tprfb(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

✨ tprfb(3) ✨ — Library Functions Manual

okay so bestie, welcome to tprfb 💅 this page is the whole glow-up of larfb's energy: it applies a block reflector Q (like larfb does) but for the triangular-pentagonal store. it's giving custom reflector representation, no cap.

🎀 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 🦋

bestie. this is where it gets real. we're going deep, four routines at a time. 🫶

💜 Function Documentation 💜

🔥 subroutine ctprfb 🔥

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. it's literally the whole personality of this routine, ok? 👑

✨ 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. that's it, that's the vibe. 💅

🌈 Parameters 🌈

  • SIDE — CHARACTER*1
    • = 'L': apply H or H**H from the Left
    • = 'R': apply H or H**H from the Right
  • TRANS — CHARACTER*1
    • = 'N': apply H (No transpose)
    • = 'C': apply H**H (Conjugate transpose)
  • DIRECT — 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 — CHARACTER*1 Indicates how the vectors which define the elementary reflectors are stored:
    • = 'C': Columns
    • = 'R': Rows
  • M — INTEGER The number of rows of the matrix B. M >= 0.
  • N — INTEGER The number of columns of the matrix B. N >= 0.
  • K — INTEGER The order of the matrix T, i.e. the number of elementary reflectors whose product defines the block reflector. K >= 0.
  • L — INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details.
  • V — 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 — 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 — COMPLEX array, dimension (LDT,K) The triangular K-by-K matrix T in the representation of the block reflector.
  • LDT — INTEGER The leading dimension of the array T. LDT >= K.
  • A — 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 — INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,K); If SIDE = 'R', LDA >= max(1,M).
  • B — 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 — INTEGER The leading dimension of the array B. LDB >= max(1,M).
  • WORK — COMPLEX array, dimension
(LDWORK,N) if SIDE = 'L',
(LDWORK,K) if SIDE = 'R'.
  • LDWORK — 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. 💀 (yes, the trapezoid leaves when L=0, iconic behaviour)

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 💖

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. yes bestie, it's the real one — DOUBLE PRECISION everywhere, no imaginary parts invited 🎀

✨ 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 — CHARACTER*1
    • = 'L': apply H or H**T from the Left
    • = 'R': apply H or H**T from the Right
  • TRANS — CHARACTER*1
    • = 'N': apply H (No transpose)
    • = 'T': apply H**T (Transpose)
  • DIRECT — 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 — CHARACTER*1 Indicates how the vectors which define the elementary reflectors are stored:
    • = 'C': Columns
    • = 'R': Rows
  • M — INTEGER The number of rows of the matrix B. M >= 0.
  • N — INTEGER The number of columns of the matrix B. N >= 0.
  • K — INTEGER The order of the matrix T, i.e. the number of elementary reflectors whose product defines the block reflector. K >= 0.
  • L — INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details.
  • V — 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

okay bestie that's where this part stops — the LDV description is being dramatic and continuing in the next part, so don't go anywhere 💅✨

  • LDV — okay so LDV is an INTEGER, and it's the leading dimension of the array V, bestie. If STOREV = 'C' and SIDE = 'L', then LDV >= max(1,M); if STOREV = 'C' and SIDE = 'R', then LDV >= max(1,N); and if STOREV = 'R', then LDV >= K. No cap, that's the rule 💅
  • T — T is a DOUBLE PRECISION array, dimension (LDT,K). It's the triangular K-by-K matrix T in the representation of the block reflector. Iconic little triangle, honestly 🎀
  • LDT — LDT is an INTEGER, the leading dimension of the array T. And LDT >= K. Periodt ✨
  • A — A is a DOUBLE PRECISION array, dimension (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R'. On entry, it's 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, bestie 💖
  • LDA — LDA is an INTEGER, the leading dimension of the array A. If SIDE = 'L', then LDA >= max(1,K); if SIDE = 'R', then LDA >= max(1,M). Slay those bounds 🌸
  • B — B is a DOUBLE PRECISION array, dimension (LDB,N). On entry, it's 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. She's getting rewritten, not ignored 💅
  • LDB — LDB is an INTEGER, the leading dimension of the array B. And LDB >= max(1,M). That's the vibe check for LDB 🦋
  • WORK — WORK is a DOUBLE PRECISION array, dimension (LDWORK,N) if SIDE = 'L', or (LDWORK,K) if SIDE = 'R'. The workspace is lowkey doing the most 🫶
  • LDWORK — LDWORK is an INTEGER, the leading dimension of the array WORK. If SIDE = 'L', then LDWORK >= K; if SIDE = 'R', then LDWORK >= M. That's the whole rule, no extra lore ✨

