ZTBSV(3)

💖 Library Functions Manual 💖

okay so bestie, welcome to the Library Functions Manual page for /home/abui...SRC/ztbsv.f — yes that whole path is the name, and we're about to make it make sense. ✨

🌸 NAME 🌸

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

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine ZTBSV (uplo, trans, diag, n, k, a, lda, x, incx) — this is the whole vibe, bestie. It's the ZTBSV subroutine and it's here to solve your triangular band system. 💅

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📓 Function/Subroutine Documentation 📓

here's the full signature, character for character:

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 — yes that's the name again, slay. 👑

🎯 Purpose 🎯

okay so here's the tea: ZTBSV solves one of these 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.

⚠️ bestie listen: no test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. so do your vibe check before you call it, 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*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.

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.

👑 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 ztbsv.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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