la_lapack_others_sm Module Reference

Extra-precise refinement helpers: condition numbers and pivot growth. More...

Functions/Subroutines
pure real(sp) function, public	la_sla_gerpvgrw (n, ncols, a, lda, af, ldaf)
	SLA_GERPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.
pure real(dp) function, public	la_dla_gerpvgrw (n, ncols, a, lda, af, ldaf)
	DLA_GERPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.
pure real(qp) function, public	la_qla_gerpvgrw (n, ncols, a, lda, af, ldaf)
	QLA_GERPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.
subroutine, public	la_sla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
	SLA_SYAMV: performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, "symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.
subroutine, public	la_dla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
	DLA_SYAMV: performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, "symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.
subroutine, public	la_qla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
	QLA_SYAMV: performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, "symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.
real(sp) function, public	la_sla_syrcond (uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)
	SLA_SYRCOND: estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C) The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number.
real(dp) function, public	la_dla_syrcond (uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)
	DLA_SYRCOND: estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C) The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number.
real(qp) function, public	la_qla_syrcond (uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)
	QLA_SYRCOND: estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C) The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number.
real(sp) function, public	la_sla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
	SLA_SYRPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.
real(dp) function, public	la_dla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
	DLA_SYRPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.
real(qp) function, public	la_qla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
	QLA_SYRPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.
pure real(sp) function, public	la_cla_gerpvgrw (n, ncols, a, lda, af, ldaf)
	CLA_GERPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.
pure real(dp) function, public	la_zla_gerpvgrw (n, ncols, a, lda, af, ldaf)
	ZLA_GERPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.
pure real(qp) function, public	la_wla_gerpvgrw (n, ncols, a, lda, af, ldaf)
	WLA_GERPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.
subroutine, public	la_cla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
	CLA_SYAMV: performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, "symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.
subroutine, public	la_zla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
	ZLA_SYAMV: performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, "symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.
subroutine, public	la_wla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
	WLA_SYAMV: performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, "symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.
real(sp) function, public	la_cla_gbrcond_c (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork)
	CLA_GBRCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector.
real(dp) function, public	la_zla_gbrcond_c (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork)
	ZLA_GBRCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
real(qp) function, public	la_wla_gbrcond_c (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork)
	WLA_GBRCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a QUAD PRECISION vector.
real(sp) function, public	la_cla_gercond_c (trans, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
	CLA_GERCOND_C: computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector.
real(dp) function, public	la_zla_gercond_c (trans, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
	ZLA_GERCOND_C: computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
real(qp) function, public	la_wla_gercond_c (trans, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
	WLA_GERCOND_C: computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a QUAD PRECISION vector.
real(sp) function, public	la_cla_hercond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
	CLA_HERCOND_C: computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector.
real(dp) function, public	la_zla_hercond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
	ZLA_HERCOND_C: computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
real(qp) function, public	la_wla_hercond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
	WLA_HERCOND_C: computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a QUAD PRECISION vector.
real(sp) function, public	la_cla_porcond_c (uplo, n, a, lda, af, ldaf, c, capply, info, work, rwork)
	CLA_PORCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector.
real(dp) function, public	la_zla_porcond_c (uplo, n, a, lda, af, ldaf, c, capply, info, work, rwork)
	ZLA_PORCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
real(qp) function, public	la_wla_porcond_c (uplo, n, a, lda, af, ldaf, c, capply, info, work, rwork)
	WLA_PORCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a QUAD PRECISION vector.
real(sp) function, public	la_cla_syrcond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
	CLA_SYRCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector.
real(dp) function, public	la_zla_syrcond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
	ZLA_SYRCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
real(qp) function, public	la_wla_syrcond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
	WLA_SYRCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a QUAD PRECISION vector.
real(sp) function, public	la_cla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
	CLA_SYRPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.
real(dp) function, public	la_zla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
	ZLA_SYRPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.
real(qp) function, public	la_wla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
	WLA_SYRPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

Detailed Description

Extra-precise refinement helpers: condition numbers and pivot growth.

