--- rpl/lapack/lapack/zpbtf2.f 2010/12/21 13:53:53 1.7
+++ rpl/lapack/lapack/zpbtf2.f 2016/08/27 15:35:03 1.15
@@ -1,9 +1,151 @@
+*> \brief \b ZPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZPBTF2 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZPBTF2( UPLO, N, KD, AB, LDAB, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, KD, LDAB, N
+* ..
+* .. Array Arguments ..
+* COMPLEX*16 AB( LDAB, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZPBTF2 computes the Cholesky factorization of a complex Hermitian
+*> positive definite band matrix A.
+*>
+*> The factorization has the form
+*> A = U**H * U , if UPLO = 'U', or
+*> A = L * L**H, if UPLO = 'L',
+*> where U is an upper triangular matrix, U**H is the conjugate transpose
+*> of U, and L is lower triangular.
+*>
+*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the upper or lower triangular part of the
+*> Hermitian matrix A is stored:
+*> = 'U': Upper triangular
+*> = 'L': Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] KD
+*> \verbatim
+*> KD is INTEGER
+*> The number of super-diagonals of the matrix A if UPLO = 'U',
+*> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] AB
+*> \verbatim
+*> AB is COMPLEX*16 array, dimension (LDAB,N)
+*> On entry, the upper or lower triangle of the Hermitian band
+*> matrix A, stored in the first KD+1 rows of the array. The
+*> j-th column of A is stored in the j-th column of the array AB
+*> as follows:
+*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
+*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
+*>
+*> On exit, if INFO = 0, the triangular factor U or L from the
+*> Cholesky factorization A = U**H *U or A = L*L**H of the band
+*> matrix A, in the same storage format as A.
+*> \endverbatim
+*>
+*> \param[in] LDAB
+*> \verbatim
+*> LDAB is INTEGER
+*> The leading dimension of the array AB. LDAB >= KD+1.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -k, the k-th argument had an illegal value
+*> > 0: if INFO = k, the leading minor of order k is not
+*> positive definite, and the factorization could not be
+*> completed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date September 2012
+*
+*> \ingroup complex16OTHERcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> The band storage scheme is illustrated by the following example, when
+*> N = 6, KD = 2, and UPLO = 'U':
+*>
+*> On entry: On exit:
+*>
+*> * * a13 a24 a35 a46 * * u13 u24 u35 u46
+*> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
+*> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
+*>
+*> Similarly, if UPLO = 'L' the format of A is as follows:
+*>
+*> On entry: On exit:
+*>
+*> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
+*> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
+*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
+*>
+*> Array elements marked * are not used by the routine.
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE ZPBTF2( UPLO, N, KD, AB, LDAB, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* September 2012
*
* .. Scalar Arguments ..
CHARACTER UPLO
@@ -13,80 +155,6 @@
COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
-*
-* ZPBTF2 computes the Cholesky factorization of a complex Hermitian
-* positive definite band matrix A.
-*
-* The factorization has the form
-* A = U' * U , if UPLO = 'U', or
-* A = L * L', if UPLO = 'L',
-* where U is an upper triangular matrix, U' is the conjugate transpose
-* of U, and L is lower triangular.
-*
-* This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* Specifies whether the upper or lower triangular part of the
-* Hermitian matrix A is stored:
-* = 'U': Upper triangular
-* = 'L': Lower triangular
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* KD (input) INTEGER
-* The number of super-diagonals of the matrix A if UPLO = 'U',
-* or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
-*
-* AB (input/output) COMPLEX*16 array, dimension (LDAB,N)
-* On entry, the upper or lower triangle of the Hermitian band
-* matrix A, stored in the first KD+1 rows of the array. The
-* j-th column of A is stored in the j-th column of the array AB
-* as follows:
-* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
-* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
-*
-* On exit, if INFO = 0, the triangular factor U or L from the
-* Cholesky factorization A = U'*U or A = L*L' of the band
-* matrix A, in the same storage format as A.
-*
-* LDAB (input) INTEGER
-* The leading dimension of the array AB. LDAB >= KD+1.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -k, the k-th argument had an illegal value
-* > 0: if INFO = k, the leading minor of order k is not
-* positive definite, and the factorization could not be
-* completed.
-*
-* Further Details
-* ===============
-*
-* The band storage scheme is illustrated by the following example, when
-* N = 6, KD = 2, and UPLO = 'U':
-*
-* On entry: On exit:
-*
-* * * a13 a24 a35 a46 * * u13 u24 u35 u46
-* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
-* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
-*
-* Similarly, if UPLO = 'L' the format of A is as follows:
-*
-* On entry: On exit:
-*
-* a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
-* a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
-* a31 a42 a53 a64 * * l31 l42 l53 l64 * *
-*
-* Array elements marked * are not used by the routine.
-*
* =====================================================================
*
* .. Parameters ..
@@ -137,7 +205,7 @@
*
IF( UPPER ) THEN
*
-* Compute the Cholesky factorization A = U'*U.
+* Compute the Cholesky factorization A = U**H * U.
*
DO 10 J = 1, N
*
@@ -165,7 +233,7 @@
10 CONTINUE
ELSE
*
-* Compute the Cholesky factorization A = L*L'.
+* Compute the Cholesky factorization A = L*L**H.
*
DO 20 J = 1, N
*