double_blas_level2(3)

📦
version 3.11.0 · 2 versions
, in debian bookworm

double_blas_level2 💖 — aka the Level 2 BLAS glow-up for DOUBLE PRECISION

okay so bestie, you opened double_blas_level2(3) and it's giving a lot, but don't panic 🫶 this is just the LAPACK manual page for the double flavor of the LEVEL 2 BLAS crew — all the matrix-vector and rank-update routines, in DOUBLE PRECISION, living their best lives. ✨

NAME 🌸

double_blas_level2 — double

(yes that's literally the whole name section. iconic minimalism. no notes. 💅)

SYNOPSIS 🦋

Functions

  • subroutine dgbmv (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) — DGBMV
  • subroutine dgemv (TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) — DGEMV
  • subroutine dger (M, N, ALPHA, X, INCX, Y, INCY, A, LDA) — DGER
  • subroutine dsbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) — DSBMV
  • subroutine dspmv (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY) — DSPMV
  • subroutine dspr (UPLO, N, ALPHA, X, INCX, AP) — DSPR
  • subroutine dspr2 (UPLO, N, ALPHA, X, INCX, Y, INCY, AP) — DSPR2
  • subroutine dsymv (UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) — DSYMV
  • subroutine dsyr (UPLO, N, ALPHA, X, INCX, A, LDA) — DSYR
  • subroutine dsyr2 (UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA) — DSYR2
  • subroutine dtbmv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX) — DTBMV
  • subroutine dtbsv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX) — DTBSV
  • subroutine dtpmv (UPLO, TRANS, DIAG, N, AP, X, INCX) — DTPMV
  • subroutine dtpsv (UPLO, TRANS, DIAG, N, AP, X, INCX) — DTPSV
  • subroutine dtrmv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX) — DTRMV

Detailed Description 💙

This is the group of double LEVEL 2 BLAS routines. periodt. 🎀

Function Documentation 🔥

subroutine dgbmv

subroutine dgbmv (character TRANS, integer M, integer N, integer KL, integer
    KU, 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)

DGBMV 🌈

Purpose:

DGBMV 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 band matrix, with kl sub-diagonals and ku super-diagonals. no cap, that's the whole vibe. ✨

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.
  • KL — KL is INTEGER. On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL.
  • KU — KU is INTEGER. On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU.
  • 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 ( kl + ku + 1 ) by n part of the array A must contain the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( ku + 1 ) of the array, the first super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer a band matrix from conventional full matrix storage to band storage:
DO 20, J = 1, N
   K = KU + 1 - J
   DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
      A( K + I, J ) = matrix( I, J )
 10    CONTINUE
 20 CONTINUE
  • 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 ( kl + ku + 1 ).
  • 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, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.
  • 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.

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. 🌈

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.
  • 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.

subroutine 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)

DGER 🍓

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

…and bestie we are literally only getting started — there's so much more of this page to go. 🦋✨

  • INCX — INTEGER, bestie. On entry, INCX says what the increment is for the elements of X, and it is absolutely not allowed to be zero. Zero increment = chaos, we don't do that. 💅
  • Y — DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before you come in here, the incremented array Y has gotta contain the n element vector y. That's the vibe. ✨
  • INCY — INTEGER. On entry, INCY is the increment for the elements of Y. And same rule as its sibling: INCY must not be zero. 🚫
  • A — 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 gets overwritten by the updated matrix — so like, don't be attached to what you put in there, she's evolving. 🦋
  • 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 shortcuts, she will notice. 👑

🌸 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.

🦋 subroutine dsbmv 🦋

subroutine dsbmv (character UPLO, integer N, integer K, 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)

DSBMV

✨ Purpose ✨

Okay so DSBMV performs the matrix-vector operation

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

where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric band matrix, with k super-diagonals. Yes she's banded, yes she's symmetric, yes she ate. 💅

🎀 Parameters 🎀

  • UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the band matrix A is being supplied, as follows:
    • UPLO = 'U' or 'u' — The upper triangular part of A is being supplied.
    • UPLO = 'L' or 'l' — The lower triangular part of A is being supplied.
  • N — N is INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. (Zero is fine bestie, she can be nothing, no stress.) 🫶
  • K — K is INTEGER. On entry, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K.
  • ALPHA — ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.
  • A — A is DOUBLE PRECISION array, dimension ( LDA, N ).

Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the symmetric matrix, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced.

The following program segment will transfer the upper triangular part of a symmetric band matrix from conventional full matrix storage to band storage:

      DO 20, J = 1, N
         M = K + 1 - J
         DO 10, I = MAX( 1, J - K ), J
            A( M + I, J ) = matrix( I, J )
   10    CONTINUE
   20 CONTINUE

Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the symmetric matrix, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced.

The following program segment will transfer the lower triangular part of a symmetric band matrix from conventional full matrix storage to band storage:

      DO 20, J = 1, N
         M = 1 - J
         DO 10, I = J, MIN( N, J + K )
            A( M + I, J ) = matrix( I, J )
   10    CONTINUE
   20 CONTINUE
  • 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 ( k + 1 ).
  • X — X is DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). 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.
  • Y — Y is DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. 🦋
  • 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.