Function/Subroutine Documentation

la_cla_gbrcond_c()

real(sp) function, public la_lapack_others_sm::la_cla_gbrcond_c	(	character, intent(in)	trans,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	kl,
		integer(ilp), intent(in)	ku,
		complex(sp), dimension(ldab,*), intent(in)	ab,
		integer(ilp), intent(in)	ldab,
		complex(sp), dimension(ldafb,*), intent(in)	afb,
		integer(ilp), intent(in)	ldafb,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(sp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(sp), dimension(*), intent(out)	work,
		real(sp), dimension(*), intent(out)	rwork )

CLA_GBRCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector.

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la_cla_gercond_c()

real(sp) function, public la_lapack_others_sm::la_cla_gercond_c	(	character, intent(in)	trans,
		integer(ilp), intent(in)	n,
		complex(sp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(sp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(sp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(sp), dimension(*), intent(out)	work,
		real(sp), dimension(*), intent(out)	rwork )

CLA_GERCOND_C: computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector.

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la_cla_gerpvgrw()

pure real(sp) function, public la_lapack_others_sm::la_cla_gerpvgrw	(	integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	ncols,
		complex(sp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(sp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf )

CLA_GERPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

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la_cla_hercond_c()

real(sp) function, public la_lapack_others_sm::la_cla_hercond_c	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		complex(sp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(sp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(sp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(sp), dimension(*), intent(out)	work,
		real(sp), dimension(*), intent(out)	rwork )

CLA_HERCOND_C: computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector.

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la_cla_porcond_c()

real(sp) function, public la_lapack_others_sm::la_cla_porcond_c	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		complex(sp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(sp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		real(sp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(sp), dimension(*), intent(out)	work,
		real(sp), dimension(*), intent(out)	rwork )

CLA_PORCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector.

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la_cla_syamv()

subroutine, public la_lapack_others_sm::la_cla_syamv	(	integer(ilp), intent(in)	uplo,
		integer(ilp), intent(in)	n,
		real(sp), intent(in)	alpha,
		complex(sp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(sp), dimension(*), intent(in)	x,
		integer(ilp), intent(in)	incx,
		real(sp), intent(in)	beta,
		real(sp), dimension(*), intent(inout)	y,
		integer(ilp), intent(in)	incy )

CLA_SYAMV: performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, "symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.

la_cla_syrcond_c()

real(sp) function, public la_lapack_others_sm::la_cla_syrcond_c	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		complex(sp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(sp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(sp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(sp), dimension(*), intent(out)	work,
		real(sp), dimension(*), intent(out)	rwork )

CLA_SYRCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector.

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la_cla_syrpvgrw()

real(sp) function, public la_lapack_others_sm::la_cla_syrpvgrw	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	info,
		complex(sp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(sp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(sp), dimension(*), intent(out)	work )

CLA_SYRPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

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la_dla_gerpvgrw()

pure real(dp) function, public la_lapack_others_sm::la_dla_gerpvgrw	(	integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	ncols,
		real(dp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		real(dp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf )

DLA_GERPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

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la_dla_syamv()

subroutine, public la_lapack_others_sm::la_dla_syamv	(	integer(ilp), intent(in)	uplo,
		integer(ilp), intent(in)	n,
		real(dp), intent(in)	alpha,
		real(dp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		real(dp), dimension(*), intent(in)	x,
		integer(ilp), intent(in)	incx,
		real(dp), intent(in)	beta,
		real(dp), dimension(*), intent(inout)	y,
		integer(ilp), intent(in)	incy )

DLA_SYAMV: performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, "symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.

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la_dla_syrcond()

real(dp) function, public la_lapack_others_sm::la_dla_syrcond	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		real(dp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		real(dp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		integer(ilp), intent(in)	cmode,
		real(dp), dimension(*), intent(in)	c,
		integer(ilp), intent(out)	info,
		real(dp), dimension(*), intent(out)	work,
		integer(ilp), dimension(*), intent(out)	iwork )

DLA_SYRCOND: estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C) The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number.

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la_dla_syrpvgrw()

real(dp) function, public la_lapack_others_sm::la_dla_syrpvgrw	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	info,
		real(dp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		real(dp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(dp), dimension(*), intent(out)	work )

DLA_SYRPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

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la_qla_gerpvgrw()

pure real(qp) function, public la_lapack_others_sm::la_qla_gerpvgrw	(	integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	ncols,
		real(qp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		real(qp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf )

QLA_GERPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

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la_qla_syamv()

subroutine, public la_lapack_others_sm::la_qla_syamv	(	integer(ilp), intent(in)	uplo,
		integer(ilp), intent(in)	n,
		real(qp), intent(in)	alpha,
		real(qp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		real(qp), dimension(*), intent(in)	x,
		integer(ilp), intent(in)	incx,
		real(qp), intent(in)	beta,
		real(qp), dimension(*), intent(inout)	y,
		integer(ilp), intent(in)	incy )

QLA_SYAMV: performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, "symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.

