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ASL Shared Memory Parallel Functions (for Fortran)

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Chapter 1  INTRODUCTION

1.1
OVERVIEW
1.1.1
Introduction to The Advanced Scientific Library ASL
1.1.2
Distinctive Characteristics of ASL
1.2
KINDS OF LIBRARIES
1.3
ORGANIZATION
1.3.1
Introduction
1.3.2
Organization of Subroutine Description
1.3.3
Contents of Each Item
1.4
SUBROUTINE NAMES
1.5
ASL SHARED MEMORY PARALLEL FUNCTIONS
1.5.1
Overview of Shared Memory Parallel Functions
1.5.2
Performance Improvement Due to Parallel Functions
1.5.3
General Notes Concerning the Use of shared memory Parallel Functions
1.6
NOTES

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Chapter 2  BASIC MATRIX ALGEBRA

2.1
INTRODUCTION
2.1.1
Notes
2.1.2
Algorithms Used
2.1.2.1
Matrix Multiplication
2.2
BASIC MATRIX ALGEBRA
2.2.1
QAM1MU, PAM1MU
Multiplying Real Matrices (Two-Dimensional Array Type)
2.2.2
QAM1MM, PAM1MM
Multiplying Real Matrices (Two-Dimensional Array Type) (C=C± AB)
2.2.3
QAM1MT, PAM1MT
Multiplying Real Matrices (Two-Dimensional Array Type) (C=C± ABT)
2.2.4
QAM1TM, PAM1TM
Multiplying Real Matrices (Two-Dimensional Array Type) (C=C± ATB)
2.2.5
QAM1TT, PAM1TT
Multiplying Real Matrices (Two-Dimensional Array Type) (C=C± ATBT)
2.2.6
HAM1MM, GAM1MM
Multiplying Complex Matrices (Two-Dimensional Array Type) (Real Argument Type) (C=C± AB)
2.2.7
HAM1MH, GAM1MH
Multiplying Complex Matrices (Two-Dimensional Array Type) (Real Argument Type) (C=C± AB*)
2.2.8
HAM1HM, GAM1HM
Multiplying Complex Matrices (Two-Dimensional Array Type) (Real Argument Type) (C=C± A*B)
2.2.9
HAM1HH, GAM1HH
Multiplying Complex Matrices (Two-Dimensional Array Type) (Real Argument Type) (C=C± A*B*)
2.2.10
HAN1MM, GAN1MM
Multiplying Complex Matrices (Two-Dimensional Array Type) (Complex Argument Type) (C=C± AB)
2.2.11
HAN1MH, GAN1MH
Multiplying Complex Matrices (Two-Dimensional Array Type) (Complex Argument Type) (C=C± AB*)
2.2.12
HAN1HM, GAN1HM
Multiplying Complex Matrices (Two-Dimensional Array Type) (Complex Argument Type) (C=C± A*B)
2.2.13
HAN1HH, GAN1HH
Multiplying Complex Matrices (Two-Dimensional Array Type) (Complex Argument Type) (C=C± A*B*)

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Chapter 3  SIMULTANEOUS LINEAR EQUATIONS (DIRECT METHOD)