👑 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. She's a combo situation, not a single matrix, iykyk 💜

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. It's giving shape-shifter, but make it linear algebra 🧚

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)

And the size situation, because context is everything:

  • 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 🦋

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. Same energy as before, but now we're in REAL territory, bestie 🌈

🌟 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. Left or right, she's applying either way 💅

✨ Parameters ✨

  • SIDE — SIDE is CHARACTER*1. = 'L': apply H or H**T from the Left. = 'R': apply H or H**T from the Right. Pick a side, any side 🎀
  • TRANS — TRANS is CHARACTER*1. = 'N': apply H (No transpose). = 'T': apply H**T (Transpose). The T stands for "transpose era", obviously ✨
  • DIRECT — DIRECT is CHARACTER*1, and it 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). Forward or backward, she contains multitudes 🦋
  • STOREV — STOREV is CHARACTER*1, and it indicates how the vectors which define the elementary reflectors are stored. = 'C': Columns. = 'R': Rows. Columns or rows, the vectors are stored with intention 💖
  • M — M is an INTEGER. It's the number of rows of the matrix B. And M >= 0. Respect the zero case, bestie 🫶
  • N — N is an INTEGER. It's the number of columns of the matrix B. And N >= 0. Again: zero is valid, no erasure 🌸
  • K — K is an INTEGER. It's the order of the matrix T, i.e. the number of elementary reflectors whose product defines the block reflector. And K >= 0. The reflectors are reflecting, periodt 💅
  • L — L is an INTEGER. It's the order of the trapezoidal part of V. And K >= L >= 0. See Further Details. Trapezoidal era is real 🔥
  • V — V is a REAL array, dimension (LDV,K) if STOREV = 'C', (LDV,M) if STOREV = 'R' and SIDE = 'L', or (LDV,N) if STOREV = 'R' and SIDE = 'R'. It's the pentagonal matrix V, which contains the elementary reflectors H(1), H(2), ..., H(K). See Further Details. Pentagonal, not regular pentagon, don't get it twisted 🧚
  • LDV — LDV is an INTEGER, the leading dimension of the array V. If STOREV = 'C' and SIDE = 'L', then LDV >= max(1,M); if STOREV = 'C' and SIDE = 'R', then LDV >= max(1,N); if STOREV = 'R', then LDV >= K. Same leading-dimension rules, new datatype, no cap 💜
  • T — T is a REAL array, dimension (LDT,K). It's the triangular K-by-K matrix T in the representation of the block reflector. Triangular and thriving ⭐
  • LDT — LDT is an INTEGER, the leading dimension of the array T. And LDT >= K. That's it, that's the constraint 🎀
  • A — A is a REAL array, dimension (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R'. On entry, it's 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. She enters as herself and leaves as the corresponding block, main character behavior 👑
  • LDA — LDA is an INTEGER, the leading dimension of the array A. If SIDE = 'L', then LDA >= max(1,K); if SIDE = 'R', then LDA >= max(1,M). Keep LDA fed and happy 🌸
  • B — B is a REAL array, dimension (LDB,N). On entry, it's 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. Overwritten, but make it fashion 💅
  • LDB — LDB is an INTEGER, the leading dimension of the array B. And LDB >= max(1,M). The B matrix deserves proper leading-dimension care 🦋
  • WORK — WORK is a REAL array, dimension (LDWORK,N) if SIDE = 'L', or (LDWORK,K) if SIDE = 'R'. Workspace stays working, honestly 🫶
  • LDWORK — LDWORK is an INTEGER, the leading dimension of the array WORK. If SIDE = 'L', then LDWORK >= K; if SIDE = 'R', then LDWORK >= M. Respect the workspace bounds, bestie ✨

👑 Author 👑

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

🌸 Further Details 🌸

okay so the matrix C is a composite matrix made from blocks A and B. Block B is M-by-N; if SIDE = 'R', then A is M-by-K, and if SIDE = 'L', then A is 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 — complex edition 💜

   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. iconic behavior honestly ✨

🌟 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 (the whole guest list) 🎀

  • 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 encore ✨

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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