lauum(3)

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version 3.12.1 · 9 versions
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okay bestie, welcome to lauum(3) from the LAPACK Library Functions Manual — the page for the triangular multiply glow-up U^H U. It's giving four subroutines, one iconic blocked-algorithm vibe, and absolutely zero chill about overwriting your matrix. 💅✨

🌸 NAME 🌸

lauum - lauum: triangular multiply: U^H U

🌈 SYNOPSIS 🌈

Functions

  • subroutine clauum (uplo, n, a, lda, info) — CLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).
  • subroutine dlauum (uplo, n, a, lda, info) — DLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).
  • subroutine slauum (uplo, n, a, lda, info) — SLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).
  • subroutine zlauum (uplo, n, a, lda, info) — ZLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).

✨ DETAILED DESCRIPTION ✨

lowkey, this section is just the vibe check before the main character energy: the real details are in Function Documentation below. The name already told you the assignment — lauum is the triangular multiply U^H U — and the four precision-besties are waiting for you. 🫶

🧚 FUNCTION DOCUMENTATION 🧚

💖 subroutine clauum

subroutine clauum (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer info)

Purpose

okay so CLAUUM computes the product U * U**H or L**H * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. 💖

  • If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A.
  • If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A.
  • This is the blocked form of the algorithm, calling Level 3 BLAS. 🔥

Parameters

  • UPLO — UPLO is CHARACTER*1; specifies whether the triangular factor stored in the array A is upper or lower triangular: = 'U': Upper triangular; = 'L': Lower triangular.
  • N — N is INTEGER; the order of the triangular factor U or L. N >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). On entry, the triangular factor U or L. On exit, if UPLO = 'U', the upper triangle of A is overwritten with the upper triangle of the product U * U**H; if UPLO = 'L', the lower triangle of A is overwritten with the lower triangle of the product L**H * L.
  • LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,N).
  • INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -k, the k-th argument had an illegal value.

Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 101 of file clauum.f.

💖 subroutine dlauum

subroutine dlauum (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer info)

Purpose

DLAUUM computes the product U * U**T or L**T * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. 💜

  • If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A.
  • If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A.
  • This is the blocked form of the algorithm, calling Level 3 BLAS. 🔥

Parameters

  • UPLO — UPLO is CHARACTER*1; specifies whether the triangular factor stored in the array A is upper or lower triangular: = 'U': Upper triangular; = 'L': Lower triangular.
  • N — N is INTEGER; the order of the triangular factor U or L. N >= 0.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the triangular factor U or L. On exit, if UPLO = 'U', the upper triangle of A is overwritten with the upper triangle of the product U * U**T; if UPLO = 'L', the lower triangle of A is overwritten with the lower triangle of the product L**T * L.
  • LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,N).
  • INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -k, the k-th argument had an illegal value.

Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 101 of file dlauum.f.

💖 subroutine slauum

subroutine slauum (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer info)

Purpose

SLAUUM computes the product U * U**T or L**T * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. 🦋

  • If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A.
  • If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A.
  • This is the blocked form of the algorithm, calling Level 3 BLAS. 🔥

Parameters

  • UPLO — UPLO is CHARACTER*1; specifies whether the triangular factor stored in the array A is upper or lower triangular: = 'U': Upper triangular; = 'L': Lower triangular.
  • N — N is INTEGER; the order of the triangular factor U or L. N >= 0.
  • A — A is REAL array, dimension (LDA,N). On entry, the triangular factor U or L. On exit, if UPLO = 'U', the upper triangle of A is overwritten with the upper triangle of the product U * U**T; if UPLO = 'L', the lower triangle of A is overwritten with the lower triangle of the product L**T * L.
  • LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,N).
  • INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -k, the k-th argument had an illegal value.

Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 101 of file slauum.f.

💖 subroutine zlauum

subroutine zlauum (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer info)

Purpose

ZLAUUM computes the product U * U**H or L**H * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. 🎀

  • If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A.
  • If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A.
  • This is the blocked form of the algorithm, calling Level 3 BLAS. 🔥

Parameters

  • UPLO — UPLO is CHARACTER*1; specifies whether the triangular factor stored in the array A is upper or lower triangular: = 'U': Upper triangular; = 'L': Lower triangular.
  • N — N is INTEGER; the order of the triangular factor U or L. N >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the triangular factor U or L. On exit, if UPLO = 'U', the upper triangle of A is overwritten with the upper triangle of the product U * U**H; if UPLO = 'L', the lower triangle of A is overwritten with the lower triangle of the product L**H * L.
  • LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,N).
  • INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -k, the k-th argument had an illegal value.

Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 101 of file zlauum.f.

🫶 AUTHOR 🫶

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💖 xoxo, bestie — that's the whole lauum(3) manual page from LAPACK Version 3.12.0; the footer didn't print a date, so no date is claimed here. Slay and happy triangular multiplying. 🎀🦋

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