3.1
INTRODUCTION
3.1.1
Methods of using subroutines
3.1.2
Notes
3.1.3
Algorithms Used
3.1.3.1
Solution of Simultaneous Linear Equations
3.1.3.2
LU Decomposition (Gauss Method)
3.1.4
Reference Bibliography
3.2
REAL MATRIX (TWO-DIMENSIONAL ARRAY TYPE)
3.2.1
QBGMSM
Simultaneous Linear Equations with Multiple Right-Hand Sides (Real Matrix)
3.2.2
QBGMSL
Simultaneous Linear Equations (Real Matrix)
3.2.3
QBGMLU
LU Decomposition of a Real Matrix
3.2.4
QBGMLC
LU Decomposition and Condition Number of a Real Matrix
3.3
COMPLEX MATRIX (TWO-DIMENSIONAL ARRAY TYPE) (REAL ARGUMENT TYPE)
3.3.1
HBGMSM
Simultaneous Linear Equations with Multiple Right-Hand Sides (Complex Matrix)
3.3.2
HBGMSL
Simultaneous Linear Equation (Complex Matrix)
3.3.3
HBGMLU
LU Decomposition of a Complex Matrix
3.3.4
HBGMLC
LU Decomposition and Condition Number of a Complex Matrix
3.4
COMPLEX MATRIX (TWO-DIMENSIONAL ARRAY TYPE) (COMPLEX ARGUMENT TYPE)
3.4.1
HBGNSM
Simultaneous Linear Equations with Multiple Right-Hand Sides (Complex Matrix)
3.4.2
HBGNSL
Simultaneous Linear Equations (Complex Matrix)
3.4.3
HBGNLU
LU Decomposition of a Complex Matrix
3.4.4
HBGNLC
LU Decomposition and Condition Number of a Complex Matrix
3.5
REAL SYMMETRIC MATRIX (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE)
3.5.1
QBSPSL, PBSPSL
Simultaneous Linear Equations (Real Symmetric Matrix)
3.5.2
QBSPUD, PBSPUD
LDLT Decomposition of a Real Symmetric Matrix
3.6
REAL SYMMETRIC MATRIX (TWO-DIMENSIONAL ARRAY TYPE, LOWER TRIANGULAR TYPE) (NO PIVOTING)
3.6.1
QBSNSL, PBSNSL
Simultaneous Linear Equations (Real Symmetric Matrix) (No Pivoting)
3.6.2
QBSNUD, PBSNUD
UTDU Decomposition of a Real Symmetric Matrix (No Pivoting)
3.7
HERMITIAN MATRIX (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE) (REAL ARGUMENT TYPE)
3.7.1
HBHPSL, GBHPSL
Simultaneous Linear Equations (Hermitian Matrix)
3.7.2
HBHPUD, GBHPUD
LDL* Decomposition of a Hermitian Matrix
3.8
HERMITIAN MATRIX (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE) (REAL ARGUMENT TYPE) (NO PIVOTING)
3.8.1
HBHRSL, GBHRSL
Simultaneous Linear Equations (Hermitian Matrix) (No Pivoting)
3.8.2
HBHRUD, GBHRUD
LDL* Decomposition of a Hermitian Matrix (No Pivoting)
3.9
HERMITIAN MATRIX (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE) (COMPLEX ARGUMENT
TYPE)
3.9.1
HBHFSL, GBHFSL
Simultaneous Linear Equations (Hermitian Matrix)
3.9.2
HBHFUD, GBHFUD
LDL* Decomposition of a Hermitian Matrix
3.10
HERMITIAN MATRIX (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE) (COMPLEX ARGUMENT TYPE) (NO PIVOTING)
3.10.1
HBHESL, GBHESL
Simultaneous Linear Equations (Hermitian Matrix) (No Pivoting)
3.10.2
HBHEUD, GBHEUD
LDL* Decomposition of a Hermitian Matrix (No Pivoting)

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Chapter 4  SIMULTANEOUS LINEAR EQUATIONS (ITERATIVE METHOD)

4.1
INTRODUCTION
4.1.1
Notes
4.1.2
Algorithms Used
4.1.2.1
Nonstationary iterative method (for Symmetric Matrix only)
4.1.2.2
Nonstationary iterative method (for Asymmetric Matrix)
4.1.2.3
Preconditioned Iterative Method
4.1.2.4
Preconditioning Methods
4.1.2.5
Advanced Techniques for Improving Performance
4.1.3
Reference Bibliography
4.2
SPARSE MATRIX--NONSTATIONARY ITERATIVE METHODS (BASIC ITERATION METHOD ROUTINES)
4.2.1
QXE010, PXE010
Positive Definite Symmetric Sparse Matrix (ELLPACK Format) (CG method)
4.2.2
QXE020, PXE020
Asymmetric Sparse Matrix (ELLPACK Format) (CGS method)
4.2.3
QXE030, PXE030
Asymmetric Sparse Matrix (ELLPACK Format) (BiCGSTAB method)
4.2.4
QXE040, PXE040
Asymmetric Sparse Matrix (ELLPACK Format) (GMRES (m) method)

