BLAS/SRC/stbsv.f(3)

okay bestie, this is the BLAS/SRC/stbsv.f(3) page from the Library Functions Manual, and it’s giving old-school BLAS but make it make sense. 💅

💖 NAME 💖

BLAS/SRC/stbsv.f — that’s the page name, bestie. It’s all about the stbsv subroutine.

✨ SYNOPSIS ✨

💫 Functions/Subroutines 💫

• subroutine stbsv (uplo, trans, diag, n, k, a, lda, x, incx) — STBSV

🎀 Function/Subroutine Documentation 🎀

Here’s the full signature, no cap:

subroutine stbsv (character uplo, character trans, character diag, integer n, integer k, real, dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx)

STBSV

🌸 Purpose 🌸

STBSV solves one of the systems of equations

A*x = b,   or   A**T*x = b,

where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals.

⚠️ Big caution, bestie: no test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. Like, you gotta check that yourself first. 💀

🌸 Parameters 🌸

UPLO

UPLO is CHARACTER*1. On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows:

• UPLO = 'U' or 'u' — A is an upper triangular matrix.
• UPLO = 'L' or 'l' — A is a lower triangular matrix.

TRANS

TRANS is CHARACTER*1. On entry, TRANS specifies the equations to be solved as follows:

• TRANS = 'N' or 'n' — A*x = b.
• TRANS = 'T' or 't' — A**T*x = b.
• TRANS = 'C' or 'c' — A**T*x = b.

DIAG

DIAG is CHARACTER*1. On entry, DIAG specifies whether or not 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.

N

N is INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.

K

K is INTEGER. On entry with UPLO = 'U' or 'u', K specifies the number of super-diagonals of the matrix A. On entry with UPLO = 'L' or 'l', K specifies the number of sub-diagonals of the matrix A. K must satisfy 0 .le. K.

A

A is REAL array, dimension ( LDA, N ).

Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced.

The following program segment will transfer an upper triangular band matrix from conventional full matrix storage to band storage:

                 DO 20, J = 1, N
                    M = K + 1 - J
                    DO 10, I = MAX( 1, J - K ), J
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced.

The following program segment will transfer a lower triangular band matrix from conventional full matrix storage to band storage:

                 DO 20, J = 1, N
                    M = 1 - J
                    DO 10, I = J, MIN( N, J + K )
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE

Note that when DIAG = 'U' or 'u' the elements of the array A corresponding to the diagonal elements of the matrix are not referenced, but are assumed to be unity.

LDA

LDA is INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( k + 1 ).

X

X is REAL array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ).

Before entry, the incremented array X must contain the n element right-hand side vector b. On exit, X is overwritten with the solution vector x.

INCX

INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero.

👑 Author 👑

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

🔥 Further Details 🔥

Level 2 Blas routine.

-- Written on 22-October-1986.

• Jack Dongarra, Argonne National Lab.
• Jeremy Du Croz, Nag Central Office.
• Sven Hammarling, Nag Central Office.
• Richard Hanson, Sandia National Labs.

Definition at line 188 of file stbsv.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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💖 okay bestie, that’s the whole BLAS/SRC/stbsv.f(3) page! Signing off from LAPACK, Version 3.12.0 — with that 22-October-1986 date energy — and yes, it was generated automatically by Doxygen for LAPACK from the source code. Mwah! 🎀✨