hesv(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

okay so welcome to hesv(3) from the Library Functions Manual — this is the bestie-coded page for hesv - {he,sy}sv: rook (v1) 💅. It’s giving linear algebra but make it group chat. No cap, we’re keeping every deet.

💖 NAME 💖

hesv — {he,sy}sv: rook (v1) ✨

✨ SYNOPSIS ✨

🌸 Functions 🌸

  • subroutine chesv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — CHESV computes the solution to system of linear equations A * X = B for HE matrices 💖
  • subroutine csysv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — CSYSV computes the solution to system of linear equations A * X = B for SY matrices ✨
  • subroutine dsysv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — DSYSV computes the solution to system of linear equations A * X = B for SY matrices 🦋
  • subroutine ssysv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — SSYSV computes the solution to system of linear equations A * X = B for SY matrices 🌸
  • subroutine zhesv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — ZHESV computes the solution to system of linear equations A * X = B for HE matrices 🔥
  • subroutine zsysv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — ZSYSV computes the solution to system of linear equations A * X = B for SY matrices 👑

🌈 Detailed Description 🌈

(the original leaves this section literally empty — no deets, no drama, just vibes)

🔥 Function Documentation 🔥

🧮 chesv — Hermitian bestie 🧮

subroutine chesv (character uplo, integer n, integer nrhs, complex,
     dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,
     complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * )
     work, integer lwork, integer info)

CHESV computes the solution to system of linear equations A * X = B for HE matrices. 🫶

🎯 Purpose 🎯

okay so CHESV solves a complex system of linear equations:

A * X = B

where A is an N-by-N Hermitian matrix, and X and B are N-by-NRHS matrices.

It uses the diagonal pivoting method to factor A as:

A = U * D * U**H,  if UPLO = 'U', or
A = L * D * L**H,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. Then the factored form of A is used to solve the system of equations A * X = B. ✨

🎀 Parameters 🎀

  • UPLO — UPLO is CHARACTER*1. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
  • N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by CHETRF. 💜
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D, as determined by CHETRF. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. 🔥
  • B — B is COMPLEX array, dimension (LDB,NRHS). On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. 🦋
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 💅
  • LWORK — LWORK is INTEGER. The length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for CHETRF. for LWORK < N, TRS will be done with Level BLAS 2; for LWORK >= N, TRS will be done with Level BLAS 3. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 🌸
  • INFO — INFO is INTEGER. = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value; > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed. 💀

👑 Author 👑

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

Definition at line 169 of file chesv.f.

🧚 csysv — symmetric slay 🧚

subroutine csysv (character uplo, integer n, integer nrhs, complex,
     dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,
     complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * )
     work, integer lwork, integer info)

CSYSV computes the solution to system of linear equations A * X = B for SY matrices. 🫶

🎯 Purpose 🎯

CSYSV solves a complex system of linear equations:

A * X = B

where A is an N-by-N symmetric matrix, and X and B are N-by-NRHS matrices.

It uses the diagonal pivoting method to factor A as:

A = U * D * U**T,  if UPLO = 'U', or
A = L * D * L**T,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B. ✨

🎀 Parameters 🎀

  • UPLO — UPLO is CHARACTER*1. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
  • N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by CSYTRF. 💜
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D, as determined by CSYTRF. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. 🔥
  • B — B is COMPLEX array, dimension (LDB,NRHS). On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. 🦋
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 💅
  • LWORK — LWORK is INTEGER. The length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for CSYTRF. for LWORK < N, TRS will be done with Level BLAS 2; for LWORK >= N, TRS will be done with Level BLAS 3. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 🌸
  • INFO — INFO is INTEGER. (the source part 1 cuts off right here — part 2 has the rest of the INFO deets, bestie!)
  • INFO — INFO is INTEGER, the receipts on how it all went 📋
    • = 0: successful exit — we ate and left no crumbs ✨
    • < 0: if INFO = -i, the i-th argument had an illegal value (so like… you passed me something cursed 💀)
    • > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed. bestie, it's giving dead end 😭

Author

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

Definition at line 169 of file csysv.f.

🦋 subroutine dsysv 💜

subroutine dsysv (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer lwork, integer info)

DSYSV computes the solution to system of linear equations A * X = B for SY matrices — that's the whole vibe, honestly 👑

Purpose:

okay so, DSYSV computes the solution to a real system of linear equations

A * X = B,

where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices. no cap, that's it 🌸

The diagonal pivoting method is used to factor A as

A = U * D * U**T,  if UPLO = 'U', or
A = L * D * L**T,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B. literally factorize then solve, iconic behaviour 🫶

Parameters

  • UPLO — UPLO is CHARACTER*1, aka which triangle are we even talking about 🎀
    • = 'U': Upper triangle of A is stored
    • = 'L': Lower triangle of A is stored
  • N — N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0. (zero is allowed bestie, it's a valid vibe)
  • NRHS — NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N) 💖 On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. (translation: we read one triangle and ghost the other one entirely 🙈)

On exit, if INFO = 0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by DSYTRF. she's a whole new matrix now ✨