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la_qla_syrcond()

real(qp) function, public la_lapack_others_sm::la_qla_syrcond	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		real(qp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		real(qp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		integer(ilp), intent(in)	cmode,
		real(qp), dimension(*), intent(in)	c,
		integer(ilp), intent(out)	info,
		real(qp), dimension(*), intent(out)	work,
		integer(ilp), dimension(*), intent(out)	iwork )

QLA_SYRCOND: estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C) The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number.

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la_qla_syrpvgrw()

real(qp) function, public la_lapack_others_sm::la_qla_syrpvgrw	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	info,
		real(qp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		real(qp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(qp), dimension(*), intent(out)	work )

QLA_SYRPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

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la_sla_gerpvgrw()

pure real(sp) function, public la_lapack_others_sm::la_sla_gerpvgrw	(	integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	ncols,
		real(sp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		real(sp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf )

SLA_GERPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

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la_sla_syamv()

subroutine, public la_lapack_others_sm::la_sla_syamv	(	integer(ilp), intent(in)	uplo,
		integer(ilp), intent(in)	n,
		real(sp), intent(in)	alpha,
		real(sp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		real(sp), dimension(*), intent(in)	x,
		integer(ilp), intent(in)	incx,
		real(sp), intent(in)	beta,
		real(sp), dimension(*), intent(inout)	y,
		integer(ilp), intent(in)	incy )

SLA_SYAMV: performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, "symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.

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la_sla_syrcond()

real(sp) function, public la_lapack_others_sm::la_sla_syrcond	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		real(sp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		real(sp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		integer(ilp), intent(in)	cmode,
		real(sp), dimension(*), intent(in)	c,
		integer(ilp), intent(out)	info,
		real(sp), dimension(*), intent(out)	work,
		integer(ilp), dimension(*), intent(out)	iwork )

SLA_SYRCOND: estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C) The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number.

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la_sla_syrpvgrw()

real(sp) function, public la_lapack_others_sm::la_sla_syrpvgrw	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	info,
		real(sp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		real(sp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(sp), dimension(*), intent(out)	work )

SLA_SYRPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

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la_wla_gbrcond_c()

real(qp) function, public la_lapack_others_sm::la_wla_gbrcond_c	(	character, intent(in)	trans,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	kl,
		integer(ilp), intent(in)	ku,
		complex(qp), dimension(ldab,*), intent(in)	ab,
		integer(ilp), intent(in)	ldab,
		complex(qp), dimension(ldafb,*), intent(in)	afb,
		integer(ilp), intent(in)	ldafb,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(qp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(qp), dimension(*), intent(out)	work,
		real(qp), dimension(*), intent(out)	rwork )

WLA_GBRCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a QUAD PRECISION vector.

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la_wla_gercond_c()

real(qp) function, public la_lapack_others_sm::la_wla_gercond_c	(	character, intent(in)	trans,
		integer(ilp), intent(in)	n,
		complex(qp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(qp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(qp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(qp), dimension(*), intent(out)	work,
		real(qp), dimension(*), intent(out)	rwork )

WLA_GERCOND_C: computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a QUAD PRECISION vector.

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la_wla_gerpvgrw()

pure real(qp) function, public la_lapack_others_sm::la_wla_gerpvgrw	(	integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	ncols,
		complex(qp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(qp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf )

WLA_GERPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

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la_wla_hercond_c()

real(qp) function, public la_lapack_others_sm::la_wla_hercond_c	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		complex(qp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(qp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(qp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(qp), dimension(*), intent(out)	work,
		real(qp), dimension(*), intent(out)	rwork )

WLA_HERCOND_C: computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a QUAD PRECISION vector.

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la_wla_porcond_c()

real(qp) function, public la_lapack_others_sm::la_wla_porcond_c	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		complex(qp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(qp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		real(qp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(qp), dimension(*), intent(out)	work,
		real(qp), dimension(*), intent(out)	rwork )

WLA_PORCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a QUAD PRECISION vector.