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Chapter 5  EIGENVALUES AND EIGENVECTORS

5.1
INTRODUCTION
5.1.1
Notes
5.1.2
Algorithms Used
5.1.2.1
Transforming a real symmetric matrix to a real symmetric tridiagonal matrix
5.1.2.2
Transforming a Hermitian matrix to a real symmetric tridiagonal matrix
5.1.2.3
The Householder transformation by block algorithm
5.1.2.4
QR method
5.1.2.5
root-free QR method
5.1.2.6
Bisection method
5.1.2.7
Accumulation of similarity (unitary) transformation by block algorithm
5.1.2.8
Inverse iteration method
5.1.2.9
Generalized eigenvalue problem
5.1.3
Reference Bibliography
5.2
REAL SYMMETRIC MATRIX (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE)
5.2.1
QCSMAA, PCSMAA
All Eigenvalues and All Eigenvectors of a Real Symmetric Matrix
5.2.2
QCSMAN, PCSMAN
All Eigenvalues of a Real Symmetric Matrix
5.2.3
QCSMSS, PCSMSS
Eigenvalues and Eigenvectors of a Real Symmetric Matrix
5.2.4
QCSMSN, PCSMSN
Eigenvalues of a Real Symmetric Matrix
5.3
HERMITIAN MATRIX (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE) (REAL ARGUMENT TYPE)
5.3.1
HCHRAA, GCHRAA
All Eigenvalues and All Eigenvectors of a Hermitian Matrix
5.3.2
HCHRAN, GCHRAN
All Eigenvalues of a Hermitian Matrix
5.3.3
HCHRSS, GCHRSS
Eigenvalues and Eigenvectors of a Hermitian Matrix
5.3.4
HCHRSN, GCHRSN
Eigenvalues of a Hermitian Matrix
5.4
HERMITIAN MATRIX (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE) (COMPLEX ARGUMENT TYPE)
5.4.1
HCHEAA, GCHEAA
All Eigenvalues and All Eigenvectors of a Hermitian Matrix
5.4.2
HCHEAN, GCHEAN
All Eigenvalues of a Hermitian Matrix
5.4.3
HCHESS, GCHESS
Eigenvalues and Eigenvectors of a Hermitian Matrix
5.4.4
HCHESN, GCHESN
Eigenvalues of a Hermitian Matrix
5.5
GENERALIZED EIGENVALUE PROBLEM FOR A REAL SYMMETRIC MATRIX (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE) (Ax = λBx)
5.5.1
QCGSAA, PCGSAA
All Eigenvalues and All Eigenvectors of a Real Symmetric Matrix (Generalized Eigenvalue Problem Ax = λBx, B: Positive)
5.5.2
QCGSAN, PCGSAN
All Eigenvalues of a Real Symmetric Matrix (Generalized Eigenvalue Problem Ax = λBx, B: Positive)
5.5.3
QCGSSS, PCGSSS
