ger(3)

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version 3.12.1 · 9 versions
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🎀 ger(3) — general matrix rank-1 update 🎀

okay so bestie, welcome to ger(3) from the Library Functions Manual. This is the general matrix rank-1 update page, and the whole squad is here to update your matrix with main character energy. 💅✨

🌸 NAME 🌸

ger — ger: general matrix rank-1 update

✨ SYNOPSIS ✨

Functions 🫶

  • subroutine cgerc (m, n, alpha, x, incx, y, incy, a, lda) — CGERC
  • subroutine cgeru (m, n, alpha, x, incx, y, incy, a, lda) — CGERU
  • subroutine dger (m, n, alpha, x, incx, y, incy, a, lda) — DGER
  • subroutine sger (m, n, alpha, x, incx, y, incy, a, lda) — SGER
  • subroutine zgerc (m, n, alpha, x, incx, y, incy, a, lda) — ZGERC
  • subroutine zgeru (m, n, alpha, x, incx, y, incy, a, lda) — ZGERU

📚 DETAILED DESCRIPTION 📚

okay bestie, this is the ger family: general matrix rank-1 update. The synopsis gives you six subroutines to pick from — cgerc, cgeru, dger, sger, zgerc, and zgeru — and then the Function Documentation section breaks down the ones in this part. No cap, the whole vibe is “update A with a rank 1 operation” 💅🔥

💖 FUNCTION DOCUMENTATION 💖

🦋 cgerc — CGERC 🦋

subroutine cgerc (integer m, integer n, complex alpha, complex, dimension(*) x, integer incx, complex, dimension(*) y, integer incy, complex, dimension(lda,*) a, integer lda)

Purpose: 🎯

CGERC performs the rank 1 operation

A := alpha*x*y**H + A,

where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. 💖

Parameters 📋

  • M — M is INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. 🫶
  • N — N is INTEGER. On entry, N specifies the number of columns 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 + ( m - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m 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 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. 🙈
  • A — A is COMPLEX array, dimension ( LDA, N ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by 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, m ). 👑

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 129 of file cgerc.f. 💜

🌈 cgeru — CGERU 🌈

subroutine cgeru (integer m, integer n, complex alpha, complex, dimension(*) x, integer incx, complex, dimension(*) y, integer incy, complex, dimension(lda,*) a, integer lda)

Purpose: 🎯

CGERU performs the rank 1 operation

A := alpha*x*y**T + A,

where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. 💖

Parameters 📋

  • M — M is INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. 🫶
  • N — N is INTEGER. On entry, N specifies the number of columns 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 + ( m - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m 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 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. 🙈
  • A — A is COMPLEX array, dimension ( LDA, N ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by 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, m ). 👑

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 129 of file cgeru.f. 💜

🍓 dger — DGER 🍓

subroutine dger (integer m, integer n, double precision alpha, double precision, dimension(*) x, integer incx, double precision, dimension(*) y, integer incy, double precision, dimension(lda,*) a, integer lda)

Purpose: 🎯

DGER performs the rank 1 operation

A := alpha*x*y**T + A,

where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. 💖

Parameters 📋

  • M — M is INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. 🫶
  • N — N is INTEGER. On entry, N specifies the number of columns 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 + ( m - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m 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, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by 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, m ). 👑

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 129 of file dger.f. 💜

🧚 sger — SGER 🧚

subroutine sger (integer m, integer n, real alpha, real, dimension(*) x, integer incx, real, dimension(*) y, integer incy, real, dimension(lda,*) a, integer lda)

Purpose: 🎯

SGER performs the rank 1 operation

A := alpha*x*y**T + A,

where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. 💖

Parameters 📋

  • M — M is INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. 🫶
  • N — N is INTEGER. On entry, N specifies the number of columns 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 + ( m - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m 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 — INTEGER. On entry, INCY tells us the increment for the elements of Y. And bestie, INCY must not be zero 🚫 like fr fr, zero is not the vibe here.
  • A — REAL array, dimension ( LDA, N ). Before entry, the leading m by n part of the array A has to contain the matrix of coefficients. On exit, A gets overwritten by the updated matrix 💅 (she's not preserving your originals, she's a rank-1-update machine).
  • LDA — INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ) ✨ no negotiating on that one.

🎀 Author 🎀

The absolute legends behind this:

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

🌸 Further Details: 🌸

Level 2 Blas routine.

And the origin story, preserved exactly:

-- 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 129 of file sger.f 📍

🦋 subroutine zgerc (integer m, integer n, complex*16 alpha, complex*16, dimension() x, integer incx, complex16, dimension() y, integer incy, complex16, dimension(lda,*) a, integer lda) 🦋

Okay so this one's called ZGERC, the complex flavour 🧚 — hold onto your brain because the math is coming:

💜 Purpose:

ZGERC performs the rank 1 operation

A := alpha*x*y**H + A,

where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. Note the **H — that's the conjugate-transpose move, iykyk 💅

✨ Parameters ✨

  • M — INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero.
  • N — INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero.
  • ALPHA — COMPLEX*16. On entry, ALPHA specifies the scalar alpha. That's the main character of the operation ngl 🔥
  • X — COMPLEX*16 array, dimension at least ( 1 + ( m - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m element vector x.
  • INCX — INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero — same rule as always, don't test me 🙈
  • Y — 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 — INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Periodt 🫶
  • A — COMPLEX*16 array, dimension ( LDA, N ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by the updated matrix. She ate and left no crumbs 💀
  • LDA — INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ).

👑 Author 👑

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

🌈 Further Details: 🌈

Level 2 Blas routine.

The lore, verbatim, from way back:

-- 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 129 of file zgerc.f 📍

💖 subroutine zgeru (integer m, integer n, complex*16 alpha, complex*16, dimension() x, integer incx, complex16, dimension() y, integer incy, complex16, dimension(lda,*) a, integer lda) 💖

And last but never least, ZGERU — the unconjugated sibling 🦋 lowkey the chill one of the family.

🍓 Purpose:

ZGERU performs the rank 1 operation

A := alpha*x*y**T + A,

where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. See the **T? Plain old transpose — no conjugate, that's the whole difference between her and ZGERC bestie, that's it 💅

⭐ Parameters ⭐

  • M — INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero.
  • N — INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero.
  • ALPHA — COMPLEX*16. On entry, ALPHA specifies the scalar alpha.
  • X — COMPLEX*16 array, dimension at least ( 1 + ( m - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m element vector x.
  • INCX — INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
  • Y — 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 — INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero 🙈
  • A — COMPLEX*16 array, dimension ( LDA, N ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by the updated matrix.
  • LDA — INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ).

🧚 Author 🧚

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

💀 Further Details: 💀

Level 2 Blas routine.

Once more, with feeling — the original credits, exactly:

-- 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 129 of file zgeru.f 📍

Okay that's the whole page bestie, you made it 🫶✨ This gorgeous thing was generated automatically by Doxygen for LAPACK from the source code — no human typed it out by hand, it's giving machine-made icon behaviour 💅 And the version? LAPACK Version 3.12.0, dated to that ger(3) footer, slay 🎀 Byeee, go update some matrices 🌸

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