/home/abui...RC/ztfsm.f(3)

🎀 NAME 🎀

okay so bestie, this page is literally about a file, not a command — it's the man page for

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ztfsm.f

which is a Fortran source file from LAPACK, and the little star in ztfsm.f doesn't mean anything cutesy, it's just how Fortran files get documented. anyway, welcome to the group chat 💅

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine ZTFSM (transr, side, uplo, trans, diag, m, n, alpha, a, b,
    ldb)

so like, ZTFSM solves a matrix equation where one operand is a triangular matrix in RFP format. that's the whole vibe 🔥

🦋 Function/Subroutine Documentation 🦋

subroutine ZTFSM (character transr, character side, character uplo,
    character trans, character diag, integer m, integer n, complex*16 alpha,
    complex*16, dimension( 0: * ) a, complex*16, dimension( 0: ldb-1, 0: * )
    b, integer ldb)

ZTFSM solves a matrix equation (one operand is a triangular matrix in RFP format). icon behavior, honestly 👑

🌸 Purpose 🌸

it's a Level 3 BLAS like routine for A in RFP Format. ZTFSM solves the matrix equation

op( A )*X = alpha*B  or  X*op( A ) = alpha*B

where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of

op( A ) = A   or   op( A ) = A**H.

A is in Rectangular Full Packed (RFP) Format.

the matrix X is overwritten on B. not me giving you the answer by destroying your input array 😭 that's just how it is bestie.

💜 Parameters 💜

TRANSR — TRANSR is CHARACTER*1
- = 'N': The Normal Form of RFP A is stored;
- = 'C': The Conjugate-transpose Form of RFP A is stored.
SIDE — SIDE is CHARACTER*1 On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows:
- SIDE = 'L' or 'l' → op( A )*X = alpha*B.
- SIDE = 'R' or 'r' → X*op( A ) = alpha*B.

Unchanged on exit.

UPLO — UPLO is CHARACTER*1 On entry, UPLO specifies whether the RFP matrix A came from an upper or lower triangular matrix as follows:
- UPLO = 'U' or 'u' → RFP A came from an upper triangular matrix
- UPLO = 'L' or 'l' → RFP A came from a lower triangular matrix

Unchanged on exit.

TRANS — TRANS is CHARACTER*1 On entry, TRANS specifies the form of op( A ) to be used in the matrix multiplication as follows:
- TRANS = 'N' or 'n' → op( A ) = A.
- TRANS = 'C' or 'c' → op( A ) = conjg( A' ).

Unchanged on exit.

DIAG — DIAG is CHARACTER*1 On entry, DIAG specifies whether or not RFP A is unit triangular as follows:
- DIAG = 'U' or 'u' → A is assumed to be unit triangular.
- DIAG = 'N' or 'n' → A is not assumed to be unit triangular.

Unchanged on exit.

M — M is INTEGER On entry, M specifies the number of rows of B. M must be at least zero. Unchanged on exit.
N — N is INTEGER On entry, N specifies the number of columns of B. N must be at least zero. Unchanged on exit.
ALPHA — ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry. Unchanged on exit.
A — A is COMPLEX*16 array, dimension (N*(N+1)/2) NT = N*(N+1)/2. On entry, the matrix A in RFP Format. RFP Format is described by TRANSR, UPLO and N as follows: If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A as defined when TRANSR = 'N'. The contents of RFP A are defined by UPLO as follows: If UPLO = 'U' the RFP A contains the NT elements of upper packed A either in normal or conjugate-transpose Format. If UPLO = 'L' the RFP A contains the NT elements of lower packed A either in normal or conjugate-transpose Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and is N when is odd. See the Note below for more details. Unchanged on exit.
B — B is COMPLEX*16 array, dimension (LDB,N) Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.
LDB — LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ). Unchanged on exit.

🫶 heads up bestie: B gets absolutely demolished — it comes in as your right-hand side and leaves as X. copy it first if you still need it, iykyk.

👑 Author 👑

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

the whole squad really said "we built this" 💅

🌈 Further Details: 🌈

okay this is the part where it gets lowkey gorgeous — the diagrams are literally art. keeping them exactly as they are because you do NOT want me paraphrasing linear algebra ASCII, bestie.

First, Standard Packed Format when N is even. Example where N = 6.

    AP is Upper             AP is Lower

 00 01 02 03 04 05       00
    11 12 13 14 15       10 11
       22 23 24 25       20 21 22
          33 34 35       30 31 32 33
             44 45       40 41 42 43 44
                55       50 51 52 53 54 55

Let TRANSR = 'N'. RFP holds AP as follows: For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last three columns of AP upper. The lower triangle A(4:6,0:2) consists of conjugate-transpose of the first three columns of AP upper. For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first three columns of AP lower. The upper triangle A(0:2,0:2) consists of conjugate-transpose of the last three columns of AP lower. To denote conjugate we place -- above the element. This covers the case N even and TRANSR = 'N'.

       RFP A                   RFP A

                            -- -- --
    03 04 05                33 43 53
                               -- --
    13 14 15                00 44 54
                                  --
    23 24 25                10 11 55

    33 34 35                20 21 22
    --
    00 44 45                30 31 32
    -- --
    01 11 55                40 41 42
    -- -- --
    02 12 22                50 51 52

Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-transpose of RFP A above. One therefore gets:

       RFP A                   RFP A

 -- -- -- --                -- -- -- -- -- --
 03 13 23 33 00 01 02    33 00 10 20 30 40 50
 -- -- -- -- --                -- -- -- -- --
 04 14 24 34 44 11 12    43 44 11 21 31 41 51
 -- -- -- -- -- --                -- -- -- --
 05 15 25 35 45 55 22    53 54 55 22 32 42 52

Next, Standard Packed Format when N is odd. Example where N = 5.

   AP is Upper                 AP is Lower

 00 01 02 03 04              00
    11 12 13 14              10 11
       22 23 24              20 21 22
          33 34              30 31 32 33
             44              40 41 42 43 44

Let TRANSR = 'N'. RFP holds AP as follows: For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last three columns of AP upper. The lower triangle A(3:4,0:1) consists of conjugate-transpose of the first two columns of AP upper. For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first three columns of AP lower. The upper triangle A(0:1,1:2) consists of conjugate-transpose of the last two columns of AP lower. To denote conjugate we place -- above the element. This covers the case N odd and TRANSR = 'N'.

       RFP A                   RFP A

                               -- --
    02 03 04                00 33 43
                                  --
    12 13 14                10 11 44

    22 23 24                20 21 22
    --
    00 33 34                30 31 32
    -- --
    01 11 44                40 41 42

Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-transpose of RFP A above. One therefore gets:

       RFP A                   RFP A

 -- -- --                   -- -- -- -- -- --
 02 12 22 00 01             00 10 20 30 40 50
 -- -- -- --                   -- -- -- -- --
 03 13 23 33 11             33 11 21 31 41 51
 -- -- -- -- --                   -- -- -- --
 04 14 24 34 44             43 44 22 32 42 52

Definition at line 296 of file ztfsm.f. 📍

💀 Author 💀

Generated automatically by Doxygen for LAPACK from the source code.

yes bestie, a robot wrote the documentation about the code. it's giving meta. it's giving full circle. 🌀

LAPACK · Version 3.12.0 · /home/abui...RC/ztfsm.f(3)

and that's the whole page, bestie — slayed, documented, and every last -- in place. periodt. 💖✨🎀🦋

📦 where this page comes from

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opensuse-leap 16.0: lapack-man 3.12.0-160000.2.2 · BSD-3-Clause
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💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms