her2(3)

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💖 her2(3) — Library Functions Manual 💖

okay so bestie, welcome to her2, which is literally the umbrella name for four lil BLAS routines — cher2, dsyr2, ssyr2, and zher2 — all doing that rank-2 update thing on Hermitian/symmetric matrices. the full name is literally "{he,sy}r2: Hermitian/symmetric rank-2 update" and yes, that brace notation is giving old-school C preprocessor energy, we love a naming convention 😌

✨ NAME ✨

her2 — {he,sy}r2: Hermitian/symmetric rank-2 update

🌸 SYNOPSIS 🌸

🎀 Functions 🎀

  • subroutine cher2 (uplo, n, alpha, x, incx, y, incy, a, lda) — CHER2
  • subroutine dsyr2 (uplo, n, alpha, x, incx, y, incy, a, lda) — DSYR2
  • subroutine ssyr2 (uplo, n, alpha, x, incx, y, incy, a, lda) — SSYR2
  • subroutine zher2 (uplo, n, alpha, x, incx, y, incy, a, lda) — ZHER2

🦋 Detailed Description 🦋

so like… this page is basically the BLAS level-2 gym membership for rank-2 updates. four routines, same shape of API, different precision/complexity vibes. scroll for the full docs on each one 💅

👑 Function Documentation 👑

💜 subroutine cher2 (character uplo, integer n, complex alpha, complex, dimension(*) x, integer incx, complex, dimension(*) y, integer incy, complex, dimension(lda,*) a, integer lda) 💜

CHER2

🌈 Purpose:

!>
!> CHER2  performs the hermitian rank 2 operation
!>
!>    A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
!>
!> where alpha is a scalar, x and y are n element vectors and A is an n
!> by n hermitian matrix.
!>

so yeah — note the conjg( alpha ) on the second term, that's the Hermitian part doing its little ✨conjugate✨ moment. not to be confused with the symmetric girls below, no cap 🔥

🍓 Parameters

  • UPLO
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the array A is to be referenced as
!>           follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of A
!>                                  is to be referenced.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of A
!>                                  is to be referenced.
!>
  • N
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A.
!>           N must be at least zero.
!>
  • ALPHA
!>          ALPHA is COMPLEX
!>           On entry, ALPHA specifies the scalar alpha.
!>
  • X
!>          X is COMPLEX array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCX ) ).
!>           Before entry, the incremented array X must contain the n
!>           element vector x.
!>
  • INCX
!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X. INCX must not be zero.
!>
⚠️ bestie, INCX must not be zero — that's a whole "do not do this" moment 🙈
  • Y
!>          Y is COMPLEX array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCY ) ).
!>           Before entry, the incremented array Y must contain the n
!>           element vector y.
!>
  • INCY
!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y. INCY must not be zero.
!>
⚠️ same energy: INCY must not be zero. periodt 💀
  • A
!>          A is COMPLEX array, dimension ( LDA, N )
!>           Before entry with  UPLO = 'U' or 'u', the leading n by n
!>           upper triangular part of the array A must contain the upper
!>           triangular part of the hermitian matrix and the strictly
!>           lower triangular part of A is not referenced. On exit, the
!>           upper triangular part of the array A is overwritten by the
!>           upper triangular part of the updated matrix.
!>           Before entry with UPLO = 'L' or 'l', the leading n by n
!>           lower triangular part of the array A must contain the lower
!>           triangular part of the hermitian matrix and the strictly
!>           upper triangular part of A is not referenced. On exit, the
!>           lower triangular part of the array A is overwritten by the
!>           lower triangular part of the updated matrix.
!>           Note that the imaginary parts of the diagonal elements need
!>           not be set, they are assumed to be zero, and on exit they
!>           are set to zero.
!>

the way that last bit matters 😭 — imaginary parts of the diagonal don't need to be set on entry (assumed zero), and on exit they get set to zero. so don't come for me if your diagonal's imaginary bits get tidied up 🧚

  • 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
!>           max( 1, n ).
!>

🫶 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 149 of file cher2.f.

💙 subroutine dsyr2 (character uplo, integer n, double precision alpha, double precision, dimension(*) x, integer incx, double precision, dimension(*) y, integer incy, double precision, dimension(lda,*) a, integer lda) 💙

DSYR2

🌈 Purpose:

!>
!> DSYR2  performs the symmetric rank 2 operation
!>
!>    A := alpha*x*y**T + alpha*y*x**T + A,
!>
!> where alpha is a scalar, x and y are n element vectors and A is an n
!> by n symmetric matrix.
!>

see how both terms are just alpha? no conjg in sight — that's the symmetric difference, iykyk 🦋

