CTBSV(3)

🦋 CTBSV(3) — Library Functions Manual 🦋

okay bestie, this is the manual page for CTBSV(3) from the Library Functions Manual. It's giving very specific triangular band-solve energy, and we're gonna get through every detail together. No cap.

🌸 NAME 🌸

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

That's the source-file glow-up for this routine, periodt.

✨ 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 🎯

Okay so CTBSV solves one of these systems of equations, literally:

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.

⚠️ Real talk: no test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. Do that first, bestie, fr fr.

🎀 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**H*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 COMPLEX 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 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.

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