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la_wla_syamv()

subroutine, public la_lapack_others_sm::la_wla_syamv	(	integer(ilp), intent(in)	uplo,
		integer(ilp), intent(in)	n,
		real(qp), intent(in)	alpha,
		complex(qp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(qp), dimension(*), intent(in)	x,
		integer(ilp), intent(in)	incx,
		real(qp), intent(in)	beta,
		real(qp), dimension(*), intent(inout)	y,
		integer(ilp), intent(in)	incy )

WLA_SYAMV: performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, "symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.

la_wla_syrcond_c()

real(qp) function, public la_lapack_others_sm::la_wla_syrcond_c	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		complex(qp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(qp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(qp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(qp), dimension(*), intent(out)	work,
		real(qp), dimension(*), intent(out)	rwork )

WLA_SYRCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a QUAD PRECISION vector.

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la_wla_syrpvgrw()

real(qp) function, public la_lapack_others_sm::la_wla_syrpvgrw	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	info,
		complex(qp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(qp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(qp), dimension(*), intent(out)	work )

WLA_SYRPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

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la_zla_gbrcond_c()

real(dp) function, public la_lapack_others_sm::la_zla_gbrcond_c	(	character, intent(in)	trans,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	kl,
		integer(ilp), intent(in)	ku,
		complex(dp), dimension(ldab,*), intent(in)	ab,
		integer(ilp), intent(in)	ldab,
		complex(dp), dimension(ldafb,*), intent(in)	afb,
		integer(ilp), intent(in)	ldafb,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(dp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(dp), dimension(*), intent(out)	work,
		real(dp), dimension(*), intent(out)	rwork )

ZLA_GBRCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.

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la_zla_gercond_c()

real(dp) function, public la_lapack_others_sm::la_zla_gercond_c	(	character, intent(in)	trans,
		integer(ilp), intent(in)	n,
		complex(dp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(dp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(dp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(dp), dimension(*), intent(out)	work,
		real(dp), dimension(*), intent(out)	rwork )

ZLA_GERCOND_C: computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.

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la_zla_gerpvgrw()

pure real(dp) function, public la_lapack_others_sm::la_zla_gerpvgrw	(	integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	ncols,
		complex(dp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(dp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf )

ZLA_GERPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

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la_zla_hercond_c()

real(dp) function, public la_lapack_others_sm::la_zla_hercond_c	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		complex(dp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(dp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(dp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(dp), dimension(*), intent(out)	work,
		real(dp), dimension(*), intent(out)	rwork )

ZLA_HERCOND_C: computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.

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la_zla_porcond_c()

real(dp) function, public la_lapack_others_sm::la_zla_porcond_c	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		complex(dp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(dp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		real(dp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(dp), dimension(*), intent(out)	work,
		real(dp), dimension(*), intent(out)	rwork )

ZLA_PORCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.

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la_zla_syamv()

subroutine, public la_lapack_others_sm::la_zla_syamv	(	integer(ilp), intent(in)	uplo,
		integer(ilp), intent(in)	n,
		real(dp), intent(in)	alpha,
		complex(dp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(dp), dimension(*), intent(in)	x,
		integer(ilp), intent(in)	incx,
		real(dp), intent(in)	beta,
		real(dp), dimension(*), intent(inout)	y,
		integer(ilp), intent(in)	incy )

ZLA_SYAMV: performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, "symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.

la_zla_syrcond_c()

real(dp) function, public la_lapack_others_sm::la_zla_syrcond_c	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		complex(dp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(dp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(dp), dimension(*), intent(in)	c,
		logical(lk), intent(in)	capply,
		integer(ilp), intent(out)	info,
		complex(dp), dimension(*), intent(out)	work,
		real(dp), dimension(*), intent(out)	rwork )

ZLA_SYRCOND_C: Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.

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la_zla_syrpvgrw()

real(dp) function, public la_lapack_others_sm::la_zla_syrpvgrw	(	character, intent(in)	uplo,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	info,
		complex(dp), dimension(lda,*), intent(in)	a,
		integer(ilp), intent(in)	lda,
		complex(dp), dimension(ldaf,*), intent(in)	af,
		integer(ilp), intent(in)	ldaf,
		integer(ilp), dimension(*), intent(in)	ipiv,
		real(dp), dimension(*), intent(out)	work )

ZLA_SYRPVGRW: computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

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