BLAS/SRC/ctbsv.f(3)

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🌈 BLAS/SRC/ctbsv.f(3) — the CTBSV page, bestie 🌈

Okay so this is the BLAS/SRC/ctbsv.f(3) page from the Library Functions Manual, and it's giving “one BLAS routine, full documentation, no skips.” 💅

🌸 NAME 🌸

BLAS/SRC/ctbsv.f

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine ctbsv (uplo, trans, diag, n, k, a, lda, x, incx)
    CTBSV

💖 Function/Subroutine Documentation 💖

subroutine ctbsv (character uplo, character trans, character diag, integer
    n, integer k, complex, dimension(lda,*) a, integer lda, complex,
    dimension(*) x, integer incx)
    CTBSV

🎯 Purpose

The way that CTBSV is out here solving one of the systems of equations, periodt:

A*x = b,   or   A**T*x = b,   or   A**H*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. No cap.

🚨 Not me being the responsible bestie: no test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. fr fr.

🌟 Parameters 🌟

UPLO

UPLO is CHARACTER*1, lowkey the matrix-shape vibe check.

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, and it picks which equation we're solving. 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**H*x = b.

DIAG

DIAG is CHARACTER*1, the unit-triangular check. 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. main character dimension energy, honestly.

K

K is INTEGER, the diagonal-count bestie.

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 COMPLEX array, dimension ( LDA, N ) — the storage plot twist.

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 COMPLEX 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 ctbsv.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

Okay bestie, that's the whole page — source/version sign-off: LAPACK Version 3.12.0, and the footer's page stamp is BLAS/SRC/ctbsv.f(3) (Doxygen-generated, and no extra calendar date is shown). 💖✨🎀

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