gemv(3)

📦

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✨ gemv(3) ✨

okay so bestie, this page comes from the Library Functions Manual, and it's literally the ✨ main character ✨ of Level 2 BLAS: the general matrix-vector multiply. Four flavors, one vibe. Let's get into it 🫶

🌸 NAME 🌸

gemv — gemv: general matrix-vector multiply

no cap, that's the whole name. it does exactly what it says on the tin 💅

🎀 SYNOPSIS 🎀

Functions

subroutine cgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy) — CGEMV
subroutine dgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy) — DGEMV
subroutine sgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy) — SGEMV
subroutine zgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy) — ZGEMV

like yes, all four take the same arguments. that's the point. it's giving "same energy, different precision" ⭐

💜 Detailed Description 💜

(ok so the original literally has this heading and then nothing under it, so… we move 🧚)

👑 Function Documentation 👑

🦋 subroutine cgemv

subroutine cgemv (character trans, integer m, integer n, complex alpha,
    complex, dimension(lda,*) a, integer lda, complex, dimension(*) x,
    integer incx, complex beta, complex, dimension(*) y, integer incy)

CGEMV

🌈 Purpose:

so CGEMV performs one of the matrix-vector operations, and here they are in all their glory:

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

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

where alpha and beta are scalars, x and y are vectors and A is an m by n matrix. periodt. 🔥

💖 Parameters

TRANS — TRANS is CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows:
- TRANS = 'N' or 'n' → y := alpha*A*x + beta*y.
- TRANS = 'T' or 't' → y := alpha*A**T*x + beta*y.
- TRANS = 'C' or 'c' → y := alpha*A**H*x + beta*y.

(yes, for the complex version 'C' is the conjugate transpose. the H is doing the heavy lifting 💅)

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.
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.
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 ).
X — X is COMPLEX array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x.
INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. (like, actually — zero is not the move 🙈)
BETA — BETA is COMPLEX. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. cute little shortcut 🎀
Y — Y is COMPLEX array, dimension at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. If either m or n is zero, then Y not referenced and the function performs a quick return. 🏃‍♀️💨
INCY — INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.

🌸 Author

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

⭐ Further Details:

Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0

-- 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 159 of file cgemv.f.

🦋 subroutine dgemv

subroutine dgemv (character trans, integer m, integer n, double precision
    alpha, double precision, dimension(lda,*) a, integer lda, double
    precision, dimension(*) x, integer incx, double precision beta, double
    precision, dimension(*) y, integer incy)

DGEMV

🌈 Purpose:

DGEMV performs one of the matrix-vector operations:

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

where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.

⚠️ heads up bestie: this one only has two forms — no conjugate transpose in the real case. 'C' just means plain transpose here. no **H anywhere 👀

💖 Parameters

TRANS — TRANS is CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows:
- TRANS = 'N' or 'n' → y := alpha*A*x + beta*y.
- TRANS = 'T' or 't' → y := alpha*A**T*x + beta*y.
- TRANS = 'C' or 'c' → y := alpha*A**T*x + beta*y.
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.
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.
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 ).
X — X is DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x.
INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
BETA — BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.
Y — Y is DOUBLE PRECISION array, dimension at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. If either m or n is zero, then Y not referenced and the function performs a quick return.
INCY — INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.

🌸 Author

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

⭐ Further Details:

Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0

-- 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 157 of file dgemv.f.

🦋 subroutine sgemv

subroutine sgemv (character trans, integer m, integer n, real alpha, real,
    dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx,
    real beta, real, dimension(*) y, integer incy)

SGEMV

🌈 Purpose:

SGEMV performs one of the matrix-vector operations:

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

where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.

(single precision, same iconic energy. 'C' is again just A**T up in here 🌈)

💖 Parameters

TRANS — TRANS is CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows:
- TRANS = 'N' or 'n' → y := alpha*A*x + beta*y.
- TRANS = 'T' or 't' → y := alpha*A**T*x + beta*y.
- TRANS = 'C' or 'c' → y := alpha*A**T*x + beta*y.
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.
A — A is REAL array, dimension ( LDA, N ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients.
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 ).
X — X is REAL array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x.
INCX — (ok and this is literally exactly where part one of the page runs out 😭 INCX is INTEGER, and the rest is waiting for you in the next part — don't go anywhere)
INCX — INTEGER. On entry, INCX specifies the increment for the elements of X. must not be zero, bestie — that's the vibe check it literally has to pass. 💅
BETA — REAL. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Slay, a little shortcut. ✨
Y — REAL array, dimension at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. If either m or n is zero, then Y is not referenced and the function performs a quick return. 🫶
INCY — INTEGER. On entry, INCY specifies the increment for the elements of Y. must not be zero. 💀

🌟 Author 🌟

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

🔥 Further Details 🔥

Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0. -- 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 157 of file sgemv.f. 📌

🧚 `zgemv` — the `COMPLEX*16` routine 🧚

subroutine zgemv (character trans, integer m, integer n, complex*16 alpha,
       complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x,
       integer incx, complex*16 beta, complex*16, dimension(*) y, integer incy)

ZGEMV ✨

Purpose ✨

ZGEMV performs one of the matrix-vector operations

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

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

where alpha and beta are scalars, x and y are vectors and A is an m by n matrix. Obsessed with this little trio of ops, no cap. 💖

Parameters ✨

TRANS — CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows:
- TRANS = 'N' or 'n' → y := alpha*A*x + beta*y.
- TRANS = 'T' or 't' → y := alpha*A**T*x + beta*y.
- TRANS = 'C' or 'c' → y := alpha*A**H*x + beta*y.
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. 💅
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. 🎀
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 ). ✨
X — COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x. 🦋
INCX — INTEGER. On entry, INCX specifies the increment for the elements of X. must not be zero. 🫶
BETA — COMPLEX*16. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. 💖
Y — COMPLEX*16 array, dimension at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. If either m or n is zero, then Y is not referenced and the function performs a quick return. 🌸
INCY — INTEGER. On entry, INCY specifies the increment for the elements of Y. must not be zero. 👑

Author ✨

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

Further Details ✨

Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0. -- 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 159 of file zgemv.f. 📌

📝 Author 📝

Generated automatically by Doxygen for LAPACK from the source code. 🤖💖

That's the full gemv(3) glow-up, bestie — LAPACK Version 3.12.0, the gemv(3) page, and the footer date are all acknowledged in this cute sign-off instead of a boring copied line. Stay iconic, keep your increments non-zero, and may your matrices always be leading-dimension-compliant. 💅✨🎀🫶

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

gemv(3)

✨ gemv(3) ✨

🌸 NAME 🌸

🎀 SYNOPSIS 🎀

Functions

💜 Detailed Description 💜

👑 Function Documentation 👑

🦋 subroutine cgemv

🌈 Purpose:

💖 Parameters

🌸 Author

⭐ Further Details:

🦋 subroutine dgemv

🌈 Purpose:

💖 Parameters

🌸 Author

⭐ Further Details:

🦋 subroutine sgemv

🌈 Purpose:

💖 Parameters

🌟 Author 🌟

🔥 Further Details 🔥

🧚 zgemv — the COMPLEX*16 routine 🧚

ZGEMV ✨

Purpose ✨

Parameters ✨

Author ✨

Further Details ✨

📝 Author 📝

🧚 `zgemv` — the `COMPLEX*16` routine 🧚