BLAS/SRC/ztbsv.f(3)

✨ ztbsv ✨ (the BLAS/SRC/ztbsv.f page, section 3 of the manual, bestie)

okay so welcome to the glow-up of BLAS/SRC/ztbsv.f 💅 this is a LAPACK/BLAS situation and honestly? it ate.

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🌸 NAME 🌸

BLAS/SRC/ztbsv.f — that's the file, that's the vibe 🦋

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🎀 SYNOPSIS 🎀

Functions/Subroutines

• subroutine ztbsv (uplo, trans, diag, n, k, a, lda, x, incx) — ZTBSV, the main character 👑

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💖 Function/Subroutine Documentation 💖

subroutine ztbsv (character uplo, character trans, character diag, integer n, integer k, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx)

ZTBSV 🫶

⭐ Purpose

ZTBSV solves one of the systems of equations

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.

🚨 not me telling you this but like... seriously: no test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. it's giving "you gotta do your own homework first" 😭

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🌈 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*16 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. no cap.

• 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*16 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.

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👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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🔥 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 ztbsv.f.

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💜 Author

Generated automatically by Doxygen for LAPACK from the source code.

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that's it bestie, you understood the whole thing, iconic behavior honestly 🌈💅

Version 3.12.0 — Tue Nov 28 2023 12:08:41 — BLAS/SRC/ztbsv.f(3) 🎀 bye pookie, go solve something symmetric 💖