🧚 subroutine dspmv 🧚

subroutine dspmv (character UPLO, integer N, double precision ALPHA, double
    precision, dimension(*) AP, double precision, dimension(*) X, integer
    INCX, double precision BETA, double precision, dimension(*) Y, integer
    INCY)

DSPMV

✨ Purpose ✨

DSPMV performs the matrix-vector operation

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

where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form. Packed and iconic, no wasted space, she's efficient like that. 💅

🎀 Parameters 🎀

  • UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP, as follows:
    • UPLO = 'U' or 'u' — The upper triangular part of A is supplied in AP.
    • UPLO = 'L' or 'l' — The lower triangular part of A is supplied in AP.
  • 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.
  • 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 part of the symmetric 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 part of the symmetric 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. ✨

  • 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. 🚫
  • 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. Big convenience energy, honestly. 💖
  • 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. On exit, Y is overwritten by the updated vector y. 🦋
  • 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.

🌸 subroutine dspr 🌸

subroutine dspr (character UPLO, integer N, double precision ALPHA, double
    precision, dimension(*) X, integer INCX, double precision, dimension(*)
    AP)

DSPR

✨ Purpose ✨

DSPR performs the symmetric rank 1 operation

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

where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix, supplied in packed form. Rank one update, no notes, she's that girl. 👑

🎀 Parameters 🎀

  • UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP, as follows:
  • UPLO — bestie, UPLO is a CHARACTER*1. on entry it tells us whether the upper or lower triangular part of A is supplied in AP, and it's giving options:
    • UPLO = 'U' or 'u' — the upper triangular part of A is supplied in AP. 👑
    • UPLO = 'L' or 'l' — the lower triangular part of A is supplied in AP. 💅
  • N — N is INTEGER. on entry, N specifies the order of the matrix A. N must be at least zero. no cap, fr fr. 💀
  • ALPHA — ALPHA is DOUBLE PRECISION. on entry, ALPHA specifies the scalar alpha. periodt. ✨
  • 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. don't even think about setting it to zero, bestie. 🚫
  • 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 part of the symmetric 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. on exit, the array AP is overwritten by the upper triangular part of the updated matrix. before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric 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. on exit, the array AP is overwritten by the lower triangular part of the updated matrix. it's giving packed realness, iykyk. 🎀

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.

subroutine dspr2 (character UPLO, integer N, double precision ALPHA, double precision, dimension() X, integer INCX, double precision, dimension() Y, integer INCY, double precision, dimension(*) AP)

DSPR2

Purpose

DSPR2 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, supplied in packed form. slay, bestie. 💅

Parameters

  • UPLO — UPLO is CHARACTER*1. on entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows:
    • UPLO = 'U' or 'u' — the upper triangular part of A is supplied in AP.
    • UPLO = 'L' or 'l' — the lower triangular part of A is supplied in AP.
  • 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.
  • 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 part of the symmetric 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. on exit, the array AP is overwritten by the upper triangular part of the updated matrix. before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric 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. on exit, the array AP is overwritten by the lower triangular part of the updated matrix.

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.

subroutine dsymv (character UPLO, 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)

DSYMV

Purpose

DSYMV performs the matrix-vector operation

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

where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix. main character energy, fr fr. 🌟

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.
  • 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. 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.
  • 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 ).
  • 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.
  • 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. bestie, that's a time saver. ✨
  • 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. on exit, Y is overwritten by the updated vector y.
  • 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.

subroutine dsyr (character UPLO, integer N, double precision ALPHA, double precision, dimension() X, integer INCX, double precision, dimension(lda,) A, integer LDA)

DSYR

Purpose

DSYR performs the symmetric rank 1 operation

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

where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix. serving looks, 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 DOUBLE PRECISION. on entry, ALPHA specifies the scalar alpha.
  • X —

X

X is a DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. bestie, that's the whole vibe ✨

INCX

INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. like. ever. 💀

A

A is a 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.

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.

🦋 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. two vectors, one glow-up, 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. the moment ✨

X

X is a 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 a 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 a 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.

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.

🎀 subroutine dtbmv (character UPLO, character TRANS, character DIAG, integer N, integer K, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(*) X, integer INCX)

DTBMV

Purpose:

DTBMV performs one of the matrix-vector operations

x := A*x,   or   x := A**T*x,

where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals. band matrix girlies rise 🧚

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 operation to be performed as follows:

  • TRANS = 'N' or 'n' — x := A*x.
  • TRANS = 'T' or 't' — x := A**T*x.
  • TRANS = 'C' or 'c' — x := A**T*x.

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.

K

K is INTEGER. On entry with UPLO = 'U' or 'u', K specifies the number of super-diagonals of the matrix A. On entry with UPLO = 'L' or 'l', K specifies the number of sub-diagonals of the matrix A. K must satisfy 0 .le. K.

A

A is a DOUBLE PRECISION array, dimension ( LDA, N ).

Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced.

