trsm(3)

📦
version 3.12.0 · 4 versions
, in centos-stream 10, fedora 43, fedora 44

💖 trsm(3) — LAPACK 💖

okay bestie, sit DOWN, because we're about to talk about trsm, aka the triangular matrix-matrix solve 💅✨ This is a LAPACK girlie and she is booked and busy solving matrix equations for you.

✨ NAME ✨

trsm — it's giving triangular matrix-matrix solve 🎀 no cap.

🦋 SYNOPSIS 🦋

Functions

  • subroutine ctrsm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb) — CTRSM 💜
  • subroutine dtrsm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb) — DTRSM 💜
  • subroutine strsm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb) — STRSM 💜
  • subroutine ztrsm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb) — ZTRSM 💜

🌸 Detailed Description 🌸

(like, the whole breakdown lives down here, keep scrolling bestie 🫶)

👑 Function Documentation 👑

💅 subroutine ctrsm

subroutine ctrsm (character side, character uplo, character transa,
    character diag, integer m, integer n, complex alpha, complex,
    dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer
    ldb)

CTRSM ✨

🍓 Purpose:

CTRSM solves one of the matrix equations, and yes she does it in ONE go:

op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,

where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of

op( A ) = A   or   op( A ) = A**T   or   op( A ) = A**H.

The matrix X is overwritten on B. (iconic behaviour, honestly — she does NOT ask permission, she just writes over it 💀)

🌈 Parameters

  • SIDE — SIDE is CHARACTER*1. On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows:
SIDE = 'L' or 'l'   op( A )*X = alpha*B.

SIDE = 'R' or 'r'   X*op( A ) = alpha*B.
  • UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the matrix A 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.
  • TRANSA — TRANSA is CHARACTER*1. On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows:
TRANSA = 'N' or 'n'   op( A ) = A.

TRANSA = 'T' or 't'   op( A ) = A**T.

TRANSA = 'C' or 'c'   op( A ) = A**H.
  • 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.
  • M — M is INTEGER. On entry, M specifies the number of rows of B. M must be at least zero.
  • N — N is INTEGER. On entry, N specifies the number of columns of B. N must be at least zero.
  • ALPHA — ALPHA is COMPLEX. On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry. (she's literally like "no thoughts, no setup, just vibes" when alpha is zero 😭)
  • A — A is COMPLEX array, dimension ( LDA, k ), where k is m when SIDE = 'L' or 'l' and k is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k 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 k by k 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.
  • LDA — LDA is INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ).
  • B — B is COMPLEX array, dimension ( LDB, N ). Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.
  • LDB — LDB is INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).

🌟 Author

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

💫 Further Details:

Level 3 Blas routine.

-- Written on 8-February-1989.
   Jack Dongarra, Argonne National Laboratory.
   Iain Duff, AERE Harwell.
   Jeremy Du Croz, Numerical Algorithms Group Ltd.
   Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 179 of file ctrsm.f. 📌

🧚 subroutine dtrsm

subroutine dtrsm (character side, character uplo, character transa,
    character diag, integer m, integer n, double precision alpha, double
    precision, dimension(lda,*) a, integer lda, double precision,
    dimension(ldb,*) b, integer ldb)

DTRSM ✨

🍓 Purpose:

DTRSM solves one of the matrix equations:

op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,

where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of

op( A ) = A   or   op( A ) = A**T.

The matrix X is overwritten on B. (again — no hesitation, she just does it 💅)

🌈 Parameters

  • SIDE — SIDE is CHARACTER*1. On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows:
SIDE = 'L' or 'l'   op( A )*X = alpha*B.

SIDE = 'R' or 'r'   X*op( A ) = alpha*B.
  • UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the matrix A 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.
  • TRANSA — TRANSA is CHARACTER*1. On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows:
TRANSA = 'N' or 'n'   op( A ) = A.

TRANSA = 'T' or 't'   op( A ) = A**T.

TRANSA = 'C' or 'c'   op( A ) = A**T.
  • 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.
  • M — M is INTEGER. On entry, M specifies the number of rows of B. M must be at least zero.
  • N — N is INTEGER. On entry, N specifies the number of columns of B. N must be at least zero.
  • ALPHA — ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.
  • A — A is DOUBLE PRECISION array, dimension ( LDA, k ), where k is m when SIDE = 'L' or 'l' and k is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k 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 k by k 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.
  • LDA — LDA is INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ).
  • B — B is DOUBLE PRECISION array, dimension ( LDB, N ). Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.
  • LDB — LDB is INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).

🌟 Author

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

💫 Further Details:

Level 3 Blas routine.