  • LDA — LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). respect the boundary fr fr
  • IPIV — IPIV is INTEGER array, dimension (N) 🍓 Details of the interchanges and the block structure of D, as determined by DSYTRF. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. negative means 2-by-2 block, that's the whole tell 😌
  • B — B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. she literally transforms in place, main character energy 💅
  • LDB — LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
  • WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. (yes, it puts the answer in slot one, sneaky but cute 🧚)
  • LWORK — LWORK is INTEGER The length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for DSYTRF.

for LWORK < N, TRS will be done with Level BLAS 2 for LWORK >= N, TRS will be done with Level BLAS 3

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. lowkey my fave hack — ask for the size before you commit, that's just good boundaries 🔥

  • INFO — INFO is INTEGER
    • = 0: successful exit ✨
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed. like… the math said no 😭

Author

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

Definition at line 169 of file dsysv.f.

🌈 subroutine ssysv 🎀

subroutine ssysv (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info)

SSYSV computes the solution to system of linear equations A * X = B for SY matrices — same plot as dsysv but she's single precision, we love a sibling 💜

Purpose:

SSYSV computes the solution to a real system of linear equations

A * X = B,

where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices. 🦋

The diagonal pivoting method is used to factor A as

A = U * D * U**T,  if UPLO = 'U', or
A = L * D * L**T,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B. same recipe, different dtype, periodt 🫶

Parameters

  • UPLO — UPLO is CHARACTER*1
    • = 'U': Upper triangle of A is stored
    • = 'L': Lower triangle of A is stored
  • N — N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • NRHS — NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • A — A is REAL array, dimension (LDA,N) 🌸 On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, if INFO = 0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by SSYTRF. 🌟

  • LDA — LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — IPIV is INTEGER array, dimension (N) 💀 Details of the interchanges and the block structure of D, as determined by SSYTRF. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. iykyk 🤫
  • B — B is REAL array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. the glow-up is real 💅
  • LDB — LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
  • WORK — WORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 🧚
  • LWORK — LWORK is INTEGER The length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for SSYTRF.

for LWORK < N, TRS will be done with Level BLAS 2 for LWORK >= N, TRS will be done with Level BLAS 3

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 🍓

  • INFO — INFO is INTEGER
    • = 0: successful exit 👑
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed. 😭

Author

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

Definition at line 169 of file ssysv.f.

subroutine zhesv

subroutine zhesv (character uplo, integer n, integer nrhs, complex*16,
    dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,
    complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( *
    ) work, integer lwork, integer info)

ZHESV computes the solution to system of linear equations A * X = B for HE matrices

🎯 Purpose

Okay so ZHESV is here to solve a complex system of linear equations like:

A * X = B,

where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS matrices.

It uses the diagonal pivoting method to factor A as:

A = U * D * U**H,  if UPLO = 'U', or
A = L * D * L**H,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. Then it uses that factored form to solve the system of equations A * X = B. Slay.

📋 Parameters

  • UPLO — CHARACTER*1. It's literally telling you which triangle of A is stored: 'U' means the upper triangle of A is stored; 'L' means the lower triangle of A is stored.
  • N — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • A — COMPLEX*16 array, dimension (LDA,N). On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by ZHETRF.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D, as determined by ZHETRF. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
  • B — COMPLEX*16 array, dimension (LDB,NRHS). On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
  • LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • WORK — COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  • LWORK — INTEGER. The length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for ZHETRF. For LWORK < N, TRS will be done with Level BLAS 2; for LWORK >= N, TRS will be done with Level BLAS 3. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
  • INFO — INTEGER. Exit status: = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value; > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.

👑 Author

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

Definition at line 169 of file zhesv.f.

subroutine zsysv

subroutine zsysv (character uplo, integer n, integer nrhs, complex*16,
    dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,
    complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( *
    ) work, integer lwork, integer info)

ZSYSV computes the solution to system of linear equations A * X = B for SY matrices

🎯 Purpose

Okay so ZSYSV is here to solve a complex system of linear equations like:

A * X = B,

where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices.

It uses the diagonal pivoting method to factor A as:

A = U * D * U**T,  if UPLO = 'U', or
A = L * D * L**T,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. Then it uses that factored form to solve the system of equations A * X = B. Periodt.

📋 Parameters

  • UPLO — CHARACTER*1. It's literally telling you which triangle of A is stored: 'U' means the upper triangle of A is stored; 'L' means the lower triangle of A is stored.
  • N — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • A — COMPLEX*16 array, dimension (LDA,N). On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by ZSYTRF.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D, as determined by ZSYTRF. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
  • B — COMPLEX*16 array, dimension (LDB,NRHS). On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
  • LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • WORK — COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  • LWORK — INTEGER. The length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for ZSYTRF. For LWORK < N, TRS will be done with Level BLAS 2; for LWORK >= N, TRS will be done with Level BLAS 3. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
  • INFO — INTEGER. Exit status: = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value; > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.

👑 Author

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

Definition at line 169 of file zsysv.f.

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