Eigenvalues and Eigenvectors of a Real Symmetric Matrix (Generalized Eigenvalue Problem Ax = λBx, B: Positive)
5.5.4
QCGSSN, PCGSSN
Eigenvalues of a Real Symmetric Matrix (Generalized Eigenvalue Problem Ax = λBx, B: Positive)
5.6
GENERALIZED EIGENVALUE PROBLEM FOR REAL SYMMETRIC MATRICES (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE) (ABx = λx)
5.6.1
QCGJAA, PCGJAA
All Eigenvalues and All Eigenvectors of Real Symmetric Matrices (Generalized Eigenvalue Problem ABx = λx, B: Positive)
5.6.2
QCGJAN, PCGJAN
All Eigenvalues of Real Symmetric Matrices (Generalized Eigenvalue Problem ABx = λx, B: Positive)
5.7
GENERALIZED EIGENVALUE PROBLEM FOR REAL SYMMETRIC MATRICES (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE) (BAx = λx)
5.7.1
QCGKAA, PCGKAA
All Eigenvalues and All Eigenvectors of Real Symmetric Matrices (Generalized Eigenvalue Problem BAx = λx, B: Positive)
5.7.2
QCGKAN, PCGKAN
All Eigenvalues of Real Symmetric Matrices (Generalized Eigenvalue Problem BAx = λx, B: Positive)
5.8
GENERALIZED EIGENVALUE PROBLEM (Az = λBz) FOR HERMITIAN MATRICES (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE) (REAL ARGUMENT TYPE)
5.8.1
HCGRAA, GCGRAA
All Eigenvalues and All Eigenvectors of Hermitian Matrices (Generalized Eigenvalue Problem Az = λBz, B: Positive)
5.8.2
HCGRAN, GCGRAN
All Eigenvalues of Hermitian Matrices (Generalized Eigenvalue Problem Az = λBz, B: Positive)
5.9
GENERALIZED EIGENVALUE PROBLEM (ABz = λz) FOR HERMITIAN MATRICES (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE) (REAL ARGUMENT TYPE)
5.9.1
HCGJAA, GCGJAA
All Eigenvalues and All Eigenvectors of Hermitian Matrices (Generalized Eigenvalue Problem ABz = λz, B: Positive)
5.9.2
HCGJAN, GCGJAN
All Eigenvalues of Hermitian Matrices
(Generalized Eigenvalue Problem ABz = λz, B: Positive)
5.10
GENERALIZED EIGENVALUE PROBLEM (BAz = λz) FOR HERMITIAN MATRICES (TWO-DIMENSIONAL ARRAY TYPE) (UPPER TRIANGULAR TYPE) (REAL ARGUMENT TYPE)
5.10.1
HCGKAA, GCGKAA
All Eigenvalues and All Eigenvectors of Hermitian Matrices (Generalized Eigenvalue Problem BAz = λz, B: Positive)
5.10.2
HCGKAN, GCGKAN
All Eigenvalues of Hermitian Matrices (Generalized Eigenvalue Problem BAz = λz, B: Positive)

