDV,N) if STOREV = 'R' and SIDE = 'R'
              The pentagonal matrix V, which contains the elementary reflectors
              H(1), H(2), ..., H(K).  See Further Details.

    LDV

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

    T

              T is COMPLEX*16 array, dimension (LDT,K)
              The triangular K-by-K matrix T in the representation of the
              block reflector.

    LDT

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

    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
              H*C or H**H*C or C*H or C*H**H.  See Further Details.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.
              If SIDE = 'L', LDA >= max(1,K);
              If SIDE = 'R', LDA >= 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
              H*C or H**H*C or C*H or C*H**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, dimension
              (LDWORK,N) if SIDE = 'L',
              (LDWORK,K) if SIDE = 'R'.

    LDWORK

              LDWORK is INTEGER
              The leading dimension of the array WORK.
              If SIDE = 'L', LDWORK >= K;
              if SIDE = 'R', LDWORK >= M.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      The matrix C is a composite matrix formed from blocks A and B.
      The block B is of size M-by-N; if SIDE = 'R', A is of size M-by-K,
      and if SIDE = 'L', A is of size K-by-N.
      If SIDE = 'R' and DIRECT = 'F', C = [A B].
      If SIDE = 'L' and DIRECT = 'F', C = [A]
                                          [B].
      If SIDE = 'R' and DIRECT = 'B', C = [B A].
      If SIDE = 'L' and DIRECT = 'B', C = [B]
                                          [A].
      The pentagonal matrix V is composed of a rectangular block V1 and a
      trapezoidal block V2.  The size of the trapezoidal block is determined by
      the parameter L, where 0<=L<=K.  If L=K, the V2 block of V is triangular;
      if L=0, there is no trapezoidal block, thus V = V1 is rectangular.
      If DIRECT = 'F' and STOREV = 'C':  V = [V1]
                                             [V2]
         - V2 is upper trapezoidal (first L rows of K-by-K upper triangular)
      If DIRECT = 'F' and STOREV = 'R':  V = [V1 V2]
         - V2 is lower trapezoidal (first L columns of K-by-K lower triangular)
      If DIRECT = 'B' and STOREV = 'C':  V = [V2]
                                             [V1]
         - V2 is lower trapezoidal (last L rows of K-by-K lower triangular)
      If DIRECT = 'B' and STOREV = 'R':  V = [V2 V1]
         - V2 is upper trapezoidal (last L columns of K-by-K upper triangular)
      If STOREV = 'C' and SIDE = 'L', V is M-by-K with V2 L-by-K.
      If STOREV = 'C' and SIDE = 'R', V is N-by-K with V2 L-by-K.
      If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.
      If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.

Definition at line 249 of file ztprfb.f.

Author

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