The following program segment will transfer an upper triangular band matrix from conventional full matrix storage to band storage:

DO 20, J = 1, N
   M = K + 1 - J
   DO 10, I = MAX( 1, J - K ), J
      A( M + I, J ) = matrix( I, J )
10    CONTINUE
20 CONTINUE

Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced.

The following program segment will transfer a lower triangular band matrix from conventional full matrix storage to band storage:

DO 20, J = 1, N
   M = 1 - J
   DO 10, I = J, MIN( N, J + K )
      A( M + I, J ) = matrix( I, J )
10    CONTINUE
20 CONTINUE

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

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 ( k + 1 ).

X

X is a DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the transformed vector x. glow-up complete, iconic 🔥

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.

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.

dtbsv — solving triangular band systems, she's so real for that 🦋

subroutine dtbsv (character UPLO, character TRANS, character DIAG, integer
    N, integer K, double precision, dimension(lda,*) A, integer LDA, double
    precision, dimension(*) X, integer INCX)

Purpose ✨

okay so DTBSV solves one of these systems of equations, bestie:

   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 band matrix, with ( k + 1 ) diagonals. band storage, we love to see it 💅

🚨 Important, no cap: no test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. She is not gonna hold your hand and tell you the matrix is cursed — you have to check that yourself, fr fr. 💀

Parameters 🎀

  • UPLO — 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 — 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 — 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 — INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
  • K — INTEGER. On entry with UPLO = 'U' or 'u', K specifies the number of super-diagonals of the matrix A. On entry with UPLO = 'L' or 'l', K specifies the number of sub-diagonals of the matrix A. K must satisfy 0 .le. K.
  • A — DOUBLE PRECISION array, dimension ( LDA, N ).

Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced. 🫶

The following program segment will transfer an upper triangular band matrix from conventional full matrix storage to band storage:

      DO 20, J = 1, N
         M = K + 1 - J
         DO 10, I = MAX( 1, J - K ), J
            A( M + I, J ) = matrix( I, J )
   10    CONTINUE
   20 CONTINUE

Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced. 🌸

The following program segment will transfer a lower triangular band matrix from conventional full matrix storage to band storage:

      DO 20, J = 1, N
         M = 1 - J
         DO 10, I = J, MIN( N, J + K )
            A( M + I, J ) = matrix( I, J )
   10    CONTINUE
   20 CONTINUE

Note that when DIAG = 'U' or 'u' the elements of the array A corresponding to the diagonal elements of the matrix are not referenced, but are assumed to be unity. iconic behaviour honestly ✨

  • LDA — INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( k + 1 ).
  • X — 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 — 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.

dtpmv — packed triangular matrix-vector multiply, main character energy 👑

subroutine dtpmv (character UPLO, character TRANS, character DIAG, integer
    N, double precision, dimension(*) AP, double precision, dimension(*) X,
    integer INCX)

Purpose ✨

DTPMV performs one of the matrix-vector operations

   x := A*x,   or   x := A**T*x,

where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix, supplied in packed form. no wasted space, we stan a compact queen 🎀

Parameters 🎀

  • UPLO — 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 — CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows:
    • TRANS = 'N' or 'n' → x := A*x.
    • TRANS = 'T' or 't' → x := A**T*x.
    • TRANS = 'C' or 'c' → x := A**T*x.
  • DIAG — 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 — INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
  • AP — 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 — DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the transformed vector x. 💜
  • INCX — 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.
  • 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.

dtpsv — packed triangular solve, the solver bestie 💅

subroutine dtpsv (character UPLO, character TRANS, character DIAG, integer
    N, double precision, dimension(*) AP, double precision, dimension(*) X,
    integer INCX)

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.

🚨 Heads up, bestie: no test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. she trusts you, which is honestly a lot 😭

Parameters 🎀

  • UPLO — 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 — 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 — 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 — INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.

AP

Okay so AP is a DOUBLE PRECISION array, and its dimension is at least ( ( n*( n + 1 ) )/2 ). That's the packed tea.

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. Column by column, no cap.

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. So they're just there for the vibe, not the math.

X

Next up, X is a 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. So it's a total glow-up.

INCX

And INCX is INTEGER.

On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Periodt.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

These are the icons who wrote this, btw.

✨ 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.

So vintage, so iconic.

🦋 dtrmv

   subroutine dtrmv (character UPLO, character TRANS, character DIAG, integer
       N, double precision, dimension(lda,*) A, integer LDA, double precision,
       dimension(*) X, integer INCX)

Purpose

DTRMV performs one of the matrix-vector operations

x := A*x,   or   x := A**T*x,

where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.

Basically, it's the triangular matrix-vector multiply, and it's lowkey a bop.

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 operation to be performed as follows:
    • TRANS = 'N' or 'n' x := A*x.
    • TRANS = 'T' or 't' x := A**T*x.
    • TRANS = 'C' or 'c' x := A**T*x.
  • 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.
  • 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 matrix and the strictly lower triangular part of A is not referenced.

Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced.

Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. Again, not even looking at them.
  • 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 ).
  • 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. On exit, X is overwritten with the transformed 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. 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.

👑 Author

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