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Chapter 6  FOURIER TRANSFORMS AND THEIR APPLICATIONS

6.1
INTRODUCTION
6.1.1
Notes
6.1.2
Algorithms Used
6.1.2.1
Two-dimensional complex Fourier transform
6.1.2.2
Two-dimensional real Fourier transform
6.1.2.3
Three-dimensional complex Fourier transform
6.1.2.4
Three-dimensional real Fourier transform
6.1.3
Reference Bibliography
6.2
MULTIPLE ONE-DIMENSIONAL COMPLEX FOURIER TRANSFORM (REAL ARGUMENT TYPE)
6.2.1
[DEPRECATED]QFCMFB, PFCMFB
Multiple One-Dimensional Complex Fourier Transforms (Include Initialization)
6.2.2
[DEPRECATED]QFCMBF, PFCMBF
Multiple One-Dimensional Complex Fourier Transforms (After Initialization)
6.3
MULTIPLE ONE-DIMENSIONAL COMPLEX FOURIER TRANSFORM (COMPLEX ARGUMENT TYPE)
6.3.1
[DEPRECATED]HFCMFB, GFCMFB
Multiple One-Dimensional Complex Fourier Transforms (Include Initialization)
6.3.2
[DEPRECATED]HFCMBF, GFCMBF
Multiple One-Dimensional Complex Fourier Transforms (After Initialization)
6.4
MULTIPLE ONE-DIMENSIONAL REAL FOURIER TRANSFORM
6.4.1
[DEPRECATED]QFRMFB, PFRMFB
Multiple One-Dimensional Real Fourier Transforms (Including Initialization)
6.4.2
[DEPRECATED]QFRMBF, PFRMBF
Multiple One-Dimensional Real Fourier Transforms (After Initialization)
6.5
TWO-DIMENSIONAL COMPLEX FOURIER TRANSFORM (REAL ARGUMENT TYPE)
6.5.1
[DEPRECATED]QFC2FB, PFC2FB
Two-Dimensional Complex Fourier Transform (Including Initialization)
6.5.2
[DEPRECATED]QFC2BF, PFC2BF
Two-Dimensional Complex Fourier Transform (After Initialization)
6.6
TWO-DIMENSIONAL COMPLEX FOURIER TRANSFORM (COMPLEX ARGUMENT TYPE)
6.6.1
[DEPRECATED]HFC2FB, GFC2FB
Two-Dimensional Complex Fourier Transform (Including Initialization)
6.6.2
[DEPRECATED]HFC2BF, GFC2BF
Two-Dimensional Complex Fourier Transform (After Initialization)
6.7
TWO-DIMENSIONAL REAL FOURIER TRANSFORM
6.7.1
[DEPRECATED]QFR2FB, PFR2FB
Two-Dimensional Real Fourier Transform (Including Initialization)
6.7.2
[DEPRECATED]QFR2BF, PFR2BF
Two-Dimensional Real Fourier Transform (After Initialization)
6.8
THREE-DIMENSIONAL COMPLEX FOURIER TRANSFORM (REAL ARGUMENT TYPE)
6.8.1
[DEPRECATED]QFC3FB, PFC3FB
Three-Dimensional Complex Fourier Transform (Including Initialization)
6.8.2
[DEPRECATED]QFC3BF, PFC3BF
Three-Dimensional Complex Fourier Transform (After Initialization)
6.9
THREE-DIMENSIONAL COMPLEX FOURIER TRANSFORM (COMPLEX ARGUMENT TYPE)
6.9.1
[DEPRECATED]HFC3FB, GFC3FB
Three-Dimensional Complex Fourier Transform (Including Initialization)
6.9.2
[DEPRECATED]HFC3BF, GFC3BF
Three-Dimensional Complex Fourier Transform (After Initialization)
6.10
THREE-DIMENSIONAL REAL FOURIER TRANSFORM
6.10.1
[DEPRECATED]QFR3FB, PFR3FB
Three-Dimensional Real Fourier Transform (Including Initialization)
6.10.2
[DEPRECATED]QFR3BF, PFR3BF
Three-Dimensional Real Fourier Transform (After Initialization)
6.11
CONVOLUTIONS
6.11.1
QFCN2D, PFCN2D
Two-Dimensional Convolutions
6.11.2
QFCN3D, PFCN3D
Three-Dimensional Convolutions
6.12
CORRELATIONS
6.12.1
QFCR2D, PFCR2D
Two-Dimensional Correlations
6.12.2
QFCR3D, PFCR3D
Three-Dimensional Correlations
6.13
POWER SPECTRUM ANALYSIS
6.13.1
QFPS2D, PFPS2D
Two-Dimensional Fourier Periodograms
6.13.2
QFPS3D, PFPS3D
Three-Dimensional Fourier Periodograms

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Chapter 7  SORTING

7.1
INTRODUCTION
7.1.1
Notes
7.1.2
Algorithms Used
7.1.3
Reference Bibliography
7.2
SORTING
7.2.1
QSSTA1, PSSTA1
Sorting a List of Data
7.2.2
QSSTA2, PSSTA2
Sorting a List of Pairwise Data

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Appendix

Appendix A
METHODS OF HANDLING ARRAY DATA
A.1
Methods of handling array data corresponding to matrix
A.2
Data storage modes
A.2.1
Real matrix (two-dimensional array type)
A.2.2
Complex matrix
A.2.3
Real symmetric matrix and positive symmetric matrix
A.2.4
Hermitian matrix
A.2.5
Random sparse matrix (For symmetric matrix only)
A.2.6
Random sparse matrix
Appendix B
MACHINE CONSTANTS USED IN ASL
B.1
Units for Determining Error
B.2
Maximum and Minimum Values of Floating Point Data