-- Written on 8-February-1989.
   Jack Dongarra, Argonne National Laboratory.
   Iain Duff, AERE Harwell.
   Jeremy Du Croz, Numerical Algorithms Group Ltd.
   Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 180 of file dtrsm.f. 📌

🌈 subroutine strsm

subroutine strsm (character side, character uplo, character transa,
    character diag, integer m, integer n, real alpha, real, dimension(lda,*)
    a, integer lda, real, dimension(ldb,*) b, integer ldb)

STRSM ✨

🍓 Purpose:

STRSM solves one of the matrix equations:

op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,

where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of

op( A ) = A   or   op( A ) = A**T.

The matrix X is overwritten on B. (the audacity?? love that for her 🫶)

🌈 Parameters

  • SIDE — SIDE is CHARACTER*1. On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows:
SIDE = 'L' or 'l'   op( A )*X = alpha*B.

SIDE = 'R' or 'r'   X*op( A ) = alpha*B.
  • UPLO
  • UPLO — CHARACTER*1. On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix, and it's giving triangle realness 🔺:
    • UPLO = 'U' or 'u' → A is an upper triangular matrix. ✨
    • UPLO = 'L' or 'l' → A is a lower triangular matrix. 💅
  • TRANSA — CHARACTER*1. On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication, no cap 🧮:
    • TRANSA = 'N' or 'n' → op( A ) = A.
    • TRANSA = 'T' or 't' → op( A ) = A**T.
    • TRANSA = 'C' or 'c' → op( A ) = A**T.
  • DIAG — CHARACTER*1. On entry, DIAG specifies whether or not A is unit triangular, bestie 🫶:
    • DIAG = 'U' or 'u' → A is assumed to be unit triangular.
    • DIAG = 'N' or 'n' → A is not assumed to be unit triangular.
  • M — INTEGER. On entry, M specifies the number of rows of B. M must be at least zero. 📏
  • N — INTEGER. On entry, N specifies the number of columns of B. N must be at least zero. 📐
  • ALPHA — REAL. On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry. 🔥
  • A — REAL array, dimension ( LDA, k ), where k is m when SIDE = 'L' or 'l', and k is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k 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 k by k 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. 👑
  • LDA — INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ). 📏
  • B — REAL array, dimension ( LDB, N ). Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X. 💖
  • LDB — INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ). 📐

🫶 Author

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

🔥 Further Details

Level 3 Blas routine.

-- Written on 8-February-1989.
   Jack Dongarra, Argonne National Laboratory.
   Iain Duff, AERE Harwell.
   Jeremy Du Croz, Numerical Algorithms Group Ltd.
   Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 180 of file strsm.f.

💜 ZTRSM 💜

   subroutine ztrsm (character side, character uplo, character transa,
       character diag, integer m, integer n, complex*16 alpha, complex*16,
       dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer
       ldb)

🎯 Purpose

ZTRSM solves one of the matrix equations

op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,

where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of

op( A ) = A   or   op( A ) = A**T   or   op( A ) = A**H.

The matrix X is overwritten on B.

📋 Parameters

  • SIDE — CHARACTER*1. On entry, SIDE specifies whether op( A ) appears on the left or right of X, and it's giving directional energy 🧭:
    • SIDE = 'L' or 'l' → op( A )*X = alpha*B.
    • SIDE = 'R' or 'r' → X*op( A ) = alpha*B.
  • UPLO — CHARACTER*1. On entry, UPLO specifies whether the matrix A 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.
  • TRANSA — CHARACTER*1. On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication, and it's lowkey important 🧮:
    • TRANSA = 'N' or 'n' → op( A ) = A.
    • TRANSA = 'T' or 't' → op( A ) = A**T.
    • TRANSA = 'C' or 'c' → op( A ) = A**H.
  • DIAG — CHARACTER*1. On entry, DIAG specifies whether or not A is unit triangular, fr fr:
    • DIAG = 'U' or 'u' → A is assumed to be unit triangular.
    • DIAG = 'N' or 'n' → A is not assumed to be unit triangular.
  • M — INTEGER. On entry, M specifies the number of rows of B. M must be at least zero.
  • N — INTEGER. On entry, N specifies the number of columns of B. N must be at least zero.
  • ALPHA — COMPLEX*16. On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.
  • A — COMPLEX*16 array, dimension ( LDA, k ), where k is m when SIDE = 'L' or 'l' and k is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k 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 k by k 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.
  • LDA — INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ).
  • B — COMPLEX*16 array, dimension ( LDB, N ). Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.
  • LDB — INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).

🫶 Author

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

🔥 Further Details

Level 3 Blas routine.

-- Written on 8-February-1989.
   Jack Dongarra, Argonne National Laboratory.
   Iain Duff, AERE Harwell.
   Jeremy Du Croz, Numerical Algorithms Group Ltd.
   Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 179 of file ztrsm.f.

Author

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