Library Functions Manual

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

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

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

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

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

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

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

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

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

!>          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 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 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 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, complex16, dimension( ldv, ) v, integer ldv, complex16, dimension( ldt, ) t, integer ldt, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ldb, ) b, integer ldb, complex16, 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  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 is INTEGER
!>          The number of rows of the matrix B.
!>          M >= 0.
!>

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

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

!>          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 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 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 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.

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