tpsv(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

🌸 tpsv(3) 🌸

okay so this is tpsv(3) from the Library Functions Manual, and bestie, it's a whole family of routines — ctpsv, dtpsv, stpsv, ztpsv — all doing the same iconic thing in different precisions. It's giving "one job, four outfits" 💅

✨ NAME ✨

tpsv — tpsv: triangular matrix-vector solve

like, that's literally it. triangular matrix, vector, solve, slay 🎀

🦋 SYNOPSIS 🦋

💖 Functions 💖

  • subroutine ctpsv (uplo, trans, diag, n, ap, x, incx) — CTPSV
  • subroutine dtpsv (uplo, trans, diag, n, ap, x, incx) — DTPSV
  • subroutine stpsv (uplo, trans, diag, n, ap, x, incx) — STPSV
  • subroutine ztpsv (uplo, trans, diag, n, ap, x, incx) — ZTPSV

🌈 Detailed Description 🌈

no cap, the whole thing is just the four function docs below. pick your precision, live your truth ✨

👑 Function Documentation 👑

🫶 subroutine ctpsv (character uplo, character trans, character diag, integer n, complex, dimension(*) ap, complex, dimension(*) x, integer incx) 🫶

CTPSV

🌸 Purpose 🌸

!>
!> CTPSV  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 matrix, supplied in packed form.
!>
!> No test for singularity or near-singularity is included in this
!> routine. Such tests must be performed before calling this routine.
!>

so real talk: it solves A*x = b, 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 matrix, supplied in packed form.

🚨 big mood warning: there is no test for singularity or near-singularity in this routine. none. zero. you gotta do those checks yourself before you call it, bestie. this thing will not warn you 😭

🌸 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.
  • AP — AP is COMPLEX array, dimension at least ( ( n*( n + 1 ) )/2 ).

Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on.

Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on.

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

  • 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. so like, your input becomes your output, no extra storage era 💅

  • 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.
!>

a Level 2 BLAS routine, written on 22-October-1986 by Jack Dongarra (Argonne National Lab), Jeremy Du Croz (Nag Central Office), Sven Hammarling (Nag Central Office) and Richard Hanson (Sandia National Labs). literal legends, we stan 🫡

Definition at line 143 of file ctpsv.f.

🦋 subroutine dtpsv (character uplo, character trans, character diag, integer n, double precision, dimension(*) ap, double precision, dimension(*) x, integer incx) 🦋

DTPSV

🌸 Purpose 🌸

!>
!> DTPSV  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 matrix, supplied in packed form.
!>
!> No test for singularity or near-singularity is included in this
!> routine. Such tests must be performed before calling this routine.
!>

double precision twin of ctpsv 💜 solves A*x = b or A**T*x = b, same deal: b and x are n element vectors, A is n by n unit or non-unit, upper or lower triangular, supplied in packed form.

🚨 again, no singularity check in here. do your own tests before calling, or you're on your own 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**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.
  • AP — AP is DOUBLE PRECISION array, dimension at least ( ( n*( n + 1 ) )/2 ).

Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on.

Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on.

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

  • X — X is DOUBLE PRECISION 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.
!>

Level 2 BLAS routine, written on 22-October-1986 by Jack Dongarra (Argonne National Lab), Jeremy Du Croz (Nag Central Office), Sven Hammarling (Nag Central Office), Richard Hanson (Sandia National Labs). same iconic lineup 💖

Definition at line 143 of file dtpsv.f.

⭐ subroutine stpsv (character uplo, character trans, character diag, integer n, real, dimension(*) ap, real, dimension(*) x, integer incx) ⭐

STPSV

🌸 Purpose 🌸

!>
!> STPSV  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 matrix, supplied in packed form.
!>
!> No test for singularity or near-singularity is included in this
!> routine. Such tests must be performed before calling this routine.
!>

the single-precision one 🍓 solves A*x = b or A**T*x = b — b and x are n element vectors, A is n by n unit or non-unit, upper or lower triangular, supplied in packed form.

🚨 same disclaimer, same energy: no singularity or near-singularity testing lives in here. run those tests before you call this routine, bestie 😭

🌸 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.
  • AP — (…and we're picking this back up in part 2, bestie 💅)

AP 🌸

AP is a REAL array, dimension at least ( ( n*( n + 1 ) )/2 ).

Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on.

Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on.

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

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 143 of file stpsv.f.

subroutine ztpsv 💜

subroutine ztpsv (character uplo, character trans, character diag, integer n, complex*16, dimension(*) ap, complex*16, dimension(*) x, integer incx)

ZTPSV — yes bestie, the COMPLEX*16 sibling is here. 👑

Purpose 🎯

ZTPSV 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 matrix, supplied in packed form.

No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. 😭

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.

AP

AP is COMPLEX*16 array, dimension at least ( ( n*( n + 1 ) )/2 ).

Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on.

Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on.

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

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 143 of file ztpsv.f.

Author 🫶 (the meta one 👀)

Generated automatically by Doxygen for LAPACK from the source code.

Okay bestie, that’s the whole tea ☕: LAPACK Version 3.12.0, footer vibe tpsv(3) — signed off with love and packed triangular realness. 💖

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