🍓 Parameters

  • UPLO
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the array A is to be referenced as
!>           follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of A
!>                                  is to be referenced.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of A
!>                                  is to be referenced.
!>
  • N
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A.
!>           N must be at least zero.
!>
  • ALPHA
!>          ALPHA is DOUBLE PRECISION.
!>           On entry, ALPHA specifies the scalar alpha.
!>
  • 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 vector x.
!>
  • INCX
!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X. INCX must not be zero.
!>
  • Y
!>          Y is DOUBLE PRECISION array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCY ) ).
!>           Before entry, the incremented array Y must contain the n
!>           element vector y.
!>
  • INCY
!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y. INCY must not be zero.
!>
  • A
!>          A is DOUBLE PRECISION array, dimension ( LDA, N )
!>           Before entry with  UPLO = 'U' or 'u', the leading n by n
!>           upper triangular part of the array A must contain the upper
!>           triangular part of the symmetric matrix and the strictly
!>           lower triangular part of A is not referenced. On exit, the
!>           upper triangular part of the array A is overwritten by the
!>           upper triangular part of the updated matrix.
!>           Before entry with UPLO = 'L' or 'l', the leading n by n
!>           lower triangular part of the array A must contain the lower
!>           triangular part of the symmetric matrix and the strictly
!>           upper triangular part of A is not referenced. On exit, the
!>           lower triangular part of the array A is overwritten by the
!>           lower triangular part of the updated matrix.
!>

lowkey notice: no imaginary-diagonal note here, because symmetric means real. the vibes are simpler 💀

  • 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
!>           max( 1, n ).
!>

🫶 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 146 of file dsyr2.f.

💚 subroutine ssyr2 (character uplo, integer n, real alpha, real, dimension(*) x, integer incx, real, dimension(*) y, integer incy, real, dimension(lda,*) a, integer lda) 💚

SSYR2

🌈 Purpose:

!>
!> SSYR2  performs the symmetric rank 2 operation
!>
!>    A := alpha*x*y**T + alpha*y*x**T + A,
!>
!> where alpha is a scalar, x and y are n element vectors and A is an n
!> by n symmetric matrix.
!>

literally dsyr2's single-precision twin, same exact formula, just REAL instead of DOUBLE PRECISION. slay, consistency 💅

🍓 Parameters

  • UPLO
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the upper or lower
!>           triangular part of the array A is to be referenced as
!>           follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of A
!>                                  is to be referenced.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of A
!>                                  is to be referenced.
!>
  • N
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A.
!>           N must be at least zero.
!>
  • ALPHA
!>          ALPHA is REAL
!>           On entry, ALPHA specifies the scalar alpha.
!>
  • X
!>          X is REAL array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCX ) ).
!>           Before entry, the incremented array X must contain the n
!>           element vector x.
!>
  • INCX
!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X. INCX must not be zero.
!>
  • Y
!>          Y is REAL array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCY ) ).
!>           Before entry, the incremented array Y must contain the n
!>           element vector y.
!>
  • INCY
!>          INCY is INTEGER
!>           On entry, INCY specifies the increment for the elements of
!>           Y. INCY must not be zero.
!>
  • A

(and bestie, this is exactly where part 1 runs out of page — the A array description, plus LDA, the authors, the further details, the zher2 whole section, and everything after are coming at you in part 2 🫶 don't go anywhere)

  • A — okay so A is a REAL array, dimension ( LDA, N ). 💖 Before you come in with UPLO = 'U' or 'u', the leading n by n upper triangular part of A has to contain the upper triangular part of the symmetric matrix, and the strictly lower triangular part of A is literally not referenced, periodt. On exit, the upper triangular part of A gets overwritten by the upper triangular part of the updated matrix. Same energy for UPLO = 'L' or 'l': the leading n by n lower triangular part of A must contain the lower triangular part of the symmetric matrix, the strictly upper triangular part is not referenced, and on exit the lower triangular part is overwritten by the lower triangular part of the updated matrix. 🦋
  • 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 max( 1, n ). No cap, just facts. 💅

👑 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 146 of file ssyr2.f. 🎀

subroutine zher2

subroutine zher2 (character uplo, integer n, complex*16 alpha, complex*16,
    dimension(*) x, integer incx, complex*16, dimension(*) y, integer incy,
    complex*16, dimension(lda,*) a, integer lda)

Okay bestie, this is the ZHER2 glow-up and she is iconic. 💜

🦋 Purpose:

ZHER2 performs the hermitian rank 2 operation fortran A := alpha*x*y**H + conjg( alpha )*y*x**H + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix.

🌸 Parameters

  • UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced, and the options are giving:
    • UPLO = 'U' or 'u' — only the upper triangular part of A is to be referenced. ✨
    • UPLO = 'L' or 'l' — only the lower triangular part of A is to be referenced. ✨
  • N — N is INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Lowkey non-negotiable. 💀
  • ALPHA — ALPHA is COMPLEX*16. On entry, ALPHA specifies the scalar alpha. Main character scalar, honestly. 👑
  • 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 vector x. 🫶
  • INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Fr fr, not zero. 🚫
  • Y — Y is COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. 🍓
  • INCY — INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Again: not zero, bestie. 💅
  • A — A is COMPLEX*16 array, dimension ( LDA, N ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the hermitian matrix, and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the hermitian matrix, and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix. 🎀 And a very important lil note: the imaginary parts of the diagonal elements need not be set — they are assumed to be zero, and on exit they are set to zero. The way that detail matters, iykyk. 😭
  • 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 max( 1, n ). Same rule as before, no exceptions. 🌈

👑 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 149 of file zher2.f. 💖

🧚 Author

Generated automatically by Doxygen for LAPACK from the source code.

And that's the whole vibe check, bestie — LAPACK Version 3.12.0, page her2(3), signed, sealed, and slaying. 💅🎀✨

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