/home/abui...RC/stfsm.f(3)
🌸 NAME 🌸
bestie, this is the manpage for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/stfsm.f — like, yes, that's the whole path, we don't gatekeep here 💅
It's part of the Library Functions Manual, and it's giving "serious linear algebra but make it cute". STFSM solves a matrix equation where one operand is a triangular matrix in RFP format. Periodt. ✨
🎀 SYNOPSIS 🎀
Functions/Subroutines
subroutine STFSM (transr, side, uplo, trans, diag, m, n, alpha, a, b,
ldb)STFSM solves a matrix equation (one operand is a triangular matrix in RFP format). That's the whole vibe. 🦋
👑 Function/Subroutine Documentation 👑
subroutine STFSM (character transr, character side, character uplo,
character trans, character diag, integer m, integer n, real alpha, real,
dimension( 0: * ) a, real, dimension( 0: ldb-1, 0: * ) b, integer ldb)STFSM solves a matrix equation (one operand is a triangular matrix in RFP format).
🌈 Purpose
!>
!> Level 3 BLAS like routine for A in RFP Format.
!>
!> STFSM 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**T.
!>
!> A is in Rectangular Full Packed (RFP) Format.
!>
!> The matrix X is overwritten on B.
!>okay so literally: 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 either A or A**T. And the solution X? It gets written straight over B. no extra storage for you, we love a low-waste moment 💖
✨ Parameters ✨
TRANSR
!> TRANSR is CHARACTER*1
!> = 'N': The Normal Form of RFP A is stored;
!> = 'T': The 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 = 'T' or 't' op( A ) = 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 REAL
!> 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.
!>ngl this is the good stuff: ifalphais zero,Ais literally not even referenced andBdoesn't need to be set before entry. free real estate 😭
A
!> A is REAL array, dimension (NT)
!> 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 = 'T' then RFP is the 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
!> transpose Format. If UPLO = 'L' the RFP A contains
!> the NT elements of lower packed A either in normal or
!> transpose Format. The LDA of RFP A is (N+1)/2 when
!> TRANSR = 'T'. 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.
!>like, NT = N*(N+1)/2, got it? and yes — see the Note below, we're getting to the diagrams, don't worry 🫶
B
!> B is REAL 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.
!>🧚 Author 🧚
- Univ. of Tennessee
- Univ. of California Berkeley
- Univ. of Colorado Denver
- NAG Ltd.
iconic collaboration, honestly 👑
🦋 Further Details 🦋
buckle up bestie, this is the diagram section and it ATE 💅
!>
!> We first consider Rectangular Full Packed (RFP) Format when N is
!> even. We give an 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
!> the 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
!> the transpose of the last three columns of AP lower.
!> 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 = 'T'. RFP A in both UPLO cases is just the
!> 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
!>
!>
!> We then consider Rectangular Full Packed (RFP) Format when N is
!> odd. We give an 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
!> the 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
!> the transpose of the last two columns of AP lower.
!> 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 = 'T'. RFP A in both UPLO cases is just the
!> 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 275 of file stfsm.f. 📍
💜 Author 💜
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